Probabilistic formulation of AVO modeling and AVO-attribute-based facies classification using well logs

Grana, Dario; Bronston, Mark

doi:10.1190/geo2014-0518.1

Cited by 10 publications

(5 citation statements)

References 24 publications

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“…In the seismic examples the Chapman-Kolmogorov equation is used to correctly propagate the uncertainty affecting the estimated Ip values into the uncertainties that are associated to the final porosity and facies models: p(m, f|s) = p(m, f|d)p(d|s)dd (13) In all applications, the porosity and facies profiles are derived by applying Equation (4) point-by point to each Ip value derived from well log data or inferred from post-stack seismic inversion. This relies on the assumption that the litho-fluid facies are spatially independent, and that the underlying vertical continuity is preserved due to the continuity of the seismic or well log data.…”

Section: Methodsmentioning

confidence: 99%

“…The outcomes of this first step are the input for the second step of porosity estimation and facies classification. Note that the uncertainties affecting the estimated impedance values are correctly propagated into the estimated porosity and facies profiles through Equation (13). Figure 13 represents the results that were obtained for Well A when the non-parametric p(m, d|f) distribution is employed.…”

Section: Post-stack Data Applicationmentioning

confidence: 99%

“…In this context, both analytical and numerical methods have been extensively applied [7][8][9][10][11][12]. The input data to the estimation and classification processes can be logged data (i.e., seismic velocities or seismic impedance values; [13]) or post/pre-stack seismic data [14,15]. In any case, the key ingredient for the estimation of reservoir properties is the petrophysical model that links the elastic attributes (i.e., seismic impedances) to the sought petrophysical properties and/or litho-fluid facies.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Different Statistical Models in Probabilistic Joint Estimation of Porosity and Litho-Fluid Facies from Acoustic Impedance Values

Aleardi

2018

Geosciences

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We discuss the influence of different statistical models in the prediction of porosity and litho-fluid facies from logged and inverted acoustic impedance (Ip) values. We compare the inversion and classification results that were obtained under three different statistical a-priori assumptions: an analytical Gaussian distribution, an analytical Gaussian-mixture model, and a non-parametric mixtu re distribution. The first model assumes Gaussian distributed porosity and Ip values, thus neglecting their facies-dependent behaviour related to different lithologic and saturation conditions. Differently, the other two statistical models relate each component of the mixture to a specific litho-fluid facies, so that the facies-dependency of porosity and Ip values is taken into account. Blind well tests are used to validate the final predictions, whereas the analysis of the maximum-a-posteriori (MAP) solutions, the coverage ratio, and the contingency analysis tools are used to quantitatively compare the inversion outcomes. This work points out that the correct choice of the statistical petrophysical model could be crucial in reservoir characterization studies. Indeed, for the investigated zone, it turns out that the simple Gaussian model constitutes an oversimplified assumption, while the two mixture models provide more accurate estimates, although the non-parametric one yields slightly superior predictions with respect to the Gaussian-mixture assumption.

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Section: Methodsmentioning

confidence: 99%

Section: Post-stack Data Applicationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of Different Statistical Models in Probabilistic Joint Estimation of Porosity and Litho-Fluid Facies from Acoustic Impedance Values

Aleardi

2018

Geosciences

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“…To this end, a prior mixture model is necessary to infer the correct statistical information about the parameters of interest. Additionally, the mixture models provide good fit to heavy-tailed data (Mukerji et al, 2009;Grana & Bronston, 2015). Grana & Della Rossa (2010) proposed a Gaussian mixture model for the litho-fluid classes.…”

Section: Introductionmentioning

confidence: 99%

AVA Inversion of PP Reflection in a VTI Medium using Proximal Splitting Algorithm

Zidan

Cheng

2022

Preprint

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Amplitude variation with offset (AVO) inversion, particularly for more than two model parameters, is a highly ill-posed problem and, hence, regularization is indispensable. Here, we propose a regularized inverse problem to mitigate the ill-posedness of the amplitude inversion. The regularization is added to measure the difference in information between the a priori probability density function and the predicted probability density of the inverted parameters. Information theory provides a collection of contrast functions which quantify the divergence from one probability distribution to another, such as the relative entropy. The a priori density is approximated by a Gaussian mixture model, obtained from well logs and rock physics model. The mixture model is a density estimator, providing the statistical properties of the model parameters of interest. The likelihood of the data and the divergence are combined in an augmented Lagrangian scheme, the alternating direction method of multipliers (ADMM), to obtain a unique solution that best generate the recorded seismic data and satisfy the geological constraints conveyed by the a priori probability density function. The proposed inversion scheme is then applied to the anisotropy AVO inversion, for estimating the elastic and seismic anisotropy parameters of shale formations.

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“…Many models exist (Mavko et al, 2009). The basis of these techniques is the combination of expectations through prior probability information along with a forward and inverse model through a likelihood probability function (Avseth et al, 2005;Duda et al, 2000;Buland and Omre, 2003;Grana and Della Rosa, 2010;Grana, 2014;Grana and Bronston, 2015). When selected, the model can explain general trends and can be used to predict situations not observed in the data set of interest using a statistical approach.…”

Section: Introductionmentioning

confidence: 99%

Statistical Rock-Property Estimates from Inverted Impedances and Rock-Physics Modeling

Spikes¹

2016

Day 2 Tue, May 03, 2016

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This work provides an example of a technique to estimate reservoir properties from inverted seismic impedances. High-quality seismic data has made inversion of that data for elastic properties reliable. Petrophysical and elastic properties from well-log data, along with a rock-physics model, explain the relationships among the elastic properties and the reservoir properties of interest. However, ambiguity and non-uniqueness are present in those relationships. The inversion of seismic data for P-impedance (I P ) and S-impedance (I S ) requires pre-stack seismic data, and a particular algorithm to combine low-frequency information. The inversion provides I P and I S for every time sample at each CDP. A calibrated rock-physics model translates seismic-scale impedances to reservoir properties. The calibration of the model typically is done using well-log curve information around the interval of interest. This paper demonstrates the seismic inversion routine and the subsequent mapping of the inverted impedances to rock properties using data from the Marco Polo field. The rock-physics model chosen was the soft-sand model because of the geological trends identified from well data and the interpretation of the depositional environment. In addition, the well-log data indicated the presence of five facies, including a gas-sand, oil-sand, two brine-sands, and shale facies. A Bayesian classification technique mapped the seismic impedances to the most likely facies. A statistical technique was necessary to account for the non-unique relationships among the elastic and reservoir properties. The results are realizations of the most likely facies. Probabilistic estimates of porosity and saturation for the hydrocarbon-bearing facies came from joint conditional distributions of I P and the ratio of P-to S-velocity (V P /V S ). Maps of the probabilities contain the associated uncertainty in each results. Limitations to this technique are three-fold. First is that the relationship is non-unique between impedances and the rock properties, whereby one value of impedance relates to different combinations of rock properties. Second, the resolution of the seismic data is the resolution of the rock properties. Third, the rock-property estimates have errors in them due to errors in the rock physics model, errors in the inverted data, and errors in the match between the data and the model.

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Probabilistic formulation of AVO modeling and AVO-attribute-based facies classification using well logs

Cited by 10 publications

References 24 publications

Analysis of Different Statistical Models in Probabilistic Joint Estimation of Porosity and Litho-Fluid Facies from Acoustic Impedance Values

Analysis of Different Statistical Models in Probabilistic Joint Estimation of Porosity and Litho-Fluid Facies from Acoustic Impedance Values

AVA Inversion of PP Reflection in a VTI Medium using Proximal Splitting Algorithm

Statistical Rock-Property Estimates from Inverted Impedances and Rock-Physics Modeling

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