Edge-preserving Traveltime Tomography with a Model Sparsity Constraint

Abstract:

The first-arrival traveltime tomography is applied to image the near surface as the first step in the procedures of reflection seismic data processing. Tomographic velocity model is used to calculate statics or further input to waveform inversion in exploration geophysics. In the traveltime tomography, Tikhonov regularization always produces a model with highly smooth structures. However, the real underground structure may not be smooth. Since traveltime tomography is an inverse problem which is often ill-posed and non-unique, it suffers from a multi-solution problem. Smoothing may help to reduce its non-uniqueness. To produce a velocity model that is reliable and also offers high resolution, we develop a new alternative edge-preserving traveltime tomography based on sparse model constraint. This new methodology is based on a hypothesis that velocity model can be represented sparsely in a known basis. In our synthetic and real data test, we choose orthogonal wavelet basis created by ‘symN’ as the sparse transform matrix. We provide two different alternative schemes, and one can choose one scheme or combine two schemes according to one’s request, like the sharpness degree of the inversion result. We estimate the effect of the new method by applying it to synthetic and real data respectively. The results show that this method can provide an image with sharper boundary in the same data fitting level comparing with the conventional traveltime tomography.