Nonlinear high‐resolution three‐dimensional seismic travel time tomography

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 spatially 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.