VTI Waveform Inversion with Practical Strategies: Application to 3D Real Data

Abstract

The term of "Waveform inversion" (WFI) refers to a collection of techniques that use the information from seismic data to derive high-fidelity earth models for seismic imaging. The attractiveness of WFI lies mainly in its lack of approximations, at least in a theoretical sense, in contrast to other model determination techniques such as semblance or tomography. However, a whole raft of approximations must be made to make the technique viable with today's computing technology and restrictions of seismic acquisition. These are collectively referred to as "waveform inversion strategies" and in this paper we mainly discuss regularization and preconditioning strategies. WFI is a highly nonlinear, ill-posed problem. As such regularization techniques from optimization theory are beneficial for its solution. Regularization involves introducing additional constraints on the problem usually by restricting smoothness or sharpness of model parameters. These restrictions are driven by a priori geophysical information. In this paper, we apply total variation regularization (TV), a popular method which involves 1-norm of the model derivatives. Real data examples show that edge locations of velocity anomalies tend to be preserved using TV regularization. Compared to inverting the Helmholtz operator, time domain implementation is straightforward and relatively fast. Therefore we present the methodology, strategies, and 3D data examples for time domain WFI with TV regularization. We pursue a vertical transverse isotropic (VTI) acoustic formulation which accounts for the effects of anisotropy. Our WFI is a joint inversion for model parameter and source delay time. Model can be parametrized by P-wave velocity and/or anisotropy parameters, ε and δ. Various preconditioning strategies are also discussed in order to increase the convergence rate for this iterative scheme and reduce the risk of converging to local minima. This paper presents the time domain acoustic VTI WFI implementation. It also discusses practical strategies for regularization and preconditioning and their influences on the models that are obtained from WFI. These approaches will be illustrated on 3D marine data from the Green Canyon area of the Gulf of Mexico.

Time‐lapse seismic imaging using regularized full‐waveform inversion with a prior model: which strategy?

“…Recently, some authors have suggested to introduce prior models in the multiplicative (Hu, Abubakar and Habashy ) and additive (Wang et al . ; Asnaashari et al . ) regularization terms of the FWI workflow.…”

“…One may want to use prior model information in the FWI scheme as is done in other velocity building techniques (Le Stunff and Grenier 1998;Tarantola 2005). Recently, some authors have suggested to introduce prior models in the multiplicative ) and additive (Wang et al 2012;Asnaashari et al 2013) regularization terms of the FWI workflow. Taking into account prior information could be very valuable for monitoring purposes, where many types of precise prior information have been collected for the target zone, in a way similar to the model-based regularization used on time-lapse electrical resistivity tomography (Oldenborger et al 2007;Miller et al 2008).…”

Multiparameter Full-waveform Inversion for Acoustic VTI Medium with Surface Seismic Data

“…To date, most real-world applications of FWI still remain in isotropic medium, and only a few studies have been shown to account for anisotropy. And most of those studies only account for anisotropy in waveform simulation but do not invert for those anisotropy fields (Wang et al, 2012;Warner et al, 2013). Multiparameter inversion for anisotropy fields, even in VTI medium, remains a hot topic in the field (Plessix and Cao, 2011;Gholami et al, 2013a,b).…”

Anisotropic Waveform Inversion with Well Constraints

“…The ALM with well constraints provides a more useful and reliable recovery of velocity profiles from well logs and seismic data including a better delineation of velocity at or close to well locations. Regularization techniques such as total variation regularization (TV) or Tikhonov regularization are also beneficial for the solution of this problem (Wang et al, 2012). Then conjugate gradient methods or qusi-Newton methods can be applied to solve this nonlinear unconstrained optimization problem.…”