Non-linear non-parametric geostatistical rock-physics inversion of elastic attributes for petrophysical properties using direct multivariate simulation

Abstract

The estimation of subsurface petrophysical properties plays an essential role in the reservoir characterization and forecasting process. In this work, we present a novel algorithm for geostatistical rock-physics inversion of elastic properties that assumes a non-linear forward model and a non-parametric multivariate joint distribution. The inversion method is based on the numerical solution for data conditioning of the joint probability distribution and it combines statistical rock-physics models and stepwise conditional transformations applied to non-parametric geostatistical simulations. Specifically, we apply a data conditioning approach of Direct Multivariate Simulation to obtain the petrophysical properties conditioned to the measured elastic properties. The approach can be applied to estimate median models or to simulate multiple geostatistical realizations conditioned on direct measurements. We validate the approach through two applications: a 1D study using real well logs for the estimation of petrophysical volumetric fractions using a 6-variate joint distribution and a synthetic time-lapse seismic study for the estimation of porosity and fluid changes using a 7-variate joint distribution. We discuss the computational advantages of the proposed implementation in terms of computational time and RAM usage. The efficient implementation makes this method applicable to high-dimensional problems. The algorithm effectively preserves the non-linear and heteroscedastic relationships among variables, providing accurate estimations of petrophysical properties while maintaining spatial correlations and incorporating hard data conditioning.