First steps on modelling wave propagation in isotropic-heterogeneous media: Numerical simulation of P-SV waves

TL;DR

This paper provides a pedagogical approach to modeling seismic wave propagation in isotropic-heterogeneous media using finite-difference methods, including detailed equations, numerical solutions, and illustrative simulations for educational purposes.

Contribution

It offers explicit instructions and detailed modeling of P-SV wave propagation in heterogeneous media, aimed at enhancing undergraduate education in computational geophysics.

Findings

Velocity maps illustrating wave propagation in x-z plane

Time series of z-velocity at detector points

Successful simulation of wave behavior in different media

Abstract

In geophysics, wave propagation in elastic media is a crucial subject. In this context, seismology has made significant progress as a result of numerous advances, among these stands out the advancement of numerical methods such as the finite-difference one. Usually, seismic wave propagation in elastic media results in complex systems of partial differential equations, whose solutions cannot be obtained in an analytical way, especially when dealing with heterogeneous media. In consequence, there exists a necessity to implement numerical methods. However, the available information about the construction of a numerical solution of these equations is not as explicit as it should be. Our main goal is to provide pedagogical instructions for undergraduate students who want to improve their computational skills as well as their knowledge of the subject. The last through current teaching methods involving challenging problems and transversal tools. Particularly, we provide a brief description of the equations and a detailed description of the numerical solution of the seismic wave equation. Furthermore, we model two different seismic explosive sources in both homogeneous and heterogeneous media as an illustrative example. In the results, we include velocity maps showing wave propagation in the x-z plane, and the z-velocity as a function of time measured in a series of detectors distributed in the numerical domain.