Nonlinear high‐resolution three‐dimensional seismic travel time tomography

Abstract

A tomographic inversion procedure is described and applied to a synthetic three-dimensional (3-D) seismic refraction data set, demonstrating that tomography is capable of determining a densely sampled velocity model with large velocity contrasts. Forward and inverse modeling procedures are chosen to minimize the computational costs of the inversion. Parameterizing the linearized inversion using functions defined along the ray paths, simple backprojection with zero pixel size is shown to exactly solve the linear problem, producing the smallest model for the slowness perturbation. For small grid cells, simple backprojection closely approximates the exact solution and is a sufficient solution for an iterative nonlinear inversion. This eliminates the need to store or solve a large system of linear.equations. Accurate first arrival travel times are rapidly computed using a finite difference algorithm. Forward modeling between each simple backprojection allows the procedure to correctly account for the locations of the rays. This becomes more important as the spatial resolution of the model is improved. The computational efficiency of the entire nonlinear procedure allows the model to be densely sampled, providing a spatia!ly well-resolved 3-D tomographic image. The synthetic refraction survey is designed to be similar to a published 3-D survey over the East Pacific Rise. Tests based on this example and others show that 3-D tomography is capable of inverting a large travel time data set for detailed earth structure with large lateral velocity variations and is stable in the presence of noisy data. INTRODUCTIONInformation about the three-dimensional seismic velocity structure of the earth can be obtained through the inversion of seismic travel times. Although the word tomograph means "slice picture" and was adopted by the medical community to describe two-dimensional (2-D) image reconstruction from line integrals, geophysicists use "seismic tomography" to describe two-and three-dimensional (3-D) imaging. Aki et al. [1977] divides the earth into a number of constant velocity blocks to invert teleseismic travel times. Thurber [1983] uses velocities interpolated between regularly spaced grid points to invert local earthquake and explosion source travel times. Other 3-D model parameterizations include those of Hawley et al. [1981], Thomson and Gubbins [1982], and Tarantola and Nercessian [1984]. The development of 2-D tomography applied to cross-borehole seismic data has paralleled that of 3-D tomography, and the formulation of the problem is very similar [e.g., Dines and Lytle, 1979; Wong et al., 1983; McMechan, 1983; Peterson et al., 1985; Scales, 1987; Bregman et al., 1989]. Most of the 3-D tomographic interpretations published to date are limited because of two factors. The first limitation lies in the nonlinearity of the seismic travel time problem. Many tomographic inversion techniques avoid the fact that the ray paths depend on the unknown velocity structure by assuming that the velocity variations are small enough t...

Three‐dimensional seismic velocity structure of the San Francisco Bay area

“…Times and rays are recomputed and inverted in an iterative nonlinear scheme that allows for arbitrarily complex velocity structure and ray paths. Nonlinear inversion becomes more important as the spatial resolution of the model improves [Hole, 1992] Table 1).…”

“…Coherency of the first arrival in a receiver gather from spatially nonaliased sources improved the quality of the picks. Since the travel times represent only a subset of the redundant information and, unlike the earthquakes, the source locations are known, the BASIX data were given 10 times weighting in the A linearized velocity inversion is performed through simple backprojection [Hole, 1992]. Times and rays are recomputed and inverted in an iterative nonlinear scheme that allows for arbitrarily complex velocity structure and ray paths.…”

Three‐dimensional velocity structure of the Kilauea Caldera, Hawaii

“…The tomographic technique used in this study is described in detail by Hole (1992) and Benz et al, (1996) and solves for both P-and S-wave velocity structure while simultaneously solving for earthquake locations. Vp/V s velocity structure is derived by directly comparing the two models.…”

East Greenland Ridge in the North Atlantic Ocean: An integrated geophysical study of a continental sliver in a boundary transform fault setting

“…[22] The tomographic inversion was calculated by application of the nonlinear tomographic inversion procedure of Hole [1992]. Perturbations of the slowness function are found by solving a linear relationship between the slowness perturbation and the traveltime residual using Fermat's principle.…”