ESTIMATING VERTICAL STOCHASTIC SCALE PARAMETERS FROM SEISMIC REFLECTION DATA: DECONVOLUTION WITH NON-WHITE REFLECTIVITY

Abstract

Seismic wavefields reflected from the Earth's crystalline crust often appear quite complex due to the non-horizontally layered, seemingly random spatial patterns of velocity structure. Deterministic mapping of such a velocity field is often impractical, therefore, we rely on stochastic descriptions to quantify textural aspects of a given Earth model. This paper introduces an iterative method to invert (in 1-D) a reflected seismic wavefield for vertical stochastic parameters. In a previous method, standard deconvolution is used to form an estimate of the Earth's reflectivity. Numerical integration of the resulting reflectivity is an estimate of the binary velocity perturbation model to which we can fit a theoretical von Kármán stochastic autocorrelation function. In this paper, an improved iterative model-based approach is introduced. The algorithm estimates the vertical von Kármán stochastic parameters by iteratively modifying a deconvolution filter based on previously estimated von Kármán model parameters. By inverting synthetic seismic data, its shown that this iterative approach is more stable numerically than an earlier algorithm, and is able to recover both the vertical characteristic length and the Hurst exponent. The method is sensitive to noise in the data because the noise has a stochastic behaviour similar to that of the data. This new method is applied to a single common shot record that was recorded as part of the PASSCAL Basin and Range experiment and recovers values of stochastic parameters that are consistent with observations of exposed crustal sections.