Bayesian inversion of seismic and electromagnetic data for marine gas reservoir characterization using multi-chain Markov chain Monte Carlo sampling
Introduction
Successful marine gas reservoir characterization requires accurate estimation of reservoir properties such as porosity and fluid/gas saturations, and the quantification of errors/uncertainties in these estimates. Controlled-Source Electromagnetic (CSEM) data are known to be sensitive to the presence of hydrocarbons — as shown in Archie's law (Archie, 1942), the electrical resistivity of reservoir rocks is highly sensitive to gas saturation through the link to water saturation. Such a dependence of bulk resistivity on gas saturation makes it possible to discriminate between economic and non-economic gas saturations. However, the CSEM data are insensitive to geological structural details, which makes standalone CSEM inversion challenging to interpret. Seismic data, on the other hand, provide detailed structural information and can help resolve rock properties such as porosity, but cannot distinguish fluid properties given the inadequate contrast in density and seismic velocities. Since seismic velocity and density have low sensitivity to variations in gas saturation (Castagna and Backus, 1993, Dȩbski and Tarantola, 1995, Plessix and Bork, 2000), both fluid and pressure changes have approximately the same degree of impact on the seismic Amplitude Versus Angle (AVA) data according to Gassmann's equations (Gassmann, 1951). The two types of data (seismic AVA and CSEM) can therefore be used as supplementary information to each other to provide adequate constraints on reservoir properties. There have been successful applications of joint inversion of seismic AVA and CSEM data for characterizing marine reservoirs (e.g., Aki and Richards, 1980, Chen et al., 2007, Du and MacGregor, 2010, Fliedner et al., 2011, Hou et al., 2006, Lang and Grana, 2015).
Although joint inversion of seismic AVA and CSEM data can provide better estimates of gas saturation and porosity than inversion of individual data sets (Chen et al., 2004, Chen et al., 2007, Hou et al., 2006), the integration of two types of data can be challenging due to the high dimensionality of the unknown parameter space. Consequently, parameter estimates and their uncertainties may vary significantly given the choice of inversion approaches (e.g., deterministic versus stochastic), designs of objective and likelihood functions and the transformation and weighting of observational data.
In typical geophysical characterization, the existence of noise and the inadequacy (e.g., spatial and temporal coverage and resolution) of the data imply that the problem is ill constrained and therefore, geophysical characterization is a good target for statistical inference. Since there is usually an infinite number of models that can fit the data, it is useful to employ stochastic approaches (e.g., Bayesian), where unknowns are inferred in the form of a posterior probability density function (PDF), thus automatically quantifying the uncertainty in the estimates of the unknowns. The estimation problem is posed as a statistical inverse problem, which provides an expression for the posterior density (alternatively, the joint PDF of the unknowns of interest). The PDF is realized by drawing samples using a method such as Markov chain Monte Carlo (MCMC). MCMC (Liang et al., 2011) methods describe a random walk in the parameter space. Each step in the walk is evaluated by running a forward model to gauge the quality of a new parameter proposal (alternatively, a proposed step in the random walk). Most proposed steps are rejected, making MCMC very expensive, since a sufficient number of samples need to be taken to recover the PDF. To reduce computational time, multi-chain (i.e., parallel) MCMC methods have been developed. Our MCMC procedure starts with 4 chains running DREAM (DiffeRential Evolution Adaptive Metropolis; Vrugt et al., 2009). When a sufficient number of samples have been collected by DREAM to make a useful proposal distribution, the MCMC method transitions to a parallel (4 chains) AM (Adaptive Metropolis; Haario et al., 2006), implemented in a manner identical to Solonen's method (Solonen et al., 2012).
In our paper, we considered a five-layer reservoir model, similar to the synthetic model setup in (Hou et al., 2006), to demonstrate the accuracy and efficiency of the newly developed multi-chain MCMC-Bayesian approach. The unknowns include gas saturation and porosity in each layer in the reservoir. We also investigated the performance of the proposed approach under different levels of noise in both seismic AVA and CSEM observational data, and evaluated the efficiency and scalability of the multi-chain MCMC.
The paper is organized as follows. Section 2 introduces the methodology, followed by the results and discussions in Section 3. Concluding remarks are presented in Section 4.
Section snippets
Seismic AVA and CSEM modeling
In seismic modeling, the reservoir variables of interest are porosity (φ), water (Sw) and gas saturation (Sg) within the reservoir. The Zoeppritz equation (Aki and Richards, 1980) was used to model the angle-dependent reflectivity, which is convolved with the compressional wave reflection coefficient to form the calculated seismic AVA responses (Shuey, 1985). ρ, Vp and Vs (density, compressional and shear wave velocities) of the reservoir are calculated from water and gas saturation and
Synthetic studies
As shown in Fig. 1, a realistic layered reservoir model (Chen et al., 2004, Hou et al., 2006) is considered in our study. The synthetic reservoir model includes five layers with a thickness of 50 m and zero oil saturation. Thus Sw + Sg = 1 in any layer. The target horizon is 1050 m below the seafloor that includes 500 m of seawater and a 550 m thick overburden under the seawater. From the upper to the bottom layers, the true gas saturation values are 0.05, 0.95, 0.4, 0.9 and 0.1, respectively. The
Conclusion
In this study, we propose a multi-chain MCMC-Bayesian framework to estimate marine reservoir gas saturation and porosity using seismic AVA and marine CSEM data. We demonstrate the ability of our approach to solve nonlinear statistical inverse problems by constructing a 10-dimensional posterior density for gas saturations and porosities of a layered underwater gas reservoir. The posterior density is complex and is approximated by samples drawn by a multi-chain MCMC technique that is a hybrid of
Acknowledgments
This work is supported by the Office of Science Advanced Scientific Computing Research (ASCR). Pacific Northwest National Laboratory is operated for the DOE by Battelle Memorial Institute under Contract DE-AC05-76RLO1830. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy’s National Nuclear Security Administration
References (26)
- Aki, K., and Richards, P., 1980, Quantitative Seismology: Theory and Methods: Freeman and Company, v....
- Archie, G. E., 1942, The electrical resistivity log as an aid in determining some reservoir characteristics: Trans....
- et al.
AVO analysis-tutorial and review: offset-dependent reflectivity
- et al.
Joint inversion of seismic AVO and EM data for gas saturation estimation using a sampling-based stochastic model
- Chen, J., Hoversten, G. M., Vasco, D., Rubin, Y., and Hou, Z., 2007, A Bayesian model for gas saturation estimation...
- Dȩbski, W., and Tarantola, A., 1995, Information on elastic parameters obtained from the amplitudes of reflected waves:...
- et al.
Reservoir characterization from joint inversion of marine CSEM and seismic AVA data using Genetic Algorithms: a case study based on the Luva gas field
- Dvorkin, J., and Nur, A., 1996, Elasticity of high-porosity sandstones: theory for two North Sea data sets: Geophysics,...
- Fliedner, M., Treitel, S., Frenkel, M., and MacGregor, L., 2011, Fast stochastic inversion of marine CSEM and seismic...
- Gassmann, F., 1951, Elastic waves through a packing of spheres: Geophysics, v. 16, no. 4, p....
Cited by (9)
Realization ranking of seismic geostatistical inversion based on a Bayesian lithofacies classification - A case study from an offshore field
2019, Journal of Applied GeophysicsCitation Excerpt :These local PDFs do not give a unique answer, and as a result, we can produce an arbitrary number of possible models of elastic properties using a random number generator and defining a threshold for the match between real and synthetic seismic data. In this study, 250 realizations of IP and IS were produced by the sampling of the local PDFs at each trace locations using Markov Chain Monte Carlo algorithm (Mosegaard, 1998; Ren et al., 2017). The Mont Carlo approach refers to a stochastic process in which the random numbers between 0 and 1 are generated by a random machine generator and used to sample the PDFs, while, the Markov Chain principle is dealing with how the new random number is affected by the previous one in a sequential process.
Pre-stack elastic parameter inversion of ray parameters
2019, Journal of Applied GeophysicsCitation Excerpt :Therefore, compared with angle gather conversion, P gather conversion is more accurate. Probability inversion method represented by Bayesian inversion has been widely used because it takes the uncertainty of observed data and the prior information of parameter into consideration (Hao and Zong, 2012; Ren et al., 2017). Cauchy prior distribution can improve the reliability of inversion (Sachhi and Uirych, 1995; Alemie and Sacchi, 2011).
The accuracy of AVA approximations in isotropic media assessed via synthetic numerical experiments: Implications for the determination of porosity
2018, Journal of Petroleum Science and EngineeringCitation Excerpt :In order to check the accuracy of P-wave reflection coefficient approximations for AVO inversions, we tried to retrieve true reservoir porosity (0.15) from synthetic reflection coefficient and amplitude data (with 25% noise/uncertainty/standard deviation of observed seismic data) using the Bayesian approach and the Monte Carlo method discussed in Section 3. Normally, the uncertainty (standard deviation/noise level) in seismic AVA data is within the range of 10–30% (Ren et al., 2017). Noise represents the uncertainty left in the observed data after the application of sophisticated seismic AVA-processing algorithms such as amplitude preserving migration (Grossman, 2003; Zhang et al., 2014).
Inferring the most probable maps of underground utilities using Bayesian mapping model
2018, Journal of Applied GeophysicsCitation Excerpt :Bayesian data fusion models have been utilized for numerous applications and there is a large body of literature proposing Bayesian modeling for data fusion and uncertainty management, thus, providing motivation for the work proposed in this study. To date, Bayesian modeling has been successfully implemented in similar applications, such as seismic/Magnetotelluric inversion (Dettmer et al., 2014; Guo et al., 2011), water distribution management, modeling for rock-physics analysis, gas and buried near-surface utility mapping (Ristić et al., 2017; Ji et al., 2016; Wang and Lu, 2016; Ren et al., 2017; Aleardi et al., 2017; Fernández-Martínez et al., 2013). Among several impactful studies using Bayesian modeling, the approach of combining multiple data sources and Bayesian data fusion for bedrock tracking has been of significant interest such as (Fiannacca et al., 2017; Christensen et al., 2015; Oldenborger et al., 2016).
Computational Geo-Electromagnetics: Methods, Models, and Forecasts
2020, Computational Geo-Electromagnetics: Methods, Models, and Forecasts