Three‐dimensional seismic refraction tomography: A comparison of two methods applied to data from the Faeroe Basin

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Abstract
This paper presents a comparison of two tomographic methods for determining three‐dimensional (3‐D) velocity structure from first‐arrival travel time data. The first method is backprojection in which travel time residuals are distributed along their ray paths independently of all other rays. The second method is regularized inversion in which a combination of data misfit and model roughness is minimized to provide the smoothest model appropriate for the data errors. Both methods are nonlinear in that a starting model is required and new ray paths are calculated at each iteration. Travel times are calculated using an efficient implementation of an existing method for solving the eikonal equation by finite differencing. Both inverse methods are applied to 3‐D ocean bottom seismometer (OBS) data collected in 1993 over the Faeroe Basin, consisting of 53,479 travel times recorded at 29 OBSs. This is one of the most densely spaced, large‐scale, 3‐D seismic refraction experiments to date. Different starting models and values for the free parameters of each tomographic method are tested. A new form of backprojection that converges more rapidly than similar methods compares favorably with regularized inversion, but the latter method provides a simpler model for little additional computational expense when applied to the Faeroe Basin data. Bounds on two model features are assessed using regularized inversion with combined smoothness and flatness constraints. An inversion of synthetic data corresponding to 100% data recovery from the real experiment shows a marked improvement in lateral resolution at deeper depths and demonstrates the potential of currently feasible 3‐D refraction experiments to provide well‐resolved, long‐wavelength velocity models. The similarity of the final models derived from the two tomographic methods suggests that the results from the new form of backprojection can be relied on when limited computational resources rule out regularized inversion.