Two-Dimensional Seismic Refraction Tomography

Abstract

S U M M A R YAn iterative tomographic inversion scheme is presented for determination of 2-D velocity structure from seismic refraction first-arrival traveltimes. The method is suited to refraction profiles where source/receiver spacings are denser than for conventional profiles. The inversion method is based on an iterative solution of the linearized problem, and allows for determination of continuous velocity variations as well as geometry of subhorizontal interfaces. In each iteration, two-point ray tracing is performed using a shooting method to construct the linear system. The velocity field is defined using triangular cells within which the velocity gradient is constant, allowing analytic calculation of ray paths. Two different inversion techniques are considered, based on distinct linearized formulations of the forward problem. Inversion using a linearized traveltime-velocity Jacobian produced better results than a slowness formulation more akin to common series expansion techniques. Resolution examples reveal horizontal smearing due to ray geometry, drop-off in resolution with depth, as well as the effect of source-receiver geometry and velocity structure on resolution.Inversion examples indicate that a global norm produces solutions closer to the true model than solutions calculated using a smallest perturbation approach, when a good starting model is available. Streak effects caused by inhomogeneous ray coverage and the removal of these effects are demonstrated.

Crustal velocity structure of the Superior and Grenville provinces of the southeastern Canadian Shield

“…A smoothing constraint could then be used to reduce the roughness of the over parameterized solution. This may either be applied inside the inversion routine (as in the case of this study ) or after the solution is obtained (White, 1989;White and Boland, 1992 given velocity value such that a linear gradient within each block is established. Also note that the lateral variation can still generdly be recovered.…”

Seismic Traveltime Tomography of the Crust and Lithosphere

“…White (1989) describes a method of 2-D refraction tomography in which a rectangular grid of nodes is used to define triangular regions of constant velocity gradient (see Fig. 3c).…”

Nonlinear refraction traveltime tomography

“…For refraction traveltime tomography, most methods attempt to apply ad hoc constraints to keep the inversion stable. These include filling with nonzero sensitivity between rays (Hole, 1992;Cai and Qin, 1994), applying model gradient derivatives to damp model stepsize in a creeping manner (White, 1989;Stefani, 1995), or using a posterior lowpass filter to smooth the model after each iteration (Zhu and McMechan, 1989). We chose to solve an inverse problem that explicitly minimizes data misfit as well as model roughness using Tikhonov regularization (Tikhonov and Arsenin, 1977).…”

“…Zhu and McMechan (1989) perform refraction tomography using an analytic traveltime solution and applying an inversion method that is the same for the crosshole geometry (McMechan et at., 1987) except for an initial model requiring positive velocity gradients. Stefani (1995) demonstrates a turning-ray tomography which is similar to White's (1989) but inverts velocities only. Using Vidale's (1988) finite-difference approach to solve an eikonal equation without involving rays, Ammon and Vidale (1993) developed a refraction traveltime tomography regularizing the inverse problem with second-order model derivatives in a jumping fashion (Scales et aI., 1990;.…”