The Role of Synthetic Reconstruction Tests in Seismic Tomography

Abstract:

Synthetic reconstruction tests are widely used in seismic tomography as a means for assessing the robustness of solutions produced by linear or iterative non-linear inversion schemes. The most common test is the so-called checkerboard resolution test, which uses an alternating pattern of high and low wavespeeds (or some other seismic property such as attenuation). However, checkerboard tests have a number of limitations, including that they (1) only provide indirect evidence of quantitative measures of reliability such as resolution and uncertainty; (2) give a potentially misleading impression of the range of scale-lengths that can be resolved; (3) don't give a true picture of the structural distortion or smearing caused by the data coverage; and (4) result in an inverse problem that is biased towards an accurate reconstruction. The widespread use of synthetic reconstruction tests in seismic tomography is likely to continue for some time yet, so it is important to implement best practice where possible. The goal here is to provide a general set of guidelines, derived from the underlying theory and illustrated by a series of numerical experiments, on their implementation in seismic tomography. In particular, we recommend (1) using a sparse distribution of spikes, rather than the more conventional tightly-spaced checkerboard; (2) using the identical data coverage (e.g. geometric rays) for the synthetic model that was computed for the observation-based model; (3) carrying out multiple tests using anomalies of different scale length; (4) exercising caution when analysing synthetic recovery tests that use anomaly patterns that closely mimic the observation-based model; (5) investigating the trade-off between data noise levels and the minimum wavelength of recovered structure; (6) where possible, test the extent to which preconditioning (e.g. identical parameterization for input and output models) influences the recovery of anomalies.