Least-squares wave-equation migration for AVP/AVA inversion

We present an acoustic migration/inversion algorithm that uses extended double-square-root wave-equation migration and modeling operators to minimize a constrained least-squares data misfit function (least-squares migration). We employ an imaging principle that allows for the extraction of ray-parameter-domain common image gathers (CIGs) from the propagated seismic wave-field. The CIGs exhibit amplitude variations as a function of half-offset ray parameter (AVP) closely related to the amplitude variation with reflection angle (AVA). Our least-squares wave-equation migration/inversion is constrained by a smoothing regularization along the ray parameter. This approach is based on the idea that rapid amplitude changes or discontinuities along the ray parameter axis result from noise, incomplete wavefield sampling, and numerical operator artifacts. These discontinuities should therefore be penalized in the inversion. The performance of the proposed algorithm is examined with two synthetic examples. In the first case, we generated acoustic finite difference data for a horizontally layered model. The AVP functions based on the migrated/inverted ray parameter ClGs were converted to AVA plots. The AVA plots were then compared to the true acoustic AVA of the reflectors. The constrained least-squares inversion compares favorably with the conventional migration, especially when incompleteness compromises the data. In the second example, we use the Marmousi data set to test the algorithm in complex media. The result shows that least-squares migration can mitigate kinematic artifacts in the ray-parameter domain CIGs effectively.