Estimation of reservoir properties from seismic data through a Markov Chain Monte Carlo-AVA inversion algorithm

2018 ◽  
Vol 49 (5) ◽  
pp. 688-703 ◽  
Author(s):  
Mattia Aleardi ◽  
Fabio Ciabarri ◽  
Alfredo Mazzotti
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Seismic Data ◽  
Inversion Algorithm ◽  
Reservoir Properties

Markov chain Monte Carlo for petrophysical inversion

Geophysics ◽  
2021 ◽  
pp. 1-60
Author(s):  
Dario Grana ◽  
Leandro de Figueiredo ◽  
Klaus Mosegaard
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Approach ◽  
Seismic Data ◽  
Correlation Model ◽  
Proposal Distribution ◽  
Reservoir Properties ◽  
Spatially Correlated ◽  
Vertical Correlation

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.

scholarly journals Monte Carlo reservoir analysis combining seismic reflection data and informed priors

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. R31-R41 ◽  
Author(s):  
Andrea Zunino ◽  
Klaus Mosegaard ◽  
Katrine Lange ◽  
Yulia Melnikova ◽  
Thomas Mejer Hansen
Keyword(s):  
Monte Carlo ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Probabilistic Approach ◽  
Multiple Point ◽  
Petroleum Reservoir ◽  
Inversion Algorithm ◽  
Reservoir Properties ◽  
Seismic Reflection Data ◽  
Reflection Data

Determination of a petroleum reservoir structure and rock bulk properties relies extensively on inference from reflection seismology. However, classic deterministic methods to invert seismic data for reservoir properties suffer from some limitations, among which are the difficulty of handling complex, possibly nonlinear forward models, and the lack of robust uncertainty estimations. To overcome these limitations, we studied a methodology to invert seismic reflection data in the framework of the probabilistic approach to inverse problems, using a Markov chain Monte Carlo (McMC) algorithm with the goal to directly infer the rock facies and porosity of a target reservoir zone. We thus combined a rock-physics model with seismic data in a single inversion algorithm. For large data sets, the McMC method may become computationally impractical, so we relied on multiple-point-based a priori information to quantify geologically plausible models. We tested this methodology on a synthetic reservoir model. The solution of the inverse problem was then represented by a collection of facies and porosity reservoir models, which were samples of the posterior distribution. The final product included probability maps of the reservoir properties in obtained by performing statistical analysis on the collection of solutions.

Gaussian mixture Markov chain Monte Carlo method for linear seismic inversion

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. R463-R476 ◽  
Author(s):  
Leandro Passos de Figueiredo ◽  
Dario Grana ◽  
Mauro Roisenberg ◽  
Bruno B. Rodrigues
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Elastic Properties ◽  
Posterior Distribution ◽  
Seismic Data ◽  
Gaussian Mixture ◽  
Gaussian Component ◽  
Well Test ◽  
Mcmc Method

We have developed a Markov chain Monte Carlo (MCMC) method for joint inversion of seismic data for the prediction of facies and elastic properties. The solution of the inverse problem is defined by the Bayesian posterior distribution of the properties of interest. The prior distribution is a Gaussian mixture model, and each component is associated to a potential configuration of the facies sequence along the seismic trace. The low frequency is incorporated by using facies-dependent depositional trend models for the prior means of the elastic properties in each facies. The posterior distribution is also a Gaussian mixture, for which the Gaussian component can be analytically computed. However, due to the high number of components of the mixture, i.e., the large number of facies configurations, the computation of the full posterior distribution is impractical. Our Gaussian mixture MCMC method allows for the calculation of the full posterior distribution by sampling the facies configurations according to the acceptance/rejection probability. The novelty of the method is the use of an MCMC framework with multimodal distributions for the description of the model properties and the facies along the entire seismic trace. Our method is tested on synthetic seismic data, applied to real seismic data, and validated using a well test.

Seismic inversion and uncertainty quantification using transdimensional Markov chain Monte Carlo method

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. R321-R334 ◽  
Author(s):  
Dehan Zhu ◽  
Richard Gibson
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Uncertainty Quantification ◽  
Seismic Inversion ◽  
Inversion Algorithm ◽  
Seismic Attribute ◽  
Data Set ◽  
Location Uncertainty ◽  
Parameter Values

We applied a transdimensional stochastic inversion algorithm, reversible jump Markov chain Monte Carlo (rjMCMC), to angle-stack seismic inversion for characterization of reservoir acoustic and shear impedance with uncertainty quantification. The rjMCMC is able to infer the number of parameters for the model as well as the parameter values. In our case, the number of parameters depends on the number of model layers for a given data set. We also use this method in uncertainty quantification because a transdimensional sampling helps prevent underparameterization or strong overparameterization. An ensemble of models with proper parameterization can improve parameter estimation and uncertainty quantification. Our new results in uncertainty analysis indicate that (1) the uncertainty in seismic inversion, including uncertainty in earth properties and their locations, is related to the discontinuity of property across an interface, and (2) there is a trade-off between property uncertainty and location uncertainty. A stronger discontinuity will induce more property uncertainty but less location uncertainty at the discontinuity interface. Therefore, we further use the inversion uncertainty as a novel seismic attribute to assist in delineation of subsurface discontinuity interfaces and quantify the magnitude of the discontinuities, which further facilitates quantitative interpretation and stratigraphic interpretation.

scholarly journals Temperature and Salinity Inverted for a Mediterranean Eddy Captured With Seismic Data, Using a Spatially Iterative Markov Chain Monte Carlo Approach

2021 ◽  
Vol 8 ◽  
Author(s):  
Wuxin Xiao ◽  
Katy Louise Sheen ◽  
Qunshu Tang ◽  
Jamie Shutler ◽  
Richard Hobbs ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Seismic Data ◽  
Imaging Method ◽  
Hydrographic Data ◽  
Prior Model ◽  
Acoustic Reflection ◽  
Starting Model ◽  
The Impact

Ocean submesoscale dynamics are thought to play a key role in both the climate system and ocean productivity, however, subsurface observations at these scales remain rare. Seismic oceanography, an established acoustic imaging method, provides a unique tool for capturing oceanic structure throughout the water column with spatial resolutions of tens of meters. A drawback to the seismic method is that temperature and salinity are not measured directly, limiting the quantitative interpretation of imaged features. The Markov Chain Monte Carlo (MCMC) inversion approach has been used to invert for temperature and salinity from seismic data, with spatially quantified uncertainties. However, the requisite prior model used in previous studies relied upon highly continuous acoustic reflection horizons rarely present in real oceanic environments due to instabilities and turbulence. Here we adapt the MCMC inversion approach with an iteratively updated prior model based on hydrographic data, sidestepping the necessity of continuous reflection horizons. Furthermore, uncertainties introduced by the starting model thermohaline fields as well as those from the MCMC inversion itself are accounted for. The impact on uncertainties of varying the resolution of hydrographic data used to produce the inversion starting model is also investigated. The inversion is applied to a mid-depth Mediterranean water eddy (or meddy) captured with seismic imaging in the Gulf of Cadiz in 2007. The meddy boundary exhibits regions of disrupted seismic reflectivity and rapid horizontal changes of temperature and salinity. Inverted temperature and salinity values typically have uncertainties of 0.16°C and 0.055 psu, respectively, and agree well with direct measurements. Uncertainties of inverted results are found to be highly dependent on the resolution of the hydrographic data used to produce the prior model, particularly in regions where background temperature and salinity vary rapidly, such as at the edge of the meddy. This further advancement of inversion techniques to extract temperature and salinity from seismic data will help expand the use of ocean acoustics for understanding the mesoscale to finescale structure of the interior ocean.

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