Irregular interface parametrization in 3-D wide-angle seismic traveltime tomography

Abstract

SUMMARY We investigate the potential advantages and pitfalls of using an irregular interface parametrization in 3‐D wide‐angle seismic traveltime tomography. Several synthetic tests are performed using an interface surface consisting of a mosaic of cubic B‐spline surface patches and a source–receiver array designed to produce a highly variable distribution of refracted and reflected ray paths. In such circumstances, an irregular parametrization can be adapted to suit the data coverage, resulting in fewer parameters being needed to describe the solution model, faster computation time and a better determined inverse problem. We demonstrate that a judicious parameter distribution can also result in a solution that is well constrained everywhere, satisfies the data to an acceptable level and extracts more information from the data than a regular parametrization. However, introducing an irregular parametrization means that the minimum wavelength of structure permitted in the model will vary both spatially and directionally. Careful consideration of surface patch size and shape, in addition to resolution estimates and data fit, is therefore required to meaningfully interpret this class of solution. An application of the irregular parametrization method to 3‐D wide‐angle data collected in Tasmania is also presented, and reveals several features consistent with the known geology that were not recovered with a regular parametrization.

2-D/3-D irregular shortest-path ray tracing for multiple arrivals and its applications

“…Sambridge et al 1995), to improve the computational efficiency by varying the grid resolution in response to the wave front curvature (e.g. Kimmel & Sethian 1998), to stabilize the inverse problem by reducing the unknown parameters and to help extract structural information by accounting for the interface curvature and velocity discontinuities (Michelini 1995; Curtis & Snieder 1997; Vesnaver et al 2000; Spakman & Bijwaard 2001; Rawlinson & Sambridge 2003; Sambridge & Faletic 2003; Sambridge & Rawlinson 2005).…”

Crust and Lithospheric Structure - Active Source Studies of Crust and Lithospheric Structure

“…They claim this balances the contribution from short and long ray paths and enhances resolution and convergence speed . Rawlinson et al (2001) and Rawlinson and Sambridge (2003b) developed an algorithm for the inversion of refraction and reflection times using a 3-D multilayered model parameterization. Interfaces are defined by a nonuniform node distribution, and velocities vary linearly with depth so ray paths are calculated analytically as piecewise circular arcs using a shooting method.…”

Seismic tomography with irregular meshes

“…), an optimal coverage of sources and receivers is often hard to achieve, and 20 heterogeneous path coverage remains an issue with many of these datasets, especially those created using 3-D arrays. Rawlinson and Sambridge [2003] examine the use of irregular meshes in the imaging of interface structure with 3-D wide-angle seismic data. Wide-angle data is recorded by receivers at significant offsets to surface sources, and typical seismograms exhibit both refracted and reflected phases.…”

“…The presence of reflected arrivals allows the geometry of sub-surface interfaces to be imaged. The tomographic method used by Rawlinson and Sambridge [2003] was first presented by Rawlinson et al [2001a], and uses a shooting method of ray tracing to determine source-receiver paths and travel times, and a subspace inversion method to solve the inverse problem. Structure is represented by a set of sub horizontal layers separated by smoothly varying interfaces.…”

“…This latter property stems from being able to arbitrarily locate control vertices, although it should be noted that a rectangular association still exists between control vertices on the grid. Rawlinson and Sambridge [2003], there is one that investigates the use of irregular interface meshes with observed data; we focus on this example here. The wide-angle dataset used was recorded in Tasmania, SE In an earlier article, Rawlinson et al [2001b] inverted 2148 P m P and 442 P n travel times from this dataset for the structure of the Moho surface using the scheme outlined above.…”