Characterizing the degree of amplitude-variation-with-offset nonlinearity in seismic physical modelling reflection data

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Abstract

The nonlinearity of the seismic amplitude-variation-with-offset response is investigated with physical modelling data. Nonlinearity in amplitude-variation-with-offset becomes important in the presence of large relative changes in acoustic and elastic medium properties. A procedure for pre-processing physical modelling reflection data is enacted on the reflection from a water-plexiglas boundary. The resulting picked and processed amplitudes are compared with the exact solutions of the plane-wave Zoeppritz equations, as well as Symbol approximations that are first, second, and third order in Symbol, Symbol, and Symbol. In the low angle range of 0°–20°, the third-order plane-wave approximation is sufficient to capture the nonlinearity of the amplitude-variation-with-offset response of a liquid-solid boundary with Symbol, Symbol, and ρ contrasts of 1485–2745 m/s, 0–1380 m/s, and 1.00–1.19 gm/cc respectively, to an accuracy value of roughly 1%. This is in contrast to the linear Aki–Richards approximation, which is in error by as much as 25% in the same angle range. Even-order nonlinear corrective terms are observed to be primarily involved in correcting the angle dependence of Symbol, whereas the odd-order nonlinear terms are involved in determining the absolute amplitude-variation-with-offset magnitudes.

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