Theory and Observations - Forward Modeling and Synthetic Seismograms: 3-D Numerical Methods

We provide an overview of the numerical methods used to simulate seismic wave propagation at the scale of the globe. These numerical techniques may be subdivided in terms of methods based upon a differential or strong form of the equation of motion and methods based upon an integral or weak representation. In the former category we discuss finite difference and pseudospectral methods, whereas in the latter category we consider coupled mode direct solution, finite element, and spectral element techniques. To date, only coupled mode, direct solution, and spectral element methods have been able to simulate three-dimensional seismic wave propagation throughout the entire globe. We have now reached a stage where fully three-dimensional numerical methods can be effectively used to address the inverse problem. In this regard, adjoint methods appear to be particularly promising.