Modeling seismic wave propagation in complex media

We review the studies on modeling seismic wave propagation in complex media, which were carried out during the past 10 years by researchers at Japanese institutions. Special emphasis is placed on those works which are perceived as important but had little exposure outside Japan. We can say that the fundamental development of method for seismogram synthesis in the (3, 1) dimension was completed, where the first and second numbers in parentheses are the space dimensions of the wavefield and the heterogeneity of the medium. However, seismologists have been eager to model seismic propagation in the (2, 2), (3, 2), and (3, 3) dimensions during the last 10 years. Modeling seismic wave propagation in a full (3, 3) dimension is now limited to simple small-scale problems because of the extensive computation and large memory, even when using a supercomputer. Nevertheless, in laterally and vertically heterogeneous media, we have to calculate 3-dimensional wavefields in order to analyze real seismic records quantitatively. There exist two potential breakthroughs. One is to assume the medium is axisymmetric and the other to model (3, 2) dimensional wave propagation (the so-called 2.5 dimensional problem). Numerical methods have the potential to simulate seismic wave propagation in realistic environments of substantial spatio-temporal extent. Since we are not used to processing such an abundance of information, we have to investigate methods for analyzing and interpreting large volumes of computational data. These studies may well challenge our conception of seismic wave propagation.