Stochastic Rock Physics Inversion
Authors: Cobos Carlos Manuel , Castagna John P. 
Published: May 2016

Abstract
The purpose of this paper is to introduce a stochastic seismic inversion algorithm based on Markov Chain Monte Carlo Simulation. The suggested inversion scheme generates a set of possible combinations of rock properties that can explain seismic amplitude responses in terms of lithology, pore structure and fluid variations. The result of the probabilistic seismic inversion is a seismic lithofacies catalog than can describe the elastic response of the studied subsurface interval. The main advantage of this technique is that the results consist of multiple equally probable rock properties models as an alternative to multiple elastic properties scenarios. Therefore, no post facto elastic to rock properties conversion is needed. The method might be used either in exploratory areas or hydrocarbon field development. In exploratory areas, the stochastic rock physics inversion can support the evaluation for hydrocarbon potential considering the effects of reservoir properties on seismic signatures for different geologic scenarios and physical conditions, with the prime goal of minimizing uncertainties and risk. In field development areas, stochastic seismic inversion produces multiple equally probable rock properties models that can explain the real 3D seismic response and can be used to constrain possible reservoir models used for hydrocarbon reserve estimation and reservoir production simulation. The probabilistic inversion algorithm was tested on a synthetic model that is based on real well log data. The objective of the synthetic test is to demonstrate the feasibility of the estimation of critical rock properties for hydrocarbon exploration, such as total porosity and reservoir fraction. The synthetic test results confirmed the capability of the proposed inversion technique to accurately predict the rock properties of the reservoir seismic lithofacies, even for seismically thin layers.

Introduction
Conventional seismic reservoir characterization (SRC) techniques were developed more than forty years ago for exploration plays where the hydrocarbon's seismic responses were relatively easy to identify. Early reservoir characterization workflows were usualy based on direct hydrocarbon indicator (DHI) identification techniques centered on post stack seismic amplitude analysis and AVO inversion. DHIs plays are usually related to shallow high porosity reservoirs with significantly lower acoustic impedance than the surrounding rocks. The associated seismic signatures of these hydrocarbon filled high porosity reservoirs can be anomalous high amplitude reflections called "bright spots". Nowadays, conventional seismic reservoir characterization techniques are becoming obsolete, since the oil industry is moving to explore areas were the hydrocarbons are located in deeper and more complex reservoirs. These new hydrocarbon plays are characterized by low porosity and low permeability reservoirs with near to undetectable pore fluid response. It means that the future seismic reservoir caracterization goal is to predict rock properties such as porosity, lithology and rock fabric of compacted and cemented porous rock. The second more important SRC challenge is to improve the seismic vertical resolution. Currently, seismic inversion resolution is still low for the new exploration/development challenges and improvement of seismic derived elastic parameters is paramount for the application of reservoir properties prediction. Techniques such as stochastic inversion have been initially developed in an attempt to obtain from seismic data quantitative information about subsurface rock properties on a very detailed scale. The goal of this paper is to introduce an inversion technique based on Markov Chain Monte Carlo simulation that can be implemented in a stochastic petrophysical inversion scheme. The stochastic seismic inversion's objective is to produce a set of equiprobable rock properties volumes that can describe the elastic seismic response of the studied interval and their associated uncertainties. The main advantage of this petrophysical inversion technique is that the results are multiple equally probable rock properties models instead of multiple elastic properties scenarios. Therefore, no elastic to rock properties conversion is needed after the inversion is performed. The method might be used either in exploratory or development areas.