MODEL-BASED INVERSION OF AMPLITUDE-VARIATIONS-WITH-OFFSET DATA USING A GENETIC ALGORITHM

I cast the inversion of amplitude-variation-with-offset (AVO) data int o the framework of Bayesian statistics. Under such a framework, the mo del parameters and the physics of the forward problem are used to gene rate synthetic data. These synthetic data are then matched with the ob served data to obtain an a-posteriori probability density (PPD) functi on in the model space. The genetic algorithm (GA) uses a directed rand om search technique to estimate the shape of the PPD. Unlike the class ical inversion methods, GA does not depend upon the choice of an initi al model and is well suited for the AVO inversion. For the single-laye r AVO inversion where the amplitudes from a single reflection event ar e inverted, GA estimates the normal incidence reflection coefficient ( R(0)) and the contrast of the Poisson's ratio (Delta sigma) to reasona ble 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-sq uares fit to the approximate reflection coefficients as is usually pra cticed 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, Po isson's ratios, and densities. However, by applying simplified approxi mations to the P-wave reflection coefficient, I verify that Ro, the co ntrast in the acoustic impedance (Delta A), and the gradient in the re flection coefficient (G), can be estimated from such an inversion. Fro m the GA estimated values of R(0), Delta A, and G, and from reliable e stimates of velocity and Poisson's ratio at the start time of the inpu t 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. Compar ison of the log data from a nearby well shows that the GA inversion ob tains both the low- and the high-frequency trends (within the bandwidt h of seismic resolution) of the P-wave acoustic impedance. In addition to P-wave acoustic impedance, GA also obtains an estimate of the Pois son's ratio, an extremely important parameter for the direct detection of hydrocarbons from seismic data.