Implementation of adaptive edge-preserving smoothing regularisation technique for simultaneous multi-frequency full waveform inversion

Abstract

The regularisation method simply involves adding a regularisation term to a misfit function, thereby generally stabilising ill-posed inverse problems. In this paper, a pure-gradient based full waveform inversion is carried out in the frequency domain, and smoothing regularisation is exploited in the form of preconditioning, contrary to conventional regularisations in general inverse theory. For more accurate descriptions of subsurface structures, we select adaptive regularisation rather than isotropic smoothing regularisation. The adaptive smoothing regularisation method is used to both smooth the image and differentiate between layers and boundaries. Dip information is estimated using the Hilbert transform, an adaptive smoothing filter with an edge-preserving property is designed from the estimated dip information, and full waveform inversion is then performed using the adaptive smoothing filter. The adaptive smoothing filter is periodically updated during inversion iterations to adapt to the inverted velocity model. We conducted numerical experiments to test our adaptive smoothing filter on a simple model, the Marmousi model, and the SEG/EAGE salt model, and the results demonstrated that our adaptive smoothing regularisation method yields more reliable and precise information compared with the conventional regularisation method.