Bernstein copula-based spatial cosimulation for petrophysical property prediction conditioned to elastic attributes

Abstract

A new methodology for the simulation of spatially distributed petrophysical properties conditioned by elastic attributes as secondary variables is presented. The method, namely Bernstein copula-based spatial cosimulation (BCSCS), is based on Bernstein copula for the estimation of the joint probability function and simulated annealing for the spatial simulation. The proposed method can model complex non-linear relationships between variables in a fully nonparametric approach. The main advantage is that it does not require linear dependence between variables nor any distribution constraint. This method is first validated in a 1-dimensional case at the well-log scale and it is applied in a 2-dimensional case at the seismic scale to predict effective porosity conditioned to P-impedance in a marine hydrocarbon reservoir located offshore Mexico. The uncertainty quantification analysis shows that the BCSCS method significantly reduces the uncertainty compared to the traditional sequential Gaussian cosimulation method.