Tomographic traveltime inversion using natural pixels

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Abstract
Traditionally in the problem of tomographic traveltime inversion, the model is divided into a number of rectangular cells of constant slowness. Inversion consists of finding these constant values using the measured traveltimes. The inversion process can demand a large computational effort if a high‐resolution result is desired. We show how to use a different kind of parameterization of the model based on beam propagation paths. This parameterization is obtained within the framework of reconstruction in Hilbert spaces by minimizing the error between the true model and the estimated model. The traveltimes are interpreted as the projections of the slowness along the beampaths. Although the actual beampaths are described by complicated spatial functions, we simplify the computations by approximating these functions with functions of constant width and height, i.e., “fat” rays, which collectively form a basis set of natural pixels. With a simple numerical example we demonstrate that the main advantage of this parameterization, compared with the traditional decomposition of the model in rectangular pixels, is that 2-D reconstructed images of similar quality can be obtained with considerably less computational effort. This result suggests that the natural pixels can provide considerable computational advantage for 3-D problems.

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