Travel time tomography with adaptive dictionaries

TL;DR

This paper introduces a novel 2D travel time tomography method that employs adaptive dictionary learning to model both smooth and discontinuous features in slowness maps, improving inversion accuracy.

Contribution

It develops a locally-sparse tomography approach using adaptive dictionaries, combining small-scale and large-scale feature modeling in a unified framework.

Findings

Outperforms traditional smoothness and total variation regularization methods.

Effectively models both smooth and discontinuous features.

Demonstrates superior results on synthetic data with irregular sampling.

Abstract

We develop a 2D travel time tomography method which regularizes the inversion by modeling groups of slowness pixels from discrete slowness maps, called patches, as sparse linear combinations of atoms from a dictionary. We propose to use dictionary learning during the inversion to adapt dictionaries to specific slowness maps. This patch regularization, called the local model, is integrated into the overall slowness map, called the global model. The local model considers small-scale variations using a sparsity constraint and the global model considers larger-scale features constrained using $\ell_2$ regularization. This strategy in a locally-sparse travel time tomography (LST) approach enables simultaneous modeling of smooth and discontinuous slowness features. This is in contrast to conventional tomography methods, which constrain models to be exclusively smooth or discontinuous. We develop a $\textit{maximum a posteriori}$ formulation for LST and exploit the sparsity of slowness patches using dictionary learning. The LST approach compares favorably with smoothness and total variation regularization methods on densely, but irregularly sampled synthetic slowness maps.