Acoustic velocities and electrical properties of frozen sandstones and shales

M. S. KING Department of Geological Sciences, Universiiy of Saskatchewan, Saskatoon, Sask., Canada S7N OW0

Received 4 October 1976 Revision accepted for publication 26 November 1976

Ultrasonic velocities and electrical properties have been measured in the laboratory at perma- frost temperatures on a number of samples of sandstones and a shale which had been recovered from boreholes in the arctic and stored in their natural frozen state. Compressional and shear- wave velocities, electrical resistivity, and phase-angle relationships in the frequency range 0.005-100 kHz have been measured on the permafrost samples, at temperatures in the range - 18°C- +4"C.

Results of the tests show that, at a particular temperature, there is a small decrease in the electrical resistivity measured on all samples tested as the frequency is increased. The phase- angle differences measured show no consistent relationship with either frequency or temper- ature, but they are all less than 12" in magnitude. The electrical resistivity at a particular frequency and the ultrasonic velocities are affected in a similar manner by changes in tempera- ture. Whereas the sandstones show a sharp reduction in velocities and resistivity as the tempera- ture is raised to 0°C or above, the shale shows little dependence of these parameters on changes in temperature in the range tested. An increase in shale content of the sandstone results in behavior intermediate between that of a clean sandstone and that of a shale.

On a mes1rr6 en labomtoire a w temptratutes du pergilisol les vitesses ultrasoniques er les propriitks ilectriques d'un nombre d'echantillonsde &set de schistes argileux qu'on a pslevks par forage dam I1'Arctique er qu'on a en t r epo i dans leur etat gele naturel. On a dttermine les vitesses des andes de compression et de cisaillement, la ksistivitP ilectrique et les relations de phase a desfrkquences allant de 5 Hz a 100 kHz des tchantillons de pergilisol & des tempiratures de - 18°C- +4T.

Ces esultat5 montrent que. pour une temperature donnte. il y a une faible diminution de risistiviti electrique dam les echantillons analyls lorsqu'on augmente la fniquence. Les differences de phase mesurkes ne montrent aucune relation bien ddinie avec la frequence ou la ternp6ratu~. mais elles writ toures plus fatbles que 12"en vdeur absolue. La risistiviti ilectrique i une fniquence donnbe ct les vitesses ultrasoniques se component de f a ~ o n semhlable sous les variations de tempkrature. Alors que les g k s montrent une diminution nette dans les vitesses et lesn5sisrivitEs lorsque latemperature augmentejusqu'gO0C et plus. les schistes argileuxmontrent une fdble dipendance de ces paramt~res aux changements de tempkrature dans I'intervalle utilise. Une augmentation de la proportion de schiste argileux dans le grks amkne un wmpone- ment i michemin entre celui d'un gres pur et celui d'un schiste arg~leux.

[Traduit par le journal] Can. J. Earth Sci.. 14. I O W l R 1 3 (1977)

Introduction The interpretation of surface seismic, electrical

resistivity, and electromagnetic surveys in areas of permafrost requires a knowledge of the acoustic-wave velocities and electrical properties of the underlying permafrost. It is generally accepted that the freezing process radically alters the elastic-wave propagation and electrical properties of water-saturated porous media. Laboratory measurements of elastic-wave veloci- ties in water-saturated porous materials at perma- frost temperatures have been reported by Frolov (1961), Antsyferov et al. (1964), Timur (1968), Nakano et al. (1972), Kurfurst and King (1972), Nakano and Froula (1973), and King and Bamford (1974). These workers all observed

abrupt increases in velocity as the temperature was decreased below O°C, with the degree of I increase depending on the water content of the material. Laboratory measurements of electrical I resistivities of these materials have been re- ported by Ananyan (1958), Parkhomenko (1967), and Hoekstra and McNeill (1973). These workers all reported pronounced increases in resistivity as the temperature was decreased i below 0°C. Collett (1974) concludes that this increase depends on the water content of the material, the chemical composition of the electrolyte, and the composition and grain size of the mineral component.

In this paper are reported the results of tests on a number of samples of permafrost from two

Can

. J. E

arth

Sci

. Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

UN

IV C

HIC

AG

O o

n 11

/13/

14Fo

r pe

rson

al u

se o

nly.

KING 1005

stratigraphic control boreholes in the arctic islands of the Northwest Territories. These rock samples, sealed in polythene bags, were shipped in their natural frozen state and stored in a laboratory freezer cabinet maintained at a temperature of approximately - 10°C.

A number of test specimens were prepared from the samples in their frozen state. There were a total of two shale and six sandstone specimens. Owing to difficulties caused by the presence of planes of weakness in three of the sandstone specimens, it was found impossible to subject them to the stress conditions required in the tests described below. The two shale and three remaining sandstone specimens were subjected to a series of tests intended to measure their acoustic compressional and shear-wave veloci- ties, and their electrical resistivity and phase- angle relationships as a function of frequency. Each series of tests was performed at a number of temperatures in the range - 18- +4"C.

Specimen Preparation

The permafrost samples were received in the form of short lengths of BX-sized core, sealed in polythene bags. The test specimens were machined on a multi-purpose grinding machine to a diameter of 3.8 cm, using a diamond grinding wheel and DC200 silicone fluid chilled to -9°C as a coolant. The preparation room was itself maintained at a temperature of -9°C during the machining process. Each specimen was cut to a suitable length (up to 6.4 cm) on a diamond saw in the preparation room and the flat surfaces were then ground to a tolerance of 0.0015 cm on the multi-purpose grinder, again using chilled DC200 silicone fluid as the coolant.

On completion, each specimen was carefully cleaned, weighed to 0.005 g and tightly sealed in polythene film before returning it to the freezer cabinet for storing prior to preparation for testing. At each stage during the preparation and testing of specimens, they were weighed to 0.005 g to ensure that no moisture had been lost.

Specimens were mounted between the trans- ducer holders for the acoustic tests and the electrode holders for the resistivity tests in the preparation room, which was maintained at -9°C. Each specimen was enclosed in a rubber jacket which was, in turn, wrapped tightly with plastic adhesive tape, so that the tape overlapped itself and the transducer or electrode holders. In this way the specimen was entirely sealed

from the atmosphere in the test chamber. Checks on the weight before and after each series of tests indicated that any loss of weight was in all cases negligible.

After the tests the specimens were removed from the transducer or electrode holders, tightly wrapped in polythene film, and stored in the freezer cabinet.

Apparatus

A block diagram of the acoustic-velocity apparatus is shown in Fig. 1. The specimen is mounted between transducer holders of the type described by King (1970) to measure sequen- tially compressional and shear-wave velocities, but designed to suit specimens of 3.8 cm diameter. The uniaxial load on the transducer holders and specimen is applied by compressed nitrogen. The acoustic velocity measurements are made in the same manner and with the same precision as those described by Kurfurst and King (1972). Temperatures within the test chamber, which can be maintained within the limits a 0.05"C in the range - 18- + 21°C, are monitored by platinum resistance sensors located in the chamber and on the lower transducer holder adjacent to the specimen.

A block diagram of the electrical resistivity apparatus is shown in Fig. 2. A variable- frequency oscillator applies an alternating voltage of constant amplitude across the speci- men, which is mounted between stainless steel electrodes with a thin layer of graphite. A pre- cision amplifier and ac voltmeter are used to measure the voltage drop across a precision resistor in a series with the specimen. In this way, the complex resistivity of the specimen can be calculated. Phase-angle relationships are mea- sured from Lissajous patterns on an oscilloscope screen. The operating frequency range for the system is 5-lo5 Hz. Hydrostatic stress is applied to the jacketed specimen between the electrode holders in a small pressure cell in the constant- temperature test chamber. The specimen and chamber temperatures are monitored in the same manner as described above for the acoustic velocity tests.

Operational Procedure The operational procedure for both acoustic

velocity and electrical resistivity tests is basically similar. Specimens mounted between the trans- ducer or electrode holders are placed in the test

Can

. J. E

arth

Sci

. Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

UN

IV C

HIC

AG

O o

n 11

/13/

14Fo

r pe

rson

al u

se o

nly.

CAN. I. EARTH SCI. VOL. 14, 1977

- - GENERATOR

FIG. 1 . Block diagram of acoustic velocity apparatus.

VARIABLE CIJS4JOUS A.C PREClStON

FREQUEMCY VOLTMETER AMPLIFIER OSCl LLATOR

j o /

, I I

STAINLESS STEEL ELECTRODES

BLOCK DIAGRAM OF ELECTRICAL

FIG. 2. Block diagram of elec

chamber at a temperature of approximately -9°C. The test chamber is then reduced in temperature to approximately - 18°C and left at this level for one day.

Acoustic velocity or electrical resistivity mea- surements are first made at the lowest tempera- ture. These are followed by measurements made at successively higher temperatures, allowing

RESIST IV ITY APPARATUS

:trical resistivity apparatus.

the specimens to come to thermal equilibrium with their surroundings for one day at each temperature step. Previous experiments have shown that one day provides ample time for this purpose. The temperature is finally allowed to rise to levels above 0°C. On completion of each test, the temperature in the chamber is reduced to -4°C before the specimen is removed in its

Can

. J. E

arth

Sci

. Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

UN

IV C

HIC

AG

O o

n 11

/13/

14Fo

r pe

rson

al u

se o

nly.

KING

TABLE 1. Specimens prepared

Specimen Borehole Depth No. description no. m Notes

SH2 SSl SS2

Black shale

Black shale Clean sandstone Shaly sandstone

Shaly sandstone

Shaly sandstone Shaly sandstone Shaly sandstone

Failed in acoustic velocity test

Successfully tested Successfully tested Prominent discontinuity

at acute angle Prominent discontinuity

at acute angle Successfully tested Successfully tested Prominent discontinuity

at acute angle

TABLE 2. Physical properties of specimens

Property SH2 SS1 SS4(shaly) SSS(sha1y) -

Bulk density, frozen, g/cm3 2.332 2.453 2.374 2.327 Bulk density, dry, g/cm3 2.205 2.329 2.237 2.167 Porosity, fraction 0.13 0 .14 0.15 0.17 Moisture content, fraction 0.058 0.053 0.061 0.074

dry weight

frozen state. In a number of cases, acoustic velocity and electrical resistivity measurements have been made during this temperature reduc- tion to observe any hysteresis effects.

Each test specimen was first subjected to a series of acoustic velocity tests a t different temperatures. The uniaxial stress on the speci- men was raised in steps of 0.7 MPa to a maxi- mum of 3.5 MPa at each temperature level. Between runs, while the chamber temperature was being changed to a new level, the uniaxial stress on the specimen was reduced to and maintained constant a t 70 kPa.

On completion of the acoustic velocity test, each specimen was prepared for the electrical resistivity test. When placed in the resistivity cell, the specimen was subjected to a hydrostatic stress of 0.35 MPa at each temperature while resistivity and phase-angle measurements were made. Between runs, the hydrostatic stress on the specimen was reduced to and maintained at 70 kPa.

On removal from each of the tests described above, the specimens were weighed to check for loss of moisture. On completion of the resistivity tests, the specimens were dried in a vacuum oven maintained at a temperature of 105°C and a vacuum of 1 Torr (133.3 Pa) for 24 h. The loss

in moisture for each specimen was noted and its porosity calculated. The sandstone specimens were then resaturated with distilled water and reweighed.

Results

The five specimens tested are described as two shales, SH1 and SH2, and three sandstones, SS1, SS4, and SS5. They are identified in Table 1, together with those specimens not tested.

In Table 2 are shown the densities, porosities, and moisture contents of the specimens success- fully tested, calculated from the frozen saturated weights and from the dry weights determined after completion of the drying cycle referred to above.

Results of the acoustic velocity tests are shown in Figs. 3 and 4. In Fig. 3 are shown the com- pressional-wave velocities, at an axial stress of 3.5 MPa, plotted as a function of temperature, for specimens SH1, SH2, SSl, SS4, and SS5. Figure 4 shows the shear-wave velocities for the specimens, plotted in the same way. However, it was difficult to determine the shear-wave velocity for specimen SS4 unequivocally at temperatures above -3°C. It should be noted that shale specimen SHl failed in uniaxial

Can

. J. E

arth

Sci

. Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

UN

IV C

HIC

AG

O o

n 11

/13/

14Fo

r pe

rson

al u

se o

nly.

CAN. J. EARTH SCI. VOL. 14, 1977

-15 -10 - 5 0 5

TEMPERATURE ('C)

FIG. 3. Compressional-wave velocity as a function of temperature at an axial stress of 3.5 MPa.

L

SS5 ,

SS 4

SHI 0

- - - 0

SH 2 SH2

0 I I I I

-15 -10 - 5 0 5

TEMPERATURE P C )

FIG. 4. Shear-wave velocity as a function of temperature at an axial stress of 3.5 MPa.

compression during testing at a temperature of there is a reduction in velocity, which becomes - 7°C. more marked as the temperature approaches

Figures 3 and 4 indicate the important effect 0°C. At temperatures above O°C, the velocities of temperature on the velocities of compressional remain constant. At temperatures above approxi- and shear waves in the sandstone specimens. As mately - 3°C it was observed that, for the shaly the temperature is raised from its lowest level, sandstones SS4 and SS5, the character of the

Can

. J. E

arth

Sci

. Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

UN

IV C

HIC

AG

O o

n 11

/13/

14Fo

r pe

rson

al u

se o

nly.

KING

received waveform changed, with the elimination of high frequency components in the signal at this temperature. This behaviour was not ob- served with the clean sandstone SS1 and the shale SH2, for which the high frequency com- ponents of the received waveform were not eliminated as the temperature was raised to 4°C. For the frozen sandstone specimens it was observed that the change in uniaxial stress from 0.7 MPa to 3.5 MPa at a particular temperature caused very little change in either compressional or shear-wave velocity. For the unfrozen speci- mens, however, there was a slight increase (less than 1%) in velocity when the stress was in- creased over this range.

In contrast to the temperature dependent behavior noted for the sandstones, shale speci- men SH2 showed very little dependence of either compressional or shear-wave velocity on tem- perature over the range - 17- +4"C tested. For this shale specimen, the temperature was first raised in steps from - 17°C to 4°C and then reduced by the same steps to - 17°C again. The measured differences in velocities at 3.5 MPa uniaxial stress between the ascending and de- scending temperature runs were negligible. The change in uniaxial stress from 0.7 MPa to 3.5 MPa caused a slight increase (3% approximately) in the compressional and shear-wave velocities measured on this shale specimen.

The velocities were also measured on sand- stone specimen SS5 as the temperature was reduced from 1.7"C to - 3.9"C in preparation for removal from the test chamber. In this case, some hysteresis was noted between the velocities measured on ascending and descending tem- perature runs. This point will be referred to further, when the electrical resistivity results are presented.

Results of the electrical resistivity tests are shown in Figs. 5-9. In Fig. 5 are shown the resistivities measured at a frequency of I kHz as a function of temperature, with the specimens

I subjected to a hydrostatic stress of 0.35 MPa. I It was observed that whereas there was a small

I reduction in resistivity as the hydrostatic stress in the cell was raised from 70 kPa to 0.35 MPa at a particular temperature and frequency, there was a negligible increase when the stress was then raised to 0.7 MPa.

Comparison of the results shown in Fig. 5 with those shown for acoustic velocities in Figs. 3 and 4, indicates that the electrical resistivity of

-15 -10 - 5 0 5 10

TEMPERATURE P C )

FIG. 5. Resistivity as a function of temperature at a frequency of 1 kHz.

these specimens behaves in a similar manner to that of the acoustic velocities. The sandstone specimens show large reductions in resistivity as the temperature is raised to 0°C. There is only a small change in resistivity at temperatures in excess of 0°C. The shale specimen, in contrast, shows little variation of resistivity with tempera- tures in the range - 17- + 2°C.

It is interesting to note that the variations in resistivity for the sandstone specimens show a similar hysteresis effect as did the variations in velocities when the temperature was reduced from a level above 0°C. It is also interesting to observe that the resistivities show the same de- creasing order in magnitude (SSI, SS5, SS4, SH2) at low temperatures and at temperatures in excess of 0°C (SS1, SH2, SS4, SS5) as do the acoustic velocities.

Figures 6, 7, 8, and 9 show the variation of electrical resistivity for the shale and sandstone specimens subjected to 0.35 MPa hydrostatic stress as a function of frequency in the range 5-10' Hz. In all cases, there is a decrease in resistivity as the frequency is increased, for the specimen subjected to a constant temperature.

Phase-angle measurements were also made

Can

. J. E

arth

Sci

. Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

UN

IV C

HIC

AG

O o

n 11

/13/

14Fo

r pe

rson

al u

se o

nly.

CAN. J. EARTH SCI. VOL. 14, 1977

F RESULTS PLOTTED FOR ASCENDING TEMPERATURES r DESCENDING TEMPERATURE

F R E Q U E N C Y (HZ)

FIG. 6. Resistivity as a function of frequency and temperature: sandstone No. 1 .

RESULTS PLOTTED FOR ASCENDING TEMPERATURES * DESCENDING TEMPERATURE

F R E Q U E N C Y (Hz)

FIG. 7. Resistivity as a function of frequency and temperature: sandstone No. 4.

from Lissajous patterns on the oscilloscope than 12' in magnitude was observed at any screen. Difficulties were experienced in making frequency or at any temperature. these measurements precisely because in all cases the phase angles were small. Although Discussion

there is some scatter in the results for different For the frozen, water-saturated sandstone specimens, no phase-angle difference greater specimens, the acoustic velocity and electrical

Can

. J. E

arth

Sci

. Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

UN

IV C

HIC

AG

O o

n 11

/13/

14Fo

r pe

rson

al u

se o

nly.

KING

RESULTS PLOTTED FOR ASCENDING TEMPERATURES + DESCENDING TEMPERATURE

F R E Q U E N C Y (Hz)

FIG. 8. Resistivity as a function of frequency and temperature: sandstone N o 5.

RESULTS PLOTTED FOR ASCENDING TEMPERATURES

10 10 l o 3 l o 4 1 0 5

F R E Q U E N C Y (Hz)

FIG. 9. Resistivity as a function of frequency and temperature: shale No. 2.

resistivity tests show that these properties are strongly affected by changes in temperature. Sharp decreases in both acoustic velocity and electrical resistivity were observed as the tem- perature was increased above 0°C. It has been argued (e.g. by Timur 1968) that, as the tem- perature is reduced below O°C, ice forms first in the larger pore spaces of a sandstone and then

in progressively smaller ones as the temperature is reduced still further. In the tests described here, the converse is probably true for ascending temperatures.

Changes in temperature did not greatly affect the measured acoustic velocities or electrical resistivity of the shale specimen tested. This can probably be attributed to the fine-grained struc-

Can

. J. E

arth

Sci

. Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

UN

IV C

HIC

AG

O o

n 11

/13/

14Fo

r pe

rson

al u

se o

nly.

1012 CAN. 3 . EARTH SCI. VOL. 14. 1977

ture of this material and to the salinity of the pore water. Timur (1968) observed a lowering of the beginning of freezing to - 8°C for a black shale. He attributed this behaviour to large interfacial forces associated with large surface areas, coupled with the salinity of the interstitial liquid.

Hysteresis effects were observed with two of the sandstones specimens between ascending and descending temperature runs. The results were similar in nature. for both the acoustic velocity and electrical resistivity tests. This type of be- haviour has been reported for other sedimentary rock types by King and Bamford (1974). The reason for the observed hysteresis probably is supercooling of the pore water on the descending temperature cycle.

The acoustic velocities and electrical resis- tivities reported for sandstone samples SS4 and SS5 as a function of changes in temperature are explained satisfactorily by the relative shale contents and porosities of these two specimens. With its higher shale content, SS4 showed a greater freezing-point depression than SS5. The acoustic velocities and resistivity for SS4 appeared to be between these values measured for SS1 and SH2. The lower values of these parameters observed at temperatures above 0°C reflect the higher porosity of SS4. With its lower shale content than SS4, but higher porosity than either SS1 or SS4, SS5 behaved in the manner expected, with velocities and resistivities lower than those reported for SSI. The relative values of these parameters for SS4 and SS5 may be explained by the differences in shale content and porosity.

The compressional-wave velocities measured in the laboratory are in reasonable agreement with those values measured using crystal cables in the stratigraphic boreholes, at the depths from which the samples reported here were obtained. At the depth of 170 m from which the

Conclusions

1. Acoustic velocities and electrical resistivities of frozen, water-saturated sandstones are strongly dependent on temperature in the range - 17-O°C, with a reduction in value of these parameters as the temperature rises to 0°C. The changes in velocity and resistivity appear to be functions of the porosity and shale content of the sandstones and the salinity of the pore fluid.

2. The acoustic velocities and electrical re- sistivity of certain shales of low porosity are relatively insensitive to changes in temperature in the range - 17- +4"C.

3. The electrical resistivity of sandstones and shales of low porosity are relatively insensitive to changes in frequency in the range 5-lo5 Hz.

Acknowledgements

Provision of the permafrost test samples by Panarctic Oils Ltd. is gratefully acknowledged, as is the continued interest shown in the research by Mr. Peter Carroll of that organization.

Financial support for the research from the Defence Research Board of Canada (Grant No. 951 1-72), the National Research Council of Canada (Grant No. A4229) and the Department of Energy, Mines and Resources (Contract No. OSU 3-0541) is also gratefully acknowledged.

Appreciation is expressed to Dr. T. J. Katsube of the Geological Survey of Canada for his advice on the design of the electrical resistivity apparatus.

ANANYAN, A. A. 1958. Dependence of electrical conduc- tivity of frozen rocks on moisture content. Izvestiya Academy of Sciences USSR, Geophysics Series, pp. 878-881.

ANTSYFEROV, M. S. , ANTSYFEROVA, N. G., and KAGAN, YA. 1964. A study of the propagation velocities and absorption of elastic waves in frozen sand. Izvestiya Academy of Sciences USSR, Geophysics Series, pp. 85-89.

sandstone samples were obtained, the tempera- COLLETT, L. S. 1974. Geophysical parameters of perma-

ture was -gOc and the compressiona~-wave frost. Proceedings Symposium Permafrost Geophys- ics, Associate Committee on Geotechnical Research,

4500 m/s. At the of 365 from National Research Council of Canada, Technical which the shale sample SH2 was obtained, the ~~~~~~d~~ 113. pp, 1-16. temperature was - 7 " ~ and the compressional- FROLOV, A. D. 1961. The propagation of ultrasonic waves wave velocity 3000 m/s. Any differences existing in frozen sandy-clayey rock. Izvestiya Academy of Sci-

ences USSR, Geophysics Series, pp. 732-736. may be attributed to the HOEKSTRA, p, and MCNEILL, D. 1973, Electromagnetic in reproducing in situ borehole conditions in the probing ofpermafrost. permafrost: the ~~~h laboratory. can contribution to the Second International Confer-

Can

. J. E

arth

Sci

. Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

UN

IV C

HIC

AG

O o

n 11

/13/

14Fo

r pe

rson

al u

se o

nly.

KING 1013

ence, Yakutsk, USSR. National Academy of Sciences, Washington, DC, pp. 517-526.

KING, M. S. 1970. Static and dynamic elastic moduli of rocks under pressure. In Rock mechanics: theory and practice, (W. H. Somerton, Ed.). American Institute of Mining, Metallurgical and Petroleum Engineers, New York, NY, pp. 329-351.

KING, M. S. ~ ~ ~ B A M F O R D , T. S. 1974. Ultrasonicvelocity measurements on frozen rocks. Earth Research, 1, pp. 4349.

KURFURST, P. J. and KING, M. S. 1972. Staticand dynamic elastic properties of two sandstones at permafrost tem- peratures. Transactions of the Society of Petroleum En- gineers of the American Institute of Mining, Metal- lurgical and Petroleum Engineers, 253, pp. 495-504.

NAKANO, Y., MARTIN, R. J., and SMITH, M. 1972. U1- trasonic velocities of the dilatational and shear waves in frozen soils. Water Resources Research, 8, pp. 1024-1030.

NAKANO, Y. and FROULA, N. H. 1973. Sound and shock transmission in frozen soils. In Permafrost: the North American contribution to the Second International Con- ference, Yakutsk, USSR. National Academy of Sci- ences, Washington, DC, pp. 359-369.

PARKHOMENKO, E. I. 1967. Electrical properties of rocks. Plenum Press, New York, NY, 314 p.

TIMUR, A. 1968. Velocity of compressional waves in po- rous media at permafrost temperatures. Geophysics, 33, pp. 584-597.

Can

. J. E

arth

Sci

. Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

UN

IV C

HIC

AG

O o

n 11

/13/

14Fo

r pe

rson

al u

se o

nly.