In 1980, Aki and Richards published linearized formulations of the Zoeppritz equations from 1919. From then on, many flavors and variations of the P-P reflection mode so-called amplitude variation with offset (AVO) equations have been published and used. Assuming the earth is isotropic, these equations are used day in and day out in the industry for reservoir characterization and to find oil and gas in the subsurface. Some publications have shown that using the P-P and P-S reflections in a joint inversion can increase the accuracy of the inverted parameters. Technically, however, there has been little divergence from the linearized Zoeppritz equations until lately when full-waveform inversion started to gain traction, initially for velocity model estimation and imaging and more recently applied to reservoir characterization.

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