Regularization tunnelling for full waveform inversion

Prior knowledge can be a powerful source of information in seismic inversion, leading to substantially more accurate models than those derived from seismic data alone. Prior knowledge about clustering of rock physics properties, supplied by appropriate rock physics models, or nearby well-logs, may be especially informative. However, incorporating general forms of this type of information into local optimization methods, such as those used in full waveform inversion (FWI), is problematic, since it will often call for model updates involving a departure from the basin of a local minimum. Here, we propose an optimization strategy for FWI, in which global regularization information is partially accounted for, and in which a model can, under the right circumstances, 'tunnel' between basins, to honour prior information. The process is based on standard FWI updates and begins with an initial model in which every model grid cell is in one of a range of pre-defined clusters. At each iteration, a standard update is computed, but it is then followed by a second update, in which each grid cell tunnels to a new cluster if the move is warranted by the update history of the model (its 'momentum') and the model regularization penalty (its 'potential'). To limit the ability of the tunnelling procedure from introducing spatial variations on scales smaller than those contained in the seismic data, these conditions are considered in combination with a small mode filter. We implement the procedure by building on an existing 2-D viscoelastic FWI algorithm, limited such that only the P-wave velocity and density are updated, and evaluate it by subjecting it to a variety of basic tests involving simulated data. We conclude that the basic approach, and this specific implementation, using a simple initial model, provides a combination of well-resolved structures and grid cells occupying appropriate clusters that cannot be produced by standard means.