Accurate subsurface modeling and characterization requires the prediction of facies and rock properties within the reservoir model. This is commonly achieved by inverting geophysical data, such as seismic reflection data, using a two-step approach either in the discrete or the continuous domain. We propose an iterative simultaneous method, namely, stochastic perturbation optimization, to invert seismic reflection data jointly for facies and rock properties. Facies are first simulated according to a Markov chain model, rock properties are then generated with stochastic sequential simulation and co-simulation conditioned to each facies. Elastic and seismic data are computed by applying a rock physics model to the realizations of petrophysical properties and a seismic convolutional model. The similarity between observed and synthetic seismic data is used to update the solution by perturbing facies and rock properties until convergence. Coupling the discrete and continuous domains ensures a consistent perturbation of the reservoir models throughout the iterations. We test the method in a one-dimensional synthetic example for the estimation of facies and porosity from zero-offset seismic data assuming a linear rock physics model to demonstrate the validity of the method. Then, we apply the method to a real three-dimensional dataset from the North Sea for the joint estimation of facies and petrophysical properties from pre-stack seismic data. The results show spatially consistent rock and fluid inverted models where the predicted facies reproduce the vertical ordering as observed in the well data.
Contents of this paper were reviewed by the Technical Committee of the 16 th International Congress of the Brazilian Geophysical Society and do not necessarily represent any position of the SBGf, its officers or members. Electronic reproduction or storage of any part of this paper for commercial purposes without the written consent of the Brazilian Geophysical Society is prohibited.
Stochastic petrophysical inversion is a method to predict reservoir properties from seismic data. Recent advances in stochastic optimization allow generating multiple realizations of rock and fluid properties conditioned on seismic data. To match the measured data and represent the uncertainty of the model variables, a large number of realizations is generally required. Stochastic sampling and optimization of spatially correlated models are computationally demanding. Monte Carlo methods allow quantifying the uncertainty of the model variables but are impractical for high-dimensional models with spatially correlated variables. We propose a Bayesian approach based on an efficient implementation of the Markov chain Monte Carlo method for the inversion of seismic data for the prediction of reservoir properties. The proposed Bayesian approach includes an explicit vertical correlation model in the proposal distribution. It is applied trace by trace and the lateral continuity model is imposed by using the previously simulated values at the adjacent traces as conditioning data for simulating the initial model at the current trace. The methodology is first presented for a one-dimensional problem to test the vertical correlation and it is extended to two-dimensional problems by including the lateral correlation and comparing two novel implementations based on sequential sampling. The proposed method is applied to synthetic data to estimate the posterior distribution of the petrophysical properties conditioned on the measured seismic data. The results are compared with a McMC implementation without lateral correlation and demonstrate the advantage of integrating a spatial correlation model.
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 seismic (or elastic) inversion i.e., the estimation of elastic properties, such as seismic velocities or impedances, from seismic amplitudes and travel times. The estimation of petrophysical properties, such as porosity, lithology, and fluid saturations, can also be formulated as an inverse problem and is generally referred to as rock physics inversion (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 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.
Seismic reservoir characterization is a subfield of geophysics that combines seismic and rock physics modeling with mathematical inverse theory to predict the reservoir variables from the measured seismic data. An open-source comprehensive modeling library that includes the main concepts and tools is still missing. We present a Python library named SeReMpy with the state of the art of seismic reservoir modeling for reservoir properties characterization using seismic and rock physics models and Bayesian inverse theory. The most innovative component of the library is the Bayesian seismic and rock physics inversion to predict the spatial distribution of petrophysical and elastic properties from seismic data. The inversion algorithms include Bayesian analytical solutions of the linear-Gaussian inverse problem and Markov chain Monte Carlo (McMC) numerical methods for non-linear problems. The library includes four modules: geostatistics, rock physics, facies, and inversion, as well as several scripts with illustrative examples and applications. We present a detailed description of the scripts that illustrate the use of the functions of module and describe how to apply the codes to practical inversion problems using synthetic and real data. The applications include a rock physics model for the prediction of elastic properties and facies using well log data, a geostatistical simulation of continuous and discrete properties using well logs, a geostatistical interpolation and simulation of two-dimensional maps of temperature, an elastic inversion of partial stacked seismograms with Bayesian linearized AVO inversion, a rock physics inversion of partial stacked seismograms with McMC methods, and a two-dimensional seismic inversion.
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