Antialiasing and wave equation statics by series approximation and inversion
Robert James Ferguson
To address the problems of irregular trace spacing and statics correction, simultaneous regularization and wave equation statics (WE statics) is implemented by least-squares inversion. In general, inversion is found to be intractable currently in 3D, so series approximation is made to reduce significantly the number of required integrals. The resulting operator is suitable for both direct inversion, or for use with gradient methods.
Real and synthetic data are used to demonstrate the viability of the inversion. Synthetic data show that even for severe velocity variation and topography, inversion converges to an acceptable solution, and that aliasing is significantly reduced. Similarly for real data, inversion is shown to return a regularized result with WE statics applied that is anti-aliased.