Robust Waveform Inversion with Adaptive Regularization

Derivation of detailed maps of elastic properties in the seismic frequency band and beyond is a highly challenging task. Global optimization methods have been highly successful in that they are not dependant on the choice of starting solution, they explore the model space extensively and reflections from all angles including post-critical arrivals can be included without difficulty. However for large models, they are computationally intensive and they are more prone to non-uniqueness. Regularization in global optimization is trivial, in theory but difficult in practice since it slows down the algorithm. We have developed local optimization methods with adaptive regularization that can be used efficiently in conjunction with global optimization for analysis of large volume of seismic data. In particular, our conjugate gradient-adaptive regularization scheme has been implemented on three processes that are vital to seismic data analysis, namely, wavelet estimation, impedance inversion from post-stack data and pre-stack inversion for estimation of Vp, Vs and density. Use of a new method of computing differential seismograms combined with sparse gradient matrix makes our algorithm computationally very efficient. We have applied these techniques successfully in the analysis of field data from the Gulf of Thailand and the Oregon coast.