Traveltime tomography: A comparison of popular methods

Abstract

Noisy or inconsistent traveltime data yielded tomographic images that contain geologically unrealistic fluctuations. In addition to diverting attention away from structural patterns, these high‐wavenumber fluctuations can generate shadow zones and caustics that destabilize iterative solution schemes requiring ray tracing. We evaluated the performance of a number of popular methods that have been designed to reduce this effect, using synthetic crosswell data containing Gaussian noise. Quantitative comparisons between tomography methods were based on the misfit with the true model, solution stability under different sets of noise of the same level, and resolution‐covariance relationships. Other important factors included versatility and simplicity. Versatility is the ability to treat data with a wide range of noise levels as well as data generated by different structures. Simplicity is characterized by the number of adjustable inputs such as smoother shape, starting model, and damping or regularization parameters that may be required. Constraint parameters such as damping must be chosen before performing an inversion. The smallest‐misfits between solutions and true models were found for constraint parameters lying just below a “kink” or change in slope of the rms residual versus constraint parameter curve. The kink separates regions in which either data or smoothing constraints dominate the solution and provides a means for choosing the optimal constraint parameter. A first difference regularization method performed the best overall and proved both simple to use and versatile in terms of the range of noise levels for which it could be used effectively. Second difference schemes were not tested since the problem is singular in the limited coverage crosswell geometries that we used. Convolutional quelling proved the best of the damped least‐squares methods, but had resolution limited by the dimension and shape of the smoothing function. A simple averaging smoother worked reasonably well on data generated by a smooth model, while a median performed better on data generated by a model with large contrasts. An iterative [Formula: see text] norm method did not function well with Gaussian noise, but was effective in tests with long‐tailed noise distributions.