Original Research Article1234

The Prognosticating Aspects of the Developed5Cosmic Geophysics Concerning to the Subsequent6

Forthcoming Intensifications of the Global Seismicity,7Volcanic and Climatic Activity of the Earth in the 21st8

Century AD91011

Sergey V. Simonenko1213

V.I. Il’ichev Pacific Oceanological Institute, Far Eastern Branch of Russian14Academy of Sciences, 43 Baltiyskaya St., Vladivostok, 690041, Russia15

1617

ABSTRACT1819

The article presents the fundamentals of the thermohydrogravidynamic theory20of the global seismotectonic, volcanic and climatic activity of the Earth based on21the author’s generalized differential formulation of the first law of22thermodynamics extending the classical Gibbs’ formulation by taking into account23the infinitesimal increment of the macroscopic kinetic energy dK , the24infinitesimal increment of the gravitational potential energy τπd , the generalized25expression for the infinitesimal work np,δA done by the non-potential terrestrial26stress forces acting on the boundary of the continuum region , the infinitesimal27increment dG of energy due to the cosmic and terrestrial non-stationary energy28gravitational influence on the continuum region . Based on the established29fundamental global seismotectonic, volcanic and climatic periodicities fclim,vol,tec,T30(702 ±6) years and fclim,vol,tec,T (3510±30) years (determined by the combined31predominant non-stationary energy gravitational influences on the Earth of the32system Sun-Moon, the Venus, the Mars, the Jupiter and the Sun owing to the33gravitational interactions of the Sun with the Jupiter and the Saturn), the author34explains the cosmic energy gravitational genesis of the previous global35seismotectonic, volcanic and climatic activity of the Earth from the planetary36disaster near the evaluated dates (10584±36) BC to the subsequent intensifications37of the global seismicity and volcanic activity in the end of the 19 th century and in38the beginning of the 20th century, in the end of the 20th century, and in the39

beginning of the 21st century AD. Combining all established links and the40established new fundamental global seismotectonic, volcanic and climatic time41periodicities T cfclim, vol,tec, (1581±189) years, T sfclim, vol,tec, (6321±3) years, the42author presents the mathematical evidence of the validity of the subsequent43subranges: (2023±3) AD, (2040.38±3) AD and (2059.5±4.5) AD of the increased44intensifications of the global seismotectonic, volcanic and climatic activity of the45Earth during the 21st century AD (since 2016 AD). Based on the generalized46differential formulation of the first law of thermodynamics, author presents the47foundation of the useful technological basis for the practical prognostication of the48regional seismotectonic activity of the Earth by using the combination of the49generalized decompositions for evaluation of the date 1) t(jP of the next50forthcoming strong earthquake (near the considered region P by taking into51account the initial date )P( t0 of the previous strong earthquake and the next dates52 t(k) (k= 1, 2, …, Pj ) of the realized strong earthquakes) and by using the53established local energy prediction thermohydrogravidynamic principles54(determining the maximal and minimal local gravity accelerations, which are55preferable for realization of strong earthquakes).56

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Keywords - cosmic geophysics (thermohydrogravidynamic theory),59generalized differential formulation of the first law of thermodynamics, non-60stationary cosmic gravitation, global seismicity, global volcanic and climatic61activity of the Earth, natural disasters.62

631. INTRODUCTION64

65The problems of the long-term predictions of the strong earthquakes [1-8],66

the volcanic eruptions [8-10] and the global climatic processes of the Earth [11]67are the significant problems of the modern geophysics. In the special issue of the68International Journal of Geophysics [12], Console et al. assessed the status of the69art of earthquake forecasts and their applicability. It was pointed out [12] that70“although many methods have been claimed to be capable of predicting71earthquakes (as numerous presentations on earthquake precursors regularly show72at every international meeting), the problem of formulating such predictions in a73quantitative, rigorous, and repeatable way is still open”.74

Taking into account the year 1923 AD of the strongest Japanese earthquake75near the Tokyo region, we predicted “the time range 2010 2011 AD of the76next sufficiently strong Japanese earthquake near the Tokyo region” [13, 14]77based on the established time periodicities 83)(T 3ЗJ, years (determined by the78non-stationary energy gravitational influences on the Earth of the Jupiter) and79

88 years 118 years (determined by the combined non-stationary energy80gravitational influences on the Earth of the system Sun-Moon, the Venus, the81Jupiter and the Mars). The proposed [13-15] cosmic energy gravitational genesis82of the strongest Japanese earthquakes was confirmed by occurrence of the strong83Japanese earthquakes on 14 March, 2010 and on 11 March, 2011. In the special84issue on “Geophysical Methods for Environmental Studies” of the International85Journal of Geophysics, Tinivella et al. [16] pointed out that the article [17]86“proposes a possible cosmic energy gravitational genesis of the strong Chinese872008 and the strong Japanese 2011 earthquakes, based on the established88generalized differential formulation of the first law of thermodynamics”.89

The time periodicity 88 years (of the global seismotectonic and volcanic90activity and the global climate variability) is related with recurrence of the91maximal combined energy gravitational influence on the Earth of the system Sun-92Moon, the Venus, the Mars, the Jupiter [13-15] and the Sun owing to the93gravitational interaction of the Sun with the Jupiter [18]). The time periodicity 8894years is in good agreement with the estimated (based on the spectral Fourier95analysis) climatic time periodicity 88 years [19] obtained from the studies of96sediments from Siberian and Mongolian lakes.97

The analysis of the period 1977-1993 revealed [20] “an extremely strong98tendency for the earthquakes to decrease the global gravitational energy”99confirming the inherent relation of the earthquakes with the transformation of the100Earth’s gravitational energy into the seismic-wave energy and frictional heat. It is101clear that the great volcanic eruptions are related with the transformation of the102internal energy accumulated in magma chambers to the macroscopic kinetic103energy and to the potential energy of the eruptive volumes of magma during the104volcanic eruptions. Owing to these combined energy conservation for seismic and105volcanic events, it was pointed out [13-15, 17, 18] that the seismotetonic and106volcanic processes should be considered in the frame of the synthetic107thermohydrogravidynamic theory.108

The analysis of the period 1977-1985 revealed [21] the strongly non-random109tendencies in the earthquake-induced geodetic changes (owing to the mass110redistribution of material inside of the Earth) related with the change of the111angular velocity of the Earth’s rotation and the Earth’s gravitational field. It is112clear that the great volcanic eruptions are related also with the mass redistribution113of material inside of the Earth related with the change of the angular velocity of114the Earth’s rotation and the Earth’s gravitational field. The analysis of the period1151977-1993 (characterized by 11015 major earthquakes) revealed [22] the strong116earthquakes’ tendency to increase the Earth’s spin (rotational) energy.117

Based on “analysis of all the reliable historical observations in the period 700118BC to AD 1990” including “records of solar and lunar eclipses in the period 700119BC to AD 1600, originating from the ancient and medieval civilizations of120Babylon, China, Europe and the Arab world” [23] is was revealed [23] a long-121

term fluctuation in the length of the mean solar day (related with a long-term122fluctuation in the Earth’s angular velocity of rotation and the related rotational123energy of the Earth) “with a semi-amplitude of ~ 4 ms and a period of ~ 1500 yr”124[23]. In Section 3 we shall present the evidence that this time periodicity of ~ 1500125years is related with the time periodicity near 1500 years of the periodic tectonic-126volcanic intensification (determined by the periodic combined cosmic non-127stationary energy gravitational influences on the Earth) related with the periodic128mass redistribution of the terrestrial material inside the Earth and the periodic129change (characterized by the same periodicity of ~ 1500 yr [23]) of the angular130velocity of the Earth’s rotation.131

According to the thermohydrogravidynamic theory [13-15, 17, 18], the same132time periodicity near 1500 years [23] is related with the global climatic processes133of the Earth. The validity of this conclusion is in agreement with the revealing134(based on the spectral Fourier analysis) of the climatic time periodicity 1500 years135[19] obtained from the studies of sediments from Siberian and Mongolian lakes.136The same climatic cycle near 1500 years was revealed also [24] for North Atlantic.137The revealed time periodicity of ~ 1500 years [23] for the long-term fluctuation in138the length of the mean solar day (related with a long-term fluctuation in the139Earth’s angular velocity of rotation and the related rotational energy of the Earth)140is also in a good agreement with the estimated (based on the spectral Fourier141analysis) empirical climatic time periodicity 1600 years [25] of Holocene.142

We present in this article the developed thermohydrogravidynamic theory143[13-15, 17, 18, 26] intended for combined consideration of the global144seismotetonic, volcanic and climatic processes of the Earth. The145thermohydrodynamic theory of the global seismotectonic, volcanic and climatic146processes [13-15, 17, 18, 26] is based on the author’s generalized differential147formulation [15, 26] of the first law of thermodynamics (FLOT):148

dKdU τπd dGδAQ np, (1)149extending the classical formulation [27] by taking into account (along with the150classical infinitesimal change of heat Q and the classical infinitesimal change of151the internal energy τdU ) the infinitesimal increment of the macroscopic kinetic152energy dK , the infinitesimal increment of the gravitational potential energy τπd ,153the generalized expression for the infinitesimal work np,δA done by the non-154potential terrestrial stress forces (determined by the symmetric stress tensor T )155acting on the boundary of the continuum region , the infinitesimal increment156dG of energy due to the cosmic and terrestrial non-stationary energy gravitational157influence on the continuum region during the infinitesimal time dt .158

In this article, by accepting with gratitude to Managing Editor, Ms.159Samapika Mondal, the personal invitation from the British Journal of Environment160and Climate Change, we present the article, which develops the prognostic aspects161of the thermohydrogravidynamic theory [13-15, 17, 18, 26] by taking into account162

the “outstanding climate anomaly 8200 years” before the present (B.P.) in the163North Atlantic” [28] as the result of weakened overturning circulation (which164“begins at ~ 8.38 thousand years P.P.” [28]) triggered by the freshwater outburst165related with catastrophic drainage of Lake Agassiz. We establish the links between166the great volcanic eruptions in the ancient history of humankind from the different167distinct eruptions of the Thera (dated in the following ranges: (1700÷1640) BC168[29, 30], (16281626) BC [31], (1627÷1600) BC [32], (1600÷1500) BC [33],169(1628÷1450) BC [34]) and “the greatest earthquake ever experienced” [35]170destroyed in 63 BC many cities of the ancient Pontus located in Asia Minor to the171increase of the global seismicity and the global volcanic activity in the end of the17219th century and in the beginning of the 20th century [4], the subsequent increase173of the global seismicity and the volcanic activity in the end of the 20 th century [6],174and the subsequent increase of the global seismicity and the volcanic activity in175the beginning of the 21st century [13-15, 17, 18]. We establish the links between176the outstanding climate anomaly related with weakened overturning circulation177during the range 8380÷8200 B.P. [28] and the date 1450 BC [34] of last major178eruption of Thera.179

To demonstrate and explain the mention links, in Section 2 we present the180generalized differential formulation of the first law of thermodynamics and the181related evidence of the cosmic and terrestrial energy gravitational genesis of the182seismotectonic, volcanic and climatic activity of the Earth. In Section 2.1 we183present the generalized differential formulation [15, 17, 26] of the first law of184thermodynamics (for the Galilean frame of reference) for non-equilibrium shear-185rotational states of the deformed one-component individual finite continuum186region (characterized by the symmetric stress tensor Т ) subjected to the non-187stationary Newtonian gravitational field. In Section 2.2 we present the evidence of188the cosmic and terrestrial energy gravitational genesis [13-15, 17] of the global189seismic, volcanic and climatic activity of the Earth determined by the combined190cosmic and terrestrial non-stationary energy gravitational influences on the191individual continuum region (of the Earth) and by the non-potential terrestrial192stress forces acting on the boundary surface of the continuum region . We193take into account the subsequent development of the cosmic geophysics [13-15,19417] by taking into account the very significant energy gravitational influence of195the Sun on the Earth (owing to the gravitational interaction of the Sun with the196outer large planets [18 , 36]) along with the previously established [13-15, 17]197energy gravitational influences on the Earth of the Moon and the planets of the198Solar System. We take into account the foundation of the planetary integral199energy gravitational influences on the Earth [13-15, 17], the lunar integral energy200gravitational influences on the Earth [14-15, 17] and the energy gravitational201influences of the Sun on the Earth [18, 36] owing to the gravitational interaction202of the Sun with the outer large planets (the Jupiter, the Saturn, the Uranus and the203Neptune) of the Solar System.204

In Section 3 we present the foundation of the fundamental global time205periodicities [18, 36] of the periodic global seismotectonic, volcanic and climatic206activity of the Earth. We present the foundation [18, 36] of the formulae (41) and207(42) for the fundamental global time periodicities of the periodic global208seismotectonic, volcanic and climatic activity of the Earth determined by the209different combinations of the non-stationary energy gravitational influences on the210Earth of the system Sun-Moon, the Venus, the Mars, the Jupiter and the Sun211owing to the gravitational interactions of the Sun with the Jupiter, the Saturn, the212Uranus and the Neptune. Especially, we present the foundation of the established213fundamental global seismotectonic, volcanic and climatic time periodicities214(3510±30) years [18, 36] and (702 ±6) [18, 36] years of the periodic global215seismotectonic, volcanic and climatic activity determined by the combined non-216stationary energy gravitational influences on the Earth of the system Sun-Moon,217the Venus, the Mars, the Jupiter and the Sun owing to the gravitational218interactions of the Sun with the Jupiter and the Saturn. In addition to previously219established different fundamental global time periodicities [18, 36], we present the220foundation of the new combined fundamental global seismotectonic, volcanic and221climatic periodicity T cfclim, vol,tec, )1891581( years determined by the combined222predominant non-stationary energy gravitational influences on the Earth of the223system Sun-Moon, the Venus, the Mars, the Jupiter and the Sun owing to the224gravitational interactions of the Sun with the Jupiter and the Saturn.225

In Section 4 we present the evidence of the fundamental global226seismotectonic, volcanic and climatic time periodicities (3510±30) years [18, 36]227and (702 ±6) [18, 36] years related with the Earth’s seismotectonic, volcanic and228climatic activity. This evidence is based on the established links [37] between the229great volcanic eruptions, earthquakes and the outstanding climate anomalies in the230history of humankind including the subsequent intensifications of the global231seismicity and volcanic activity of the Earth in the end of the 19 th century and in232the beginning of the 20th century [4], in the end of the 20th century [6], and in the233beginning of the 21st century AD [13-15, 18].234

In Subsection 4.1 we present the evidence of the founded range of the235fundamental global seismotectonic, volcanic and climatic periodicities 696 ÷708236years based on the established link between the outstanding climate anomaly237during 8380÷8200 years BP [28] in the North Atlantic and the different volcanic238eruptions of Hekla in Iceland BC [38].239

In Subsection 4.2. we present the evidence of the founded range of the240fundamental global periodicities (3510±30) years based on the established link241[37] of the eruption of Thera (Santorini) in the range 1627 1600 BC [32] and the242Eruptions of Santorini in 1866 AD and 1925 AD [39]. The evidence of the243founded range of the fundamental global periodicities (3510±30) years is based244also on the established link of the eruption of Thera (Santorini) in the range245

1627 1600 BC [32] and the increase of the global seismicity in the end of the24619th century and in the beginning of the 20th Century AD [4].247

In Subsection 4.3 we present the evidence of the founded range of the248fundamental global periodicities 696 ÷708 years based on the established link249[37] between the last major eruption of Thera (1450 ±14 BC), the greatest250earthquake destroyed the ancient Pontus (63 BC) [35] and the strong volcanic251eruptions during (50±30) BC [38]. The evidence of the founded range of the252fundamental global periodicities 696 ÷708 years is based also on the established253link [37] between the last major eruption of Thera (1450 ±14 BC), the great frost254event (628 AD) [31] related with the atmospheric veil induced by the great255unknown volcanic eruption (apparently, Rabaul’ [31], and the strong Japanese256earthquake (684 AD) [40] near the Tokyo region. This evidence is based also on257the established link [37] between the last major eruption of Thera (1450 ±14 BC)258and the strong earthquakes occurred in England (1318 AD and 1343 AD) [40],259Armenia (1319 AD) [40], Portugal (1320 AD, 1344 AD and 1356 AD) [40],260Japan (1361 AD) [40] and the volcanic eruptions in Iceland on the Hekla volcanic261system (1341 AD and 1389 AD) [41] and on the Katla volcanic system (1357 AD)262[41].263

In Subsection 4.4 we present the evidence of the evaluated [37] moderate264intensification of the global seismotectonic, volcanic and climatic activity of the265Earth (from 2014÷2016 AD) related with the last major eruption of Thera (1450266±14 BC).267

In Section 5 we present the additional evidences of the forthcoming268intensification of the global seismotectonic, volcanic and climatic activity of the269Earth in the 21st century AD (since 2016 AD) related with the forthcoming strong270synchronization of the mean periodicities 702 years and 1581 years of the founded271ranges of the fundamental global seismotectonic, volcanic and climatic time272periodicities T fclim, vol,tec, (702 ±6) years [18, 36] and T cfclim, vol,tec, (1581±189)273years founded in Section 3.274

In Subsection 5.1 we present the evidence of the founded range of the275fundamental global periodicities 696 ÷708 years [18, 36] based on the276established link between the last major eruption of Thera (1450 ±14 BC) and the277outstanding climate anomaly during 8380÷8200 years BP in the North Atlantic278[28].279

In Subsection 5.2 we present the evidence of the founded range of the280fundamental global periodicities 696÷708 years [18, 36] based on the established281link between the outstanding climate anomaly during 8380÷8200 years BP in the282North Atlantic [28] and the great planetary disasters in the Central Asia (near28310555 BC) [42] and Egypt (near 10450 BC) [43].284

In Subsection 5.3 we present the mathematical foundation of the synchronic285fundamental seismotectonic, volcanic and climatic time periodicity286

T sfclim, vol,tec, (6321±3) years characterizing the time synchronization of the mean287

periodicities 702 years and 1581 years of the fundamental global seismotectonic,288volcanic and climatic time periodicities T fclim, vol,tec, (702 ±6) years [18, 36]289and T cfclim, vol,tec, (1581±189) years.290

In Subsection 5.4 we present the mathematical evidence of the291forthcoming intensification of the global seismotectonic, volcanic and climatic292activity of the Earth in the 21st Century AD (since 2016 AD) related with the293outstanding climate anomaly during 8380÷8200 years BP in the North Atlantic294[28] owing to the very probable catastrophic seismotectonic event (near 6372 BC)295close to Lake Agassiz.296

In Subsection 5.5 we present the evidence of the intensification of the global297seismotectonic, volcanic and climatic activity of the Earth in the beginning of the29821st century AD related with the intensification of the oscillatory motion of the299internal rigid core relative to the fluid core of the Earth.300

In Subsection 5.6 we present the practical forecasting aspects of the301thermohydrogravidynamic theory related with the regional seismotectonic and302volcanic activity of the Earth.303

In Section 6 we present the conclusions.304305

2. THE GENERALIZED DIFFERENTIAL FORMULATION OF THE306FIRST LAW OF THERMODYNAMICS DETERMINING THE COSMIC307AND TERRESTRIAL ENERGY GRAVITATIONAL GENESIS OF THE308

GLOBAL SEISMOTECTONIC, VOLCANIC AND CLIMATIC ACTIVITY309OF THE EARTH310

311312

2.1. The Generalized Differential Formulation of the First Law of313Thermodynamics Intended for the Deformed One-component Individual314

Finite Continuum Region (considered in the Galilean Frame of Reference)315subjected to the Non-stationary Newtonian Gravitational Field316

317318

We shall assume that is an individual continuum region (bounded by the319closed continual boundary surface ) moving in the three-dimensional Euclidean320space with respect to a Cartesian coordinate system K . Following the works [17,32118], we shall consider the deformed finite one-component individual continuum322region characterized by the non-equilibrium shear-rotational states [44] related323with the Earth’s continuum deformation. We shall consider the small continuum324region in a Galilean frame of reference with respect to a Cartesian coordinate325system K centred at the origin O and determined by the axes X , X , X1 2 3 (see Fig.3261). The unit normal K -basis coordinate vectors triad 321 ,, μμμ is taken in the327directions of the axes X , X , X1 2 3 , respectively. The K -basis vector triad is328

taken to be right-handed in the order 321 ,, μμμ , see Fig. 1. g is the local gravity329acceleration. The local hydrodynamic velocity vector v is determined by the330general equation of continuum movement [45]:331

gTv +div1=dtd

(2)332

for the deformed continuum characterized by the symmetric stress tensor Т = P333[45] of general form. We take into account the time variations of the potential ψ334of the non-stationary gravitational field (characterized by the local gravity335acceleration g ψ ) inside of an arbitrary finite macroscopic individual336continuum region subjected to the non-stationary Newtonian gravitational field.337The decomposition of the pressure tensor P [46] is given by:338

ΠδΡ +p= , (3)339where δ is the Kronecker delta-tensor, П is the viscous-stress tensor [46]. The340operator v+t/=d/dt denotes the total derivative [45] following the341continuum substance. The relevant three-dimensional fields such as the velocity342and the local mass density (and also the first and the second derivatives of the343relevant fields) are assumed to vary continuously throughout the entire continuum344bulk of the continuum region .345

The specific (per unit mass) internal thermal energy u is determined by the346differential formulation of the FLOT [46] for the one-component deformed347macrodifferential continuum element with no chemical reactions:348

-dtdp

dtdq=

dtdu

vП Grad: , (4)349where 1 / is the specific volume, is the local mass density, p is the350thermodynamic pressure, dq is the differential change of heat across the351boundary of the continuum region (of unit mass) related with the thermal352molecular conductivity described by the heat equation [46] :353

qdivdtdqρ J , (5)354

where qJ is the heat flux [46].355356357

358Fig. 1. Cartesian coordinate system K of a Galilean frame of reference and the359Lagrangian coordinate system K related with the mass center C of an individual360finite continuum region (of a wide variety of sizes): the geo-block of the361lithosphere, or the magma chamber, or the oceanic / atmosperic continuum region362of the Earth, or the whole Earth, or the planet of the Solar System subjected to363the non-stationary Newtonian gravitation364

365Using the general equation (2) of continuum movement [45], the366

decomposition (3), the differential formulation (2) of the first law of367thermodynamics [46] for the one-component deformed macrodifferential368continuum element with no chemical reactions and the heat equation (5) [46], we369derived [15, 17, 26] the generalized differential formulation (for the Galilean370frame of reference) of the FLOT (for moving rotating deforming compressible371heat-conducting stratified macroscopic continuum region presented on Fig. 1):372

)U(Kd τττ π =

τ

qτ

ddt-ddt nn nJTnv + Vρdtψdt

τ , (6)373

where374K = Vd

2ρ

τ

2v (7)375

is the instantaneous macroscopic kinetic energy of the macroscopic individual376continuum region , dV is the mathematical differential of physical volume of377the continuum region;378

U dVuρ

(8)379

is the classical microscopic internal thermal energy of the macroscopic individual380continuum region ;381

Vψρd

(9)382

is the macroscopic potential energy (of the macroscopic individual continuum383region ) related with the non-stationary potential ψ of the gravitational field;384

,npA

nTnv ddt (10)385

is the differential work done during the infinitesimal time interval dt by non-386potential stress forces acting on the boundary surface of the continuum region387 ; nd is the differential element (of the boundary surface of the continuum388region ) characterized by the external normal unit vector n ; Тnt is the stress389vector [45];390

nnJ d-dtQ q (11)391

is the differential change of heat related with the thermal molecular conductivity392of heat across the boundary of the continuum region , qJ is the heat flux [46]393across the element nd of the continuum boundary surface ;394

dG = Vρdtψdt

τ (12)395

is the infinitesimal amount dG of energy [15, 17, 26] added or lost as the result of396the Newtonian non-stationary gravitational energy influence on the continuum397region during the infinitesimal time interval dt . We use the common Riemann’s398integral here and everywhere.399

The generalized differential formulation (6) of the FLOT can be rewritten as400follows [15, 17, 26]:401

dKdU τπd dGδAQ np, (13)402extending the classical [27, 47] formulations by taking into account (along with403the classical infinitesimal change of heat Q and the classical infinitesimal404change dU dU of the internal energy τU ) the infinitesimal increment dK of the405macroscopic kinetic energy K , the infinitesimal increment τπd of the406gravitational potential energy , the generalized infinitesimal work np,δA done407during the infinitesimal time interval dt by non-potential stress forces (pressure,408compressible and viscous forces for Newtonian continuum) acting on the409boundary surface of the continuum region , the infinitesimal amount dG of410energy [15, 17, 26] added or lost as the result of the Newtonian non-stationary411gravitational energy influence on the continuum region during the infinitesimal412time interval dt . The infinitesimal amount dG [15, 17, 26] of energy (added or413

lost as the result of the Newtonian non-stationary gravitational energy influence414on the continuum region ) may be interpreted [13-15, 17, 26] as the differential415energy gravitational influence dG on the continuum region during the416infinitesimal time interval dt .417

Under imposed partial conditions 0δQ , 0δA τnp, , 0dG , the418generalized differential formulation (13) of the FLOT gives the conservation law419of the total energy:420

0ddKdU τττ π , )(τconstKU τττ π (14)421of the moving deformed finite individual continuum region (characterized by422the symmetric stress tensor Т ) subjected to the stationary gravitational field. The423generalized differential formulation (13) of the first law of thermodynamics424(given for the Galilean frame of reference) is valid for non-equilibrium shear-425rotational states of the moving deformed finite individual continuum region 426(characterized by the symmetric stress tensor Т ) subjected to the non-stationary427gravitational field. The generalized differential formulation of the first law of428thermodynamics (13) is the generalization of the classical formulations [27, 47] of429the first law of thermodynamics. The generalized differential formulation (13) of430the first law of thermodynamics takes into account the significant generalized431terms: 1) the generalized expression (10) for the differential work ,npA done432during the infinitesimal time interval dt by non-potential stress forces acting on433the boundary surface of the individual continuum region and 2) the new434additional expression (12) for the differential energy gravitational influence dG435on the continuum region during the infinitesimal time interval dt related with436the time variations of the potential ψ of the non-stationary gravitational field437inside the individual continuum region due to the deformation of the individual438continuum region and due to the external (terrestrial and cosmic) gravitational439influence on the individual continuum region moving in the total (combined:440internal and external) non-stationary gravitational field.441

The generalized differential formulation (13) of the FLOT for the Newtonian442continuum can be rewritten as follows:443

dKdU τπd dGδFδAδQ vis,cp (15)444extending the classical [27, 47] formulations by taking into account (along with445the classical [27, 47] infinitesimal change of heat Q , the classical [27, 47]446infinitesimal change of the internal energy dU dU and the classical [27, 47]447differential work pδA of the hydrodynamic pressure forces) the infinitesimal448increment of the macroscopic kinetic energy dK , the infinitesimal increment of449the gravitational potential energy τπd , the infinitesimal amount dG of energy [15,45017, 26] added or lost as the result of the Newtonian non-stationary gravitational451energy influence on the continuum region during the infinitesimal time interval452

dt , and the sum cvis,δF = sc δAδA of the established differential work cδA of453the acoustic (compressible) pressure forces and the established differential work454

sδA of the viscous Newtonian forces.455The generalized differential formulation (15) is the result of generalization of456

the differential work (10) presented for Newtonian continuum as follows [15, 17,45726] :458

,npA scp δAδAδA = (16)459

=

τ

dpdt- nnv

τv ddivηη

32dt- nnvv + dt n

ταβαβ dΩen v2η

,460

where461

τ

p dp-dtδA nnv (17)462

is the differential work of the hydrodynamic pressure forces acting on the463boundary surface of the individual continuum region (bounded by the464continuum boundary surface ) during the infinitesimal time interval dt ;465

cδA =

τv ddivηη

32dt- nnvv (18)466

is the differential work (related with the combined effects of the acoustic467compressibility, molecular kinematic viscosity and molecular volume viscosity) of468the acoustic (compressible) pressure forces acting on the boundary surface of469the individual continuum region during the infinitesimal time interval dt ;470

sδA = dt nτ

αβαβ dΩen v2η

(19)471

is the differential work of the viscous Newtonian forces (related with the472combined effect of the velocity shear, i.e. the deformation of the continuum region473 , and the molecular kinematic viscosity) acting during the differential time dt on474the boundary surface of the continuum region characterized by the rate of475strain tensor αβe [17], the coefficient of molecular kinematic (shear) viscosity476 = η/ρ and the coefficient of molecular volume (second) viscosity 2ν = /ρη v .477

Under partial conditions 0dK τ , 0d τπ , 0δA c , 0δAs , 0dG , the478generalized differential formulation (15) of the FLOT can be rewritten as follows:479

τdU pδAδQ . (20)480Using the approach of the thermohydrodynamic theory [46] and assuming481

the constant pressure p (for the small macroscopic continuum region ) in the482

relation (17) for pδA , we get483

pδA = - p dV , (21)484where dV is the differential change of volume V of the small macroscopic485continuum region characterized by the thermodynamic pressure p . Using the486

relation (21), the partial formulation (20) of the FLOT can be rewritten as487follows:488

pdV-δQdUτ (22)489which is consistent with the following Gibbs’ [27] formulation of the FLOT for490the fluid body (in Gibbs’ designations):491

dW-dHdε , (23)492where dε is the differential of the internal thermal energy of the fluid body, dH is493the differential change of heat across the boundary of the fluid body related with494the thermal molecular conductivity (associated with the corresponding external or495internal heat fluxes), dW= pdV is the differential work produced by the496considered fluid body on its surroundings (surrounding fluid) under the497differential change dV of the fluid volume V under the thermodynamic pressure498p . The partial formulation (22) is consistent with the following formulation [47]499of the FLOT for the general thermodynamic system (in Landau’s and Lifshitz’s500designations [47]):501

pdV-dQdE , (24)502where pdVdA is the differential work produced by the surroundings503(surroundings of the thermodynamic system) on the thermodynamic system under504the differential change dV of volume V of the thermodynamic system505characterized by the thermodynamic pressure p ; dQ is the differential heat506transfer (across the boundary of the thermodynamic system) related with the507thermal interaction of the thermodynamic system and the surroundings508(surrounding environment); E is the energy of the thermodynamic system, which509should contain (as supposed [47] and in an agreement with the generalized510differential formulation (13) of the FLOT) the kinetic energy of the macroscopic511continuum motion.512

513514

5152.2. Cosmic and Terrestrial Energy Gravitational Genesis of the Global516Seismic, Volcanic and Climatic Activity of the Earth Determined by the517

Combined Cosmic and Terrestrial Non-stationary Energy Gravitational518Influences on the Individual Continuum Region and by the Non-519

potential Terrestrial Stress Forces Acting on the Boundary Surface 520of the Continuum Region 521

522We have the evolution equation for the total mechanical energy )(K ττ π of523

the deformed finite individual macroscopic continuum region [15, 17, 26]:524

)πττKdtd

= dtd Vρdψ

21

τ

2

v =525

= Vdpdivτ v + Vddivη-η

32

τ

2v

v – Vρdeν2

τ

2ij +526

+

τ

d nTnv + Vρdtψ

τ

(25)527

obtained from the generalized differential formulation (13) of the first law of528thermodynamics for the compressible viscous Newtonian one-component529continuum moving in the non-stationary gravity field. The evolution equation (25)530takes into account the dependences of the coefficient of molecular kinematic531viscosity = η/ρ and the coefficient of molecular volume viscosity 2ν = /ρη v on532the space (three-dimensional) Cartesian coordinates. We founded the generalized533thermohydrogravidynamic shear-rotational model [15, 17, 26] of the earthquake534focal region based on the evolution equation (25) for the Newtonian continuum535using the above three expressions (17), (18) and (19) for the differential works536

pδA , cδA and sδA together with the generalized expression [15, 17, 26, 48] for537the instantaneous macroscopic kinetic energy K of the small macroscopic538individual continuum region . Using the evolution equation (25) for the total539mechanical energy ττ πK (of the deformed finite individual macroscopic540continuum region ) and the generalized differential formulation (13) of the first541law of thermodynamics, we derived [15, 18] the evolution equation for the internal542energy τU of the macroscopic continuum region :543

τUdtd = –

τ

q d nnJ + Vρdeν2τ

2ij – Vddivη-η

32

τ

2v

v – Vdpdiv

τ v .544

(26)545If the period of variations of the potential of the external cosmic non-stationary546gravitational field (of the Sun, the Moon, the planets of the Solar System and our547Galaxy influencing on the continuum region of the Earth 3τ ) is equal to548

egT ( τ ) energyT ( τ ) then the same time periodicity egT ( τ ) energyT ( τ ) will549characterize the periodic variations of the rate of strain tensor ije [44] (along with550the divergence vdiv of the velocity vector v of the continuum motion and the551angular velocity of internal rotation ω ( v ) /2 [45]) inside of the subsystem552 of the Earth 3τ . Taking into account that the quadratic functions 2

ij )e( and553

2divv have the time period egT21

( τ ) of temporal variations, we obtained [13,554

14, 18], according to the evolution equation (26), the time periodicity )τ(Tendog555

)τ(T21)τ(T egendog (27)556

of variations of the internal energy τU of the macroscopic continuum region as557a result of the irreversible dissipation of the macroscopic kinetic energy558determined by the second and the third terms in the right-hand side of the559evolution equation (26).560

According to the generalized differential formulation (13) of the first law of561thermodynamics, the supply of energy (related with the energy flux) into the562continuum region is related with the differential work [15] (obtained previously563in [48]):564

τ

τnp, ddtδA nTnv (28)565

done by non-potential stress forces (pressure, compressible and viscous forces for566Newtonian continuum) acting on the boundary surface of the continuum region567 during the differential time interval dt .568

The considered mechanisms of the energy flux into the Earth’s569macroscopic continuum region should result to the irreversible process of the570splits formation in the rocks related with the generation of the high-frequency571acoustic waves from the focal continuum region before the earthquakes and572volcanic eruptions. Taking this into account, the sum sc δAδA (for Newtonian573continuum) in the expression (28) for τnp,A may be interpreted [13-15, 17] as the574energy flux (represented in the generalized differential formulation (15) of the first575law of thermodynamics for the Newtonian continuum)576

cvis,δF = sc δAδA (29)577directed (according to the classical hydrodynamic approach [49]) across the578boundary of the continuum region due to the compressible and viscous579forces (for Newtonian continuum) acting on the boundary surface of the580continuum region .581

The considered two mechanisms of the energy flux into the Earth’s582macroscopic continuum region should result to the significant increase of the583energy flux of the geo-acoustic energy from the focal region before the584earthquakes and volcanic eruptions. The deduced conclusion is in a good585agreement with the results of the detailed experimental studies [50].586

We founded [13-15, 26] the physical mechanisms of the energy fluxes to the587continuum region related with preparation of earthquakes and volcanic588eruptions. The generalized differential formulation (13) of the FLOT shows that589the non-stationary gravitational field (related with the non-stationary gravitational590potential ψ ) gives the following gravitational energy power591

)τ(Wgr Vρdtψ

τ =

dtdG (30)592

associated with the gravitational energy power of the total combined (external593cosmic, global terrestrial and internal related with the macroscopic continuum594region ) gravitational field. If the macroscopic continuum region is not very595

large, consequently, it cannot induce the significant time variations to the potential596ψ of the gravity field inside the continuum region . According to the generalized597differential formulation (13) of the FLOT, the energy power of the gravitational598field may produce the fractures [13-15, 26] in the terrestrial continuum region 599of the lithosphere of the Earth.600

The generalized differential formulation (13) of the first law of601thermodynamics and the expression (30) for the gravitational energy power602

)τ(Wgr show that the local time increase of the potential ψ of the gravitational603field is the gravitational energy mechanism of the gravitational energy flux into604the continuum region . The local time increase of the potential ψ of the605gravitational field inside the continuum region ( 0tψ/ ) is related [13-15,60626] with the gravitational energy flux into the continuum region . According to607the generalized differential formulation (13) of the FLOT, the total energy608

)UK( τττ π of the continuum region is increased if 0tψ/ . According to609the generalized differential formulation (13) of the FLOT, the gravitational610energy flux into the continuum region may induce the formation of fractures611[13-15, 26] (in the terrestrial continuum region of the lithosphere) related with612the production of earthquake. This conclusion corresponds to the observations [6,61320-22, 51, 52 ] of the identified anomalous variations of the gravitational field614before strong earthquakes.615

The generalized differential formulation (13) of the FLOT gives also the616theoretical foundation of the detected non-relativistic classical “gravitational”617waves [18, 36] (the propagating disturbances of the gravitational field of the618Earth) from the moving focal regions of earthquakes. The theoretical foundation619of the non-relativistic classical “gravitational” waves is based on the fact that the620gravitational energy power )τ(Wgr (in the last differential term dG of the621generalized differential formulation (13) of the FLOT) can be rewritten as [18, 36]622

)τ(Wgr ,d)(Vρdtψ

ττng nJ

(31)623

where gJ is the energy flux characterized by the divergence [18, 36]624

tψρdiv

gJ (32)625of the gravitational energy (across the boundary of the continuum region )626related with the time change of the potential ψ of the gravitational field inside the627continuum region . It was pointed out [51] that the past experience and628empirical data showed that “earthquakes typically occur within one to two years629after a period of significant gravity changes in the region in question”. The630gravitational energy power )τ(Wgr (in last differential term dG of the generalized631differential formulation (13) of the FLOT) may be considered as the useful632

theoretical component “needed to remove the subjective nature in the633determination of the timeframe of a forecasted earthquake” [51].634

The necessity to consider the gravitational field (during the strong635earthquakes) is related with the observations of the slow gravitational [53, 54]636ground waves resulting from strong earthquakes and spreading out from the focal637regions [55, 56] of earthquakes. Lomnitz pointed out [55] that the gravitational638ground waves (related with great earthquakes) “have been regularly reported for639many years and remain a controversial subject in earthquake seismology”. Richter640presented [2] the detailed analysis of these observations and made the conclusion641that “there is almost certainly a real phenomenon of progressing or standing waves642seen on soft ground in the meizoseismal areas of great earthquakes”. Lomnitz643presented [56] the real evidence of the existence of the slow gravitational waves644in sedimentary layers during strong earthquakes.645

Based on the generalized differential formulation (6) of the FLOT used for646the Earth, we obtained [15] the evaluation of the relative maximal planetary647integral energy gravitational influences on the Earth in the approximation of the648circular orbits of the planets of the Solar System. To evaluate the relative649maximal planetary integral energy gravitational influence of the inner planet τi650(the Mercury and the Venus) at the mass center ЗC of the Earth, we considered651[15, 17] the ratio652

,)t,τ(Emax

)t,τ(Emaxs(i)

1зgt

iзgt

i= 1, 2653

(33)654of the maximal positive integral energy gravitational influence )t,τ(Emax iзgt

(of655the inner planet iτ at the mass center 3C of the Earth) and the maximal positive656integral energy gravitational influence )t,τ(Emax 1зgt

of the Mercury at the mass657center 3C of the Earth. To evaluate the relative maximal planetary integral energy658gravitational influence of the outer planet iτ (the Mars, the Jupiter, the Saturn, the659Uranus, the Neptune and the Pluto) at the mass center ЗC of the Earth, we660considered [15, 17] the ratio661

,)t,τ(Emax

)t,τ(Emins(i)

1зgt

iзgt

i = 4, 5, 6, 7, 8, 9662

(34)663of the absolute (positive) value )t,τ(Emin iзgt

of the integral energy gravitational664influence t),τ(E iзg (of the outer planet iτ at the mass center 3C of the Earth)665and the maximal positive integral energy gravitational influence )t,τ(Emax 1зgt

of666the Mercury at the mass center 3C of the Earth. Based on the expressions (33)667and (34), we calculated [15] the following numerical values s(i) (characterizing668

the planetary maximal integral energy gravitational influences on the unit mass at669the mass center ЗC of the Earth): 6409.89s(2) (for the Venus), 319.31s(5) 670(for the Jupiter), 6396.2s(4) (for the Mars), 036.1s(6) (for the Saturn), 1s(1) 671(for the Mercury by definition), 0133.0s(7) (for the Uranus), 003229.0s(8) (for672the Neptune) and 7104495.1s(9) (the Pluto). The Venus and the Jupiter are673characterized by the maximal planetary integral energy gravitational influences on674the Earth.675

Based on the generalized differential formulation (6) of the FLOT used for676the Earth, we obtained [13, 14] the evaluation of the maximal integral energy677gravitational influence of the Moon on the unit mass at the mass center 3C of the678Earth in the approximation of the elliptical orbits of the Earth and the Moon679around the combined mass center MOON3,C . To evaluate the maximal positive680integral energy gravitational influence of the Moon at the mass center ЗC of the681Earth, we considered [13, 14, 17] the ratio682

)t,τ(Emax

)tMoon,(Emaxapprox.)seconds(Moon,

1зgt

зgt

683

(35)684of the maximal positive integral energy gravitational influence )tMoon,(Emax зgt

(of685the Moon on the unit mass at the mass center 3C of the Earth) and the maximal686positive integral energy gravitational influence )t,τ(Emax 1зgt

of the Mercury at the687mass center 3C of the Earth. We calculated [13, 14] the numerical values688

13.0693approx.)seconds(Moon, characterizing the lunar maximal integral energy689gravitational influence on the unit mass at the mass center ЗC of the Earth.690

Based on the generalized differential formulation (6) of the FLOT used for691the Earth, we derived [18] the relation for the maximal positive integral energy692gravitational influences t),τ(SunEΔmax j3gt

of the Sun on the Earth owing to the693gravitational interaction of the Sun with the outer large planets jτ 8)7,6,5,(j . Using694the maximal positive integral energy gravitational influence t),τ(SunEΔmax j3gt

of695the Sun on the Earth (owing to the gravitational interaction of the Sun with the696outer large planet jτ , 87,6,5,j ) and using the maximal positive integral energy697gravitational influence )t,τ(Emax 1зgt

of the Mercury on the Earth, we considered698[18] the following ratio (for 87,6,5,j )699

t),(τEΔmax

t),τ-(SunEΔmaxapprox.)first,τs(Sun

13gt

j3gtj .700

(36)701Based on the above expressions, we calculated [18] the following values702(characterizing the maximal integral energy gravitational influences of the Sun on703

the unit mass at the mass center ЗC of the Earth owing to the gravitational704interaction of the Sun with the outer large planet jτ ):705

613239.4235approx.)first,τs(Sun 5 (for the Sun owing to the gravitational706interaction of the Sun with the Jupiter), 4442965.887approx.)first,τs(Sun 6 (for707the Sun owing to the gravitational interaction of the Sun with the Saturn),708

8337322.93approx.)first,τs(Sun 7 (for the Sun owing to the gravitational interaction709of the Sun with the Uranus) and 8477601.87approx.)first,τs(Sun 8 (for the Sun710owing to the gravitational interaction of the Sun with the Neptune). Taking into711account the calculated relative values approx.)first,τs(Sun j characterizing the712maximal integral energy gravitational influences of the Sun on the unit mass at the713mass center ЗC of the Earth owing to the gravitational interaction of the Sun with714the outer large planets, we established [18] the following order of signification of715the outer large planets jτ 8)7,6,5,(j of the Solar System: the Jupiter, the Saturn,716the Uranus and the Neptune in respect of the importance of the integral energy717gravitational influences of the Sun on the Earth owing to the gravitational718interaction of the Sun with the outer large planets.719

Thus, we have the following order of the prevalent maximal integral energy720gravitational influences on the Earth [18]: 1) the integral energy gravitational721influence of the Sun on the Earth owing to the gravitational interaction of the Sun722with the Jupiter approx.)first,τ(s(Sun 5 )613239.4235 , 2) the integral energy723gravitational influence of the Sun on the Earth owing to the gravitational724interaction of the Sun with the Saturn approx.)first,τ(s(Sun 6 ),4442965.887 3) the725integral energy gravitational influence of the Sun on the Earth owing to the726gravitational interaction of the Sun with the Uranus727

)8337322.93approx.)first,τ(s(Sun 7 , 4) the integral energy gravitational influence of728the Venus on the Earth )6409.89(s(2) , 5) the integral energy gravitational729influence of the Sun on the Earth owing to the gravitational interaction of the Sun730with the Neptune approx.)first,τ(s(Sun 8 )8477601.87 , 6) the integral energy731gravitational influence of the Jupiter on the Earth )319.31(s(5) , 7) the integral732energy gravitational influence of the Moon on the Earth733

13.0693)approx.)second(s(Moon, and 8) the integral energy gravitational influence of734the Mars on the Earth ( 6396.2s(4) ).735

The revealed [13, 14, 17] small difference of the maximal energy736gravitational influence of each planet at the surface point ЗD and at the mass737center ЗC of the Earth must lead to the small difference of the combined maximal738energy gravitational influences of the planets of the Solar System at the points 3C739and ЗD of the Earth. It was recognized [13, 14] that the small difference of the740combined planetary maximal energy gravitational influences at the surface point741

ЗD and at the mass center ЗC of the Earth can contribute to the following related742geophysical phenomena: the small oscillatory motion of the internal rigid core of743the Earth relative to the fluid core of the Earth; the small oscillation of the Earth’s744pole (i.e., the Chandler’s wobble of the Earth’s pole [57]); the small oscillations of745the boundary of the Pacific Ocean (i.e., the seismic zone of the Pacific Ring); the746oscillations, rotations and deformations of the geo-blocks weakly coupled with the747surrounding plastic layers in all seismic zones of the Earth and the formation of748fractures related with the strong earthquakes and the planetary cataclysms. It was749suggested [58] the hypothesis that the Chandler’s wobble of the Earth’s pole can750be generated by the motion of the internal rigid core of the Earth induced by the751disturbances in the system Sun-Earth-Moon. The obtained results [17, 18]752supported the stated [13, 14] conclusion that the related geophysical phenomena753(the small oscillatory motion of the internal rigid core of the Earth relative to the754fluid core of the Earth [58]; the small oscillation of the Earth’s pole (i.e., the755Chandler’s wobble of the Earth’s pole); the small oscillations of the boundary of756the Pacific Ocean (i.e., the seismic zone of the Pacific Ring [8]); the oscillations757[7], rotations and deformations [8] of the geo-blocks weakly coupled with the758surrounding plastic layers in all seismic zones of the Earth, and the formation of759fractures related with the strong earthquakes [15, 16] and the planetary cataclysms760[13, 14, 18] are induced by the combined non-stationary cosmic energy761gravitational influence on the Earth of the planets of the Solar System, the Sun762and the Moon.763

Using the mathematical equality764

ρ1div

ρ1

ρdiv gg

g JJJ , (37)765

the equation (32) can be rewritten as follows766t),(s

ρ)ρ(

)ψ(divtψ

ge2ge rJ

v g

, (38)767

whereρψge

gJv is the velocity of propagation of the gravitational energy, ρψ is the768

macroscopic potential energy per unit volume, t),(sge r is the space-time source of769distributed production of the gravitational energy per unit volume and per unit770time.771

The obtained equation (38) for the non-stationary gravitational potential ψ772is analogous to the generalized hydrodynamic continuity equation (for the local773macroscopic density ρ of mass distribution and the local hydrodynamic velocity v774of the macroscopic velocity field)775

)t,(s)ρ(divtρ

m rv 776

(39)777generalizing the classical hydrodynamic continuity equation (considered usually778under condition 0)t,(sm r ) by taking into account the function 0)t,(sm r779

determining the space-time source )t,(sm r of distributed mass output per unit780volume and per unit time. The non-stationary gravitational potential ψ (the781macroscopic potential energy per unit mass of the continuum) is analogous to the782local non-stationary macroscopic density ρ (the macroscopic mass per unit783volume of the continuum). The velocity

ρψgegJ

v of propagation of the gravitational784

energy is analogous to the local hydrodynamic velocity v of the macroscopic785velocity field. The space-time source )t,(sm r of distributed mass output per unit786volume and per unit time is analogous to the space-time source t),(sge r of787distributed production of the gravitational energy per unit volume and per unit788time.789

The obtained equation (38) for the non-stationary gravitational potential790ψ (the macroscopic potential energy per unit mass of the continuum) means that791the strong density gradients 0ρ inside of the continuum of the Earth792(especially, in the heterogeneous region between the rigid core of the Earth and793the fluid core of the Earth) are related with the sources 0t),(sge r of distributed794production of the gravitational energy radiating under the oscillatory motion of795the rigid core of the Earth relative to the fluid core of the Earth owing to planetary796and lunar energy gravitational influences on the Earth [13, 14, 17] and owing to797the energy gravitational influences of the Sun on the Earth [18, 36, 37, 59]798determined by the gravitational interaction of the Sun with the outer large planets799(the Jupiter, the Saturn, the Uranus and the Neptune) of the Solar System.800

Applying the gradient operator for the obtained equation (38) for the801non-stationary gravitational potential ψ , we obtain the evolution equation for the802local gravity acceleration g ψ (of the non-stationary gravitational field):803

,ρρ

ρρ

)div(ρ1)(rotrot

ρ1

t 22

gg

gg

JJJJg804

(40)805which determines the local gravity acceleration g ψ owing the combined806effects of the energy flux gJ of the gravitational energy, the local macroscopic807density ρ of mass distribution and the local density gradient ρ (especially, in the808heterogeneous region between the rigid core of the Earth and the fluid core of the809Earth).810

The gravitational disturbances radiating from the heterogeneous regions811(especially, between the rigid core of the Earth and the fluid core of the Earth)812should have the fundamental influence on the global seismotectonic, volcanic and813climatic activity of the Earth. We shall present in the next section the fundamental814global seismotectonic, volcanic and climatic time periodicities of the815seismotectonic, volcanic and climatic activity of the Earth related with the same816fundamental global time periodicities of the periodic oscillatory motion (related817

with the periodic time variations of the gravitational field on the surface of the818Earth) of the internal rigid core of the Earth (relative to the fluid core of the Earth)819induced by the combined non-stationary cosmic energy gravitational influence on820the Earth of the planets of the Solar System, the Sun and the Moon.821

8223. THE FUNDAMENTAL GLOBAL TIME PERIODICITIES OF THE823

PERIODIC GLOBAL SEISMOTECTONIC, VOLCANIC AND824CLIMATIC ACTIVITY OF THE EARTH825

826Based on the generalized differential formulation (13) of the FLOT used for827

the Earth as a whole, we established the successive approximations for the time828periodicities of recurrence of the maximal (instantaneous and integral) energy829gravitational influences on the Earth: 1),(iyears3}){(T iЗMOON,-S 2),(iyears8 830

years19 ,3)(i 4)(iyears27 for the system Sun-Moon [15] including 11 years (i=2)831[17, 18]; 1),(jyears3}){(T jЗV, 2)(jyears8 for the Venus [15] including 11 years832(j=3) [17, 18]; 1),(kyears15}){(T kЗMARS, 2),(kyears32 )3(kyears47 for the Mars [15];833

1),(nyears11}){(T nЗJ, 2),(nyears12 )3(nyears83 for the Jupiter [15] and for the Sun834owing to the gravitational interaction of the Sun with the Jupiter [18];835

1),(myears29}){(T mЗSAT, 2),(myears59 )3(myears265 for the Saturn [18] and for the Sun836owing to the gravitational interaction of the Sun with the Saturn [18];837

1)(qyears84}){(T qЗU, for the Uranus [18] and for the Sun owing to the gravitational838interaction of the Sun with the Uranus [18]; 1),(ryears165}){(T rЗN, ),2(ryears965 839

)3(ryears2142 for the Neptune [18] and for the Sun owing to the gravitational840interaction of the Sun with the Neptune [18].841

We founded [13-15, 17, 18] that the time periodicities of the global842seismotectonic, volcanic and climatic activity of the Earth are determined by the843combined cosmic factors: G -factor related with the combined cosmic non-844stationary energy gravitational influences on the Earth, )G(a -factor related to the845tectonic-endogenous heating of the Earth as a consequence of the periodic846continuum deformation of the Earth due to the G -factor, )G(b -factor related to the847periodic atmospheric-oceanic warming or cooling as a consequence of the848periodic variable (increasing or decreasing) output of the greenhouse volcanic849gases and the related variable greenhouse effect induced by the periodic variable850tectonic-volcanic activity (intensification or weakening) due to the G -factor, )G(c -851factor [13, 14, 18] related to the periodic variations of the solar activity owing to852the periodic variations of the combined planetary non-stationary energy853gravitational influence on the Sun. We take into account (in this article) the854combined cosmic G , )G(a and )G(b -factors related with the cosmic non-stationary855energy gravitational influences on the Earth of the system Sun-Moon, the Venus,856the Mars, the Jupiter and the Sun owing to the gravitational interaction of the Sun857

with the Jupiter, the Saturn, the Uranus and the Neptune.858Based on the generalized differential formulation (13) of the FLOT used for859

the Earth as a whole, we founded [18, 36] the fundamental sets of the860fundamental global seismotectonic and volcanic time periodicities ftec,T (of the861periodic global seismotectonic and volcanic activities owing to the G -factor) and862the fundamental global climatic periodicities fclim1,T (of the periodic global climate863variability and the global variability of the quantities of the fresh water and glacial864ice resources owing to the )G(b -factor):865

})(T,)(T,)(T,)(T,)(T,)(T,)(T.{..

TTT876542o

rЗN,qЗU,mЗSAT,nЗJ,kЗMARS,jЗV,iЗMOON,-S

fenergy,fclim1,ftec,

lllllllMCL

866

(41)867determined by the successive global fundamental periodicities fenergy,T (defined by868the least common multiples L.C.M. of various successive time periodicities related869to the different combinations of the following integer numbers: 4;3,2,1,i 2;1,j 870

3;2,1,k 3;2,1,n 3;2,1,m 1;q 3;2,1,r 1;,0o l 1;,02 l 1;,04 l 1;,05 l 1;,06 l8711;,07 l 1,08 l ) of recurrence of the maximal combined energy gravitational872

influences on the Earth of the different combined combinations of the cosmic non-873stationary energy gravitational influences on the Earth of the system Sun-Moon,874the Venus, the Mars, the Jupiter and the Sun owing to the gravitational875interactions of the Sun with the Jupiter, the Saturn, the Uranus and the Neptune.876

Based on the generalized differential formulation (13) of the FLOT used for877the Earth as a whole, we deduced [18, 36] the fundamental set of the878fundamental global seismotectonic and volcanic time periodicities fendog,-tecT (of the879periodic global seismotectonic and volcanic activities determined by the )G(a -880factor related with the tectonic-endogenous heating of the Earth as a consequence881of the periodic continuum deformation of the Earth due to the G -factor) and the882fundamental global climatic periodicities fclim2,T (of the periodic global climate883variability and the global variability of the quantities of the fresh water and glacial884ice resources owing to the )G(a and )G(b -factors):885

})(T,)(T,)(T,)(T,)(T,)(T,)(T.{..21

2/TTTT

876542orЗN,qЗU,mЗSAT,nЗJ,kЗMARS,jЗV,iЗMOON,-S

fenergy,fendog,fclim2,fendog,-tec

lllllllMCL

(42)886

determined by the successive global fundamental periodicities fenergy,T (defined by887the least common multiples L.C.M. of various successive time periodicities related888to the different combinations of the following integer numbers: 4;3,2,1,i 2;1,j 889

3;2,1,k 3;2,1,n 3;2,1,m 1;q 3;2,1,r 1;,0o l 1;,02 l 1;,04 l 1;,05 l 1;,06 l8901;,07 l 1,08 l ) of recurrence of the maximal combined energy gravitational891

influences on the Earth of the different combined combinations of the cosmic non-892stationary energy gravitational influences on the Earth of the system Sun-Moon,893the Venus, the Mars, the Jupiter and the Sun owing to the gravitational894

interactions of the Sun with the Jupiter, the Saturn, the Uranus and the Neptune.895We deduced [18] from formula (41) (for 1,o l 1,2 l ,14 l896

,15 l 1,6 l ,07 l )08 l the fundamental global seismotectonic, volcanic and897climatic periodicity (determined by the combined predominant non-stationary898energy gravitational influences on the Earth of the system Sun-Moon, the Venus,899the Mars, the Jupiter and the Sun owing to the gravitational interactions of the900Sun with the Jupiter and the Saturn)901

fenergy,fclim1,ftec, TTT years59453}59,12,15,3,3.{.. MCL = years3540 . (43)902We obtained [18] from formula (41) (for 1,o l 1,2 l ,14 l ,15 l 1,6 l903,07 l 08 l ) the fundamental global seismotectonic, volcanic and climatic904

periodicity (of the Earth’s periodic global seismotectonic and volcanic activity905and the global climate variability)906

}29,12,15,8,8.{..TTT fenergy,fclim1,ftec, MCL 6965 years = 3480 years (44)907determined by the combined predominant non-stationary energy gravitational908influences on the Earth of the system Sun-Moon, the Venus, the Mars, the Jupiter909and the Sun owing to the gravitational interactions of the Sun with the Jupiter and910the Saturn. The time periodicities (43) and (44) give the range [36] of the911following fundamental global seismotectonic, volcanic and climatic periodicities912

ftec,T = fclim1,T (determined by the G -factor related with the combined predominant913non-stationary energy gravitational influences on the Earth of the system Sun-914Moon, the Venus, the Mars, the Jupiter and the Sun owing to the gravitational915interactions of the Sun with the Jupiter and the Saturn):916

fenergy,fclim1,ftec, TTT 3480 ÷ years3540 = )708696(5 =( 303510 ) years.917(45)918

Based on the formula (42) and using the range (45), we obtain the range of919the following fundamental global seismotectonic, volcanic and climatic920periodicities fendog,-tecT (determined by the )G(a -factor related with the tectonic-921endogenous heating of the Earth as a consequence of the periodic continuum922deformation of the Earth due to the G -factor determined by the combined923predominant non-stationary energy gravitational influences on the Earth of the924system Sun-Moon, the Venus, the Mars, the Jupiter and the Sun owing to the925gravitational interactions of the Sun with the Jupiter and the Saturn):926

1517552/TTTT fenergy,fendog,fclim2,fendog,-tec years.927(46)928

We obtain from formula (41) (for 1,o l 1,2 l ,14 l ,15 l 1,6 l ,07 l92908 l ) the fundamental global seismotectonic, volcanic and climatic periodicity930

(of the Earth’s periodic global seismotectonic and volcanic activity and the global931climate variability)932

}29,12,32,8,3.{..TTT fenergy,fclim1,ftec, MCL 6964 years = 2784 years933(47)934determined by the combined predominant non-stationary energy gravitational935influences on the Earth of the system Sun-Moon, the Venus, the Mars, the Jupiter936and the Sun owing to the gravitational interactions of the Sun with the Jupiter and937the Saturn. Еhe fundamental global seismotectonic, volcanic and climatic938periodicity (47) is in good agreement with the estimated (based on the spectral939Fourier analysis) empirical climatic time periodicity 2750 years [19] obtained from940the studies of sediments from Siberian and Mongolian lakes.941

We obtain from formula (42) (for 1,o l 1,2 l ,14 l ,15 l 1,6 l ,07 l94208 l ) the fundamental global seismotectonic, volcanic and climatic periodicity943

fendog,-tecT (determined by the )G(a -factor related with the tectonic-endogenous944heating of the Earth as a consequence of the periodic continuum deformation of945the Earth due to the G -factor determined by the combined predominant non-946stationary energy gravitational influences on the Earth of the system Sun-Moon,947the Venus, the Jupiter and the Sun owing to the gravitational interactions of the948Sun with the Jupiter and the Saturn):949

2/TTTT fenergy,fendog,fclim2,fendog,-tec 6962 years = 1392 years. (48)950We obtain from formula (41) (for 1,o l 1,2 l ,04 l ,15 l 1,6 l ,07 l951

08 l ) the fundamental global seismotectonic, volcanic and climatic periodicity952(of the Earth’s periodic global seismotectonic and volcanic activity and the global953climate variability)954

}59,12,8,8.{..}59,12,8,3.{..TTT fenergy,fclim1,ftec, MCLMCL 59423 years =95514167082 years956

(49)957determined by the combined predominant non-stationary energy gravitational958influences on the Earth of the system Sun-Moon, the Venus, the Jupiter and the959Sun owing to the gravitational interactions of the Sun with the Jupiter and the960Saturn. The fundamental global seismotectonic, volcanic and climatic periodicities961(48) and (49) give the range of the combined fundamental global seismotectonic,962volcanic and climatic periodicities963

fclim2,clim1,fendog,- tectec, TT )708696(2 years = 14161392 years (50)964determined by the combined predominant non-stationary energy gravitational965influences on the Earth of the system Sun-Moon, the Venus, the Jupiter and the966Sun owing to the gravitational interactions of the Sun with the Jupiter and the967Saturn.968

The ranges of the fundamental global seismotectonic, volcanic and climatic969periodicities (46) and (50) give the total range of the combined fundamental970global seismotectonic, volcanic and climatic periodicities971

fclim2,clim1,fendog,- tectec,cfclim, vol,tec, TTT )151755()6702(2 years =972

= )151755()121404( years = )17701392( years = )1891581( years (51)973determined by the combined predominant non-stationary energy gravitational974influences on the Earth of the system Sun-Moon, the Venus, the Mars, the Jupiter975and the Sun owing to the gravitational interactions of the Sun with the Jupiter and976the Saturn. The periodic tectonic-volcanic intensification (determined by the977periodic combined non-stationary energy gravitational influences on the Earth of978the system Sun-Moon, the Venus, the Mars, the Jupiter and the Sun owing to the979gravitational interactions of the Sun with the Jupiter and the Saturn) must980generate the periodic mass redistribution of the terrestrial material inside the Earth981related with the periodic change (characterized by the same periodicity (51)) of the982angular velocity of the Earth’s rotation and related periodic intensification983(characterized by the same periodicity (51)) of the Chandler’s wobble [57] of the984Earth’s pole. The obtained mean value of 1581 years (of the total range of the985combined fundamental global seismotectonic, volcanic and climatic periodicities986(51)) is in a good agreement with the estimated (based on the spectral Fourier987analysis) empirical climatic time periodicity 1500 years [19] obtained from the988studies of sediments from Siberian and Mongolian lakes. The obtained mean value989of 1581 years (of the total range of the combined fundamental global990seismotectonic, volcanic and climatic periodicities (51)) is in a good agreement991with the revealed climatic cycle (time periodicity) near 1500 years [24] for North992Atlantic. The obtained mean value of 1581 years (of the total range of the993combined fundamental global seismotectonic, volcanic and climatic periodicities994(51)) is in a very good agreement with the estimated (based on the spectral Fourier995analysis) empirical climatic time periodicity 1600 years [25] of Holocene.996

We deduced [18, 36, 59] from the formula (41) (for 1,o l 1,2 l ,04 l997,15 l 1,6 l ,07 l 08 l ) the range of the following fundamental global998

seismotectonic, volcanic and climatic periodicities ftec,T = fclim1,T (determined by the999G -factor related with the combined predominant non-stationary energy1000gravitational influences on the Earth of the system Sun-Moon, the Venus, the1001Jupiter and the Sun owing to the gravitational interactions of the Sun with the1002Jupiter and the Saturn):1003

T fclim, vol,tec, fclim1,ftec, TT }29,12,8,3.{..( MCL })59,12,3,3.{.. MCL = years708696 , (52)1004which contains the empirical time periodicity 704 years [6] of the global1005seismotectonic activity. The founded range of the fundamental global1006seismotectonic, volcanic and climatic periodicities years708696TT fclim1,ftec, [18, 36,100759] contains the evaluated (based on the wavelet analysis) time periodicity of1008approximately 700 years [60] characterizing the regional climate variability of the1009Japan Sea. These agreements with the empirical results [6, 60] confirm the1010established cosmic energy gravitational genesis of the founded range1011

years708696TT fclim1,ftec, of the fundamental global seismotectonic, volcanic and1012climatic periodicities the global seismotectonic, volcanic and climatic activity of1013

the Earth. The range (52) of the fundamental global seismotectonic, volcanic and1014climatic periodicities years708696TT fclim1,ftec, gives the mean fundamental global1015seismotectonic, volcanic and climatic periodicity (which is near the empirical1016time periodicity 704 years [6])1017

years702TT fclim1,ftec, 1018(53)1019determined by the G -factor related with the combined predominant non-stationary1020energy gravitational influences on the Earth of the system Sun-Moon, the Venus,1021the Jupiter and the Sun owing to the gravitational interactions of the Sun with the1022Jupiter and the Saturn. Since the ratio ) /(TT 1MARS,3ftec, 46.8 is near the integer1023number 47 and the ratio ) /(TT 2MARS,3ftec, 21.937 is near the integer number 22,1024we can conclude that the time periodicities (52) are determined also by the1025contribution of the non-stationary energy gravitational influence of the Mars on1026the Earth.1027

We have (for 1,o l 1,2 l ,04 l ,15 l ,06 l ,07 l 08 l ) from the formula (41) the1028following fundamental global seismotectonic, volcanic and climatic periodicity1029

ftec,T = fclim1,T (determined by the G -factor related with the combined predominant1030non-stationary energy gravitational influences on the Earth of the system Sun-1031Moon, the Venus, the Jupiter and the Sun owing to the gravitational interactions1032of the Sun with the Jupiter):1033

fclim1,ftec, TT }11,8,11.{..}11,11,8.{..}11,8,8.{.. MCLMCLMCL = years88 ,1034(54)1035which is in agreement with the empirical time periodicity 88 years [6] of the1036global seismotectonic activity of the Earth and with the climatic periodicity 881037years [19]. Since the ratio 88 years/ ТMARS=46.786 in near the integer number 47,1038we concluded [13, 14, 17] that the time periodicity 88 years is determined also by1039the contribution of the non-stationary energy gravitational influence of the Mars1040on the Earth. We see that the range of the fundamental global seismotectonic,1041volcanic and climatic periodicities (52) contains approximately 8 cycles of the1042fundamental global seismotectonic, volcanic and climatic periodicity (54). These1043good agreements (of the independent experimental seismotectonic [6] and the1044climatic [19] periodicity 88 years with the fundamental global seismotectonic,1045volcanic and climatic periodicity (54) confirm additionally the validity of the1046thermohydrogravidynamic theory of the global seismotectonic, volcanic and1047climatic activity of the Earth [18].1048

We have (for 1,o l 1,2 l ,04 l ,15 l ,06 l ,07 l 08 l ) from the formula (42) the1049following fundamental global seismotectonic, volcanic and climatic periodicity1050

fendog,-tecT (determined by the )G(a -factor related with the tectonic-endogenous1051heating of the Earth as a consequence of the periodic continuum deformation of1052the Earth due to the G -factor determined by the combined predominant non-1053

stationary energy gravitational influences on the Earth of the system Sun-Moon,1054the Venus, the Mars, the Jupiter and the Sun owing to the gravitational1055interactions of the Sun with the Jupiter):1056

2/TTTT fenergy,fendog,fclim2,fendog,-tec1057(55)1058

= }11,8,11.{..21}11,11,8.{..

21}11,8,8.{..

21 MCLMCLMCL = years44 ,1059

which is in agreement with the empirical time periodicity 44 years [6] of the1060global seismotectonic activity of the Earth. The fundamental global periodicity1061(55) is in fairly good agreement with the time periodicity 41.6 years [58] of the1062Chandler’s wobble [57] of the Earth’s pole.1063

1064106510661067

4. THE EVDENCE OF THE FUNDAMENTAL GLOBAL1068SEISMOTECTONIC, VOLCANIC AND CLIMATIC TIME1069PERIODICITIES (702 ±6) YEARS AND (3510±30) YEARS1070

RELATED WITH THE EARTH’S ACTIVITY10711072

4.1 The Evidence of the Founded Range of the Fundamental Global1073Periodicities 696 ÷708 years Based on the Established Link Between the1074

Outstanding Climate Anomaly During 8380÷8200 years BP in the North1075Atlantic and the Different Volcanic Eruptions of Hekla in Iceland BC1076

1077It was revealed the outstanding climate anomaly 8200 years before the1078

present (B.P.) in the North Atlantic [28] as the result of weakened overturning1079circulation (which “begins at ~ 8.38 thousand years B.P.” [28]) triggered by the1080freshwater outburst related with catastrophic drainage of Lake Agassiz.1081Consequently, we can assume that the outstanding climate anomaly in the North1082Atlantic is related with the possible catastrophic seismotectonic event near Lake1083Agassiz during the following range1084

(8380÷8200) B.P. = (8290±90) B.P.1085(56)1086Taking into account the date 2008 of the article [28], the range (56) gives the1087corresponding range of the possible catastrophic seismotectonic event near Lake1088Agassiz1089

(8290±90) - 2008 =(6282±90) BC =(6372÷6192) BC.1090(57)1091It is clear that the catastrophic seismotectonic event near Lake Agassiz was1092realized near the lower date 6372 BC of the range (57). We shall present the1093additional evidence of this conclusion in Subsection 4.8.1094

Under this assumption, we can evaluate the range of the dates of the possible1095strong volcanic eruptions and strong earthquakes worldwide (after 1 cycles of the1096fundamental global periodicities fenergy,fclim1,ftec, TTT 696 ÷708 years):1097

-(6282±90)+1×(702±6)=-5580±96=(5580±96) BC=(5676÷5484) BC, (58)1098which is in a good agreement with the following time range of the possible1099volcanic eruptions of Hekla in Iceland BC [38]:1100

(5470±130) BC =(5600÷5340) BC.1101(59)1102We have the sufficiently wide intersection of the ranges (58) and (59)1103

(5600÷5484) BC = (5542±58) BC,1104(60)1105which means the strong correlation of the possible catastrophic seismotectonic1106event near Lake Agassiz (during the range (57)) and the possible volcanic1107eruptions of Hekla in Iceland (during the range (59)).1108

11091110

4.2. The Evidence of the Founded Range of the Fundamental Global1111Periodicities (3510±30) years1112

1113We find the evidence of the founded range (45) of the fundamental global1114

periodicities (3510±30) years based on the established link between the eruption1115of Thera (Santorini) in the Range 1627 1600 BC [32] and the eruptions of1116Santorini in 1866 AD and 1925 AD [39]. Papazachos [39] considered (see also1117[33]) the largest eruptions (accompanied by tsunamis) of the Santorini volcano,1118which occurred (during the last five centuries) in 1457, 1573, 1560, 1866 and11191925 AD. Using the obtained range (1627 1600) BC of the first Santorini’s1120eruption (based on the “radiocarbon wiggle-matching” dating analysis [32] with112195.4% probability), we can obtain the time duration 3509 years between the mean1122date 1895.5 AD (of eruption of Santorini in 1866 AD and 1925 AD) and the1123mean date 1613.5 BC of the obtained range (16271600) BC of the eruption of1124Santorini [32]. We get the ratio of the obtained time duration 3509 years to the1125time periodicities fenergy,fclim1,ftec, TTT ( 303510 ) years:1126

0083.19912.0)35403480(

3509)30(3510

1895.5)(1613.5

,1127

(61)1128which is very close to the integer number 1 denoting that the eruptions of1129Santorini in 1866 AD and 1925 AD are closely related with the eruption of Thera1130(Santorini) in the range (1627 1600) BC [32]. The obtained ratio (61) confirms1131the founded [36] fundamental global seismotectonic, volcanic and climatic1132periodicities fenergy,fclim1,ftec, TTT ( 303510 ) years determined by the combined1133predominant non-stationary energy gravitational influences on the Earth of the1134

system Sun-Moon, the Venus, the Mars, the Jupiter and the Sun owing to the1135gravitational interactions of the Sun with the Jupiter and the Saturn.1136

Taking into account the date 1925 AD of the previous eruption of Santorini1137[61], we see that the sum of the date 1925 AD and the fundamental global1138seismotectonic and volcanic periodicity (54) gives the date of the next possible1139intensification of Santorini volcano:1140

1925 +88 = 2013 AD,1141(62)1142which is in agreement with the modern intensification [62] of microseismic1143activity near Santorini volcano and significant ground uplift. Taking into account1144the date 1928 AD of the previous eruption of Santorini [61], we see that the sum1145of the date 1928 AD and the fundamental global seismotectonic and volcanic1146periodicity (54) gives the date of the next possible intensification of Santorini1147volcano:1148

1928 +88 = 2016 AD,1149(63)1150which cannot be considered as rigorous prediction of the next eruption of1151Santorini volcano without the detailed combined experimental studies of the1152increased microseismic activity [62] and the gravitational field in the near future1153near Santorini volcano based on the generalized differential formulation (13) of1154the FLOT.1155

We find the evidence of the founded range (45) of the fundamental global1156periodicities (3510±30) years based on the established link between the eruption1157of Thera (Santorini) in the range 1627 1600 BC [32] and the increase of the1158global seismicity in the end of the 19th century and in the beginning of the 20th1159century AD [4]. The former President of the Seismological Society of America1160made in 1969 the statement [4] about the increase of the global seismicity1161recorded in the range1162

(1896 1906) AD1163(64)1164up to 1969: “One notices with some amusement that certain religious groups have1165picked this rather unfortunate time to insist that the number of earthquakes is1166increasing. In part they are misled by the increasing number of small earthquakes1167that are being catalogued and listed by newer, more sensitive stations throughout1168the world. It is worth remarking that the number of great [that is, 8.0 and over on1169the Richter scale] earthquakes from 1896 to 1906 (about twenty-five) was greater1170than in any ten-year interval since”. We can obtain the time duration 3514.5 years1171between the mean date 1901 AD (of the range (64)) and the mean date 1613.51172BC of the obtained range (16271600) BC of the eruption of Santorini [32].1173

We get the ratio of the obtained time duration 3514.5 to the time periodicities1174 fenergy,fclim1,ftec, TTT ( 303510 ) years:1175

0099.19927.0)35403480(

5.3514)30(3510

1901)(1613.5

,1176

(65)1177which is very close to the integer number 1 denoting that the increase of the1178global seismicity in the range (64) is closely related with the eruption of Thera1179(Santorini) in the range (1627 1600) BC [32]. The obtained ratio (65) confirms1180the founded [36] fundamental global seismotectonic, volcanic and climatic1181periodicities fenergy,fclim1,ftec, TTT ( 303510 ) years determined by the combined1182predominant non-stationary energy gravitational influences on the Earth of the1183system Sun-Moon, the Venus, the Mars, the Jupiter and the Sun owing to the1184gravitational interactions of the Sun with the Jupiter and the Saturn.1185

11861187

4.3. The Evidence of the Founded Range of the Fundamental Global1188Periodicities 696 ÷708 years Based on the Established Links1189

11901191

We find the evidence of the founded range (52) of the fundamental global1192periodicities 696 ÷708 years based on the established link between the last major1193eruption of Thera (1450 ±14 BC), the greatest earthquake destroyed the ancient1194Pontus (63 BC) [35] and the strong global volcanic eruptions during (50±30) BC1195[38]. Using the date 1450 BC [34] of last major eruption of Thera and assuming1196the same ambiguity ±14 years (as in the studies [32] with 95.4% probability), we1197shall consider the range of the possible dates (1450±14) BC of the last major1198eruption of Thera. We can evaluate the range of the dates of the possible strong1199volcanic eruptions and strong earthquakes (after 2 cycles of the fundamental1200global periodicities fenergy,fclim1,ftec, TTT 696 ÷708 years):1201

-(1450±14)+2×(702±6)=-46±26 = (-72÷-20) = (7 2÷20) BC,1202(66)1203which is in a good agreement with the time range [38]1204

(50±30) BC=(80÷20) BC (67)1205of the strong global volcanic activity of the Earth.1206

The obtained range (66) and the range (67) contain the date 63 BC [35] of1207the greatest earthquake destroyed the ancient Pontus. It gives the evidence of the1208founded [18] fundamental global seismotectonic, volcanic and climatic1209periodicities fenergy,fclim1,ftec, TTT 696 ÷708 years. We get the ratio of the time1210duration (1450±14)-63 (between the date 63 BC [35] of the greatest earthquake1211destroyed the ancient Pontus and the possible dates (1450±14) BC of the last1212major eruption of Thera) to the time periodicities fenergy,fclim1,ftec, TTT 696 ÷7081213years:1214

0129.29392.1)708696()14011373(

6)(70263)-14(1450

,1215

(68)1216which is very close to the integer number 2 confirming the validity of the1217considered possible dates (1450±14) BC of the last major eruption of Thera [34].1218

We find the evidence of the founded range (52) of the fundamental global1219periodicities 696 ÷708 years based on the established link between the last major1220eruption of Thera (1450 ±14 BC), the great frost event (628 AD) [31] in Europe1221related with the atmospheric veil induced by the great unknown volcanic eruption1222[31], and the strong Japanese earthquake (684 AD) [40]. Considering the range of1223the possible dates (1450±14) BC of last major eruption of Thera, we can evaluate1224the range of the dates of the possible strong volcanic eruptions and strong1225earthquakes worldwide (after 3 cycles of the fundamental global periodicities1226

fenergy,fclim1,ftec, TTT 696 ÷708 years [18]:1227-(1450±14)+3×(702±6) = (656±32) AD = (624÷688) AD,1228

(69)1229which contains the date 626 AD of the recorded atmospheric veil (related with the1230great unknown volcanic eruption, apparently, Rabaul’ [31] in Europe and the1231resulted great frost events in 628 AD [31]. This satisfactory agreements confirm1232additionally the validity of the considered possible dates (1450±14) BC of the last1233major eruption of Thera [34]. The upper value of the range (69) is near the date1234684 AD [40] of the strong Japanese earthquake.1235

We find the evidence of the founded range (52) of the fundamental global1236periodicities 696 ÷708 years based on the established link between the last major1237eruption of Thera (1450 ±14 BC) and the strong earthquakes [40] occurred in1238England (1318 AD and 1343 AD), Armenia (1319 AD), Portugal (1320 AD, 13441239AD and 1356 AD), Japan (1361 AD) and the volcanic eruptions [41] in Iceland1240on the Hekla volcanic system (1341 AD and 1389 AD) and on the Katla volcanic1241system (1357 AD). Considering the range of the possible dates (1450±14) BC of1242last major eruption of Thera, we can evaluate the range of the dates of the possible1243strong volcanic eruptions and strong earthquakes (after 4 cycles of the1244fundamental global periodicities fenergy,fclim1,ftec, TTT 696 ÷708 years [18]:1245

-(1450±14)+4×(702±6)= (1358±38) AD = (1320÷1396) AD,1246(70)1247which is near the dates the strong earthquakes [40] occurred in England (13181248AD) and Armenia (1319 AD), respectively. The range (70) contains the date 13431249AD of the strong earthquake in England [40], the dates (1320 AD, 1344 AD and12501356 AD) of the strong earthquakes in Portugal, the date 1348 AD of the strong1251earthquake in Austria [40], the date 1361 AD of the strong earthquakes in Japan1252[40], the dates (1341 AD and 1389 AD) of the volcanic eruptions in Iceland on1253the Hekla volcanic system [41] and the date 1357 AD of the volcanic eruption on1254

the Katla volcanic system [41]. We see that mean date 1358 AD of the range (70)1255is in good agreement with the lower date 1350 AD of the range (1350÷1700) AD1256of the “Litle Ice Age” [38]. Consequently, we can conclude that the “Litle Ice1257Age” [38] is induced by the intensification of the volcanic eruptions of the Earth1258during the range (70).1259

12601261

4.4. The Possible Moderate Intensification of the Global Seismic,1262Volcanic and Climatic Activity of the Earth During 2014÷2016 AD Related1263

with the Last Major Eruption of Thera (1450 ±14 BC)12641265

We have presented above the evidence of the founded ranges of the1266fundamental global periodicities fenergy,fclim1,ftec, TTT )6702( years (given by1267(52)) and fenergy,fclim1,ftec, TTT (3510±30) years. Considering the date (13001268AD) of the eruption of Hekla (1300 AD) in Iceland [41] and the date (1303 AD)1269of great earthquake in China [40] and using the founded range of the fundamental1270global periodicities fenergy,fclim1,ftec, TTT )6702( years of the global1271seismotectonic and volcanic activities and the climate variability of the Earth [18],1272we evaluated [18] the following ranges1273

(1300+696÷1300+708)=(1996÷2008) AD,1274(71)1275

(1303+696÷1303+708)=(1999÷2011) AD,1276(72)1277which give of the next possible strong volcanic eruptions and strong earthquakes.1278We see that the date 2000 AD of the realized eruption of Hekla in Iceland [41]1279gets into the obtained range 1996÷2008 AD of the possible eruptions of Hekla.1280The date 2008 AD of realized strong Chinese 2008 earthquakes gets into the1281obtained range 1999÷2011 AD of the strong Chinese earthquakes. These1282agreements confirm the founded [18] fundamental global seismotectonic,1283volcanic and climatic periodicities fenergy,fclim1,ftec, TTT )6702( years of the1284global seismotectonic and volcanic activities and the climate variability of the1285Earth determined by the combined predominant non-stationary energy1286gravitational influences on the Earth of the system Sun-Moon, the Venus, the1287Jupiter and the Sun owing to the gravitational interactions of the Sun with the1288Jupiter and the Saturn.1289

Considering the date 1318 AD of the strong earthquake in England [40] and1290using the founded range of the fundamental global periodicities1291

fenergy,fclim1,ftec, TTT )6702( years, we evaluated [18] the following range (of the1292forthcoming possible strong earthquakes worldwide and possibly in England)1293

(1318+696÷1318+708) = (2014÷2026) AD,1294(73)1295

which contains the date 2016 AD of the evaluation (63).1296Using the obtained range (1600 1500) BC [33] of the eruption of Santorini,1297

we can evaluate the range of the dates of the possible strong volcanic eruptions1298and strong earthquakes (after 1 cycle of the fundamental global periodicities1299

energyclim1tec TTT ( 303510 ) years [36]):1300-(1550 ±50) +3510±30 = (1960 ±80) AD = (1880÷2040) AD,1301

(74)1302which explains the intensification of the global seismic and volcanic activity in1303the end of the 19th century and in the beginning of the 20th century [4], then in the1304end of the 20th century [6] and in the beginning of the 21th century [13-15].1305

Considering the range of the possible dates (1450±14) BC of the last major1306eruption of Thera, we can evaluate [37] the range of the dates of the possible1307intensification of volcanic and seismic activity (after 5 cycles of the fundamental1308global periodicities fenergy,fclim1,ftec, TTT )6702( years [18] or after 1 cycle of the1309fundamental global periodicities fenergy,fclim1,ftec, TTT ( 303510 ) years [10, 36]):1310

-(1450±14)+5×(702±6) = (2060±44)AD = (2016÷2104) AD.1311(75)1312

The intersection of the ranges (74) and (75) gives the combined range1313(determining the forthcoming intensification of the global seismic and volcanic1314activity in the beginning of the 21th century):1315

(2016÷2040) AD,1316(76)1317which contains the date 2016 AD of the evaluation (63). Consequently, the1318detailed combined experimental studies of the increased microseismic activity [62]1319and the gravitational field near the Santorini volcano can give (based on the1320generalized differential formulation (13) of the first law of thermodynamics) the1321very significant information for verification of the range (76) of the possible1322forthcoming intensification of the global seismic, volcanic and climatic activity in1323the 21th century AD.1324

The ranges (76) and (73) demonstrated [37] the possibility of the moderate1325intensification of the global seismic, volcanic and climatic activity of the Earth1326from 2014÷2016 AD. Thus, based on the possible dates (1450±14) BC of the1327last major volcanic eruption at Thera (Santorini) [34], the date 1318 AD [40] of1328the strong earthquake in England, and using the fundamental global1329seismotectonic, volcanic and climatic periodicities fenergy,fclim1,ftec, TTT )6702( 1330years [18] and fenergy,fclim1,ftec, TTT ( 303510 ) years [36], we evaluated [37] in1331advance (2013 AD) the possible forthcoming intensification (from (2014÷2016)1332AD) of the global seismotectonic, volcanic and climatic activity of the Earth1333determined by the combined predominant non-stationary energy gravitational1334influences on the Earth of the system Sun-Moon, the Venus, the Jupiter and the1335Sun owing to the gravitational interactions of the Sun with the Jupiter and the1336

Saturn.13371338

5. THE EVIDENCE OF THE FORTHCOMING INTENSIFICATION OF1339THE GLOBAL SEISMOTECTONIC, VOLCANIC AND CLIMATIC1340

ACTIVITY OF THE EARTH RALATED WITH THE1341SYNCHRONIZATION OF THE MEAN PERIODICITIES 702 YEARS1342

AND 1581 YEARS OF THE FOUNDED RANGES OF THE1343FUNDAMENTAL GLOBAL PERIODICITIES (702 ±6)1344

YEARS AND (1581±189) YEARS13451346

5.1. The Evidence of the Founded Range of the Fundamental Global1347Periodicities 696 ÷708 years Based on the Established Link Between the Last1348

Major Eruption of Thera (1450 ±14 BC) and the Outstanding Climate1349Anomaly During 8380÷8200 years BP in the North Atlantic1350

1351Based on the analysis of the outstanding climate anomaly during 8380÷82001352

years BP in the North Atlantic [28], we shall present in this Section the additional1353evidence of the lower date 2016 AD (in the range (75)) corresponding to the1354forthcoming intensification of the global seismic, volcanic and climatic activity in1355the 21th century. The outstanding climate anomaly 8200 years before the present1356(B.P.) in the North Atlantic [28] is associated with weakened overturning1357circulation (which “begins at ~ 8.38 thousand years B.P.” [28]) triggered by the1358freshwater outburst related with catastrophic drainage of Lake Agassiz. We have1359presented above the evidence that the outstanding climate anomaly in the North1360Atlantic [28] is related with the possible catastrophic seismotectonic event (related1361with catastrophic drainage of Lake Agassiz) near Lake Agassiz during the range1362(57).1363

Based on the founded range of the fundamental global seismotectonic1364and volcanic periodicities fenergy,fclim1,ftec, TTT )6702( years, we find the1365evidence of the obvious link between the last major eruption of Thera (1450 ±141366BC) and the possible catastrophic seismotectonic event near Lake Agassiz, which1367was realized more probably (to all appearances) near the lower date 6372 BC [28]1368of the range (57). We get the ratio of the time duration 6372 - (1450±14)1369(between the date 6372 BC of the possible catastrophic seismotectonic event near1370Lake Agassiz and the founded above dates (1450±14) BC of the last major1371eruption of Thera) to the mean time periodicity 702 years (of the founded range1372

fenergy,fclim1,ftec, TTT )6702( years [18]):1373

0313.79914.60199.00128.7702

14))(1450-(6372

,1374(77)1375which is very close to the integer number 7 confirming the validity of the1376considered assumption concerning to the lower date 6372 BC of the range (57) as1377

the more probable date of the catastrophic seismotectonic event near Lake1378Agassiz.1379

We get the ratio of the time duration 6192 - (1450±14) (between the date13806192 BC of the upper boundary of the range (57) and the founded above dates1381(1450±14) BC of the last major eruption of Thera) to the mean time periodicity1382702 years (of the founded range fenergy,fclim1,ftec, TTT )6702( years [18]):1383

7748.6735.60199.07549.6702

14))(1450-(6192

, (78)1384which is not close to the integer number 7 confirming the validity of the made1385above conclusion concerning to the lower date 6372 BC of the range (57) as the1386more probable date of the catastrophic seismotectonic event near Lake Agassiz.1387

The above all results give the additional evidence that the last major eruption1388of Thera (1450 BC) [34] can be really considered in the narrow range1389

(1450 ±14 BC).1390(79)1391

13925.2. The Evidence of the Founded Range of the Fundamental Global1393

Periodicities 696÷708 years Based on the Established Link Between the1394Outstanding Climate Anomaly During 8380÷8200 years BP in the North1395

Atlantic and the Great Planetary Disasters in the Central Asia (near 105551396BC) and Egypt (near 10450 BC)1397

1398We must take into account the revealed marks (presented in “Egypt’s Place1399

in Universal History” by Von Bunsen [42]) of the planetary disaster related with1400the dramatic change of the landscape of the Central Asia near 10555 BC [42],1401which is the important date reconstructing the ancient history of the humankind.1402Considering the ancient history of the humankind in his “Fingerprints of the1403Gods” [43], Graham Hancock revealed the Egyptian marks of the planetary1404disaster near 10450 BC, which should be taken also into account. It was suggested1405[13, 14] that the Bunzen’s [42] and Hancock’s [43] estimations are related with1406the planetary disaster during the possible time range1407

(10555 10450) BC1408(80)1409in the ancient history of the humankind.1410

Considering the total range (57) of the catastrophic seismotectonic event1411(near Lake Agassiz [28]) related with the outstanding climate anomaly in the1412North Atlantic [28], we can evaluate the range of dates of the previous possible1413intensification of the seismotectonic volcanic, and climatic activity (before 61414cycles of the fundamental global periodicities fenergy,fclim1,ftec, TTT )6702( years1415[18]):1416

-(6282±90)-6×(702±6) = (10494±126) BC =(10620 10368) BC, (81)1417which includes the range (80). It means the obvious link between the planetary1418

disasters in the Central Asia near 10555 BC [42], the Egypt near 10450 BC [43]1419and the catastrophic seismotectonic event near Lake Agassiz resulted to the1420outstanding climate anomaly in the North Atlantic [28]. The established link gives1421the additional evidence of the founded range of the fundamental global1422seismotectonic, volcanic and climatic periodicities fenergy,fclim1,ftec, TTT )6702( 1423years [18].1424

Taking into account that the possible catastrophic seismotectonic event near1425Lake Agassiz was realized more probably (to all appearances, as it is shown1426above) near the lower date 6372 BC of the range (57), we can evaluate the range1427of the dates of the previous possible intensification of volcanic, seismic and1428climatic activity (before 6 cycles of the fundamental global periodicities1429

fenergy,fclim1,ftec, TTT )6702( years [18]):1430-6372 -6×(702±6) = (-10584±36) =(10584±36) BC =(10620 10548) BC. (82)1431

The range (82) is more narrow than the range (81). The range (82) includes the1432approximate date 10555 BC [42] of the planetary disaster in the Central Asia. We1433can present the additional evidence of the validity of the mean value 10584 BC of1434the range (82).1435

Considering the time range (67) of the strong volcanic activity [38], we can1436evaluate the range of the dates of the previous possible intensification of volcanic,1437seismic and climatic activity (before 15 cycles of the fundamental global1438periodicities fenergy,fclim1,ftec, TTT )6702( years [18]):1439

-50±30-15×(702±6)=(-10580±120)=(10580±120) BC=(10700 10460)BC,1440(83)1441which includes the approximate date 10555 BC [42] of the planetary disaster in1442the Central Asia. The upper value 10460 BC of the range (83) is near the date144310450 BC [43] of the revealed Egyptian marks of the planetary disaster. The good1444agreement of the mean dates 10584 BC (of the range (82)) and 10580 BC (of the1445range (83)) gives the evidence of the validity of the considered assumption1446concerning to the lower date 6372 BC (of the range (57)) as the more probable1447date of the catastrophic seismotectonic event near Lake Agassiz resulted to the1448outstanding climate anomaly in the North Atlantic [28].1449

The intersection of the ranges (81), (82) and (83) gives the range (consistent1450with the range (82))1451

(10620 10548) BC,1452(84)1453which includes the approximate date 10555 BC [42] of the planetary disaster in1454the Central Asia.1455

14561457

5.3. The Synchronic Fundamental Seismotectonic, Volcanic and Climatic1458Time Periodicities T sfclim, vol,tec, (6321±3) Years Characterizing the1459

Synchronization of the Mean Periodicities 702 Years and 15811460Years of the Fundamental Global Seismotectonic, Volcanic1461

and Climatic Time Periodicities T fclim, vol,tec, (702 ±6)1462Years and T cfclim, vol,tec, (1581±189) Years1463

14641465

To present the additional evidence of the mean dates 10584 BC (of the range1466(82)) and 10580 BC (of the range (83)) and the lower date 2016 AD (in the range1467(75)) corresponding to the forthcoming intensification of the global seismic,1468volcanic and climatic activity in the 21st century, we shall take into account the1469founded (and evaluated above) ranges of the fundamental global periodicities1470

T cfclim, vol,tec, )1891581( years (given by (51)) and T fclim, vol,tec, )6702( years1471(given by (52)) based on the generalized differential formulation (13) of the FLOT1472used for the Earth as a whole. We have the periodic recurrence of the same1473combined fundamental seismotectonic, volcanic and climatic time period1474T sfclim, vol,tec, related with the integer number i of the fundamental global1475periodicity T cfclim, vol,tec, )1891581( years and the integer number k of the1476fundamental global periodicity T fclim, vol,tec, )6702( years to satisfy the1477following condition for the time period T sfclim, vol,tec,1478

702kkT1581iTiT fclim,vol,tec,cfclim, vol,tec,sfclim, vol,tec, ,1479(85)1480which results to the condition1481

,702

1581T

Tik

fclim,vol,tec,

cfclim, vol,tec, (86)1482

which means that the ratio fclim,vol,tec,cfclim, vol,tec, T/T must be approximated with some1483accuracy by the rational number .i/k We present the ratio (86) by the following1484mathematical fraction:1485

.

2128

11

13

12702

1581T

Tik

ftec,

cfclim, vol,tec,

1486

(87)1487Considering the following approximation of the ratio (87) given by the following1488rational number:1489

,49

113

12T

Tik

fclim,vol,tec,

cfclim, vol,tec,

(88)1490

we have the reasonable approximation of the relation (85):1491years,631870299Tyears632415814T4T fclim, vol,tec,cfclim, vol,tec,sfclim, vol,tec, 1492

(89)1493which denotes the existence of the following range of the synchronic fundamental1494seismotectonic, volcanic and climatic time periodicities1495

years.3)(6321years6324)(6318T sfclim, vol,tec, 1496(90)1497

Considering the range (82) of the previous possible intensification of1498volcanic, seismic and climatic activity of the Earth, we can evaluate the range of1499the dates of the next possible intensification of seismotectonic, volcanic and1500climatic activity (after 1 cycle of the fundamental global periodicities (90))1501

-10584±36+1×(6321±3)= (-4263±39) =(4263±39) BC =(4302 4224) BC,1502(91)1503which is in partial agreement with the possible range [38]1504

(4400±110) BC =(4510 4290) BC1505(92)1506of the major eruption of Mt Mazama in Oregon, USA. We have the intersection of1507the ranges (91) and (92):1508

(4302 4290) BC,1509(93)1510which confirms the validity of the founded range (90) of the synchronic1511fundamental seismotectonic, volcanic and climatic time periodicities and also the1512mean date 10584 BC of the range (82). We are finally preparing for obtaining the1513range of the next possible intensification of seismotectonic, volcanic and climatic1514activity of the Earth characterized by the range (90) of the synchronic fundamental1515seismotectonic, volcanic and climatic time periodicities.1516

15175.4. The Evidence of the Forthcoming Intensification of the Global1518

Seismotectonic, Volcanic and Climatic Activity of the Earth in the 21st1519Century AD (since 2016 AD) Related With the Outstanding1520

Climate Anomaly During 8380÷8200 years BP in the North1521Atlantic Owing to the Catastrophic Seismotectonic Event1522

(near 6372 BC) Close to Lake Agassiz15231524

Considering the range (82) of the previous possible intensification of1525seismotectonic, volcanic, and climatic activity of the Earth, we can evaluate the1526range of the dates of the forthcoming intensification of seismotectonic, volcanic1527and climatic activity (after 2 cycles of the synchronic fundamental seismotectonic,1528volcanic and climatic time periodicities (90))1529

-10584±36 +2×(6321±3)= (2058±42) AD =(2016 2100) AD1530(94)1531which is in good agreement with the obtained [36] range (75) base on the1532

possible dates (1450±14) BC of the last major eruption of Thera and the founded1533range the fundamental global seismotectonic and volcanic periodicities1534

T fclim, vol,tec, )6702( years [18].1535Considering the mean date (10584 BC) (of the range (82)) as the date of1536

previous possible intensification of seismotectonic, volcanic and climatic activity1537of the Earth, we can evaluate the range of the dates of the forthcoming1538intensification of volcanic, seismic and climatic activity (after 2 cycles of the1539synchronic fundamental seismotectonic, volcanic and climatic time periodicities1540(90))1541

-10584+2×(6321±3)= (2058±6) AD =(2052 2064) AD1542(95)1543which includes the obtained [18] third subrange1544

(2058 2064) AD1545(96)1546of the increased peak of the global seismotectonic, volcanic and climatic activity1547of the Earth in the 21st century during the evaluated range [18]1548

2020 2061AD (97)1549of the maximal seismotectonic, volcanic and climatic activities of the Earth during1550the past 708696 years of the history of humankind. The range (97) was1551evaluated based on the consideration of the dates (in the range AD13891300 ) of1552the volcanic eruptions [41] in Iceland on the Hekla (1300 AD, 1341 AD and 13891553AD) and the Katla (1357 AD) volcanic systems, and the dates (in the range1554

AD13891300 ) of the great earthquakes [40] in China (1303 AD), England (13181555AD and 1343 AD), Armenia (1319 AD), Portugal (1320 AD, 1344 AD and 13561556AD), Austria (1348 AD) and Japan (1361 AD).1557

Considering the ranges (95) and (96), we obtain the following mean range (of1558the increased global seismotectonic, volcanic and climatic activity of the Earth)1559

(2055 2064) AD = (2059.5±4.5) AD,1560(98)1561which incorporates the mean date (10584 BC) of the range (82), the synchronic1562fundamental seismotectonic, volcanic and climatic time periodicities (90) and the1563founded range the fundamental global seismotectonic and volcanic periodicities1564

T fclim, vol,tec, )6702( years (97) used previously [18] for evaluation of the range1565(97).1566

The inclusion of the previously obtained [18] subrange (96) into the1567predicted range (95) means that the obtained range (82) (of the possible dates of1568the previous possible intensification of volcanic, seismic and climatic activity of1569the Earth) is really contain the date of the planetary disaster, which was evaluated1570near 10555 BC [42] in the Central Asia.1571

Let us demonstrate that the evaluated range (95) is really corresponds to the1572dates of the forthcoming intensification of seismotectonic, volcanic and climatic1573

activity related with the synchronization of the mean periodicities 702 years and15741581 years of the fundamental global seismotectonic, volcanic and climatic time1575periodicities T fclim, vol,tec, (702 ±6) years [18] and T cfclim, vol,tec, (1581±189)1576years. To understand this, we consider the following functions )(tf702 , (t)g1581 and1577

(t)g)(tf 1581702 of date t AD (in the range 2013 2071 AD):157818

702)10584(t10584BC)(t,f)(tf 702702

,1579

(99)15808

1581)10584(t10584BC)(t,g(t)g 15811581

,1581

(100)15828

1581)10584(t18

702)10584(t(t)g)(tf 1581702

1583

(101)1584characterizing (depending on time t) the synchronizations of the mean1585periodicities 702 years and 1581 years (of the fundamental global seismotectonic,1586volcanic and climatic time periodicities T fclim, vol,tec, (702 ±6) years [18] and1587

T cfclim, vol,tec, (1581±189) years) for the considered initial time moment 10584 BC1588corresponding to the mean date (10584 BC) of the evaluated range (82). Table 11589demonstrates the calculated functions )(tff 702702 , (t)gg 15811581 and 1581702 gf (based1590on the formulas (99), (100) and (101)) for the presented dates t AD in Table 1.1591

Based on Table 1, we see that the date 2052 AD is characterized by the1592numerical value 0f702 , which means (according to (99)) that the forthcoming date15932052 AD is characterized by the time period equal to 18 cycles of the mean1594periodicity 702 years (of the fundamental global seismotectonic, volcanic and1595climatic time periodicities T fclim, vol,tec, (702 ±6) years [18]) from the initial1596date of 10584 BC appeared in the obtained range (82). Based on Table 1, we see1597that the date 2064 AD is characterized by the numerical value 0g1581 , which1598means (according to (100)) that the forthcoming date 2064 AD is characterized by1599the time period equal to 8 cycles of the mean periodicity 1581 years (of the1600fundamental global seismotectonic, volcanic and climatic time periodicities1601

T cfclim, vol,tec, (1581±189) years) from the initial date of 10584 BC appeared in the1602obtained range (82). Consequently, we obtain the range (which is perfectly1603consistent with the obtained range (95)) (2052 2064) AD related with the1604forthcoming synchronization of the mean periodicities 702 years and 1581 years1605(of the fundamental global seismotectonic, volcanic and climatic time1606periodicities T fclim, vol,tec, (702 ±6) years [18] and T cfclim, vol,tec, (1581±189)1607years) from the initial date of 10584 BC appeared in the obtained range (82). The1608sum (t)g)(tf 1581702 (given by (101) and presented in Table 1) characterizes the1609combined synchronization (for the dates t AD of the range (2013 2071) AD)1610

between the mean periodicities 702 years and 1581 years (of the fundamental1611global seismotectonic, volcanic and climatic time periodicities T fclim, vol,tec,1612(702 ±6) [18] years and T cfclim, vol,tec, (1581±189) years) from the initial date of161310584 BC appeared in the obtained range (82). Considering the Table 1, we see1614that the obtained [18] subrange (96) is characterized by the maximal combined1615synchronization for the date 2058 AD (which is characterized by the minimal1616value 702f 1581g =0.0047 for the subrange (96)) containing to the obtained [18]1617subrange (96).1618

Considering the Table 1, we have the evidence that the maximal combined1619synchronization (of the mean periodicities 702 years and 1581 years of the1620fundamental global seismotectonic, volcanic and climatic time periodicities1621

T fclim, vol,tec, (702 ±6) [18] years and T cfclim, vol,tec, (1581±189) years) from the1622initial time moment 10584 BC (corresponding to the mean date 10584 BC of the1623evaluated range (82)) is realized for the dates 2055 AD and 2056 AD, which are1624characterized by the minimal absolute (positive) values 1581702 gf =0.0014 and1625

1581702 gf =0.0006, respectively. This result is in accordance with the obtained1626ranges (95) and (98). The obtained dates 2055 AD and 2056 AD (characterized by1627the maximal combined synchronization) are in very good agreement with the1628lower date 2055 AD of the obtained mean range (98) of the increased global1629seismotectonic, volcanic and climatic activity of the Earth. This correspondence1630give the additional evidence of the validity of the obtained range (82), which1631includes the approximate date 10555 BC [42] of the planetary disaster in the1632Central Asia.1633

Considering the date (defining by the time parameter сα )1634-10584+ сα1635

(102)1636of the previous possible intensification of seismotectonic, volcanic and climatic1637activity of the Earth, we can evaluate the range of the dates of the forthcoming1638intensification of seismotectonic, volcanic and climatic activity (after 2 cycles of1639the synchronic fundamental seismotectonic, volcanic and climatic time1640periodicities (90))1641-10584+ сα +2×(6321±3)=(2058+ сα ±6)AD=(2058+ сα -6 2058+ сα +6) AD,(103)1642

which characterizes the possible dates of maximal synchronization (of the mean1643periodicities 702 years and 1581 years of the fundamental global seismotectonic,1644volcanic and climatic time periodicities T fclim, vol,tec, (702 ±6) years [18] and1645

T cfclim, vol,tec, (1581±189) years) from the initial time moment (102).16461647

Table 1. Functions 702f , 1581g and 702f 1581g for the dates t AD of the range1648(2013 2071) AD1649

1650t AD 2013 2014 2015 2016 2017 2018 2019

702f -0.0555 -0.0541 -0.0527 -0.0512 -0.0498 -0.0484 -0.0471581g -0.0322 -0.0316 -0.0309 -0.0303 -0.0297 -0.0291 -0.0284702f 1581g -0.0877 -0.0857 -0.0836 -0.0815 -0.0795 -0.0775 -0.0754

t AD 2020 2021 2022 2023 2024 2025 2026702f -0.0455 -0.0441 -0.0427 -0.0413 -0.0398 -0.0384 -0.0371581g -0.0278 -0.0272 -0.0265 -0.0259 -0.0253 -0.0246 -0.024702f 1581g -0.0733 -0.0713 -0.0692 -0.0672 -0.0651 -0.063 -0.061

t AD 2027 2028 2029 2030 2032 2034 2036702f -0.0356 -0.0341 -0.0327 -0.0313 -0.0285 -0.0256 -0.02271581g -0.0234 -0.0227 -0.022 -0.0215 -0.0202 -0.0189 -0.0177702f 1581g -0.059 -0.0568 -0.0547 -0.0528 -0.0487 -0.0445 -0.0404

t AD 2037.38 2038.38 2039.38 2040.38 2041.38 2042.38 2043.38702f -0.0208 -0.0194 -0.0179 -0.0165 -0.0151 -0.0137 -0.01221581g -0.0168 -0.0162 -0.0155 -0.0149 -0.0143 -0.0136 -0.013702f 1581g -0.0376 -0.0356 -0.0334 -0.0314 -0.0294 -0.0273 -0.0252

t AD 2051 2052 2053 2054 2055 2056 2057702f -0.0014 0 0.0014 0.0028 0.0042 0.0056 0.00711581g -0.0082 -0.0075 -0.0069 -0.0063 -0.0056 -0.005 -0.0044702f 1581g -0.0096 -0.0075 -0.0055 -0.0035 -0.0014 0.0006 0.0027

t AD 2058 2059 2060 2061 2062 2063 2064702f 0.0085 0.0099 0.0113 0.0128 0.0142 0.0156 0.0171581g -0.0038 -0.0031 -0.0025 -0.0018 -0.0012 -0.0006 0702f 1581g 0.0047 0.0068 0.0088 0.011 0.013 0.015 0.017

t AD 2065 2066 2067 2068 2069 2070 2071702f 0.0185 0.0199 0.0213 0.0227 0.0242 0.0256 0.0271581g 0.0006 0.0012 0.0018 0.0025 0.0031 0.0037 0.0044702f 1581g 0.0191 0.0211 0.0231 0.0252 0.0273 0.0293 0.0314

16511652

Equating the approximate date 10555 BC [42] of the planetary disaster in the1653Central Asia to the date (102):1654

-10555= -10584+ сα ,1655(104)1656we obtain the numerical value )10555(αс 29 years, which gives (based on1657expression (103) for corresponding date 10555 BC [42] of the planetary disaster1658in the Central Asia) the range of the dates of the forthcoming intensification of1659

seismotectonic, volcanic and climatic activity (after 2 cycles of the synchronic1660fundamental seismotectonic, volcanic and climatic time periodicities (90)):1661

(2081 2093) AD, (105)1662which belongs to the obtained range (75).1663

Equating the mean value 2058+ сα of the range (103) to the mean values 20231664AD, 2040.38 AD and 2061 AD of the evaluated subsequent subranges1665

(2023±3) AD, (2040.38±3) AD and (2061±3) AD (106)1666of the increased activization of the global seismotectonic, volcanic and climatic1667activities of the Earth in the 21st century [18], we can calculate the following1668corresponding numerical values:1669

сα =2023-2058=-35, сα =2040.38-2058=-17.62, сα =2061-2058=3, (107)1670which give (according to the relation (102)) the corresponding dates of previous1671possible intensification of the seismotectonic, volcanic and climatic activity of the1672Earth:1673

-10584-35=-10619 = 10619 BC,1674-10584-17.62=-10601.62 = 10601.62 BC,1675

(108)1676-10584+3=-10581 = 10581 BC.1677

We see that all obtained dates (108) belong to the range (84). It gives the1678additional evidence of the validity of the obtained [18] subranges (106) of the1679increased activization of the global seismotectonic, volcanic and climatic1680activities of the Earth during the obtained range (94) consistent with the1681previously established [37] range (75).1682

Taking into account the obtained results, we can understand that it is1683necessary to expend slightly the evaluated previously [18] subrange (2058 2064)1684AD = (2061±3) AD (of the increased activization of the global seismotectonic,1685volcanic and climatic activities of the Earth) into the obtained mean range1686(2055 2064) AD = (2059.5±4.5) AD (given by (98)) including the obtained dates16872055 AD and 2056 AD characterized by the maximal combined synchronization1688related jointly with the mean date 10584 BC of the obtained range (82), with the1689established synchronic fundamental seismotectonic, volcanic and climatic time1690periodicities years3)(6321T sfclim, vol,tec, (given by (90)), and with the founded1691previously [18] range of the fundamental global seismotectonic and volcanic time1692periodicities T fclim, vol,tec, )6702( years (given by (52)). Finally, equating the1693mean value 2058+ сα of the range (103) to the mean value 2059.5 AD of the1694obtained mean range (98) of the increased activization of the global1695seismotectonic, volcanic and climatic activities of the Earth in the 21 st century1696[18], we can calculate the following corresponding numerical value:1697

сα =2059.5-2058=1.5, (109)1698

which gives (according to the relation (102)) the corresponding dates of previous1699possible intensification of the seismotectonic, volcanic and climatic activity of the1700Earth:1701

-10584 +1.5=-10582.5 = 10582.5 BC, (110)1702which belongs to the range (84). The obtained date (110) is located between the1703mean date 10584 BC (of the obtained range (82)) and the mean date 10580 BC of1704the obtained range (83). It gives the convincing additional evidence of the1705validity of the obtained mean range (2055 2064) AD = (2059.5±4.5) AD (given1706by (98)) of the forthcoming increased intensification of the global seismotectonic,1707volcanic and climatic activities of the Earth.1708

Concerning the date (2016 AD) of the forthcoming intensification of the1709global seismotectonic, volcanic and climatic activity of the Earth in the 21st1710century AD, the estimation (94) (based on the synchronic fundamental1711seismotectonic, volcanic and climatic time periodicities (90)) and the previous1712[10] estimation (75) (based on the fundamental global periodicities1713

fenergy,fclim1,ftec, TTT ( 303510 ) years [36]) are perfectly consistent. It gives the1714convincing additional evidence of the validity of the obtained date (2016 AD) of1715the forthcoming moderate activization of the global seismotectonic, volcanic and1716climatic activities of the Earth. This date (2016 AD) is in perfect agreement with1717the founded same date 2016 AD (given by (63)) of the next possible1718intensification of Santorini volcano. The date 2016 AD (given by (63)) cannot be1719(as mentioned above) considered as rigorous prediction of the next eruption of1720Santorini volcano without the detailed combined analysis (based on the1721generalized differential formulation (13) of the FLOT) of experimental studies of1722the increased microseismic activity [62] and the previous and modern time1723variations of the gravitational field near Santorini volcano during the long time.1724

Concerning to the possible locations of the forthcoming intensification of1725the global seismotectonic, volcanic and climatic activity of the Earth in the 21st1726century AD, we have presented [63] the evaluation of the first forthcoming range1727

2015 2023 2027.7 AD (111)1728of the possible intensification of the seismic and volcanic activity near the Tokyo1729region based on the dates (818 AD [40]; 1605 AD [8]; 1703 AD [8]; 1855 AD1730[64]; 1923 AD and 2011 AD) of previous strong Japanese earthquakes (near the1731Tokyo region) and using the established [63] (based on the generalized differential1732formulation (13) of the FLOT) following mean fundamental global seismotectonic1733and volcanic periodicities: 702(1)Tf years, 351(2)Tf years, 176(3)Tf years,1734

88(4)Tf years, 44(5)Tf years, 33(6)Tf years, 24(7)Tf years, 16.5(8)Tf 1735years, 12(9)Tf years and 6(10)Tf years related with the periodic time1736variations of the gravitational field on the surface of the Earth owing to the1737oscillatory motion of the internal rigid core of the Earth relative to the fluid core1738of the Earth. The lower boundary 2015 AD of the range (111) is located between1739

the lower boundaries 2014 AD (of the ranges (73)) and 2016 AD (of the range1740(75)). The founded range (2014÷2016) AD [10, 37] of the moderate1741intensification of the global seismic, volcanic and climatic activity of the Earth1742contains the lower boundary 2015 AD of the range (111). The short-term1743fundamental global seismotectonic and volcanic periodicity 6(10)Tf years [63]1744(related with the periodic change of the angular velocity of the Earth’s rotation1745owing to the oscillatory motion of the internal rigid core of the Earth relative to1746the fluid core of the Earth) is in perfect agreement with “the unexplained spectral1747peak at a period of around 6 years” [65] in the spectrum of spin-rate variations of1748the Earth for the modern time.1749

17505.5. The Evidence of the Intensification of the Global Seismotectonic,1751

Volcanic and Climatic Activity of the Earth in the Beginning of the 21st1752Century AD Related with the Intensification of the Oscillatory Motion of the1753

Internal Rigid Core Relative to the Fluid Core of the Earth17541755

We can assume that the intensification of the global seismotectonic, volcanic1756and climatic activity of the Earth in the 21st century AD is related with the1757intensification of the amplitude of the oscillatory motion of the internal rigid core1758of the Earth (relative to the fluid core of the Earth), which is related with the1759intensification of the time variations of the gravitational field on the surface of the1760Earth. To confirm this assumption, let us consider the oscillatory motion of the1761internal rigid core of the Earth relative to the fluid core of the Earth owing to the1762non-stationary energy gravitational influences on the Earth of the Moon. We shall1763assume that the time displacement (t)x cr of the internal rigid core of the Earth in1764the fluid core of the Earth (relative to the mass center 3СС of the Earth) along1765some axis ix (i=1 or 2 or 3, see Fig. 1) is given by the following relation1766

)tT2πsin()T(x)tωsin()ω(xx

sdsdoisdsdoicr ,1767

(112)1768where )T(x)ω(x sdoisdoi is the amplitude of the oscillatory motion of the internal1769rigid core of the Earth along some axis ix taken from the axes 321 ,, xxx (see Fig.17701), sdsd T/2πω is the circular frequency of the oscillatory motion, t is the time,1771

h4.12Tsd is the time period of the oscillatory motion corresponding to the1772semidiurnal tidal motion related with the non-stationary gravitational field of the1773Moon. Based on the classical Newtonian gravity theory, we obtain the relation for1774the magnitude )T,Dt,(g sdirfc, of the local gravity acceleration (at the surface point1775

iD , which is the intersection of the axis ix with the surface of the Earth) created by1776the internal rigid core and the fluid core of the Earth:1777

23

3fc,fc,

2sdsdoi3

3rc,fc,rc,

sdirfc, )3(R)R(ργ4π

t))sin(ω(ωxR3)R()ρ(ργ4π

)T,Dt,(g

, (113)1778

where γ is the universal gravitational constant, rc,ρ is the mass density of the1779internal rigid core of the Earth, fc,ρ is the mass density of the fluid core of the1780Earth, rc,R is the average radius of the internal rigid core of the Earth, fc,R is the1781average radius of the fluid core of the Earth, 3R is the average radius of the1782Earth. We have the derivative of the relation (113):1783

t)cos(ω

t))sin(ω(ωxR3)(ωxω)R()ρ(ργ8π

)T,Dt,(gdtd

sd3sdsdoi3

sdoisd3

rc,fc,rc,sdirfc,

, (114)1784

which gives the characteristic maximal positive value1785

sd3

3

sdoi3

rc,fc,rc,2

sdirfc,t T)3(R)(Tx)R()ρ(ργ)16(π

)T,Dt,(gdtdmax

(115)1786

taking into account that ).(ωxR sdoi3 To estimate the characteristic maximal1787positive value (115), we shall assume that the amplitude )T(x sdoi of the oscillatory1788motion of the internal rigid core of the Earth along some axis ix is near to the1789evaluated (by Sir Horace Lamb [66]) space displacement (of 145 m [66]) of the1790resulting force of attraction of the Moon relative to the mass center 3СС of the1791Earth. We calculate the characteristic maximal positive value1792

daymGal0.4151)T,Dt,(g

dtdmax sdirfc,t

(116)1793

taking into account the following numerical values: 2-11 kgmJ106.67γ ,1794m145)T(x sdoi [66], 3

rc, mkg12800ρ [67], 3fc, mkg12200ρ [67] , km1220R rc, 1795

[67], km6371R 3 , h4.12Tsd . The calculated characteristic maximal positive1796value (116) is in good agreement with mean value mGal/day0.4 of the1797experimental range mGal/day0.5)(0.3 corresponding to the uneven (of not1798ordinary wave-like tidal nature) gravitational variations in the order of1799

mGal0.5)(0.3 per unit day [68]. It was pointed out [68] that “the measurements1800taken with gravimeter, examined daily, showed uneven gravitational variations in1801the order of mGal0.50.3 , modulated by a wave-like trace in the order of1802

mGal.511.0 ”. The good agreement between the calculated characteristic maximal1803positive value (116) and the mean value mGal/day0.4 of the experimental range1804

mGal/day0.5)(0.3 (corresponding to the uneven, i.e. not tidal gravitational1805variations) means that the adopted amplitude m145)T(x sdoi [66] of the oscillatory1806motion of the internal rigid core of the Earth is in good agreement with the1807evaluated space displacement (of 145 m [66]) of the resulting force of attraction of1808the Moon relative to the mass center 3СС of the Earth.1809

On the other hand, not assuming the equality m145)T(x sdoi [66], but taking1810into account the mean value )T,Dt,(g

dtdmax sdirfc,t

mGal/day0.4 of the experimental1811

range mGal/day0.5)(0.3 [68] of uneven gravitational variations, we can calculate1812from relation (115) the numerical value m71.139)T(x sdoi , which is in fairly good1813agreement with the evaluated displacement of 145 m [66]. It means, according to1814the relation (115), that the experimental range mGal/day0.5)(0.3 [68] of uneven1815gravitational variations may be explained by the the oscillatory motion of the1816internal rigid core characterized by the range of amplitudes1817

m)63.17478.104()T(x sdoi , which contains the evaluated space displacement (of1818145 m [66]) of the resulting force of attraction of the Moon relative to the mass1819center 3СС of the Earth. Consequently, it means the validity of the considered1820assumption that the amplitude )T(x sdoi of the modern oscillatory motion of the1821internal rigid core (related with the experimental range mGal/day0.5)(0.3 [68] of1822the modern uneven gravitational variations) is near to the evaluated [66] space1823displacement (of 145 m [66]) of the resulting force of attraction of the Moon1824relative to the mass center 3СС of the Earth. Taking into account the previous1825estimation of the amplitude (of the order of 10 m [58] made in 1996 AD) of the1826oscillatory motion of the internal rigid core of the Earth, we can conclude that the1827intensification of the global seismotectonic, volcanic and climatic activity of the1828Earth in the 21st century AD is related with the intensification of the amplitude of1829the oscillatory motion of the internal rigid core of the Earth (relative to the fluid1830core of the Earth) and related intensification of the periodic time variations of the1831gravitational field on the surface of the Earth.1832

18335.6. The Practical Forecasting Aspects of the1834

Thermohydrogravidynamic Theory Related with the1835Regional Seismotectonic and Volcanic Activity of the Earth1836

1837Concerning to the evaluation of all possible locations of the Earth (along1838

with the established Japanese region [63]) of the forthcoming intensification of1839the global seismotectonic, volcanic and climatic activity of the Earth in the 21 st1840century AD, we can generalize the obtained results [63] by taking into account1841that the founded range (2014÷2016) AD [10, 37] of the moderate intensification1842of the global seismic, volcanic and climatic activity of the Earth contains the1843lower boundary 2015 AD of the range (111) of the possible intensification of the1844seismic and volcanic activity near the Tokyo region. Using the established [63]1845fundamental global seismotectonic and volcanic periodicities 702(1)Tf years,1846

351(2)Tf years, 176(3)Tf years, 88(4)Tf years, 44(5)Tf years, 33(6)Tf 1847years, 24(7)Tf years, 16.5(8)Tf years, 12(9)Tf years and 6(10)Tf years, we1848have presented the evidence that the dates ( t(1) 1605 AD, t(2) 1703 AD,1849

t(3) 1855 AD, t(4) 1923 AD and t(5) 2011 AD) of the previous strong1850Japanese earthquakes (near the Tokyo region) may be satisfactory decomposed1851

(relative to the initial date 0 t 818 AD of the previous strong earthquake near the1852Tokyo region) into the following linear sums [63]1853

k),(tt(i)Tαtt(k) 0res

10

1ifki0

(117)1854

characterized by the different coefficients kiα (having the possible values 1αki or18550αki ) and the small residual terms k),(tt 0res for 54,3,2,1,k . Especially for the1856

date 2011 AD of the previous strong Japanese earthquakes near the Tokyo region,1857we obtained (in 2009 AD [13]) the following simple decompositions [63]:1858

t(5) 2011=1923+88, k=4,1859(118)1860

t(5) 2011=1703+176+88+44, k=3,1861(119)1862which determine the date 2011 AD of the possible strong earthquakes near the1863Tokyo region. It was the main argument to announce in 2009 [13] and in 20101864[14] “the time range 2010 2011 AD of the next sufficiently strong Japanese1865earthquake near the Tokyo region”. The occurrence (on 11 March, 2011) of the1866strong 2011 earthquake near the Tokyo region confirms the validity of the1867practical forecasting aspect related with decompositions (118) and (119).1868

Taking into account the confirmed practical forecasting aspect (related with1869occurrence on 11 March, 2011 of the strong 2011 earthquake near the Tokyo1870region) of the decompositions (117), we can generalize the previous results [63]1871for evaluation of the possible dates of the regional seismotectonic and volcanic1872activity near an arbitrary region P (of the Earth) characterized by the initial date1873

)P( t0 of the previous strong earthquake near the region P and by the next dates1874 t(k) (k= 1, 2, …, Pj ) of the previous realized strong earthquakes near the region1875P. It is necessary (as the first step) to obtain the evidence that the dates t(k) (k=18761, 2, …, Pj ) of the previous realized strong earthquakes near the region P may be1877satisfactory decomposed (relative to the initial date )P( t0 of the previous strong1878earthquake near the region P) into the following linear sums1879

k),(tt(i)TαP)(tt(k) 0res

10

1ifki0

, k= 1, 2, …, Pj1880

(120)1881characterized by the different coefficients kiα (having the possible values 1αki or1882

0αki ) and the small residual terms k),(tt 0res for k= 1, 2, …, Pj . Generalizing the1883previous results [63] in the aspect of the practical forecasting, we can state that if1884the decompositions (120) are satisfactory satisfied, then the date 1) t(jP 1885(corresponding to the next number Pj +1 ) of the next forthcoming strong1886earthquake near the region P may be satisfactory decomposed (relative to the1887initial date )P( t 0 (for 1a1 and 0b1 ) or relative to the date t(k) (for 1b and1888

0a ) of the previous strong earthquake near the region P) into the following1889

linear sums1890k)j,,(tt(i)Tβt(k)bP)(ta1)t(j 0res

10

1ifjkij0jP

(121)1891

characterized by the different coefficients ja (having the possible values 1a1 or18920a 2 ), jb (having the possible values 0b1 for 1a1 or 1b2 for 0a 2 ), and1893

jkiβ (having the possible values 1β jki or 0β jki ) and the small residual terms1894k)j,,(tt 0res . If the different decompositions (121) give the same sum 1) t(jP (as in1895

the decompositions (118) and (119)), it means the time synchronization of the1896different fundamental global seismotectonic and volcanic periodicities (i)Tf1897participating in the sums (121) with different coefficients jkiβ depending on the1898initial date )P( t 0 (for 1a1 and 0b1 ) and the different dates t(k) of the previous1899strong earthquake near the region P. Taking into account the confirmed practical1900forecasting aspect (related with occurrence on 11 March, 2011 of the strong 20111901earthquake near the Tokyo region) of the obtained [13] decompositions (118) and1902(119), the obtained forthcoming dates (characterized by the time synchronization1903of the different fundamental global seismotectonic and volcanic periodicities1904

(i)Tf ) 1) t(jP should be considered (for various regions P of the Earth) in the1905first order of priority together with analysis of the time variations of the1906gravitational field on the surface of the Earth.1907

Using the previously formulated [18] local energy prediction1908thermohydrogravidynamic principles (based on the generalized differential1909formulation (13) of the FLOT used for the macroscopic continuum region τ )1910determining the fractures formation in the macroscopic continuum region τ1911subjected to the combined integral energy gravitational influences of the planets1912of the Solar System, the Moon and the Sun owing to the gravitational interaction1913of the Sun with the outer large planets), we can deduce mathematically1914(rigorously) the practical forecasting aspects of the thermohydrogravidynamic1915theory related with the regional gravitational variations owing to the oscillatory1916motion of the internal rigid core relative to the fluid core of the Earth.1917

The local energy prediction thermohydrogravidynamic principles1918(determining the formations of fractures near some time moments t and t ,1919respectively) in the considered macroscopic continuum region τ subjected the1920combined integral energy gravitational influence of the planets of the Solar1921System, the Moon and the Sun owing to the gravitational interaction of the Sun1922with the outer large planets) are formulated mathematically as follows [18]:1923

t

to

dGt),ΔG(τ1924

,Vρdtψdt

t

t τ0

tmomenttimeformaximumlocal (122)1925

and1926

t

to

dGt)ΔG(τ,1927

,Vρdtψdt

t

t τ0

tmomenttimeforminimumlocal (123)1928

which state the attainments of the maximal and minimal integral combined energy1929gravitational influences ((122) and (123) for some time moments t and t ,1930respectively) on the considered macroscopic continuum region τ subjected the1931combined integral energy gravitational influence of the planets of the Solar1932System, the Moon and the Sun owing to the gravitational interaction of the Sun1933with the outer large planets.1934

Assuming that the time displacement (t)x cr of the internal rigid core of the1935Earth in the fluid core of the Earth (relative to the mass center 3СС of the1936Earth) along some axis ix (i=1 or 2 or 3, see Fig. 1) is given by the relation (112),1937we deduced from the local energy prediction thermohydrogravidynamic principle1938(122) (used for the energy gravitational influence of the Moon on the Earth at the1939surface point iD ) that the formulation (122) is satisfied if the magnitude1940

)T,Dt,(g sdirfc, of the local gravity acceleration (created by the internal rigid core and1941the fluid core of the Earth at the surface point iD the surface of the Earth) is in the1942state of the local maximal value (for the time moments sdsd nT/4T t , n=0, 1,19432,…):1944

23

3fc,fc,

2sdoi3

3rc,fc,rc,

sdirfc,t )3(R)R(ργ4π

)(ωxR3)R()ρ(ργ4π

)T,Dt,(gmax

(124)1945

attained for the minimal distance between the center of the internal rigid core and1946the considered surface point iD of the Earth. Consequently, according to the local1947energy prediction thermohydrogravidynamic principle (122), the formation of the1948fractures (under the energy gravitational influence of the Moon on the Earth) is1949more probable in the macroscopic continuum region τ at the surface point iD1950characterized by the maximal local gravity acceleration (124) related with the1951minimal distance between the center of the internal rigid core and the considered1952surface point iD of the Earth.1953

Assuming that the time displacement (t)x cr of the internal rigid core of the1954Earth in the fluid core of the Earth (relative to the mass center 3СС of the1955Earth) along some axis ix (i=1 or 2 or 3, see Fig. 1) is given by the relation (112),1956we deduced from the local energy prediction thermohydrogravidynamic principle1957(123) (used for the energy gravitational influence of the Moon on the Earth at the1958surface point iD ) that the formulation (123) is satisfied if the magnitude1959

)T,Dt,(g sdirfc, of the local gravity acceleration (created by the internal rigid core and1960

the fluid core of the Earth at the surface point iD the surface of the Earth) is in the1961state of the local minimal value (for the time moments sdsd nT/4T3 t , n=0, 1,19622,…):1963

23

3fc,fc,

2sdoi3

3rc,fc,rc,

sdirfc,t )3(R)R(ργ4π

)(ωxR3)R()ρ(ργ4π

)T,Dt,(gmin

(125)1964

attained for the maximal distance between the center of the internal rigid core and1965the considered surface point iD of the Earth. Consequently, according to the local1966energy prediction thermohydrogravidynamic principle (123), the formation of the1967fractures (under the energy gravitational influence of the Moon on the Earth) is1968more probable in the macroscopic continuum region τ at the surface point iD1969characterized by the minimal local gravity acceleration (125) related with the1970maximal distance between the center of the internal rigid core and the considered1971surface point iD of the Earth.1972

Thus, according to the local energy prediction thermohydrogravidynamic1973principles (122) and (123), the formation of the fractures (under the energy1974gravitational influence of the Moon on the Earth) is more probable in the1975macroscopic continuum region τ at the surface point iD characterized by the1976maximal local gravity acceleration (124) and the minimal local gravity1977acceleration (125) related with the minimal and maximal, respectively, distance1978between the center of the internal rigid core and the considered surface point iD1979of the Earth. It is clear from the physical viewpoint that the obtained (using the1980consideration of the energy gravitational influence of the Moon on the Earth)1981result is valid for the macroscopic continuum region τ subjected the combined1982integral energy gravitational influence of the planets of the Solar System, the1983Moon and the Sun owing to the gravitational interaction of the Sun with the outer1984large planets. Consequently, the formation of the fractures during the earthquake1985(under the energy gravitational influence of the planets of the Solar System, the1986Moon and the Sun owing to the gravitational interaction of the Sun with the outer1987large planets) is more probable in the macroscopic continuum region τ under the1988maximal local gravity acceleration and under the minimal local gravity1989acceleration. This conclusion is in good agreement with the experimental studies1990[69] of the time variations (before and after the large distant earthquakes) of the1991gravitational field on the surface of the Earth for various regions. Almost all large1992distant earthquakes were closely related [69] with the maximal local gravity1993accelerations and under the minimal local gravity accelerations.1994

199519961997

CONCLUSIONS19981999

Based on the generalized differential formulation (13) of the FLOT used for2000

the Earth as a whole, we have presented the fundamentals of the2001thermohydrogravidynamic theory of the global seismotectonic, volcanic and2002climatic activity of the Earth determined by very significant non-stationary energy2003gravitational influences on the Earth of the Sun [18] (owing to the gravitational2004interactions of the Sun with the Jupiter, the Saturn, the Uranus and the Neptune),2005the Moon [13, 14, 17] and the planets [13-15, 17, 18] of the Solar System. Based2006on the established links between the great volcanic eruptions, earthquakes and2007climatic anomalies in the history of humankind, we have presented the evidences2008of the established fundamental global seismotectonic, volcanic and climatic2009periodicities (702±6) years [18] and (3510±30) years [36] determined by the2010combined predominant non-stationary energy gravitational influences on the Earth2011of the system Sun-Moon, the Venus, the Mars, the Jupiter and the Sun owing to2012the gravitational interactions of the Sun with the Jupiter and the Saturn. Taking2013into account the founded possible dates (1450±14) BC (given by (79)) of the last2014major volcanic eruption at Thera [34] and the date 1318 AD of the strong2015earthquake in England [40], we have presented the evidence of the forthcoming2016intensification of the global seismotectonic, volcanic and climatic activity of the2017Earth during the range (given by (75)) (2016÷2104) AD [37] related with the2018range of the fundamental global seismotectonic, volcanic and climatic2019periodicities fclim1,ftec, TT (702±6) years [18].2020

We have shown that different distinct eruptions of the Thera (dated in the2021following ranges: (1700÷1640) BC [29, 30], (1628 1626) BC [31], (1627÷1600)2022BC [32], (1600÷1500) BC [33], (1628÷1450) BC [34]) are related with the2023subsequent intensifications of the global seismicity volcanic activity in the end of2024the 19th century and in the beginning of the 20th century [4], in the end of the 20th2025century [6], and in the beginning of the 21st century AD [13-15, 17, 18].2026

We have presented the additional evidence of the forthcoming2027intensification of the global seismotectonic, volcanic and climatic activity of the2028Earth during the range (given by (94)) (2016 2100) AD based on the following2029established links: 1) between the last major eruption of Thera (1450 ±14 BC)2030[34] and the outstanding climate anomaly during 8380÷8200 years BP in the2031North Atlantic [28] owing to the very probable catastrophic seismotectonic event2032(near 6372 BC) close to Lake Agassiz; 2) between the outstanding climate2033anomaly during 8380÷8200 years BP in the North Atlantic [28] and the great2034planetary disasters in the Central Asia (near 10555 BC) [42] and Egypt (near203510450 BC) [43].2036

We have presented the mathematical evidence of the synchronic fundamental2037seismotectonic, volcanic and climatic time periodicities T sfclim, vol,tec, (6321±3)2038years characterizing the time synchronization of the mean periodicities 702 years2039and 1581 years of the fundamental global seismotectonic, volcanic and climatic2040time periodicities T fclim, vol,tec, (702 ±6) years [18] and the established2041

fundamental global seismotectonic, volcanic and climatic time periodicities2042T cfclim, vol,tec, (1581±189) years (which is in a good agreement with the revealed2043

time periodicity of ~ 1500 years [23] for the long-term fluctuation in the length of2044the mean solar day related with a long-term fluctuation in the Earth’s angular2045velocity of rotation and the related rotational energy of the Earth), which is also in2046a good agreement with the following empirical climatic time periodicities: 15002047years obtained [19] from the studies of sediments from Siberian and Mongolian2048lakes; near 1500 years [24] for North Atlantic; 1600 years [25] for Holocene.2049Taking into account the all established links and the established fundamental2050global seismotectonic, volcanic and climatic time periodicities T fclim, vol,tec,2051(702±6) years [18], fenergy,fclim1,ftec, TTT ( 303510 ) years [36],2052

T cfclim, vol,tec, (1581±189) years, T sfclim, vol,tec, (6321±3) years, we have presented2053the mathematical evidence of the validity of the previously evaluated subsequent2054subranges [18]: (2023±3) AD, (2040.38±3) AD, and (2061±3) AD = (2058÷2064)2055AD (given by (106)) of the increased activization of the global seismotectonic,2056volcanic and climatic activities of the Earth [18] during the nearly consistent2057established ranges (2016÷2104) AD [37] (given by (75)) and (2016 2100) AD2058given by (94). We have presented the mathematical evidence that the previously2059evaluated subrange (2061±3) AD = (2058÷2064) AD [18] (of the increased2060activization of the global seismotectonic, volcanic and climatic activities of the2061Earth) should be expended slightly into the range (2055 2064) AD =2062(2059.5±4.5) AD (given by (98)), which includes the obtained dates 2055 AD and20632056 AD characterized by the maximal combined synchronization of the2064established synchronic fundamental seismotectonic, volcanic and climatic time2065periodicities years3)(6321T sfclim, vol,tec, (given by (90)) and the founded2066previously [18] range of the fundamental global seismotectonic and volcanic time2067periodicities T fclim, vol,tec, )6702( years (given by (52)).2068

Based on the founded relation (114) for the derivative of the local gravity2069acceleration (created by the internal rigid core and the fluid core of the Earth at2070the surface point of the Earth), we have presented the evidence that the2071intensification of the global seismotectonic, volcanic and climatic activity of the2072Earth in the beginning of the 21st century AD is related with the intensification of2073the oscillatory motion of the internal rigid core relative to the fluid core of the2074Earth. Based on the established [63] mean fundamental global seismotectonic and2075volcanic periodicities: 702(1)Tf years, 351(2)Tf years, 176(3)Tf years,2076

88(4)Tf years, 44(5)Tf years, 33(6)Tf years, 24(7)Tf years, 16.5(8)Tf 2077years, 12(9)Tf years and 6(10)Tf years, we have generalized the previous2078results [13, 14, 63] by founding the decomposition (121) for the date 1) t(jP 2079(corresponding to the next number Pj +1 ) of the next (forthcoming) strong2080earthquake near the region P using the information about the initial date )P( t0 of2081

the previous initial strong earthquake near the region P and the next dates t(k)2082(k= 1, 2, …, Pj ) of the previous realized strong earthquakes near the region P.2083

Based on previously formulated [18] local energy prediction2084thermohydrogravidynamic principles (122) and (123) (consistent with the2085generalized differential formulation (13) of the FLOT used for the macroscopic2086continuum region τ ), we have presented the mathematical evidence that the2087realization of the strong earthquakes (under the energy gravitational influence on2088the macroscopic continuum region τ of the planets of the Solar System, the Moon2089and the Sun owing to the gravitational interaction of the Sun with the outer large2090planets) is more probable under the maximal local gravity acceleration and under2091the minimal local gravity acceleration, that is consistent with the experimental2092studies [69] of the time variations (before and after the large distant earthquakes)2093of the gravitational field on the surface of the Earth for various regions. Finally,2094we can conclude that the combined consideration of the decompositions (121) (for2095evaluation of the date 1) t(jP of the next forthcoming strong earthquake near the2096considered region P based on the initial date )P( t0 of the previous strong2097earthquake near the region P and the next dates t(k) of the previous realized2098strong earthquakes) and the local energy prediction thermohydrogravidynamic2099principles (122) and (123) (determining the maximal and minimal local gravity2100accelerations preferable for realization of the strong earthquakes) may give the2101useful basis for the practical forecasting of the regional seismotectonic and2102volcanic activity of the Earth during the founded (since 2016 AD) forthcoming2103moderate intensification of the global seismotectonic, volcanic and climatic2104activities of the Earth.2105

21062107210821092110

REFERENCES211121122113

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