Inversion of seismic refraction and wide-angle reflection traveltimes for three-dimensional layered crustal structure

We present a method for the determination of crustal structure by simultaneous inversion of seismic refraction and wide-angle reflection traveltimes for 3-D interface geometry and layer velocity. Crustal structure is represented by layers in which velocity varies linearly with depth, separated by smooth interfaces with a cubic B-spline parametrization. Lateral variations in structure are therefore represented by variations in interface depth only. The model parametrization we have chosen means that ray paths consist of piecewise circular arc segments for which analytic expressions of trajectory and traveltime are calculated. The two-point problem of finding the first-arrival ray path and traveltime of a specified phase between a given source and receiver is solved using a shooting technique. A subspace inversion method is used to solve the inverse problem, which is formulated as a non-linear optimization problem in which we seek to minimize an objective function that consists of a data residual term and a regularization term. Before performing the inversion, each data pick must be assigned as a refraction or reflection from a particular layer or interface. Since our method represents structure in terms of interfaces, fewer parameters would generally be used in a reconstruction compared to an equivalent 3-D variable-velocity inversion. The method is well suited to wide-angle surveys that consist of many sources and relatively few receivers (or vice versa), such as marine shot lines used in conjunction with land-based receivers. Data coverage in this kind of survey is often sparse and, especially if near-offset ray paths are unavailable, highly variable. A 3-D synthetic test with an array consisting of eight sources lying within a three-sided square of 79 receivers is described. The test model consists of a three-interface structure that includes a layer pinch-out, and the synthetic data set comprises 987 refraction and 930 reflection travel times contaminated with 75 ms of data noise. Six iterations of an 18-D subspace method demonstrate that the method can produce an accurate reconstruction that satisfies the data from a 1-D starting model. We also find that estimates of a posteriori model covariance and resolution obtained from linear theory are useful in analysing solution reliability despite the nonlinear nature of the problem. Application of the method to data collected as part of the 1995 TASGO project in Tasmania shows that the method can satisfy 1345 refraction and reflection traveltime picks with a geologically reasonable and robust 254-parameter three-interface model. The inversion results indicate that the Moho beneath NW Tasmania varies in depth from 27 km near the coast to 37 km near central Tasmania, with the major increase in depth occurring across the Arthur Lineament.