Differential Semblance Optimization, a variant of output least squares inversion, successfully estimates the nonlinear P-wave background velocity and linear reflectivities. Simultaneous inversion for reflectivities and source explains substantially more of the actual data than does inversion for reflectivities with fixed source from an air gun modeler. The best reflectivity estimates conform to widely accepted lithologic relationships and closely match the filtered well logs. S. E. Minkoff, 1996.
Seismic inversion produces model estimates which are at most unique in an average sense.
The model resolution matrix quantifies the spatial extent over which the estimate averages the true model. Although the resolution matrix has traditionally been defined in terms of the singular value decomposition of the discretized forward problem, this computation is prohibitive for inverse problems of realistic size. Inversion requires one to solve a large normal matrix system which is best tackled by an iterative technique such as the conjugate gradient method. The close connection between the conjugate gradient and Lanczos algorithms allows us to construct an extremely inexpensive approximation to the model resolution matrix. Synthetic experiments indicate the data dependancy of this particular approximation.