Quantitative determination of uncertainties in seismic refraction prospecting

We present a model of the propagation of refracted seismic waves in planar (horizontal or dipping) layered structures in which we quantify the errors from various sources. The model, called the (mixed) variance component model, separates the errors originating on the surface from those due to inhomogeneities of subsurface layers. The model starts with the assumption of homogeneous (constant-velocity) layers, but by taking the principal errors into account, variations from this model (including degree of velocity inhomogeneity, vertical velocity gradients, and gradational interfaces) can be identified. A complete solution to the variance component model by Bayesian methods relies on the Gibbs sampler, a recently well-developed statistical technique. Using the Gibbs sampler and Monte Carlo methods, we can estimate the posterior distributions of any parameter of interest. Thus, in addition to estimating the various errors, we can obtain the velocity-versus-