INVERSION OF SEISMIC VELOCITIES FOR THE ANISOTROPIC ELASTIC TENSOR (ACOUSTICS).
Abstract
Two methods of obtaining the complete elastic tensor are presented. Both methods are theoretically exact and linear and therefore eliminate the error inherent in approximation methods. The first method uses phase velocity observations of both P and S waves along with estimates of the direction of polarization to solve for the elastic tensor. This is an iterative method in which polarization is updated with each iteration. It is quite robust and quickly converging. This method is applied to real data collected from dunite and bronzitite. The second method uses group velocity observations, estimates of the normal to the group velocity surface (which is parallel to slowness), and estimates of the direction of polarization to solve for the elastic tensor. This method, like the phase velocity method, is an iterative method in which both the normal to the group velocity surface and polarization are updated with each iteration. The group velocity method is less robust than the phase velocity method but quickly converging.
In addition, a number of new relationships of the elastic tensor are also presented. These relate Voight and Reuss moduli to the elastic tensor and also yield an invariant relationship between mutually orthogonal phase velocities. Specifically, this invariant is the sum of the squares of the three phase velocities propagating in each of three mutually orthogonal directions this quantity is invariant under rotation. This invariant does not depend upon the type of symmetry or strength of anisotropy but on the elastic properties of the material in which the velocities are measured.
Subject Area
Geophysics
Recommended Citation
HARDER, STEVEN HENRY, "INVERSION OF SEISMIC VELOCITIES FOR THE ANISOTROPIC ELASTIC TENSOR (ACOUSTICS)." (1986). ETD Collection for University of Texas, El Paso. AAI8629468.
https://scholarworks.utep.edu/dissertations/AAI8629468