A dictionary-based approximation approach for seismic traveltime tomography

We attempt the reconstruction of the solid earth’s interior three-dimensional structure using seismic wave observations. The interior structure of the mantle deviates moderately from spherically symmetrical reference models and therefore seismological observables also vary moderately from spherically symmetrical predictions. Hence we consider here the linearized inverse problem of seismic traveltime tomography.

Usually, the solution is approximated in a fixed basis system: either global (e.g. polynomials) or local (e.g. finite elements) basis functions. Here we use a dictionary-based approximation approach, called the Learning Regularized Functional Matching Pursuit (LRFMP). A dictionary is an intentionally redundant set of diverse trial functions from which iteratively an approximation in a best basis is built. The next best basis element is chosen such that the Tikhonov functional is minimized.

The methods have been used for a variety of spherical as well as tomographic tasks from the geosciences as well as medical imaging. Here we apply them to seismic traveltime tomography for the first time. We discuss relevant developments and challenges in the process of tailoring the methods to the problem and show first promising results.