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Gradient of image-space wave-equation tomography by the adjoint-state method

Claudio Guerra


Optimization with gradient-descent techniques requires computing the gradient of the objective function. The gradient can be determined by using the Frech $ \acute {\rm e}$t derivatives, but, for practical problems, this can be very expensive. The gradient can be more efficiently computed by the adjoint-state method, which does not require the use of the Frech $ \acute {\rm e}$t derivatives. Here, I derive the gradient of the image-space wave-equation tomography using the adjoint-state method. I also show its application with a numerical example using image-space phase-encoded gathers.