Quantitative determination of uncertainties in seismic refraction prospecting

Abstract

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-depth curve with its confidence intervals at any relevant point along the line.We analyze data from a crustal-scale refraction line to illustrate both features of this method. The results indicate that the conventional linear regression model for the first arrivals is inappropriate for this data set. As might be expected, geophone spacing strongly affects our ability to resolve the heterogeneities. Differences in the amount of velocity heterogeneity in different layers can be resolved, and may be useful for lithologic characterization. For this crustal-scale problem, a velocity profile derived from this method is an improvement over simple linear interpretations, but it could be further refined by more comprehensive methods attempting to match later arrivals and wave amplitudes as well as first arrivals. The method could also be applied to smaller-scale refraction problems, such as determination of refraction statics, or constraints on the degree of probable lateral variations in velocity of shallow layers, for improved processing of reflection data.