Image-domain wavefield tomography with extended common-image-point gathers

Waveform inversion is a velocity-model-building technique based on full waveforms as the input and seismic wavefields as the information carrier. Conventional waveform inversion is implemented in the data domain. However, similar techniques referred to as image-domain wavefield tomography can be formulated in the image domain and use a seismic image as the input and seismic wavefields as the information carrier. The objective function for the image-domain approach is designed to optimize the coherency of reflections in extended common-image gathers. The function applies a penalty operator to the gathers, thus highlighting image inaccuracies arising from the velocity model error. Minimizing the objective function optimizes the model and improves the image quality. The gradient of the objective function is computed using the adjoint state method in a way similar to that in the analogous data-domain implementation. We propose an image-domain velocity-model building method using extended common-image-point spaceand time-lag gathers constructed sparsely at reflections in the image. The gathers are effective in reconstructing the velocity model in complex geologic environments and can be used as an economical replacement for conventional common-image gathers in wave-equation tomography. A test on the Marmousi model illustrates successful updating of the velocity model using commonimage-point gathers and resulting improved image quality.