Probabilistic approach to rock physics modeling

Rock physics modeling aims to provide a link between rock properties, such as porosity, lithology, and fluid saturation, and elastic attributes, such as velocities or impedances. These models are then used in quantitative seismic interpretation and reservoir characterization. However, most of the geophysical measurements are uncertain; therefore, rock physics equations must be combined with mathematical tools to account for the uncertainty in the data. We combined probability theory with rock physics modeling to make predictions of elastic properties using probability distributions rather than definite values. The method provided analytical solutions of rock physics models in which the input is a random variable whose exact value is unknown but whose probability distribution is known. The probability distribution derived with this approach can be used to quantify the uncertainty in rock physics model predictions and in rock property estimation from seismic attributes. Examples of fluid substitution and rock physics modeling were studied to illustrate the application of the method.