Imaging earth’s structures is fundamental to the earth’s interior, yet how to reconstruct earth’s heterogeneities using full-waveform inversion of full wavefield data that includes primary reflections and multiples remains enigmatic. I develop a nonlinear Bayesian approach for full-waveform inversion method with multiple scattering. Instead of using single scattering Born approximation to formulate the sensitivity kernels, I develop multiple scattering sensitivity kernels using multiple scattering-based Green’s functions. It is based on the Lippmann-Schwinger integral and Marchenko methods, for which the Green’s functions are retrieved from reflection data by solving a Marchenko equation. To estimate the uncertainty of velocities, I apply a Bayesian framework to the inverse problem. Our results indicate that the method does not depend on the earth’s scattering potential and the full-waveform inversion method with multiple scattering is a good alternative approach to image the earth’s structures.

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