Nonlinear elastic inversion of real data

Two-component multi-offset seismic data contains many events that cannot be explained with the acoustic wave equation. These include mode converted shear waves and Rayleigh waves. By deriving a nonlinear inversion algorithm based upon the elastic wave equation, it is possible to account for all of these different waves and obtain the maximum probability compressional and shear wave velocity model. The algorithm does not assume a smooth background velocity as is typically done in migrations and Born inversions. Also, it is based on the full two-way elastic wave equation. Therefore, it can in principle obtain both interval velocities and reflectivities simultaneously (high- and low-wavenumber components of the velocity). The interval velocities are resolved by wave equation renection-tomographic terms in the inversion equations while the reflectivities are resolved by migrationlike terms in the inversion equations. All amplitudes must be accounted for by the theory assumed in the inversion (the elastic wave equation) in order that the result be accurate. However, even neglecting many effects such as source and receiver directivities, the results using real seismic data are encouraging. Ideally, such non-elastic-wave-like events should be included in the theory. After one iteration the algorithm has essentially done an elastic migration using P-P reflections and P-S mode converted waves. The best resolved part of the velocity model is the high-wavenumber perturbations in velocity that produce reflections. Some low wavenumbers are also present in the solution due to mismatches in the shapes of reflection hyperbolae.