Probabilistic petrophysical-properties estimation integrating statistical rock physics with seismic inversion

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. O21-O37 ◽  
Author(s):  
Dario Grana ◽  
Ernesto Della Rossa
Keyword(s):  
Seismic Data ◽  
Measurement Errors ◽  
Rock Physics ◽  
Seismic Inversion ◽  
Joint Estimation ◽  
Physical Models ◽  
Inversion Method ◽  
Petrophysical Properties ◽  
Reservoir Properties ◽  
Statistical Rock Physics

A joint estimation of petrophysical properties is proposed that combines statistical rock physics and Bayesian seismic inversion. Because elastic attributes are correlated with petrophysical variables (effective porosity, clay content, and water saturation) and this physical link is associated with uncertainties, the petrophysical-properties estimation from seismic data can be seen as a Bayesian inversion problem. The purpose of this work was to develop a strategy for estimating the probability distributions of petrophysical parameters and litho-fluid classes from seismics. Estimation of reservoir properties and the associated uncertainty was performed in three steps: linearized seismic inversion to estimate the probabilities of elastic parameters, probabilistic upscaling to include the scale-changes effect, and petrophysical inversion to estimate the probabilities of petrophysical variables andlitho-fluid classes. Rock-physics equations provide the linkbetween reservoir properties and velocities, and linearized seismic modeling connects velocities and density to seismic amplitude. A full Bayesian approach was adopted to propagate uncertainty from seismics to petrophysics in an integrated framework that takes into account different sources of uncertainty: heterogeneity of the real data, approximation of physical models, measurement errors, and scale changes. The method has been tested, as a feasibility step, on real well data and synthetic seismic data to show reliable propagation of the uncertainty through the three different steps and to compare two statistical approaches: parametric and nonparametric. Application to a real reservoir study (including data from two wells and partially stacked seismic volumes) has provided as a main result the probability densities of petrophysical properties and litho-fluid classes. It demonstrated the applicability of the proposed inversion method.

Incorporation of geology with rock physics enables subsalt poststack inversion: A case study in the Gulf of Mexico

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB53-WB65 ◽  
Author(s):  
Huyen Bui ◽  
Jennifer Graham ◽  
Shantanu Kumar Singh ◽  
Fred Snyder ◽  
Martiris Smith
Keyword(s):  
Seismic Data ◽  
Acoustic Impedance ◽  
Low Frequency ◽  
Rock Physics ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Reservoir Properties ◽  
Blind Test ◽  
Frequency Model ◽  
Layer Sequence

One of the main goals of seismic inversion is to obtain high-resolution relative and absolute impedance for reservoir properties prediction. We aim to study whether the results from seismic inversion of subsalt data are sufficiently robust for reliable reservoir characterization. Approximately [Formula: see text] of poststack, wide-azimuth, anisotropic (vertical transverse isotropic) wave-equation migration seismic data from 50 Outer Continental Shelf blocks in the Green Canyon area of the Gulf of Mexico were inverted in this study. A total of four subsalt wells and four subsalt seismic interpreted horizons were used in the inversion process, and one of the wells was used for a blind test. Our poststack inversion method used an iterative discrete spike inversion method, based on the combination of space-adaptive wavelet processing to invert for relative acoustic impedance. Next, the dips were estimated from seismic data and converted to a horizon-like layer sequence field that was used as one of the inputs into the low-frequency model. The background model was generated by incorporating the well velocities, seismic velocity, seismic interpreted horizons, and the previously derived layer sequence field in the low-frequency model. Then, the relative acoustic impedance volume was scaled by adding the low-frequency model to match the calculated acoustic impedance logs from the wells for absolute acoustic impedance. Finally, the geological information and rock physics data were incorporated into the reservoir properties assessment for sand/shale prediction in two main target reservoirs in the Miocene and Wilcox formations. Overall, the poststack inversion results and the sand/shale prediction showed good ties at the well locations. This was clearly demonstrated in the blind test well. Hence, incorporating rock physics and geology enables poststack inversion in subsalt areas.

Seismic inversion for reservoir properties combining statistical rock physics and geostatistics: A review

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A165-75A176 ◽  
Author(s):  
Miguel Bosch ◽  
Tapan Mukerji ◽  
Ezequiel F. Gonzalez
Keyword(s):  
Elastic Properties ◽  
Quantitative Estimation ◽  
Rock Physics ◽  
Seismic Inversion ◽  
Elastic Parameters ◽  
Reservoir Properties ◽  
Sequential Approach ◽  
Geostatistical Methods ◽  
Bayesian Formulation ◽  
Statistical Rock Physics

There are various approaches for quantitative estimation of reservoir properties from seismic inversion. A general Bayesian formulation for the inverse problem can be implemented in two different work flows. In the sequential approach, first seismic data are inverted, deterministically or stochastically, into elastic properties; then rock-physics models transform those elastic properties to the reservoir property of interest. The joint or simultaneous work flow accounts for the elastic parameters and the reservoir properties, often in a Bayesian formulation, guaranteeing consistency between the elastic and reservoir properties. Rock physics plays the important role of linking elastic parameters such as impedances and velocities to reservoir properties of interest such as lithologies, porosity, and pore fluids. Geostatistical methods help add constraints of spatial correlation, conditioning to different kinds of data and incorporating subseismic scales of heterogeneities.

Mapping lithofacies and pore‐fluid probabilities in a North Sea reservoir: Seismic inversions and statistical rock physics

Geophysics ◽  
2001 ◽  
Vol 66 (4) ◽  
pp. 988-1001 ◽  
Author(s):  
T. Mukerji ◽  
A. Jørstad ◽  
P. Avseth ◽  
G. Mavko ◽  
J. R. Granli
Keyword(s):  
North Sea ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Probability Distributions ◽  
Rock Physics ◽  
Normal Incidence ◽  
Seismic Inversion ◽  
Training Data ◽  
Well Log ◽  
Statistical Rock Physics

Reliably predicting lithologic and saturation heterogeneities is one of the key problems in reservoir characterization. In this study, we show how statistical rock physics techniques combined with seismic information can be used to classify reservoir lithologies and pore fluids. One of the innovations was to use a seismic impedance attribute (related to the [Formula: see text] ratio) that incorporates far‐offset data, but at the same time can be practically obtained using normal incidence inversion algorithms. The methods were applied to a North Sea turbidite system. We incorporated well log measurements with calibration from core data to estimate the near‐offset and far‐offset reflectivity and impedance attributes. Multivariate probability distributions were estimated from the data to identify the attribute clusters and their separability for different facies and fluid saturations. A training data was set up using Monte Carlo simulations based on the well log—derived probability distributions. Fluid substitution by Gassmann’s equation was used to extend the training data, thus accounting for pore fluid conditions not encountered in the well. Seismic inversion of near‐offset and far‐offset stacks gave us two 3‐D cubes of impedance attributes in the interwell region. The near‐offset stack approximates a zero‐offset section, giving an estimate of the normal incidence acoustic impedance. The far offset stack gives an estimate of a [Formula: see text]‐related elastic impedance attribute that is equivalent to the acoustic impedance for non‐normal incidence. These impedance attributes obtained from seismic inversion were then used with the training probability distribution functions to predict the probability of occurrence of the different lithofacies in the interwell region. Statistical classification techniques, as well as geostatistical indicator simulations were applied on the 3‐D seismic data cube. A Markov‐Bayes technique was used to update the probabilities obtained from the seismic data by taking into account the spatial correlation as estimated from the facies indicator variograms. The final results are spatial 3‐D maps of not only the most likely facies and pore fluids, but also their occurrence probabilities. A key ingredient in this study was the exploitation of physically based seismic‐to‐reservoir property transforms optimally combined with statistical techniques.

Seismic data conditioning and orthotropic rock-physics-based inversion of wide-azimuth P-wave seismic data for fracture and total organic carbon characterization in a north Kuwait unconventional reservoir

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. B229-B240 ◽  
Author(s):  
Rajive Kumar ◽  
Prashant Bansal ◽  
Bader S. Al-Mal ◽  
Sagnik Dasgupta ◽  
Colin Sayers ◽  
...  
Keyword(s):  
Organic Carbon ◽  
Total Organic Carbon ◽  
Seismic Data ◽  
Rock Physics ◽  
Seismic Inversion ◽  
P Wave ◽  
Natural Fracture ◽  
Reservoir Properties ◽  
Fluid Saturation ◽  
Fracture Intensity

Optimization of production from unconventional reservoirs requires estimates of reservoir properties such as porosity, total organic carbon (TOC) content, clay content, fluid saturation, and fracture intensity. The porosity and TOC content help to determine reservoir quality, and the natural fracture intensity provides information important for the completion strategy. Because shale reservoirs display intrinsic anisotropy due to layering and the partial alignment of clay minerals and kerogen with the bedding plane, the minimum acceptable representation of the anisotropy of naturally fractured shale-gas reservoirs is orthotropy, in which a set of vertical compliant fractures is embedded in a vertical transverse isotropic (VTI) background medium. Full-azimuth seismic data are required to characterize such reservoirs and to invert for the anisotropic elastic properties. Orthotropic inversion uses azimuthally sectored seismic data stacked according to the incident angle. Even for high-fold acquisition, this azimuth/angle grouping can result in low-fold angle stacks. Orthotropic amplitude-variation-with-offset-and-azimuth (AVOAz) inversion requires seismic preconditioning techniques that ensure proper primary amplitude preservation, noise attenuation, and data alignment, and a workflow implemented for the construction of an orthotropic rock-physics model. This model integrates well and core data to estimate reservoir properties using the results of the AVOAz inversion. The seismic inversion results include the P- and S-impedance and parameters quantifying the azimuthal anisotropy. The rock model assumes a VTI kerogen-rich layer, containing aligned vertical fractures, and it uses prestack orthotropic AVOAz inversion results to predict porosity, TOC, and fracture intensity.

Geostatistical inversion of prestack seismic data for the joint estimation of facies and impedances using stochastic sampling from Gaussian mixture posterior distributions

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. M55-M65 ◽  
Author(s):  
Xiaozheng Lang ◽  
Dario Grana
Keyword(s):  
Elastic Properties ◽  
Posterior Distribution ◽  
Seismic Data ◽  
Gaussian Mixture ◽  
Seismic Inversion ◽  
Joint Estimation ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Data Set ◽  
Geostatistical Approach

We have developed a seismic inversion method for the joint estimation of facies and elastic properties from prestack seismic data based on a geostatistical approach. The objectives of our inversion methodology are to sample from the posterior distribution of seismic properties and to simultaneously classify the lithology conditioned by seismic data. The inversion algorithm is a sequential Gaussian mixture inversion based on Bayesian linearized amplitude variation with offset inverse theory and sequential geostatistical simulations. The stochastic approach to the inversion allows generating multiple elastic models that match the seismic data. To mathematically represent the multimodal behavior of elastic properties due to their variations within different lithologies, we adopt a Gaussian mixture distribution for the prior model of the elastic properties and we use the prior probability of the facies as weights of the Gaussian components of the mixture. The solution of the inverse problem is achieved by deriving the explicit analytical expression of the posterior distribution of the elastic properties and facies and by sampling from this distribution according to a spatial correlation model. The inversion methodology has been validated using well logs and synthetic seismic data with different noise levels, and it is then applied to a real 3D seismic data set in North Sea.

Joint facies and reservoir properties inversion

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. M15-M24 ◽  
Author(s):  
Dario Grana
Keyword(s):  
Seismic Data ◽  
Joint Inversion ◽  
Convex Combination ◽  
Real Data ◽  
Joint Estimation ◽  
Reservoir Rock ◽  
Inversion Method ◽  
Simultaneous Estimation ◽  
Model Parameters ◽  
Reservoir Properties

I have developed a joint inversion of seismic data for the simultaneous estimation of facies and reservoir properties, such as porosity, mineralogy, and saturation. The inversion method is a Bayesian approach for the joint estimation of facies and reservoir rock/fluid properties based on the statistical assumption of mixtures of nonparametric distributions of the model parameters. A mixture distribution is a convex combination of distributions. In the approach, I use a mixture of [Formula: see text] nonparametric distributions, where [Formula: see text] is the number of facies, and the weights of the combination represent the probability of the facies. The statistical assumptions in the proposed Bayesian inversion allow modeling multimodal and nonsymmetric distributions of the model parameters because they are not restricted to specific shapes of the probability distributions and allow modeling multimodal distributions caused by the presence of different facies and nonlinear relations between reservoir properties and elastic data. The inversion can be applied to elastic properties from well logs or derived from seismic data, and they can be combined with traditional Bayesian linearized AVO inversion. The method provides the point-by-point posterior distribution of facies and reservoir properties, as well as the most-likely models and its associated uncertainty, and it is successfully applied to real data.

Stochastic nonlinear inversion of seismic data for the estimation of petroelastic properties using the ensemble smoother and data reparameterization

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. M25-M39 ◽  
Author(s):  
Mingliang Liu ◽  
Dario Grana
Keyword(s):  
Seismic Data ◽  
Reservoir Characterization ◽  
Computational Cost ◽  
Rock Physics ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Seismic Velocities ◽  
Reservoir Properties ◽  
Data Set ◽  
Ensemble Smoother

We have developed a new stochastic nonlinear inversion method for seismic reservoir characterization studies to jointly estimate elastic and petrophysical properties and to quantify their uncertainty. Our method aims to estimate multiple reservoir realizations of the entire set of reservoir properties, including seismic velocities, density, porosity, mineralogy, and saturation, by iteratively updating the initial ensemble of models based on the mismatch between their seismic response and the measured seismic data. The initial models are generated using geostatistical methods and the geophysical forward operators include rock-physics relations and a seismic forward model. The optimization is achieved using an iterative ensemble-based algorithm, namely, the ensemble smoother with multiple data assimilation, in which each iteration is based on a Bayesian updating step. The advantages of the proposed method are that it can be applied to nonlinear inverse problems and it can provide an ensemble of solutions from which we can quantify the uncertainty of the model properties of interest. To reduce the computational cost of the inversion, we perform the optimization in a lower dimensional data space reparameterized by singular value decomposition. The proposed methodology is validated on a synthetic case in which the set of petroelastic properties is recovered with satisfactory accuracy. Then, we applied the inversion method to a real seismic data set from the Norne field in the Norwegian Sea.

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