Institute of Computational Mathematics and Mathematical Geophysics

Abstracts

Mathematical problems in geophysical investigations of solid Earth

The basic idea of this paper is to derive approximate equations for vertical slowness for P and SV waves and PP, SS and PS traveltimes in TIV media not using a weak-anisotropy approximation. We show that the three-term Taylor series for both vertical slowness and phase velocity in TIV media have the same coefficients. These coefficients completely define all three terms approximations: vertical slowness, phase velocity and traveltime in TIV media. Comparison with the weak anisotropy approximation shows that the first and second terms in the Taylor series are the same as were used in weak anisotropy approximation, but the third term is non-linear with respect to anisotropy parameters and differs from one in weak anisotropy approximation. This fact results in different definitions of heterogeneity coefficient in the traveltime approximation, and consequently in Castle's parameter S. In derivation of approximate equation for the traveltimes we use the continued fraction approximation which gives more accurate approximations than the standard weak anisotropy approximation.

Mail to Webmaster

|Home Page| |English Part|

Go to Home