Full-Waveform Inversion with Mumford-Shah regularization

Full-waveform inversion (FWI) is a non-linear procedure to estimate subsurface rock parameters from surface measurements of induced seismic waves. This procedure is ill-posed in nature and hence, requires regularization to enhance some structure depending on the prior information. Recently, Total-Variation (TV) regularization has gained popularity due to its ability to produce blocky structures. Contrary to this, the earth behaves more like a piecewise smooth function. TV regularization fails to enforce this prior information into FWI. We propose a Mumford-Shah functional to incorporate the piecewise smooth spatial structure in the FWI procedure. The resulting optimization problem is solved by a splitting method. We show the improvement in results against TV regularization on two synthetic camembert examples.