Estimation of crustal stochastic parameters from seismic exploration data

Stochastic models for the crystalline crust produce synthetic seismograms that compare well with recorded data for a variety of crustal ages and tectonic environments. In this paper, we explore the parameter space describing such stochastic models as a basis for formulating the inverse problem; that is, we wish to estimate the parameters which define a stochastic model from the recorded backscattered wave field. We base the estimation on approximate relations between the primary reflectivity series, which is the ideal wave field response of a medium, and various seismic gathers. A two-dimensional lateral correlation method is used to investigate the sensitivity of synthetic wave fields to horizontal characteristic length. A derived empirical relationship relates the scale length to the half width of the correlation coefficient. A horizontal wavenumber-time domain spectral analysis successfully estimates the horizontal characteristic length (a(x)) and the fractal dimension (D) of the stochastic medium from which the wave field was backscattered. We employ a Monte Carlo based optimization scheme to fit the observed spectral values to a one-dimensional von Karman function and simultaneously estimate values for a, and the Hurst number v. The method yields consistent results when tested on synthetic data. Application of this technique to data sorted into different domains shows that zero-offset sections yield the best estimate. We also present results of our estimates using this method on a Program for Array Seismic Studies of the Continental Lithosphere (PASSCAL) dynamite source shot gather and a vibroseis-source Consortium for Continental Reflection Profiling (COCORP) data set recorded in the Basin and Range Province.