a spectral approach to moho depths_88

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J. Phys.Earth,36,255-266, 988

A SPECTRALAPPROACH TO MOHO DEPTHSESTIMATION FROM GRAVITY MEASUREMENTSIN EPIRUS(NW GREECE)Gerasimos-Akis TsersNrrs,l'* John DRerolouros,2

and Klisthenis DrMnnlq.ols2| furthquake Researchnstitute, The Universityof Tokyo,Bunkyo-ku,Tokyo I 13, Japan?Department f Geophysics, thens(lniversity,Panepistimiopolisthens157 84, Greece(Receivedanuary7, 1988;RevisedNovember16, 1988)

We compute rustal hicknessn Epirus NE Greece),rom spectral nalysis fthe Bouguer ravity ield.Moho depthswereestablishedrom the slopeof the og-power adialspectrumat the owerendof thewavenumber andandwere ound o vary rom 3l to 38km.This s n agreement ith the results btained y other nvestigatorsmployingseismologicalmethodsof analysis.

L lntroductionA two-dimensional set of data representing a potential field such as the gravityfield, can be thought of as a superpositionof fields due to a subsurfacedistribution

of sources.Consequently, inear methods such as two-dimensional filtering shouldbe of use in separating the various components according to their wavenumberspectrum.Spectralmethodsof gravity data processingare being ncreasinglyemployed nrecent years,owing to their elegance n handling a large amount of data and theirbuilt-in mechanism for sigaal-to-noiseratio enhancement(BuerrecHenyy.l andLEu. 1975).By Fourier transformation, the gravity field data can be representedby two-dimensional Fourier series onsistingof various frequencieswhich characterize heanomalies.Thb amplitude and phase elationship among these requencieshas beenusedextensivelyby many workers for the interpretation of gravity data, particularyin the caseof downward continuation and source depth estimation (Srncron and

GReNr,1970; nsnrr et al . , l97l ; GnrnN, 1972; IHN er al . ,1976;plr tet at . ,1979:Nscret al.,1983;Bossand SnNcuere, 984).Representinghe Moho by a variable interface,h(x), and considering a84,Greece. Present ddress: thensUniversity,Panepistimiopolisthens 157

255


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256 G.-A. Tsrt-nNus, . Duropour.os, and K. Dtutrnllolsconstant density contrast, P., the Fouriei transform of the correspondinggravityfield can be written (Mssnn and PsnsnspN,1982):

where,k is the wavenumber :liwavelength), and G is the internationalgravityconstant.Expanding the exponentialand taking into account only the first order termwhich is a very good approximation for the small wavenumbers that we areinterestedn, the above elation can be written:

/g(k) :2cPos- i tx tn"771l i Q)indicating a direct connection between the computed gravity spectra and theunknown mean depth, ho, of the interface,perturbated by the term Ah(k).

At the long wavelengths n which we are interested he non-linear effect of/h(k) is negligible Mrsrne and PsonnsEN, 982),and the relation betweengravityspectra and depth is almost log-linear. Thus, the slope of the graph provides anestimateof the depth.

For the case of two-dimensional data, it is convenient to work with theabsolute value of the radial spectrum of all the partial waves falling within afrequencyrange, as will be explained n section 3.2. Tectonics nd Geologyof the Area

The area of Epirus lies along the North-Western margin of the Greekmainland, extends nto SW Albania, and is situatedalong the Apullian and Aegeanblocks (Fie. l) .

The rocks present n the area aredivided into the lonian depositionalzone andits subzone(Gavrovo). The Adriatic-Ionian zone begins from Tirana in Albaniaand extendsalong the study area down to NW Peloponnese.t is madeup of rocksranging in age from Triassic (evaporitic facies) to upper Neocen (I.F.P., 1966).These are mainly pelagic limestones ollowed by silts, sandstones, nd conglom-eratesof typical flysch faciesof Miocene age.The subzoneof Gavrovo is exposedeast of the Ionian zone and consistsofthick, mainly neritic limestonesprotruding through the flysch. Upper Eocenelimestones ie disconformably upon Cretaceous imestones

From Eocene ime until the end of the Tertiary, detrital sediments ccumulatedin the areL reaching a few thousand meters above the Triassic evaporites.Significant ectonicactivity started n the subzoneof Gavrovo in the Oligocene,andin the Ionian zone n the Middle Miocene (I.F.P., 1966).This activity created oldsand thrust faults that generallystrike NW-SE (Fig. l).

The SW migration of deformation and fault plane solutions from a fewmoderate earthquakesnear the Ionian coast (Dnarorouros and Dsrmests, 1974;

f"o/g (k ) : (2GP^ lH I g- ikx . - l f t l r t x )6*- J - * (1 )


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Moho Depths Estimation from Gravity Measurements 257

Fig. l. Tectonic setting ofencountered.

Ittl7:; : . . 1 _ d - / - - . )li;f7i7.t-'g'",4

the general area, illustrating the tectonic zones


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25 8 G.-A. Tsu-eNrts,J. Duropoulos, and K. DtutrnllplsPnpnzrcnos et al., 1984), ogether with studies of late Cenozoic deformation(MEncmnet al., 1979), uggest hat the tectonicactivity results rom the collisionand continuing North-Westward convergence f the Northern Ionian seafloor,which s affected y the tectonicdevelopment f the Aegean egion LEPIcHoNandAucnrrnR, 1979;BuncHFrELD,980).The tectonic ramework of the area s mainly compressive, haracterized ynumerous zones of thrust faulting striking parallel to the coast (Fig. l), withearthquakes howinga predominantcompressive tress omponent.However, some seismic events have been attributed to normal faulting(Dnarorouros and DEtln.r.srs, 974;McKENZTE, 978)and a recent microearth-quake survey n the area(KINc et al., 1983) evealed hat the derived ault planesolutionsexhibita varietyof focal mechanisms, hich arenot consistentwith simplezonesof shorteningor extension.Additionally, a number of in situ stressmeasurementsn the area(PlqutN elal., 1984),ndicate he presence f a dominant E-W extensional tress egime.3. Methodof Analysis

The Bouguermap of Epirus,preparedby Mnnrs (1977),has beenused n thepresentnvestigation. he areawas surveyed ravimetrically uring theyears 97l-1973 Fig. 2), with a surveydensityof 0.075stations/km2.The datawereuniformly reduced o Bougueranomalies t meansea evel,andtopographic eductions rom 0 to 166.7 m werecomputedon a spherical arth witha uniform densityof 2.67g/cm3.The whole map was digitized and the data were gridded using a modifiedversion of an interpolation algorithm written by SwlrN (1976)which uses initedifferenceequations o producea systemwith minimum curvature.The resultinggrid wasthen contouredand inconsistent ata were dentifiedby the tight circularcontours hey producedand were removed rom the data file.Eight squaregrids,measuring160x l60km each(32x32 data points) andoverlappingby 501were used or the calculationof Moho depthsacross N-Sdirection.

For each squaregrid, the following operations were performed. First, weremoved he regional ield'by itting a planesurface o all the databy the methodofleast squares.The obtained regional field was found to be describedby theexpression:'f(x,y): -3.985x* 1.068y+0.827 (3)

wherex andy are the two axesof the grids.The residualgravity field values or each block were then transformed romthe space omain to the frequencydomain by meansof a Fast Fourier Transform(FFT).Applying an FFT algorithm to the abovedata subgridswill obviouslycausea


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259oho Depths Estimation from Gravity Measurements2tr30',I, , r - 40 : t5 /i'n

",'li,,i,, / t;;i,[, !:\\.:\r:t{\,i((rj;irl:N\N.rN\\\\N

s-,rj"-ANi : i J-Ils7.s6,Fig. 2. Bouguer ravitymapof the nvestigatedrea.Contourntervals 5mgal.

pronouncedGibbs phenomenon eading to great edgeeffects. n order to maketransitionzoneswider, weused hefollowing procedure BnerrlcHARYYAand LEu,teTs).We assume hat the residual ield vanishes t the points locateda distanceof

\ iil


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G.-A. TsneNns, J. Dnnopout-os, and K. Dnntntllts(- ru+8 DarA -J

}- O{ + }'-a rFa -iFar-- - r'+ -.| 41" 1IIIIIIIIIIIIIII

IIIIIIIIIIIIIL

Fig. 3. Dataexpansioncheme.four units of the dataspacing rom the boundaryof eachsubgrid. nclusion of thesepoints results n (N+8)x(N+8) non-equispaced ata points for an NxN block(Fig. 3). Next, bicubic splinesurfaceswere it ted to the data by employing he finiteelement technique (INouE, 1986) n such a way that the residual field and thecontinuity of the first and secondderivativesaremaintainedat eachoneof the datapoints. Thesesurfaces,were used o generate he "tapered" data set.

The Fourier transform of each data grid results in a set of Real R,n andImaginary ,l* amplitudes by meansof which the field valuesgiven at the grid points(x, y) can be representedby the sum:s(x,y): I I nf," os{2nDXN) (kx+ my)\k m

+ 1| sin 2n@XN) (kx+ my))whereDX is the grid interval.Equation 4 can be written as follows:s(x, ): T; C\cos{2nl@xN)kx*my)- Ph}

where Pl is the appropriatephaseangle andch:{(Gh)'+(t!,)r}'t '

is the amplitude of a partial field wave, with wavelengthDX'Nl(k2+m2)tt'frequencyF h:(k2 * m27rrz.

(4)

(5)

(6)and


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Moho Depths Estimation from Gravity Measurements

t l vA l , tlU t ' l8 t lSt c / $ t. :J:: , bl : . ; : : : :

Fig. 4. Schematiccomputation of the radial spectrum for the northern160 160kmblock. Spectrummatrix coefficients l are alsoshown.

In order to calculate the radial spectrum for each data grid, we calculate firstthe 2-D power spectrum:

P(1, ): R(1, )2+ Ig, n'. 0)The radial spectrum s calculatedby superposinghe 2-D spectrumwith anumberof concentricings hat arecentered t [1 1] , upperleft oint of thematrixP(1, ), which s the owest requency omponent f the data set mean alue),andwith radialdistancesescribedn Fig. 4. Next, he squares f the amplitudes f thepartialwavesoccurringbetweenwo consecutiveycles reaveraged.The schemeor computing adial spectra or the northern160x 160km data

grid is illustrated n Fig. 4. The resultingvalues orm the radial spectrum f theanomalousieldunderconsideration,nd arenormalizedo the valueCo(1, ). Bythis technique,we transform the current two-dimensional roblem to a one-dimensional ne,assuming o preferred rientation n the esponse.If the ogarithms f sucha radial spectrum replottedagainst requency, ne

261


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G.-A. TsnrrNrn,J. DnexoPoulos,and K. Dmlrntlplst

often findsa series f pointswhich may well be represented y oneor morestraightlines. From the slopeof the lines and the standard error of fi t we calculate hecorrespondingdepth and error depth to the appropriatedensitydiscontinuityforeachdata grid.4. Discussion f the Results

Figure5 shows he spectra f the northernand southern160 160 m partsofthe map respectively.The obtained 3-D representationsof the encounteredwavenumbers uggesthat the problemdue to the preferredorientation s minimal.The correspondingadial spectrumof the northernblock is shown n Fig. 6.The two linear segments f this plot correspond o two differentdensitydiscon-tinuities.The first segment anges rom wavelengths 60-40kmwhile the secondsegment anges rom 40 to 20km. Beyond the 20km wavelength, he amplitudesfoim an almostwhitespectrumwhichcorrespondso randomnoise ontainedn thedata.To estimate he depth to the deepest iscontinuity,(which is attributed to theMoho), the central axis of the area was scannedby 8 overlappinggrids of themaximum allowed grid size 32x32 data points (160x l60km), allowing thedetectionof wavelengths reater han 40km. The correspondingadial spectra redepicted n Fig. 7, while the deriveddepths o the Moho with the corresponding.rio, aregraphicallypresentedn Fig. 8. This latter figuresuggestshat the averageMoho depths n the areavary from a minimum of 32km to about 39km. A recent

Fig. 5. Three-dimensionalepresentation f the encounteredwavenumbersthe northern (A), and the southern B) blocks'

Orr{7r,


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Moho DepthsEstimation from Gravity Measurements

ltAvENUl.lBERS(CYCLES/KI'|)t

Fig. 6. Radial spectrum or the northern block.

263

---J- l0 . 5 |

km

0 , 5 I

depthsestimation.ig. Z. Radial spectrum or the eight grids used or Moho


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264 G.-A. TsnrnNrIs. J. Dnexopoulos. and K. Drurrntlors

1 2 3 4 5 6 . 7 8I r l l l l l l r--20KM-i

3040

I TI Ft f tt oV! z er

S T l | O YR I I

a a =

Fig. 8. Moho depthsraverselong N-S)Epiruswith associatedrrors.Points1,2,' . , 8 representhecentersf the160 160km rids sedor hescan.investigationn the areaemploying he analysisof P, and P,' waves Knnacosrns,1982), uggested crustal hickness f the order of 40km, while an applicationof asinglestationdeconvolutiono long-periodP-waves esulted n a crustal hicknessof about 35km (TsnrnNusand DRAKopouLos, 988).These esultsseem o be ingood agreementwith the resultsobtained rom the presentanalysis.5. Accuracyof theResults

Onecauseof discrepancyn the resultsmight be found in the effect hat everyunit of buriedmasscontributes o the total observed ravityfield, hus the spectraloverlapbetween he effectof deeperand shallowersourceswill alwaysoccur.Care also has to be taken to minimize aliasingerrorscausedby digitization.Obviously, closer digitization has the effect of incorporating high frequencycomponents, esulting in the decreaseof the slope of the log spectralcurve(Sencron,1968).One difficulty with this refinementoccursbecausehe higher wavenumbercomponentsend towards ncreasingly mallermagnitudes nd it becomes ard toseparate hem from noise.The overall effect s that the deriveddepthswill beunderestimated.ncreasing igitizationon the other hand leads o aliasingerrors,hencean optimizationof digitizationspacing s essential.6. Conclusion

As part of an extensive eophysicalnvestigationn the area of Epirus (NWGreece),'we ttempted o derive he crustal hickness rom the existinggravitydata.This was achievedby employingspectral echniquesof analysisof the Bouguergravity map of the area.


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Moho Depths Estimation from Gravity Measurements 265A series of 8 overlapping grids of maximum allowed grid size (160 x 160km),were used in an attempt to increase resolution while retaining the capacity to discerndeeper sources. For each grid, Moho depths were established from the slope of thelog-power radial spectrum at the lower end of the wavenumber band.crustal thickness in the area wa s found to vary from 3l to 39km, an d thisresult is in good agreement with the results obtained employing seismological data.

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ecrasement.Bull. Soc. Geol.Fr., 19, 437460, 1990.DrlrrrRre,ors, ., G.-A. TSELENTTS,nd K. THeN.Lssoules, basicprogram for 2-D spectralanalysisof gravity data and source-depthestimation, Comput. Geosci.,13, 549-560,1987.Dnaropouros, J. K. and N. D. Drrtsesls, On the mechanismof someearthquakesn the areaof westernGreeceand the stressproducing them, Proc. l3th Eur. Seism.Com. SpecialIssueof rechn. and Ec. studies,BucharestD-ser. Geoph.prosp.,10, 169-192, 1974.GRTEN, . G., Magnetic profile analysis,Geophys'. . R. Astron soc.London 30, 393-403.1972.HluN, A., E' G. KtNo, and D. C. Mrsune, Depth estimationof magneticsources y meansofFourier amplitude spectra.Geophys.prospect.,24, 2g7_30g,1g76.INoue, H. ' A least squares smooth fitting for irregularly spaced data-Finite elementapproachusing the cubic B-splinebasis,Geophysics, l,205l-2066, 19g6.INstIrurn FneNcnrs ou Prrnor-E (LF.p.), Etude Geologique e t'Epire,I.G.M.E., Athens,1966.K,{n,{cosrAs,G., Crustal structurefrom seismologicalnvestigations n the area of Greece.Ph.D. Diss.Seismological ab., ThessalonikiUniversity, 13 3pp., 19g2.KING,G., G.-A. TssrnNtts,P. MotN.m, S. Roncxrn, H. SrNvu,lL,c. Surr-snls, nd J. Srocr,Microearthquakeseismicityand active tectonicsof northwesternGreece,Earth planet.Sci.Lett., 6, 279288, 1983.Lr PrcsoN, X. and J. ANcErmn, The Hellenic arc and rrench system: A key to theneotectonicevolution of the E. Mediterranean arca;Tectonophysics,fi , 142, 1979.MaKnrs, J., Geophysical Investigations oJ- he Hellenides, Geophys. Eiyzel-schr., vol. 34,Hamburg University, 126 pp., 1977.McKENzrE, D. P., Active tectonics of the Alpine-Himalayan belt: The Aegean sea andsurrounding regions,Geophys. . R. Astron Soc.,55, 217_254, g7g.MEncrrR, J., N. D. Dpusassrs,A. Geur*n, J. JeRnrcr, F. Lruullr, M. SssnrpR, nd D.SonEr,La neotectoniquede l'arc Aegeen,Rev.Geor.Dyn. Geogr.phys.,2,67-92, rg./g.MISun.l, D' C. and L. B. PnoEnsrN,Statisticalanalysisof potential fields from subsurfacereliefs,Geoexploration,19,247 265, L992.Npcr, J. G., P. K. AcneweL, and K. N. N. Reo, Threedimensionalmodel of the Koyna areaof Maharashtra State (India)-based on the spectral analysis of aeromagneticdata,Geophysics,48, 964-974, 1983.


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G.-A. TsnrsNrrs.J. Duropoulos. and K. DnflrnllnrsPlr, P. c., K. K. KnuneuA, and P. UNuxnrsHNAN, wo examples f spectralapproach o

sourcedepthestimation n Gravity and Magnetics,Pageoph, 7,772-783, 1979.Pepa,z.e,cnos,., A. KrRATzr,P. HaraonrarrRrou, and A. Rocca, Seismic faults in theAegean area, Tectonophysics,06, 7l-85, 1984.P.l,qun, C., J. Brovrr, and C. ANcEuoIs, Tectonic stresses n the boundary of the Aegeandomain. In situ measurementsy overcoring,Tectonophysics,ll0,145-150,1984.Stncton, A., Spectral analysisof aeromagneticmaps, Ph.D. thesis,University of Toronto,1968.SrnctoR, A. and F. S. Gur.rr, Statistical models for interpreting aeromagneticdata,Geophys cs, 25, 293-302, 197 .Sw.LIN,C. J., A Fortran IV program for interpolating irregular spaceddata using thedifferenceequations or minimum curvature, Comput.Geosci.,1,231-240, 1976.TREITEL, ., W. G. CLuurNt, and R. K. K.lul, The spectraldetermination of depths o buriedmagneticbasement ocks, Geophys. . R. Astron: 9oc.,24, 411'/,28, 1971.TsnLnutts,G.-A. and J. Dnaropouroso Crustal structure n W. Greeceas obtained from theanalysisof surfacewaves,Pure Appl. Geophys.,1988 in press).

a spectral approach to moho depths_88

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