1-D elastic waveform inversion: A divide-and-conquer approach

Subsurface rock properties are manifested in seismic records as variations in traveltimes, amplitudes, and waveforms. It is commonly acknowledged that traveltimes are sensitive to the long wavelength part of the velocity, whereas amplitudes are sensitive to the short wavelength part of the velocity. The inherent sensitivity of seismic velocity at different wavelengths suggests an approach that decomposes the waveform data into traveltime and amplitude components. Therefore we propose a divide-and-conquer approach to the elastic waveform inversion problem. We first estimate the smoothly varying background velocity from the traveltime and the rapidly changing perturbations from the amplitude by amplitude variation with offset (AVO) inversion based on linearized reflection coefficient. Then we combine the perturbation with the background to obtain a starting model to be used in the final waveform inversion that models all converted waves and internal multiples assuming a 1-D earth model. For estimating the background velocity, we use the flatness of events as the objective criterion, and simulated annealing as a search tool. Three different model parameterization schemes (constant velocity blocks, splines, and arctangent models) are compared, with the arctangent having the most flexibility and least artifacts. Having obtained the background velocities, we analyze the AVO effects to estimate the perturbations to the background, for which we use a linearized inversion method. The combination of the perturbation and background should be sufficiently close to the true model so that the inverse problem becomes quasi-linear. A full elastic waveform inversion is used to fine-tune the combined model to obtain P-wave and S-wave velocity and density, again using either a nonlinear optimization method or an iterative linearized solution. Application of the inversion algorithm to synthetic data from an 84-layer model was able to predict the full reflectivity data and recover the true model parameters. Application to one seismic line in the Carolina Trough area found a thin gas zone which produces strong Bottom Simulating Reflectors (BSRs).