Application of Isotropic Finite Strain Theory to Ultrasonic and Seismological Data

Abstract

The finite strain expressions, originally derived by F. Birch (1938), for the compressional and shear velocities in an isotropic solid under hydrostatic pressure, when rederived to be complete to first order in the strain, are functions of both the second- and third-order elastic constants. The extra terms appearing in the complete first-order theory for the velocities and their pressure derivatives are of the order of the ordinary elastic constants. There is no longer any discrepancy between first-order finite strain theory and ultrasonic and seismic data.

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