Decomposition of acoustic and elastic RP into contributions from one-parameter reflection coefficients
Kristopher A. Innanen
In AVO/AVA inversion, a linearized form of the Zoeppritz equations known as the AkiRichards approximation and variants are used to model RP . This approximation can be viewed as a linear decomposition of the full reflection coefficient into contributions from the reflectivities of individual medium parameters. A forward/inverse series framework leads to an alternative approach to this type of decomposition. The first order terms in the decomposition are qualitatively similar to the Aki-Richards approximation, with secondand third-order terms correcting the approximation at large angle and large contrast. We test the approach both for acoustic and elastic reflection coefficients. In the elastic case, where forward/inverse methods of the kind we use require the incorporation of both RP and RS , we proceed in an approximate fashion using RP only. The elastic nonlinear corrections, in spite of the approximation, provide a significant increase in accuracy over the linear/AkiRichards approximation in several large contrast/large angle model regimes. Separately determining individual reflectivities could provide useful input to bandlimited impedance inversion algorithms, or the ability to extrapolate data from small to large angle.