Adaptive Travel Time Tomography with Local Sparsity

Abstract

We develop a 2D travel time tomography method which regularizes the inversion by modeling sparsely patches of slowness pixels from discrete slowness map, and adapts sparse dictionaries to the slowness data. This locally-sparse travel time tomography (LST) approach considers global and local behavior of slowness, whereas conventional regularization methods consider only global covariance of pixels. We develop a maximum a posteriori formulation of LST, and further exploit the sparsity of patches using dictionary learning. We demonstrate the LST method on densely, but irregularly sampled synthetic slowness maps.