Wavefield tomography based on local image correlations

The estimation of a velocity model from seismic data is a crucial step for obtaining a high-quality image of the subsurface. Velocity estimation is usually formulated as an optimization problem where an objective function measures the mismatch between synthetic and recorded wavefields and its gradient is used to update the model. The objective function can be defined in the data-space (as in full-waveform inversion) or in the image-space (as in migration velocity analysis). In general, the latter leads to smooth objective functions, which are monomodal in a wider basin about the global minimum compared to the objective functions defined in the data space. Nonetheless, migration velocity analysis requires construction of common-image gathers at fixed spatial locations and subsampling of the image in order to assess the consistency between the trial velocity model and the observed data. We present an objective function that extracts the velocity error information directly in the image domain without computing common-image gathers. Because of the dimensionality of the problem, gradient-based methods (such as the conjugate-gradient algorithm) are used in the optimization procedure. In order to include the full complexity of the wavefield in the velocity estimation algorithm, we consider a two-way (as opposed to one-way) wave operator, we do not linearize the imaging operator with respect to the model parameters (as in linearized wave-equation migration velocity analysis), and compute the gradient of the objective function using the adjoint-state method. We illustrate our velocity estimation methodology with a few synthetic examples.