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Amplitude of Pair Correlation Function to Understand Heterogeneity From Well-Log and Seismic Data

Abstract

The elastic properties of the medium are scale-dependent and therefore it would be ideal to make the best possible use of the seismic data by integrating it with the available well-log data. Effective medium theory (EMT) uses homogeneous physical properties to calculate the effective properties of a heterogeneous medium thereby bridging the gap between the macro- and micro- physical properties. Depending upon the complexity of the medium, different effective medium theories are used. Pair Correlation Function (PCF) approximation method that takes into account the effect of scattering is a very effective tool in understanding the heterogeneity of the medium. It considers the interactions between any two points of a heterogeneous medium. The maximum heterogeneity is recorded when there are fluid filled inclusions in the matrix. The study has previously been successfully carried out mostly on well-log data to distinguish the productive zones from the non- productive zones. The correlation function has two parts: amplitude and correlation radius. This work deals mainly with the amplitude part of the PCF that tends to be higher if the properties of the medium are drastically different in composition from its surroundings. The amplitudes of PCF are calculated for elastic stiffness tensors, density and porosity. The seismic and well-log data are from northern part of South Marsh Island in the Gulf of Mexico. The Tertiary sediments of interest are generally interbedded sands and shales. Apart from distinguishing the productive layer, an interesting correlation between the gamma ray-log and the amplitude of PCF has been observed through this study. This could help in quantifying the net to gross sands in a reservoir. We are also extending its application to the downscaled velocities to understand the measure of heterogeneity from 3D seismic data.