June 2001 | Volume 26 Issue 06 | View Issue
Abstract
Pre-stack seismic waveform inversion is a highly challenging task. The non-linearity and non-uniqueness together with compute intensive forward modeling often make the problem intractable. Much progress has been made in the last decade in the application of global and local optimization methods in model parameter estimation, data fitting and uncertainty estimation. In isotropic media, we found that a hybrid multi-stage waveform inversion approach based on prior travel time and AVO analysis in the plane wave (delay time – slowness or τ–p) domain is fairly robust and computationally efficient. Much of current research is focused on including the effects of transverse isotropy on AVO and pre-stack analysis. Unlike isotropic media, P wave normal moveout analysis in the delay time-ray parameters (τ–p) domain reveals that only two anisotropy parameters, namely, elliptic velocity (αel ) and k can be derived successfully in a weak transversely isotropic medium. Based on travel time analysis, an efficient strategy can be made to apply full waveform inversion for parameter estimation and uncertainty analysis. I use the αel and k derived from travel time analysis to constrain the travel time fit; the three free parameters β0 , δ and density ρ are allowed to vary within a pre-defined search window that is chosen based on a priori knowledge. As in isotropic media, I use synthetic seismograms generated by a reflectivity algorithm and a global optimization method called very fast simulated annealing (VFSA) in search for optimal earth models. An extensive uncertainty analysis is carried out using all the models sampled by multiple VFSA runs. The results are presented as approximate marginal posterior density functions of different model parameters and correlation matrices. The correlation matrices clearly demonstrate the trade-off between different anisotropy parameters. The results reveal that the acoustic impedance is the best-resolved parameter. Uncertainties in many of the parameters can be greatly reduced by joint inversion of PP and PS data as recorded by the modern Ocean bottom cables (OBC). Application of (τ–p) based waveform inversion for such multi-component data including the effects of anisotropy is fairly straightforward in that the forward modeling method remains unchanged. However, issues such as regularization, penalty functions, data and model weights and objective functions need to be re-evaluated for computational efficiency and robustness of the algorithm.