Inversion of wide‐angle seismic reflection times with damped least squares

Abstract

The wide‐angle seismic reflection times appearing in the postcritical range are used extensively to image the crustal structure in deep seismic sounding investigations. The most commonly used method to calculate interval velocities and thicknesses of a stack of horizontal layers is based on Dix’s hyperbolic equation that requires traveltimes at zero offset and a prior estimate of root‐mean‐square (rms) velocity. Since the wide‐angle reflection times are represented by the nonhyperbolic Taner and Koehler series, a forced fit of such a data set by a hyperbolic equation causes large errors in the estimation of interval velocities. We propose a fast and simple method to determine the interval velocities from wide‐angle reflection times by minimizing the squared errors between the observed traveltimes and the forward response using a damped least‐squares technique. The forward response is calculated, including higher order terms of the reflection series, through Chebychev (orthogonal) polynomial approximations. Inversion of synthetic reflection times by this method, for a given velocity model contaminated by some random errors, and starting with various initial models, produces a final model that matches the true model. This modeling serves as a good indicator of the reliability of the estimated parameters. Besides, the method provides a measure of uncertainty and resolution of estimated parameters.