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Indian Journal of Science • Analysis

Abhilash Borah, Characteristic Study of Dynamic Elastic Modulii, Physical properties of rocks in geographical South India, Indian Journal of Science, 2013, 4(11), 76-84, www.discovery.org.in http://www.discovery.org.in/ijs.htm © 2013 Discovery Publication. All Rights Reserved

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Abhilash Borah

Undergraduate Dual BS-MS Student, Indian Institute of Science Education & Research, Kolkata, Email: [email protected] Received 09 July; accepted 22 August; published online 01 September; printed 16 September 2013

ABSTRACT The laboratory measurements of physical properties such as density, porosity, ultrasonic P-wave and S-wave velocities, Poisson’s ratio, Young’s modulus, Bulk modulus, and Shear modulus have been carried out of some of the different types of rocks of southern part of geographical Indian sub-continent. The rock samples consisted of igneous, sedimentary and metamorphic origins like basalt, granite, sandstone, rhyolite, dolerite and granulite. The dynamic elastic moduli were calculated using density, P-wave and S-wave velocity data’s. The compressional P-wave and shear S-wave velocities increases with increase in density, young’s modulus, shear modulus and Bulk modulus. Based on observed experimental results the rock samples which can be classified under excellent quality rocks are NK19AY2 (Granulite) and JDP-20B (Sandstone) can be classified under good quality rocks for engineering applications. Key Words: P-wave velocity, S-wave velocity, density, elastic waves, modulus of elasticity.

To Cite This Article: Abhilash Borah. Characteristic Study of Dynamic Elastic Modulii, Physical properties of rocks in geographical South India. Indian Journal of Science, 2013,4(11),76-84

1. INTRODUCTION Rock mechanics is the discipline of engineering science that involves the relation between geology, geophysics, mathematical sciences, physical sciences, mining and civil engineering. Rock Mechanics deals with the theoretical and applied behavior of rocks: it is the branch of mechanics concerned with the response of rock to the force fields of its environment (Jumikis, 1979). Rock is a natural substance which functions under the environmental processes of load, water, temperature, pressure, plate tectonics of the earth’s crust etc which ultimately depends upon the physical and mechanical properties of those rock materials. Rock mechanics is a division of a broader discipline, Geomechanics, which is classified under geotechnical engineering. This subject basically deals with the physical and mechanical reactions of all geological elements like soil, rock, ice etc. in geographical fields. A naturally occurring material, rock has many uses and application. For example, rock is used: For laying structural foundations and to support structures. For constructing vehicular and equeous tunnels, underground power plants, and other underground openings and

cavities. As facing stone for buildings, bridges, and hydraulic structures to protect these structures from weathering. For making artificial sand from rock in regions poor in sand but rich in suitable rocks.

1.1. Rock Mechanics According to the definition put forwarded by the Committee on Rock Mechanics of the Geological Society of America in 1964, viz., of the National Academy of Sciences committee on Rock Mechanics in 1966: “Rock Mechanics is the theoretical and applied behavior of rock; it is that branch of mechanics concerned with the response of rocks to the force fields of its environment”. Some of the features of Rock Mechanics are as follows (Jumikis, 1979): Mechanically, rock is a “Multiple-body” system. In a large, solid, sound rock mass. Rock may be considered to be a continuum. In its geologic environment, rock is principally characterized by the fact that rock is not a continuum but a regulated

discontinuum because of joints, fissures, shistosity, cracks, cavities, and other possible discontinuities. Objectives of Rock Mechanics are: To carry out engineering rock surveys. To develop rational rock sampling, identification and classification methods. To collect and classify information on rocks and their physical properties in the light of fundamental knowledge of rock

mechanics, foundation engineering and hydraulic structures engineering.

RESEARCH • GEOSCIENCE Indian Journal of Science, Volume 4, Number 11, September 2013

Characteristic Study of Dynamic Elastic Modulii, Physical properties of rocks in geographical South India

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Table 1 Density of different types of rocks (Ref: Engineering properties of rocks- I.W Farmer) Serial No. Rock types Rock Density Range 1. Granite 2.6-2.7 2. Gabbro 3.0-3.1 3. Basalt 2.8-2.9 4. Dolerite 3.0-3.05 5. Gneiss 2.9-3.0 6. Rhyolite 2.4-2.6 7. Andesite 2.2-2.3 8. Sandstone 2.0-2.6 9. Shale 2.0-2.6 10. Limestone 2.2-2.6 11. Marble 2.6-2.7 12. Slate 2.6-2.7 13. Quartzite 2.6-2.65

Table 2A Density of different rocks used in the present study, Sample: AGP-I(A) Dolerite

Observation Length(cm) Diameter(cm) Volume(cc) Mass(g) Density(g/cc) 1 7.554 3.021 54.118 157.848 2.916 2 7.554 3.058 55.452 157.846 2.846

3 7.544 3.058 55.452 157.856 2.846

4 7.545 3.009 53.625 157.848 2.943

Average 7.549 3.023 54.167 157.848 2.914

Table 2B Density of different rocks used in the present study, Sample: AGP-I(B) Dolerite

Observation Length(cm) Diameter(cm) Volume(cc) Mass(g) Density(g/cc)

1 7.513 2.989 52.690 156.241 2.965

2 7.536 2.991 52.922 156.244 2.952

3 7.533 2.998 53.149 126.246 2.939

4 7.537 2.993 53.000 156.248 2.948

Average 7.529 2.992 52.940 156.244 2.951

Table 2C Density of different rocks used in the present study, Sample: KHD-III(A) Granite


1 7.407 2.963 51.047 134.830 2.641

2 7.413 2.956 50.847 134.831 2.651

3 7.410 2.956 50.827 134.831 2.652

4 7.420 2.968 51.309 134.833 2.627

Average 7.412 2.960 51.007 134.831 2.643

Table 2D Density of different rocks used in the present study, Sample: KHD-III(B) Granite


1 7.627 3.025 54.786 142.198 2..595

2 7.628 3.006 54.107 142.198 2.628

3 7.615 3.012 54.231 142.202 2.622

4 7.617 3.019 54.497 142.203 2.609

Average 7.621 3.015 54.405 142.203 2.613



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Table 2E Density of different rocks used in the present study, Sample: NGR-I(A) Dolerite


1 7.509 2.965 51.820 158.402 3.056

2 7.503 2.963 51.709 158.403 3.063

3 7.521 2.974 52.218 158.409 3.033

4 7.505 2.965 51.792 158.406 3.058

Average 7.509 2.966 51.884 158.405 3.053

Table 2F Density of different rocks used in the present study, Sample: NGR-I(B) Dolerite


1 7.654 2.975 53.178 161.065 3.028

2 7.663 2.965 52.883 161.067 3.045

3 7.664 2.973 53.175 161.070 3.029

4 7.662 2.978 53.341 161.071 3.019

Average 7.660 2.972 53.144 161.068 3.030

Table 2G Density of different rocks used in the present study, Sample: RR2-(A) Granite


1 7.553 2.991 53.042 138.595 2.612

2 7.555 2.991 53.056 138.597 2.612

3 7.556 2.990 53.027 138.599 2.613

4 7.551 2.990 52.992 138.598 2.615

Average 7.553 2.990 53.029 138.597 2.613

Table 2H Density of different rocks used in the present study, Sample: RR2-(B) Granite


1 7.514 2.994 52.874 138.158 2.612

2 7.513 2.991 52.761 138.159 2.618

3 7.530 2.993 52.951 138.162 2.609

4 7.515 2.995 52.916 138.162 2.610

Average 7.518 2.993 52.800 138.160 2.616

Table 2I Density of different rocks used in the present study, Sample: VNA II(A) Basalt


1 7.562 2.980 52.786 154.197 2.921

2 7.565 2.978 53.375 154.193 2.888

3 7.558 2.984 52.687 154.200 2.926

4 7.564 2.980 52.764 154.199 2.922

Average 7.562 2.985 52.903 154.198 2.914

Table 2J Density of different rocks used in the present study, Sample: VNA II(B) Basalt


1 7.567 2.980 52.750 154.518 2.927

2 7.569 2.978 52.693 154.516 2.930

3 7.574 2.984 52.941 154.416 2.916

4 7.572 2.980 52.785 154.412 2.925

Average 7.570 2.980 52.792 154.415 2.924



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Table 2K Density of different rocks used in the present study, Sample: JDP 10A, Sandstone


1 6.121 3.005 43.389 105.52 2.431

2 6.135 3.000 43.343 105.521 2.434

3 6.123 2.989 42.942 105.522 2.457

4 6.120 2.987 42.863 105.521 2.461

Average 6.124 2.995 43.134 105.521 2.446

Table 2L Density of different rocks used in the present study, Sample: JDP 20D, Sandstone


1 5.994 2.990 42.065 84.369 2.005

2 5.981 2.970 41.414 84.365 2.037

3 5.983 2.987 41.904 84.269 2.010

4 5.986 2.971 41.477 84.368 1.985 Average 5.986 2.979 41.715 83.842 2.009

Table 2M Density of different rocks used in the present study, Sample: UP 34AY2, Granulite


1 6.110 2.970 42.308 117.104 2.767

2 6.117 2.970 42.356 117.105 2.764

3 6.109 2.969 42.272 117.105 2.770

4 6.110 2.969 42.238 117.105 2.772

Average: 6.110 2.969 42.293 117.105 2.768

Table 2N Density of different rocks used in the present study, Sample: NK 19AY2, Granulite


1 6.197 3.039 44.927 150.464 3.349

2 6.208 3.039 45.007 150.463 3.343

3 6.189 3.039 44.869 150.464 3.353

4 6.193 3.040 44.928 150.465 3.349

Average: 6.196 3.039 44.933 150.464 3.348

Table 3 Velocity data of different rock types used in present study

OBSERVATIONS SAMPLES ROCK TYPE P-Wave velocity (m/s) S-Wave velocity (m/s) 1. AGP IA Dolerite 6797 3832 2. AGP IB Dolerite 6832 3887 3. KHD IIIA Granite 5992 3551 4. KHD IIIB Granite 5999 3676 5. NGR IA Dolerite 6855 3853 6. NGR IB Dolerite 6852 3896 7. RR-2A Granite 5695 3436 8. RR-2B Granite 5638 3470 9. JDP-10A Sandstone 4954 3080 10. JDP-20D Sandstone 4863 3023 11. UP-34AY2 Granulites 5588 3503 12. NK-19AY2 Granulites 6962 4187 13. VNA IIA Basalt 5709 3179 14. VNA IIB Basalt 5610 3255



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To study rock performance under thermal conditions and water regimen. To perform research on the mechanisms of failure in rocks. To apply the knowledge of rock mechanics for the solution of practical

engineering problems. 1.2. Physical Properties Rock is a natural substance having structural features which are not encountered in most other engineering materials. For safe and economical design of structure on and in rock, adequate knowledge about the technological properties of rock is indispensible. Some of the main technological properties of rocks necessary to consider in the design of concrete dams, rock slopes, and underground structures are (Jumikis, 1979): Unit weight Movements and deformations under load Static and dynamic strength Young’s modulus of elasticity Poisson’s ratio Density against water absorption Permeability to water Resistance to weathering Thermal properties Electrical properties etc.

The physical properties of rocks affecting design and construction in rock are: Mineralogical composition, texture, and structure Specific gravity Density Porosity Void ratio

Permeability to water Elastic waves (P-wave and S-wave) Saturation moisture content etc.

2. OBJECTIVES OF PRESENT STUDY 2.1. Determination of physical properties like density, Compressional P-wave velocity, Shear S-wave velocity of different rock types 2.1.1. Density It is the characteristic property of a substance. The density of a substance is the relationship between the mass of the substance and how much space it takes up (volume). The mass of atoms, their size, and how they are arranged determine the density of a substance. Density equals the mass of a substance divided by its volume; ƥ = m/V. Objects with the same volume but different mass have different densities (Understanding Earth- Grotzinger, Press, Jordan, Siever). A great many common rock-forming minerals, however, are too similar in density. A standard measure of density is specific gravity, which is equal volume of pure water at 40C. Density depends on the atomic mass of mineral ion’s and how closely they are packed in its crystal structure. Increase in density caused by increases in pressure affect the way minerals transmit light, heat, and earthquake waves. Rock densities are very sensitive to the minerals present in it which compose a particular rock type. Covalently bonded materials have more open packed and so have lower densities. Sedimentary rocks and granite, which are rich in quartz and feldspar, tend to be less dense than volcanic rocks while the more mafic a rock is, the greater is its density. Some of the standard density ranges are mentioned in Table 1.

2.1.2. Elastic Waves It is the motion in medium in which, when particles are displaced, a force proportional to the displacement acts on the particles to restore them to their original position. If a material has the property of elasticity and the particles in a certain region are set in vibratory motion, an elastic wave will propagate. An elastic wave is a type of mechanical wave that propagates through, or on the surface of a medium. Elastic waves are fairly common in nature. For example, sound propagating through the air or water waves propagating across the surface of a pond are elastic waves. The elasticity of the material provides the restoring force of the wave. Elastic waves occurring in the Earth as a result of an earthquake or any other disturbance, are usually called seismic waves. Earthquake shaking and damage is the result of three basic types of elastic waves. Two of the three propagates within a body of rock. The faster of these waves is called the Primary wave (P-Wave). Its motion is the same as that of a sound wave in that, as it spreads out, it alternately pushes (compresses) and pulls (dilates) the rock. These P-Waves are able to travel through both solid rock, such as Granite Mountains, and liquid material, such as volcanic magma and the water of the oceans (Lama et al. 1978). The slower wave through the body of rock is called the Secondary or S-Wave. As an S-Wave propagates, it shears the rock sideways at right angles to the direction of travel. If a liquid is sheared sideways or twisted, it will not spring back; hence S-waves cannot propagate in the liquid parts of the earth, such as oceans and lakes. The actual speed of P and S seismic waves depends on the density and elastic properties of the rocks and soil through which they pass. In most earthquakes, P waves are felt first. The effect is similar to a sonic boom that bumps and battles and rattles windows. Some seconds later, S waves arrive with their up-and-down and side-to-side motion, shaking the ground surface vertically and horizontally. This is the wave motion that is so damaging to structures. P-wave and S-wave have a characteristic which effects shaking: when they move through layers of rocks in the crust, they are reflected or refracted at the interfaces between rock types. Whenever either wave is reflected or refracted, some of the energy of one type is converted to waves of the other type.



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3. EXPERIMENTAL PROTOCOL 3.1. Sample Details The samples collected were in the shape of blocks of 25*25*25 cm for laboratory studies from different geographical areas of Southern India. The samples are of hard Basalt, vesicular Basalt, Dolerite, pink Granite, gray Granite, Sandstone, Quartzite and granulites. The cylindrical specimens 60 mm length and 30 mm diameter were prepared. The two ends of each rock cylinder were ground and lapped parallel to attain an accuracy of 0.2 mm and the ends were polished. Also, the cylindrical sides are made straight to the accuracy of 0.3 mm over the full length of each specimen.

3.2. Density The density of each core samples was measured after the removal from it. The moisture was removed by placing the rock samples in an electric oven at ~800C for about one hour and they were dried at the room conditions. The diameter and the length of each the cylindrical rock samples were measured using digital Vernier calipers for four observations, and the values were averaged for computing the volume. Several measurements were made along the core and the average values of length and diameter were used for calculating the cross-sectional area and volume of the samples. The weight (Mass) of each of the dried core was measured using an electronic balance. The density is calculated using the following equation:

Table 4 Summary of physical properties and dynamic modulii of different rock types used in present study

Observations Samples Rock type Density

(g/cc)

P-wave velocity (m/s)

S-wave Velocity

(m/s)

Elastic Properties

Serial No. Shear Modulus (GPa)

Young’s Modulus (GPa)

Bulk Modulus (GPa) Poisson’s ratio

1. AGP IA Dolerite 2.916 6797 3832 42.82178 108.5127117 77.61996545 0.267027 2. AGP IB Dolerite 2.951 6832 3887 44.58607 112.4184245 78.29344402 0.260690 3. KHD IIIA Granite 2.643 5992 3551 33..32721 81.94113533 50.45816620 0.229343 4. KHD IIIB Granite 2.613 5999 3676 35.30948 84.69874742 46.95734492 0.199377 5. NGR IA Dolerite 3.053 6855 3853 35.30948 115.0394390 83.03195059 0.269086 6. NGR IB Dolerite 3.030 6852 3896 45.32374 116.0026347 80.93575989 0.261122 7. RR 2A Granite 2.611 5695 3436 30.82574 74.83368232 43.58163821 0.213818 8. RR 2B Granite 2.612 5638 3470 31.45087 75.17430205 41.09326990 0.195107 9. JDP 10A Sandstone 2.446 4954 3080 23.20377 54.99090099 29.09165121 0.184956 10. JDP 20B Sandstone 2.009 4863 3023 18.35933 43.51528302 23.03127078 0.185100 11. UP-34AY2 Granulites 2.768 5588 3503 33.96619 79.90933016 41.14460829 0.176307 12. NK-19AY2 Granulites 3.348 6962 4187 58.6937 142.8229074 84.01742875 0.216680 13. VNA IIA Basalt 2.914 5709 3179 29.22908 75.11206599 55.70962813 0.275287 14. VNA IIB Basalt 2.924 5610 3255 30.97987 77.21744188 50.71793135 0.246252

Table 5 Physical properties that show maximum and minimum values of density, P-wave velocity, S-wave velocity, Shear Modulus, Young’s Modulus and Bulk Modulus of the different rock types in present study

Properties Maximum Minimum Density NK19AY2: 3.348 g/cc JDP20B: 2.009 g/cc

P-wave velocity NK19AY2: 6962 m/s JDP20B: 3023 m/s S-wave velocity NK19AY2: 4187 m/s JDP20B: 3023 m/s Shear Modulus NK19AY2: 58.6937 GPa JDP20B: 18.35933 GPa

Young’s Modulus NK19AY2: 142.822 GPa JDP20B: 43.51528 GPa Bulk Modulus NK19AY2: 84.0174 Gpa JDP20B: 23.03127 GPa

Table 6 Classification of different rock types under our present study (Reference: Barton N. Rock quality, seismic velocity, attenuation, and anisotropy, Taylor & Francis, 2007)

Rock types Samples No. Classification of rocks based on dynamic

young’s modulus data (Barton,N./2007,taylor & francis)

Range

N/A N/A Very poor <16.5 N/A N/A poor 16.5-23 N/A N/A Fair 23-38

Sandstone JDP20B Good 38-51 Sandstone AGP IA

Excellent

51>

Dolerite AGP IB Granite KHD IIIA Granite KHD IIIB Dolerite NGR IA Dolerite NGR IB Granite RR 2A Granite RR 2B

Granulites UP-34AY2 Granulites NK-19AY2

Basalt VNA IIA Basalt VNA IIB

Sandstone JDP10A



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(g /cm3)= mass of sample / volume of sample

3.3. Velocity Ultrasonic velocities of P-Wave and S-Wave measurements have been carried out using a high-energy pulser receiver on the driving side and a 2-channel digital storage oscilloscope on the receiving side. We determined the velocity of compressional (Vp) waves and shear waves (Vs) using the time-of-flight measurement technique at 1MHz frequency as described in detail. In this technique the test sample is placed between the transmitting transducer and receiving transducer. We have two different sets of transducers to measure P-wave and S-wave velocity measurements separately. The pulser will generate a high power DC electric pulse which is converted by the transmitting transducer into an elastic wave. This stress wave passes through the test sample and when it enters the receiving transducer the stress wave is converted back into an electric transient pulse. The electric transient pulse is viewed and stored on the receiving side with the help of a digital storage oscilloscope for the measurement of travel time and pulse width. The velocity is computed using the formula: VP

(m/sec) = length the sample/time

The Poisson’s ratio and dynamic moduli have been computed using P-wave and S-wave velocities and density data. The relation between them is given in the table below,

Figure 1 Density and P-Wave velocity relationship of different rock types

Figure 2 Density and S-Wave velocity relationship of different rock types

Figure 3 Young’s Modulus and P-Wave velocity relationship of different rock types

Figure 4 Youngs Modulus and S-Wave velocity relationship of different rock types



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Poisson’s Ratio() 1/2 *((VP/VS)2 –2))/((VP/VS)2 –1)) Young’s Modulus(E) (1+)(1-2)VP 2/(1- ) Bulk Modulus(K) E/3(1-2) Shear/Rigidity Modulus(G) E/2(1+) Where, VP =P-wave velocity in rock sample (cm/sec) VS =S-wave velocity in rock sample (cm/sec) =Density of rock sample (gm/cc)

4. OBSERVATIONS Observations are listed and shown in Table 2-6 and Figure 1-6.

5. RESULTS AND DISCUSSION The densities of different rock samples of the geographic southern India were determined. The rock sample densities found are similar to the standard values by comparing. From the measurement of elastic wave velocity measurements it is seen that the velocities depend on the elastic modulii and density. The elastic constants, and densities, in turn depend on the properties that the geologist or engineer use to characterize the rock such as porosity, fluid saturation, texture etc. It is observed from the Table-5 Rock sample, Granulite NK19AY2 has the highest maximum value of density, compressional P-wave velocity, shear S-wave velocity, Young’s Modulus, Bulk Modulus & Shear Modulus while the rock sample, Sandstone JDP20B has the lowest minimum value of density, compressional P-wave velocity, shear S-wave velocity, Young’s Modulus, Bulk Modulus & Shear Modulus. It is evident that as P-Wave velocity increases, the youngs’s modulus increases simultaneously (Figure 3) and as S-Wave velocity increases, the young’s modulus increases (Figure 4). Density is also increasing with increase in compressional P-wave velocity and shear S-wave velocity (Figure 1 & Figure 2 respectively). It is also seen that as Poisson’s ratio increases P-Wave velocity & S-Wave velocity both increases (Figure 5 & Figure 6 respectively). The density of all rock types of the present study varies from 2.009 g/cc to 3.348 g/cc with an average value of 2.774 m/s. The compressional P-Wave velocity shows a wide variation from 4863 m/s to 6962 m/s with an average value of 6024 m/s (Figure 3). The shear S-Wave velocity too shows a wide variation from 3023 m/s to 4187 m/s with an average value of 3559.143 m/s (Table 3). The physical properties are essential for classification of rock materials and judgments about their suitability for various construction purposes.

6. CONCLUSIONS Hence, from the experimental measurements of elastic waves measurement it shows that the velocities depend on the

elastic modulii and density. It is inferred from the experimental results that velocity increases with increase in density, Young’s modulus and Poisson’s

ratio. On the basis of experimental data evidences, Granulite (NK19AY2) rock is an excellent strong rock group for engineering

applications while sandstone (JDP20B) come under somewhat good quality rock. Classification of rocks based on dynamic young’s modulus data (Barton, 2007)

SUMMARY OF RESEARCH The research project analysis helped to see the various physical properties of rocks found in geographical South India. DISCLOSURE STATEMENT I thank to IAS-NASI-INSA for the research funding as a part of Research Fellowship Programme-2013

Figure 5 Poisson ratio and P-Wave velocity relationship of different rock types

Figure 6 Poisson’s ration and S-Wave velocity relationship of different rock types



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ACKNOWLEDGEMENT Thanks and appreciation to IISER-Kolkata, IAS(Banglore)-NASI(Allahabad)-INSA(New Delhi), NGRI-Dr.K.Lakshmi, Hyderabad. REFERENCE

1. Barton N. Rock quality, seismic velocity, attenuation, and anisotropy, Taylor & Francis, 2007 2. Jumikis AR. Rock Mechanics, Trans Tech Publications, Rockport USA, 1979 3. Lama RD, Vutukuri VS. Handbook on Mechanical Properties of rocks-Testing Technique and Result-Volume I Trans Tech

publications Aedermannsdorf, Switzerland, 1978 4. Lama RD, Vutukuri VS. Handbook on Mechanical Properties of rocks-Testing Technique and Result-Volume II Trans Tech

publications Aedermannsdorf, Switzerland, 1978 5. Understanding Earth- Grotzinger, Press, Jordan, Siever

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