Acoustic- and elastic-waveform inversion using a modified total-variation regularization scheme

Subsurface velocities within the Earth often contain piecewise-constant structures with sharp interfaces. Acoustic- and elastic-waveform inversion (AEWI) usually produces smoothed inversion results of subsurface geophysical properties. We develop novel AEWI methods using a modified total-variation regularization scheme to preserve sharp interfaces in piecewise-constant structures and improve the accuracy of compressional- and shear wave velocity inversion. We use an alternating-minimization algorithm to solve the minimization problem of our new waveform inversion methods. We decouple the original optimization problem into two simple subproblems: a standard waveform inversion subproblem with the Tikhonov regularization and a standard L2–TV subproblem. We solve these two subproblems separately using the non-linear conjugate-gradient and split-Bregman iterative methods. The computational costs of our new waveform inversion methods using the modified total-variation regularization scheme are comparable to those of conventional waveform inversion approaches. Our numerical examples using synthetic seismic reflection data show that our new methods not only preserve sharp interfaces of subsurface structures, but also significantly improve the accuracy of compressional- and shear wave velocity inversion.