Non-linear arrival time inversion: constraining velocity anomalies by seeking smooth models in 3-D

Abstract

SUMMARY The problem of constraining 3-D seismic anomalies using arrival times from a regional network is examined. The non-linear dependence of arrival times on the hypocentral parameters of the earthquakes and the 3-D velocity field leads to a multiparameter-type non-linear inverse problem, and the distribution of sources and receivers from a typical regional network results in an enormous 3-D variation in data constraint. To ensure computational feasibility, authors have tended to neglect the non-linearity of the problem by linearizing about some best-guess discretized earth model. One must be careful in interpreting 3-D structure from linearized inversions because the inadequacy of the data window may combine with non-linear effects to produce artificial or phantom ‘structure’. To avoid the generation of artificial velocity gradients we must determine only those velocity variations which are necessary to fit the data rather than merely estimating local velocities in different parts of the model, which is the more common practice. We present a series of inversion algorithms which seek to inhibit the generation of unnecessary structure while performing efficiently within the framework of a large-scale inversion. This is achieved by extending the subspace method of Kennett, Sambridge & Williamson (1988) and incorporating the smoothing strategy proposed by Constable, Parker & Constable (1987). A flexible model parametrization involving Cardinal spline functions is used, and full 3-D ray tracing performed. A comparison between linear and non-linear inversions shows that if a breakdown in the linearizing approximation occurs spurious velocity models may be obtained which would appear acceptable in a linear inversion. Application of the techniques to a SE Australian data set show that unnecessary structure can be suppressed. As the smoothing power of the algorithm is improved a robust low-velocity anomaly dipping to the north becomes the most dominant feature of the P-wave model and much of the complex structure of pure data-fitting models is removed.