Travel time tomography with local sparse modeling and dictionary learning

In this talk, we present a machine learning-based approach to 2D travel time tomography. Travel time tomography methods image slowness structures (e.g., Earth geology) from acoustic and seismic wave travel times across sensor arrays. Typically, slowness is obtained via an ill-posed linear inverse problem, which requires regularization to obtain physically plausible solutions. We propose to regularize this inversion by modeling rectangular groups of slowness pixels from the image, called patches, as sparse linear combinations of atoms from a dictionary. In this locally-sparse travel time tomography (LST) method, the dictionary, which represents elemental slowness features, is initially unknown and is learned from the travel time data using an unsupervised machine learning task called dictionary learning. This local model constrains small-scale slowness features, and is combined with a global model, which constrains larger-scale features with L2 regularization. In contrast to conventional regularization, which allows only for smoothness or discontinuous slowness, LST permits increased resolution where warranted by data. A maximum a posteriori formulation of LST is derived, which is solved as an iterative algorithm. LST performance is evaluated on both synthetic and real data in the context of ambient noise tomography.