Recent Trends and Future Directions Seismograms recorded at the earth's surface or in boreholes from earthquakes and man-made explosions are used extensively to infer the structure of the earth's deep interior. Thus numerical modeling of seismic wave propagation plays an important role in understanding the wiggles and obtaining meaningful images of the earth's subsurface. Elastic wave theory and linear elasticity is used for this purpose.
Numerical methods allow for realistic models but are computationally very expensive.
Fast analytic methods make several approximations and, at times, require use of very simplistic earth models. The real challenge is to develop techniques that are fairly accurate and are valid for realistic earth models. Although computation of 3D isotropic models still remains a challenging task, the new data show abundant evidence of anisotropy at all levels and at all scales of resolution. Semi-analytic approaches that make use of flat earth approximation are computationally feasible for anisotropic media. However, for general 3D models, finite differnce solutions of elastic wave equations are applied.