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Elastic Waves in Homogeneous and Inhomogeneous Media

By the time that the first seismographs were operational (1889) the mathematical theory of elastic waves was well developed and available for use in interpretation. The complexity of seismic records then encouraged further research into the propagation of elastic waves in stratified media, which has enabled the computation of theoretical seismograms for complex stratified media.

Much of the early work on elastic waves was inspired by trying to understand the propagation of light by using the model of a crystalline medium. Thus Green in 1838 made a detailed study of two-dimensional wave propagation. He introduced the concept of a strain energy function and showed that 21 elastic constants were needed for an anisotropic medium, which reduced to 2 for isotropy. Green isolated P, SV, and SH plane wave components and established the equations that hold at a planar interface between two dissimilar media. He did not attempt to solve these