A 2.5-D time-domain elastodynamic equation for a general anisotropic medium

In order to provide a quantitative analysis of real seismic records from complex regions we need to be able to calculate the wavefields in three dimensions. However, full 3-D modelling of seismic-wave propagation is still computationally intensive. An economical approach to the modelling of seismic-wave propagation which includes many important aspects of the propagation process is to examine the 3-D response of a model where the material parameters vary in two dimensions. Such a configuration, in which a 3-D wavefield is calculated for a 2-D medium, is called the '2.5-D problem'. Recently, Takenaka & Kennett (1996) proposed a 2.5-D time-domain elastodynamic equation for seismic wavefields in models with a 2-D variation in structure but obliquely incident plane waves in the absence of source. This approach is useful even for non-plane waves. In the presence of source a new 2.5-D elastodynamic equation for general anisotropic media can be derived in the time domain based on the Radon transform over slowness in the direction with constant medium properties. The approach can also be formulated in terms of velocity-stress, a representation which is well suited to the use of numerical techniques for 2-D time-domain problems such as velocity-stress finite-difference or velocity-stress pseudospectral techniques.