Image-space wave-equation tomography in the generalized source domain

Conclusions

We extend the theory of image-space wave-equation tomography to the generalized source domain. One important advantage of this new domain is that we are able to synthesize a much smaller data set while still keeping necessary velocity information for migration velocity analysis; hence the computational cost of performing image-space wave-equation tomography can be significantly reduced. We demonstrate how these new data sets can be generated by using both the data-space phase encoding method and the image-space phase encoding method. Our preliminary tests on a simple synthetic model show that with the synthesized gathers, we are able to obtain a gradient of the tomography objective functional similar to that computed using the original shot gathers, but at significantly lower cost. The correct gradient is thus important for the gradient-based optimization algorithm to converge to the correct solution.