The physics that describes the seismic response of an interval of saturated porous rocks with known petrophysical properties is relatively well understood and includes rock physics, petrophysics, and wave propagation models. The main goal of seismic reservoir characterization is to predict the rock and fluid properties given a set of seismic measurements by combining geophysical models and mathematical methods. This modeling challenge is generally formulated as an inverse problem. The most common geophysical inverse problem is the seismic (or elastic) inversion, i.e., the estimation of elastic properties, such as seismic velocities or impedances, from seismic amplitudes and traveltimes. The estimation of petrophysical properties, such as porosity, lithology, and fluid saturations, also can be formulated as an inverse problem and is generally referred to as rock-physics (or petrophysical) inversion. Several deterministic and probabilistic methods can be applied to solve seismic inversion problems. Deterministic algorithms predict a single solution, which is a “best” estimate or the most likely value of the model variables of interest. In probabilistic algorithms, on the other hand, the solution is the probability distribution of the model variables of interest, which can be expressed as a conditional probability density function or a set of model realizations conditioned on the data. The probabilistic approach provides a quantification of the uncertainty of the solution in addition to the most likely model. Our goal is to define the terminology, present an overview of probabilistic seismic and rock-physics inversion methods for the estimation of petrophysical properties, demonstrate the fundamental concepts with illustrative examples, and discuss the recent research developments.

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