SEISMIC MODELING IN THE IMPLICIT MODE *

A bstract Finite‐difference seismic models are often saddled with huge memory requirements for data manipulation, a prohibitive amount of CPU time and even approximate results. At least part of these costs may be due to the fact that most of the work reported on this subject is devoted to the development of explicit models which suffer from severe limitations of stability and necessitate extremely fine time sampling of the wavefield. A new method of seismic modeling which works in the implicit mode and is unconditionally stable is put forward. It is based on the self‐adjoint version of the acoustic wave equation. The evaluation of the wavefield is done by using a highly efficient splitting algorithm which does not require transposing the field data at the various time steps. Moreover, it can accommodate anisotropic media as well as three‐dimensional structures. Computational efficiency is achieved by introducing an unconventional procedure which yields the sum of the values of the wavefield corresponding to a new time step and a previous time step. The new value can be obtained from this sum by a simple subtraction. A number of numerical examples, some obtained by using time steps about five times larger than the largest permissible time step in the corresponding explicit model, are presented. The effect of topographic changes on the growth of the wavefield due to a source located near the surface of the ground is investigated.