Wave-equation tomography by beam focusing

Conclusions

To reliably estimate velocity using wavefield operators, I introduce a new objective function that rewards flatness of the correlation between source wavefield and receiver wavefield. The proposed objective function is maximized as a function of the slowness model through the application of residual moveout operators to the correlation. The first term of the objective function measures the power of the stack over local beams as a function of the local beam curvature. Maximization of this first term ensures global convergence in presence of large velocity errors. The second term maximizes the global power of the stack as a function of time shifts applied to the local stack over the beams. Maximization of this second term helps the estimation of localized velocity errors.

I tested the application of the proposed objective function by computing its gradients for two simple problems: the estimation of a large and spatially uniform velocity error and the estimation of a spatially localized velocity error. The computed search directions confirm the potential of the proposed method and illustrate the different roles played by the the local and the global terms of the objective function.

Wave-equation tomography by beam focusing