Implementation of Adaptive Smoothing Regularization Technique for Simultaneous Multi-frequency Full Waveform Inversion

In full waveform inversion, regularization schemes have been exploited to stabilize the inverse problem. It is apparent that full waveform inversion with regularization shows a better result than with no regularization. However, it may fail to represent layer interfaces clearly such as faults, sedimentary layers and salt boundaries. Consequently, the application of an adaptive regularization based on geological structures is required to recover accurate subsurface structures. In this paper, we suggest an adaptive smoothing regularization based on local slope. Our adaptive regularization algorithm is to apply directional smoothing based on local slope information obtained from a migrated image. Local slopes are calculated using the Hilbert transform and stabilized through isotropic and edge-enhancing smoothing before and after calculating local slopes, respectively. We apply the proposed adaptive smoothing regularization to the full waveform inversion of the SEG/EAGE salt model. The adaptive smoothing regularization filter is periodically updated as the inversion progresses. The inversion result shows that the layer interfaces are faithfully preserved and sharpened.