Mathematic Physical Equivalency of 2D Pure Waves in Seismics and Electromagnetics

Abstract

Summary For a long time people tried to find the inner connection between the seismic waves and electromagnetic (EM) waves to explain their similarity. For example, the acoustic wave and Shear Horizontal (SH) wave possess the similar mathematic expression with the Transversal Electric (TE) and Transversal Magnetic (TM) wave, respectly. In this paper, we summarize those waves into an uniform wave equation based on a concept we termed the “wave operator”. The spartial matrix derived from the wave operator consists of four parts in three directions: the direction component, the volume component, the shear component and the rotation component. We then proved the equivalency of different pure waves in 2D case using this uniform expression. Therefore the forward solver developed for the longitudinal, shear and rotation wave can be converted to each other with a simple substitution. The two numerical tests verified our proposition.