Compressibility and Anisotropy of Rocks at and near the Earth's Surface

Abstract

Purpose of the Investigation.-That remarkably active branch of geophysics, seismology, is dependent for theory and practice on accurate information regarding those physical properties of rocks that are most intimately related to the propagation of elastic waves in the earth. Most important of all for use in diagnosing the composition of hidden rocks is volume compressibility. Due to recent improvements in technique by Bridgman and others, it is now possible to measure the linear and cubic compressibility of a rock under hydrostatic pressures as high as 10,000 to 30,000 kilograms per square centimeter. This is the range of pressure at depths of roughly 35 to 100 kilometers in the earth. While Bridgman has supplied some data on the compressibility of rocks at high pressure, the greater part of the available information comes from the work of Adams and Williamson at the Geophysical Laboratory of the Carnegie Institution of Washington.I Adams and Williamson worked in a pressure range of 2000 to 10,000 "megabars" (now sometimes called "bars"), a megabar being one million dynes per square centimeter and equal to about 1.02 kilograms per square centimeter or about ninety-nine per cent of one atmosphere. Their measurements were made under two different conditions. In the one case the rock specimens were exposed directly to the fluid transmitting the pressure; in the other case the air-dried specimens were covered with thin, impermeable tin-foil which prevented the direct access of the fluid. Adams and Williamson pointed out that the measured compressibility should be the greater in the second case, provided the rock carries cracks or pores in communication. For clearly, when the pressure goes on, the cracks and pores should be more easily closed if the specimen is "covered" than if the transmitting fluid is allowed to enter cracks and pores and so add to the resistance to closure. This theoretical expectation agreed with the results of the many experiments, except in the case of three rocks: marble, Westerly granite and Stone Mountain granite. These anomalies were not explained. During the experiments reported in the present paper, twenty-eight different specimens of rock were tested in both the covered and uncovered states; in every case the behavior was that foretold by Adams and Williamson. Those authors showed that the compressibility of most rocks decreases rapidly as the pressure rises from an initial amount of three hundred 666 PROC. N. A. S.

The Elastic Properties of Rocks: A Correlation of Theory and Experiment

“…For example, a ten per cent variation in o-produces only two per cent variation in E/I computed from formula (4). Similarly a ten per cent variation in a-produces only 3.7 per cent variation in V/v from formulas (1) and (2). But aside from the quantitative difference between the discrepancies of table 1 and of table 2, the general results are very similar.…”

“…E: + 3E/,u = 9 (5) ,4_ 1 -2a (6j 3 2(1+ua) In these formulas E is Young's modulus of elasticity 3 is the cubic compressibility ,u is the modulus of rigidity a is Poisson's ratio of lateral contraction to longitudinal extension p is the density of the medium V is the velocity of a longitudinal wave in the medium v is the velocity of a transverse wave in the medium Obviously formulas (1) and (2) can be extended to express V and v in terms of any two of the four constants, E, A, ,, a.…”

“…The material in table 2 and formulas (1), (2), (3) and (4) are used for this discussion. Finally, we compare formulas (1) and (2) with experiment, by computing longitudinal and transverse wave-velocities from measured values of E, A and ,B. The computed and observed wave-velocities are compared in table 3.…”

“…This is true because of the manner in which o enters-into formulas (1), (2) and (4). For example, a ten per cent variation in o-produces only two per cent variation in E/I computed from formula (4).…”

“…This comparison is of particular interest since wave-velocities are the data of primary concern to seismologists. Table 3 contains values obtained in three ways: (A) computed by formulas (1) and (2) from laboratory determinations of Young's modulus and the modulus of rigidity; (B) obtained by Leet from time-distance curves for explosion waves; and (C) computed by formulas (1) and (2) from laboratory measurements of Young's modulus and compressibility.…”