Dynamics of SV-wave, SH-wave, and P-wave in a cross-anisotropic medium exhibiting exponential heterogeneity

Abstract

This paper investigates the dynamics of SV -waves, SH-waves, and P-waves in a continuously heterogeneous cross-anisotropic material. Two case studies have been performed, each associated with the heterogeneity involved in Young’s moduli, shear modulus, and density of the medium by means of a function of depth. With suitable analytical treatment, the equation of motion reduces to an eigenvalue problem that further helps to achieve the closed-form expression for the phase velocities in the considered framework. Based on the numerical calculations and simulations, the propagation behavior of wave along with the above-stated variation has been scrutinized and discussed. This study unfolds the remarkable influence of inhomogeneity parameters on quasi-wave velocities. The prominent effect of the dependence of wave velocity on the degree of material anisotropy has been shown using 2-dimensional and 3-dimensional graphical presentations for two alternative cases. The impact of phase angle and depth parameter has also been remarkably established. This study may help geophysicists and civil engineers in the field of theoretical foundations and practical applications related to earthquake source mechanisms.