Amplitudes vary in seismic reflection data in a complex manner. AVO problems (not to mention full waveform inversion and inverse scattering) must be supported by theory which provides insight into the relationship between medium and amplitude, leads to modeling and inversion algorithms, and scales easily between rough-approximate and detailed-accurate tools for analysis. This applies equally to AVO well-developed regimes, such as P-, S-, and C-wave AVO, as to AVO in anelastic regimes. The purpose of this paper is to extend a mode of analysis elsewhere used to study anelastic inversion of P-P data, and to use it to discuss these regimes as well as anelastic AVF behaviour. A range of conclusions are arrived at: (1) second order corrections to converted wave amplitudes can account for dependence on target VP , a dependence that is invisible to the Aki-Richards approximation. (2) Variations of anelastic reflection coefficients with angle and with frequency can be used to estimate target parameters such as QS. (3) To second order, a contrast in QS only across a boundary can cause a P-S mode conversion whereas a contrast in QP only cannot. (4) However, if a contrast occurs in both QP and QS but no other parameter, the QP contrast can alter the amplitude of the conversion.
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