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We present a method based on gradient separation and recombination to improve the long wavelength updates of full wavefield inversion (FWI) on reflection-dominant data. We decompose the FWI gradient into a tomographic and a migration term. The tomographic term is obtained by crosscorrelating wavefields traveling in similar direction (forward scatterings), whereas the migration term is obtained by crosscorrelating wavefields traveling in opposite directions (backward scatterings). We show that the tomographic component of the gradient mainly updates the long wavelengths of the model parameters, whereas the migration component of the gradient mainly updates the short wavelengths of the model parameters. We recombine these two components to form a new gradient with a higher weight on the tomographic component. We show that the tomographically enhanced gradient makes FWI converge to the correct model even in situations where the conventional FWI fails to converge. We demonstrate our method based on constant-density acoustic FWI by inverting the P-wave velocities, but the method can be easily extended to more complicated multi-parameter inversion.
Tang et al. (Mon,) studied this question.