Facies probability from mixture distributions with non‐stationary impedance errors

Gallop, Jeremy

doi:10.1190/1.2369874

Cited by 24 publications

(5 citation statements)

References 6 publications

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“…Indeed, the physical model can be any rock physics model: velocity-saturation (Mavko and Mukerji, 1998), velocity-porosity (Doyen, 1988), velocity-pressure (Doyen, 2007), amplitudes-velocities (Buland and Omre, 2003), and porosity-permeability, etc. ; it can include discrete properties such as facies classification (Eidsvik et al, 2004;Gallop, 2006), and it can involve multiple properties (Bachrach, 2006;Larsen et al, 2006;Gunning and Glinsky, 2007;Buland et al, 2008;González et al, 2008;Spikes et al, 2008;Bosch et al, 2009;Grana and Della Rossa, 2010;Rimstad and Omre, 2010;Ulvmoen and Omre, 2010). Some of these inversion methods are summarized in Doyen (2007) and Bosch et al (2010).…”

Section: Introductionmentioning

confidence: 99%

Probabilistic approach to rock physics modeling

Grana

2014

GEOPHYSICS

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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.

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Section: Introductionmentioning

confidence: 99%

Probabilistic approach to rock physics modeling

Grana

2014

GEOPHYSICS

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“…In this work, we assume a Gaussian mixture model (Gallop, 2006;Grana and Della Rossa, 2010). A Gaussian mixture model is a linear combination of Gaussian distributions.…”

Section: Methodsmentioning

confidence: 99%

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

Grana

Bronston²

2015

GEOPHYSICS

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We have developed a probabilistic formulation to derive the probability density function of amplitude variation with offset (AVO) attributes given the distribution of elastic properties, in the context of AVO analysis of well log data. The proposed probabilistic formulation includes the analytical expression of the posterior distribution and contributes to the correct propagation of the uncertainty through the AVO model. When this analysis is performed in each facies, the resulting posterior probability density functions of AVO attributes, conditioned by the elastic attributes and the underlying log-facies classification, can be used in a Bayesian inversion workflow to obtain the AVO-attribute-based facies classification. This classification is then compared with the petrophysical log-facies profile and can be extended to the entire reservoir model if inverted seismic attributes are available. We demonstrate the methodology on a data set from an onshore tight-sand gas reservoir in Texas. The main results of the application are the set of probability distributions of AVO properties as a function of elastic attributes in each facies and the corresponding AVO-based facies profile at the well location. A comparison of different statistical assumptions and a sensitivity analysis on the resolution of the elastic data set are presented.

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“…Similar modeling strategies, along with associated applications to assessment of uncertainty in estimation of rock properties, have been explored by Doyan (1988), Avseth et al (1998), Mavko and Mukerji (1998), Takahashi et al (1999aTakahashi et al ( , 1999b, Mukerji et al (2001), Bachrach and Dutta (2004), Gallop (2006), and Spikes et al (2007). Our models include distributions on porosity (), reservoir thickness (h), and water saturation (S w ).…”

Section: Seismic Models For Joint Distributionsmentioning

confidence: 96%

Quantifying the Reliability and Value of 3D Land Seismic

Bickel

Gibson

McVay

et al. 2008

SPE Reservoir Evaluation &Amp; Engineering

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Seismic data provide essential information for guiding reservoir development. Improvements in data quality hold the promise of improving performance even further, provided that the value of these data exceeds their cost. Previous work has demonstrated value-of-information (VOI) methods to quantify the value of seismic data. In these examples, seismic accuracy was obtained by means of expert assessment instead of being based on geophysical quantities. In addition, the modeled seismic information was not representative of any quantity that would be observed in a seismic image.Here we apply a more general VOI model that includes multiple targets, budgetary constraints, and quantitative models relating poststack seismic amplitudes and amplitude-variation-withoffset (AVO) parameters to the quantities of interest for reservoir characterization, such as porosity and reservoir thickness. Also, by including estimated changes in data accuracy based on signal-tonoise ratio, the decision model can provide objective estimates of the reliability of measurements derived from the seismic data. We demonstrate this methodology within the context of a west Texas 3D land survey. This example demonstrates that seismic information can improve reservoir economics and that improvements in seismic technology can create additional value. Value of Seismic (VOS) Information.Consider an exploration and production (E&P) company that is designing a land-based infill-drilling program. The company has identified m infill targets but faces a budget constraint such that it can drill only b wells. Such a constraint could be the result of a limited capital budget or of rig availability. Let d=(d 1 , . . . , d m ) be an m-vector of drilling decisions, or a drilling program where d i ‫1ס‬ if target i is to be drilled and 0 otherwise. Each drilled well will produce a value for the company, which is a function of the underlying reservoir properties (e.g., porosity, thickness, water saturation). Let v i represent the expected net present value (ENPV) (Brealey and Myers 1991) of Well i. We represent the reservoir properties at location i with the n-vector i , where n is the number of properties. Then ⍀‫(ס‬ 1 , . . . , m ) is a matrix that describes the reservoir properties at each of the m locations. If we consider only porosity, thickness, and water saturation, then each reservoir-property vector contains three elements. At the time of the drilling decision, these properties are unknown and, hence, i is a random vector with prior probability distribution f i ( i ). The joint distribution over the reservoir properties at all locations is f(⍀).* This name is based on an analogy to a hiker that wants to fill his/her knapsack with the most-valuable items but is restricted as to how much can be carried. In our setting, we want to the most-valuable wells but can select only b of them.

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Facies probability from mixture distributions with non‐stationary impedance errors

Cited by 24 publications

References 6 publications

Probabilistic approach to rock physics modeling

Probabilistic approach to rock physics modeling

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

Quantifying the Reliability and Value of 3D Land Seismic

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