Full-waveform inversion attempts to estimate a high-resolution model of the Earth by inverting all the seismic data. This procedure fails if the Earth model contains high-contrast bodies such as salt and if su ciently low frequencies are absent from the data. Salt bodies are important for hydrocarbon exploration because oil or gas reservoirs are often located on their sides or underneath. We represent the shape of the salt body with a level set, constructed from radial basis functions to keep its dimensionality low. We have shown earlier that the salt body can be completely recovered if the sediment structure is already known. In this paper, we propose a strategy to simultaneously reconstruct the sediment and the salt. The sediment is implicitly represented by a bilinear interpolation kernel with a small number of variables. An alternating minimization technique solves the resulting optimization problem. The results on a synthetic model using Gauss-Newton approximation of the Hessian shows the feasibility of the approach
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