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

Abstract

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).

Integrated Approach for the Petrophysical Interpretation of Post-and Pre-Stack 3-D Seismic Data, Well-Log Data, Core Data, Geological Information and Reservoir Production Data via Bayesian Stochastic Inversion

“…Hybrid optimization techniques have also been used to include the most important features of local and global inversion methods (Chunduru et al, 1997;Xia et al, 1998).…”

Computation of differential seismograms and iteration adaptive regularization in prestack waveform inversion

“…This is evident from the fact that most published results reported on the use of prestack waveform inversion on only a few CMP gathers or within a small time window (e.g., Xia et al, 1998;Mallick, 1999). For application to 2D or 3D seismic lines, either an AVO or a hybrid approach is employed.…”

“…A variant of SA called very fast simulated annealing (VFSA) (Ingber, 1989;Sen and Stoffa, 1995) is computationally efficient and can be a practical tool. For example, Xia et al (1998) proposed a hybrid scheme in which arc-tangent parameterization and VFSA were used in estimating background velocity, which was then used as starting solution for linearized full-waveform inversion although arc-tangent parameterization for regularization was rather ad hoc. However, they obtained a robust solution because much care was taken to define a starting model and the search space, based on traveltime and AVO inversion.…”

Optimization and geophysical inverse problems

“…For instance, Xia et al (1998) show how the long wavelength and short wavelength parts of a velocity model can be separately estimated. The primary advantage of such a separation is that different optimization procedures can be used for the different parts of the inverse problem, allowing the optimization procedure to be tailored to the particular attribute of the model that is being estimated.…”