Hierarchical Bayesian lithology/fluid prediction: A North Sea case study

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. B69-B85 ◽  
Author(s):  
Kjartan Rimstad ◽  
Per Avseth ◽  
Henning Omre
Keyword(s):  
North Sea ◽  
Rock Physics ◽  
Model Parameters ◽  
Gas Oil ◽  
Clear Fluid ◽  
Prior Model ◽  
Spatial Coupling ◽  
The North ◽  
Likelihood Model ◽  
Physics Model

Seismic 3D amplitude variation with offset (AVO) data from the Alvheim field in the North Sea are inverted into lithology/fluid classes, elastic properties, and porosity. Lithology/fluid maps over hydrocarbon prospects provide more reliable estimates of gas/oil volumes and improve the decision concerning further reservoir assessments. The Alvheim field is of turbidite origin with complex sand-lobe geometry and appears without clear fluid contacts across the field. The inversion is phrased in a Bayesian setting. The likelihood model contains a convolutional, linearized seismic model and a rock-physics model that capture vertical trends due to increased sand compaction and possible cementation. The likelihood model contains several global model parameters that are considered to be stochastic to adapt the model to the field under study and to include model uncertainty in the uncertainty assessments. The prior model on the lithology/fluid classes is a Markov random field that captures local vertical/horizontal continuity and vertical sorting of fluids. The predictions based on the posterior model are validated by observations in five wells used as blind tests. Hydrocarbon volumes with reliable gas/oil distributions are predicted. The spatial coupling provided by the prior model is crucial for reliable predictions; without the coupling, hydrocarbon volumes are severely underestimated. Depth trends in the rock-physics likelihood model improve the gas versus oil predictions. The porosity predictions reproduce contrasts observed in the wells, and mean square error is reduced by one-third compared to Gauss-linear predictions.

scholarly journals Stochastic reservoir characterization using prestack seismic data

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 978-993 ◽  
Author(s):  
Jo Eidsvik ◽  
Per Avseth ◽  
Henning Omre ◽  
Tapan Mukerji ◽  
Gary Mavko
Keyword(s):  
Reservoir Characterization ◽  
A Priori ◽  
Rock Physics ◽  
Real Data ◽  
Spatial Coupling ◽  
The North ◽  
Amplitude Versus Offset ◽  
Likelihood Model ◽  
Avo Attributes ◽  
The Impact

Reservoir characterization must be based on information from various sources. Well observations, seismic reflection times, and seismic amplitude versus offset (AVO) attributes are integrated in this study to predict the distribution of the reservoir variables, i.e., facies and fluid filling. The prediction problem is cast in a Bayesian setting. The a priori model includes spatial coupling through Markov random field assumptions and intervariable dependencies through nonlinear relations based on rock physics theory, including Gassmann's relation. The likelihood model relating observations to reservoir variables (including lithology facies and pore fluids) is based on approximations to Zoeppritz equations. The model assumptions are summarized in a Bayesian network illustrating the dependencies between the reservoir variables. The posterior model for the reservoir variables conditioned on the available observations is defined by the a priori and likelihood models. This posterior model is not analytically tractable but can be explored by Markov chain Monte Carlo (MCMC) sampling. Realizations of reservoir variables from the posterior model are used to predict the facies and fluid‐filling distribution in the reservoir. A maximum a posteriori (MAP) criterion is used in this study to predict facies and pore‐fluid distributions. The realizations are also used to present probability maps for the favorable (sand, oil) occurrence in the reservoir. Finally, the impact of seismic AVO attributes—AVO gradient, in particular—is studied. The approach is demonstrated on real data from a turbidite sedimentary system in the North Sea. AVO attributes on the interface between reservoir and cap rock are extracted from 3D seismic AVO data. The AVO gradient is shown to be valuable in reducing the ambiguity between facies and fluids in the prediction.

scholarly journals Rock physics model of glauconitic greensand from the North Sea

2010 ◽  
Author(s):  
Zakir Hossain ◽  
Tapan Mukerji ◽  
Jack Dvorkin ◽  
Ida L. Fabricius
Keyword(s):  
North Sea ◽  
Rock Physics ◽  
The North ◽  
The North Sea ◽  
Physics Model ◽  
Rock Physics Model

Statistical rock physics inversion of elastic and electrical properties for CO2 sequestration studies

2020 ◽  
Vol 223 (1) ◽  
pp. 707-724
Author(s):  
Mohit Ayani ◽  
Dario Grana
Keyword(s):  
Electrical Properties ◽  
Co2 Sequestration ◽  
Rock Physics ◽  
Real Data ◽  
Inversion Method ◽  
Model Parameters ◽  
The North ◽  
Physics Model ◽  
Rock Physics Model ◽  
Statistical Rock Physics

SUMMARY We present a statistical rock physics inversion of the elastic and electrical properties to estimate the petrophysical properties and quantify the associated uncertainty. The inversion method combines statistical rock physics modeling with Bayesian inverse theory. The model variables of interest are porosity and fluid saturations. The rock physics model includes the elastic and electrical components and can be applied to the results of seismic and electromagnetic inversion. To describe the non-Gaussian behaviour of the model properties, we adopt non-parametric probability density functions to sample multimodal and skewed distributions of the model variables. Different from machine learning approach, the proposed method is not completely data-driven but is based on a statistical rock physics model to link the model parameters to the data. The proposed method provides pointwise posterior distributions of the porosity and CO2 saturation along with the most-likely models and the associated uncertainty. The method is validated using synthetic and real data acquired for CO2 sequestration studies in different formations: the Rock Springs Uplift in Southwestern Wyoming and the Johansen formation in the North Sea, offshore Norway. The proposed approach is validated under different noise conditions and compared to traditional parametric approaches based on Gaussian assumptions. The results show that the proposed method provides an accurate inversion framework where instead of fitting the relationship between the model and the data, we account for the uncertainty in the rock physics model.

scholarly journals Bayesian survey-based assessment of North Sea plaice (Pleuronectes platessa): extracting integrated signals from multiple surveys

2009 ◽  
Vol 66 (4) ◽  
pp. 665-679 ◽  
Author(s):  
Johannes A. Bogaards ◽  
Sarah B. M. Kraak ◽  
Adriaan D. Rijnsdorp
Keyword(s):  
North Sea ◽  
Small Sample Size ◽  
Small Sample ◽  
Distribution Area ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Fishing Mortality ◽  
Pleuronectes Platessa ◽  
The North ◽  
Spawning Stock

Abstract Bogaards, J. A., Kraak, S. B. M., and Rijnsdorp, A. D. 2009. Bayesian survey-based assessment of North Sea plaice (Pleuronectes platessa): extracting integrated signals from multiple surveys. – ICES Journal of Marine Science, 66: 665–679. Dependence on a relatively small sample size is generally viewed as a big disadvantage for survey-based assessments. We propose an integrated catch-at-age model for research vessel data derived from multiple surveys, and illustrate its utility in estimating trends in North Sea plaice abundance and fishing mortality. Parameter estimates were obtained by Bayesian analysis, which allows for estimation of uncertainty in model parameters attributable to measurement error. Model results indicated constant fishing selectivity over the distribution area of the North Sea plaice stock, with decreased selectivity at older age. Whereas separate analyses of survey datasets suggested different biomass trends in the southeast than in the western and central North Sea, a combined analysis demonstrated that the observations in both subareas were compatible and that spawning-stock biomass has been increasing over the period 1996–2005. The annual proportion of fish that dispersed in a northwesterly direction was estimated to increase from about 10% at age 2 to 33% at age 5 and older. We also found higher fishing mortality rates than reported in ICES assessments, which could be the consequence of inadequate specification of catchability-at-age in this study or underestimated fishing mortality by the conventional ICES assessment, which relies on official landings figures.

Improved resolution in Bayesian lithology/fluid inversion from prestack seismic data and well observations: Part 1 — Methodology

Geophysics ◽  
2010 ◽  
Vol 75 (2) ◽  
pp. R21-R35 ◽  
Author(s):  
Marit Ulvmoen ◽  
Henning Omre
Keyword(s):  
Seismic Data ◽  
Markov Chain Model ◽  
Complete Solution ◽  
Seismic Signal ◽  
Chain Model ◽  
Prior Model ◽  
Spatial Coupling ◽  
Spatial Coverage ◽  
Convolution Model ◽  
Likelihood Model

The focus of our study is lithology/fluid inversion with spatial coupling from prestack seismic amplitude variation with offset (AVO) data and well observations. The inversion is defined in a Bayesian setting where the complete solution is the posterior model. The prior model for the lithology/fluid (LF) characteristics is defined as a profile Markov random-field model with lateral continuity. Each vertical profile is further given as an inhomogeneous Markov-chain model upward through the reservoir. The likelihood model is defined by profile, and it relates the LF characteristics to the seismic data via a set of elastic material parameters and a convolution model. The likelihood model is approximated. The resulting approximate posterior model is explored using an efficient block Gibbs simulation algorithm. The inversion approach is evaluated on a synthetic realistic 2D reservoir. Seismic AVO data and well observations are integrated in a consistent manner to obtain predictions of the LF characteristics with associated uncertainty statements. The predictions appear very reliable despite the approximation of the posterior model, and errors in seismic data are the major contributions to the uncertainty. Resolution of the inversion is improved considerably by using a spatially coupled prior LF model, and LF units of [Formula: see text] thick can be identified even with a seismic signal-to-noise ratio of two. The inversion results appear robust toward varying model parameter values in the prior model as a result of the discretization of LF characteristics and seismic data with good spatial coverage.

scholarly journals Correlations of Rock-Physics Model Parameters From Bayesian Analysis: Pressure- and Porosity-Dependent Models Applied to Unconsolidated Sands

2022 ◽  
Vol 9 ◽  
Author(s):  
Kyle T. Spikes ◽  
Mrinal K. Sen
Keyword(s):  
Reservoir Characterization ◽  
Rock Physics ◽  
Model Parameters ◽  
Data Sets ◽  
Unconsolidated Sands ◽  
Bayesian Formulation ◽  
Input Parameters ◽  
Physics Model ◽  
Rock Physics Model ◽  
Prior Models

Correlations of rock-physics model inputs are important to know to help design informative prior models within integrated reservoir-characterization workflows. A Bayesian framework is optimal to determine such correlations. Within that framework, we use velocity and porosity measurements on unconsolidated, dry, and clean sands. Three pressure- and three porosity-dependent rock-physics models are applied to the data to examine relationships among the inputs. As with any Bayesian formulation, we define a prior model and calculate the likelihood in order to evaluate the posterior. With relatively few inputs to consider for each rock-physics model, we found that sampling the posterior exhaustively to be convenient. The results of the Bayesian analyses are multivariate histograms that indicate most likely values of the input parameters given the data to which the rock-physics model was fit. When the Bayesian procedure is repeated many times for the same data, but with different prior models, correlations emerged among the input parameters in a rock-physics model. These correlations were not known previously. Implications, for the pressure- and porosity-dependent models examined here, are that these correlations should be utilized when applying these models to other relevant data sets. Furthermore, additional rock-physics models should be examined similarly to determine any potential correlations in their inputs. These correlations can then be taken advantage of in forward and inverse problems posed in reservoir characterization.

scholarly journals Bayesian Analysis to Determine Relative Significance of Inputs of a Rock-Physics Model

2021 ◽  
Vol 9 ◽  
Author(s):  
Kyle T. Spikes ◽  
Mrinal K. Sen
Keyword(s):  
Bayesian Analysis ◽  
Reservoir Characterization ◽  
Likelihood Function ◽  
Rock Physics ◽  
Rock Properties ◽  
Model Parameters ◽  
Prior Distributions ◽  
Relative Significance ◽  
Physics Model ◽  
Rock Physics Model

Rock-physics models relate rock properties to elastic properties through non-unique relationships and often in the presence of seismic data that contain significant noise. A set of inputs define the rock-physics model, and any errors in that model map directly into uncertainty in target seismic-scale amplitudes, velocities, or inverted impedances. An important aspect of using rock-physics models in this manner is to determine and understand the significance of the inputs into a rock-physics model under consideration. Such analysis enables the design of prior distributions that are informative within a reservoir-characterization formulation. We use the framework of Bayesian analysis to find internal dependencies and correlations among the inputs. This process requires the assignments of prior distributions, and calculation of the likelihood function, whose product is the posterior distribution. The data are well-log data that come from a hydrocarbon-bearing set of sands from the Gulf of Mexico. The rock-physics model selected is the soft-sand model, which is applicable to the data from the reservoir sands. Results from the Bayesian algorithm are multivariate histograms that demonstrate the most frequent values of the inputs given the data. Four analyses are applied to different subsets of the reservoir sands, and each reveals some correlations among certain model inputs. This quantitative approach points out the significance of a singular or joint set of rock-physics model parameters.

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