Introduction

Abstract

In this chapter we present the basic elements for the numerical modelling of seismic wave propagation. Following a summary of notational conventions, we introduce the elastic wave equation in its different formulations (Sect. 2.2). The acoustic wave equation is treated as a special case in Sect. 2.3. While numerical methods differ in the details of the spatio-temporal discretisation, they can still be treated within a unifying framework. The approximation of the spatial derivatives generally leads to a system of ordinary differential equations in time that is commonly referred to as the semi-discrete form of the wave equation. The semi-discrete form can be written in terms of mass and stiffness matrices (Sect. 2.4). Depending on the specifics of an application, the remaining time derivatives can then be approximated using either the Fourier transform or time-stepping algorithms such as the Newmark or leapfrog methods (Sect. 2.5).KeywordsDiscontinuous Galerkin MethodPseudospectral MethodWaveform InversionSeismic Wave PropagationStress FormulationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.