S U M M A R YIn a set of problems ranging from 4-D seismic to salt boundary estimation, updates to the velocity model often have a highly localized nature. Numerical techniques for these applications such as full-waveform inversion (FWI) require an estimate of the wavefield to compute the model updates. When dealing with localized problems, it is wasteful to compute these updates in the global domain, when we only need them in our region of interest. This paper introduces a local solver that generates forward and adjoint wavefields which are, to machine precision, identical to those generated by a full-domain solver evaluated within the region of interest. This means that the local solver computes all interactions between model updates within the region of interest and the inhomogeneities in the background model outside. Because no approximations are made in the calculation of the forward and adjoint wavefields, the local solver can compute the identical gradient in the region of interest as would be computed by the more expensive full-domain solver. In this paper, the local solver is used to efficiently generate the FWI gradient at the boundary of a salt body. This gradient is then used in a level set method to automatically update the salt boundary.

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Seismic full-waveform inversion (FWI) (Tarantola, 1984) has gained much interest because of its ability to produce highresolution earth models (Vigh and Starr, 2008; Virieux and Operto, 2009). However, the task of accurately recovering the geometry of salt bodies, typically found in geologically complex marine environments like the Gulf of Mexico, still presents a great challenge to FWI. Therefore, the salt geometry often must be manually picked by seismic interpreters, which is not only subjective but also a time-consuming and costly process. Better definition of the salt geometry has been shown to greatly improve imaging in the subsalt sedimentary regions, as shown by Vigh et al. (2010). In this paper, we present an approach to directly invert the geometry of the salt bodies, using FWI, by partitioning the inversion domain into salt and sediment regions and using a level set representation to parameterize the salt geometry.

Full-waveform inversion (FWI) is a high-resolution model-building technique that uses the entire recorded seismic data content to build the earth model. Conventional FWI usually utilizes diving and refracted waves to update the low-wavenumber/background components of the model; however, the update is often depth limited due to the limited offset range acquired. To extend conventional FWI beyond the limits of the transmitted energy, we must use reflection data. Synthetic and field data examples demonstrate that, even in a complex subsalt Gulf of Mexico setting, the background velocity model can be updated from shallow to deep water using conventional FWI followed by reflection-based FWI. A future refinement of the technique shows that, after updating the sediment model, the salt boundaries can be further updated by level-set technology.

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