Wave Propagation in Laterally Varying Media: A Model Expansion Method

摘要

A general approach, using modes defined on subregions of the medium, has beendeveloped to model seismic wave propagation in media with vertically and horizontally acoustic waves in fluid media and electromagnetic wave propagation in laterally varying media. The restriction on the medium variability is that it can be represented by step function variations in its properties in both the vertical and horizontal directions. The basic method makes use of normal mode expansion of the wave field in each partitioned sub-region of the medium within which the medium is uniform in the lateral directions. Thus the medium is partitioned into laterally uniform zones and complete normal mode solutions are obtained for each horizontally layered zone. In the analytical development the zonal eigenvalues and eigenfunctions are generated by treating each zone as a layered half space or radially layered sphere, as is appropriate for medium geometry. The resulting set of modes are then used as a basis for expansions of the wave fields in the layered subregions. The modes are then used as bases for expansions of the wave fields in each zone at the common boundaries between the zones where continuity of displacement and traction is required. This results in the definition of a lateral propagator of the wave field when applied to all the zones making up the entire medium and is, in application, very similar to the classical vertical propagator method. This method is exact when the lateral variations are actually discontinuous step changes in properties. When the actual changes can be approximated as a sequence of steps, the method should be superior in computational accuracy and speed to numerical methods.