Model‐based inversion of amplitude‐variations‐with‐offset data using a genetic algorithm

Abstract

I cast the inversion of amplitude‐variation‐with‐offset (AVO) data into the framework of Bayesian statistics. Under such a framework, the model parameters and the physics of the forward problem are used to generate synthetic data. These synthetic data are then matched with the observed data to obtain an a‐posteriori probability density (PPD) function in the model space. The genetic algorithm (GA) uses a directed random search technique to estimate the shape of the PPD. Unlike the classical inversion methods, GA does not depend upon the choice of an initial model and is well suited for the AVO inversion. For the single‐layer AVO inversion where the amplitudes from a single reflection event are inverted, GA estimates the normal incidence reflection coefficient [Formula: see text] and the contrast of the Poisson’s ratio (Δσ) to reasonable accuracy, even when the signal‐to‐noise ratio is poor. Comparisons of single‐layer amplitude inversion using synthetic data demonstrate that GA inversion obtains more accurate results than does the least‐squares fit to the approximate reflection coefficients as is usually practiced in the industry. In the multilayer AVO waveform inversion, all or a part of the prestack data are inverted. Inversion of this type is nonunique for the estimation of the absolute values of velocities, Poisson’s ratios, and densities. However, by applying simplified approximations to the P‐wave reflection coefficient, I verify that [Formula: see text], the contrast in the acoustic impedance (ΔA), and the gradient in the reflection coefficient (G), can be estimated from such an inversion. From the GA estimated values of [Formula: see text], ΔA, and G, and from reliable estimates of velocity and Poisson’s ratio at the start time of the input data, an inverted model can be generated. I apply this procedure to marine data and demonstrate that the the synthetics computed from such an inverted model match the input data to reasonable accuracy. Comparison of the log data from a nearby well shows that the GA inversion obtains both the low‐ and the high‐frequency trends (within the bandwidth of seismic resolution) of the P‐wave acoustic impedance. In addition to P‐wave acoustic impedance, GA also obtains an estimate of the Poisson’s ratio, an extremely important parameter for the direct detection of hydrocarbons from seismic data.