Using kernel principal component analysis to interpret seismic signatures of thin shaly-sand reservoirs

Dejtrakulwong, Piyapa; Mukerji, Tapan; Mavko, Gary

doi:10.1190/segam2012-1013.1

Cited by 10 publications

(8 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The basic idea of kernel principal component analysis (KPCA) is to project each sample vector x k in the input space R N into the high-dimensional feature space F by introducing a nonlinear function φ, and then Principal Component Analysis is performed in high dimensional space [8][9][10]. Duo to the high dimensional characteristics of the feature space, the nonlinear mapping and the decomposition of characteristic variables become very difficult, but the nonlinear mapping can be avoided by introducing the kernel technique [11][12][13], and the point product of the original space variables is only needed to be calculated [6].…”

Section: Kernel Principal Component Analysis (Kpca)mentioning

confidence: 99%

The Attribute Optimization Method Based on the Probability Kernel Principal Component Analysis and Its Application

Zheng¹

2019

OGCE

View full text Add to dashboard Cite

The principal component analysis (PCA) is the most common attribute optimization analysis techniques, but it is a linear method and exists the problem of lack of probability model and the absence of higher-order statistics information. It has poor comprehensive ability to complex non-linear attributes. Therefore, in order to overcome two shortcomings of the principal component analysis (PCA) and improve the effect of attribute optimization, this paper studies the probability kernel principal component analysis (PKPCA) method which is based on Bayesian theory and kernel principal component analysis (KPCA). First, the sample data are mapped to the high dimensional feature space, then define probability model of the data in high-dimensional space, and finally, expectation maximization (EM) estimated is used to get the best results. This method has both the advantage of probability analysis and kernel principal component analysis (KPCA). It is able to effectively adapt to more complex reservoir conditions and can realize the non-linear probability analysis. The probability kernel principal component analysis (PKPCA) method is applied to reservoir prediction of the Southern oil fields in China. The predicted results show that the method can improve the precision of the attribute optimization, while improving the accuracy of the forecasts of reservoir.

show abstract

Section: Kernel Principal Component Analysis (Kpca)mentioning

confidence: 99%

The Attribute Optimization Method Based on the Probability Kernel Principal Component Analysis and Its Application

Zheng¹

2019

OGCE

View full text Add to dashboard Cite

show abstract

“…The low-order DCT coefficients express most of the variability of the original signal, and the model compression is simply accomplished by zeroing the numerical coefficients of the basis functions beyond a certain threshold. However, each compression technique must be applied taking in mind that part of the information in the original (unreduced) parameter space could be lost in the reduced space and thus, the model parameterization must always constitute a compromise between model resolution and model uncertainty (Aleardi, 2020;Aleardi & Salusti, 2021;Dejtrakulwong et al, 2012;Fernández-Martínez et al, 2017;Grana et al, 2019;Lochbühler et al, 2014). Similarly, data parameterization must constitute a compromise between good data resolution (our ability to match the observed data) and accurate uncertainty quantification.…”

Section: Introductionmentioning

confidence: 99%

Ensemble-Based Electrical Resistivity Tomography with Data and Model Space Compression

Aleardi

Vinciguerra

Hojat

2021

Pure Appl. Geophys.

View full text Add to dashboard Cite

Inversion of electrical resistivity tomography (ERT) data is an ill-posed problem that is usually solved through deterministic gradient-based methods. These methods guarantee a fast convergence but hinder accurate assessments of model uncertainties. On the contrary, Markov Chain Monte Carlo (MCMC) algorithms can be employed for accurate uncertainty appraisals, but they remain a formidable computational task due to the many forward model evaluations needed to converge. We present an alternative approach to ERT that not only provides a best-fitting resistivity model but also gives an estimate of the uncertainties affecting the inverse solution. More specifically, the implemented method aims to provide multiple realizations of the resistivity values in the subsurface by iteratively updating an initial ensemble of models based on the difference between the predicted and measured apparent resistivity pseudosections. The initial ensemble is generated using a geostatistical method under the assumption of log-Gaussian distributed resistivity values and a Gaussian variogram model. A finite-element code constitutes the forward operator that maps the resistivity values onto the associated apparent resistivity pseudosection. The optimization procedure is driven by the ensemble smoother with multiple data assimilation, an iterative ensemble-based algorithm that performs a Bayesian updating step at each iteration. The main advantages of the proposed approach are that it can be applied to nonlinear inverse problems, while also providing an ensemble of models from which the uncertainty on the recovered solution can be inferred. The ill-conditioning of the inversion procedure is decreased through a discrete cosine transform reparameterization of both data and model spaces. The implemented method is first validated on synthetic data and then applied to field data. We also compare the proposed method with a deterministic least-square inversion, and with an MCMC algorithm. We show that the ensemble-based inversion estimates resistivity models and associated uncertainties comparable to those yielded by a much more computationally intensive MCMC sampling.

show abstract

“…In this case, the full state space is projected onto a limited number of basis functions and the algorithm generates samples in this reduced domain. This technique must be applied taking in mind that part of the information in the original (unreduced) parameter space could be lost in the reduced space, and, for this reason, the model parameterization must always constitute a compromise between model resolution and model uncertainty (Dejtrakulwong et al ., 2012; Lochbühler et al ., 2014; Aleardi, 2019; Grana et al ., 2019; Aleardi, 2020b).…”

Section: Introductionmentioning

confidence: 99%

A gradient‐based Markov chain Monte Carlo algorithm for elastic pre‐stack inversion with data and model space reduction

Aleardi

2021

Geophysical Prospecting

View full text Add to dashboard Cite

The main challenge of Markov chain Monte Carlo sampling is to define a proposal distribution that simultaneously is a good approximation of the posterior probability while being inexpensive to manipulate. We present a gradient‐based Markov chain Monte Carlo inversion of pre‐stack seismic data in which the posterior sampling is accelerated by defining a proposal that is a local, Gaussian approximation of the posterior model, while a non‐parametric prior is assumed for the distribution of the elastic properties. The proposal is constructed from the local Hessian and gradient information of the log posterior, whereas the non‐linear, exact Zoeppritz equations constitute the forward modelling engine for the inversion procedure. Hessian and gradient information is made computationally tractable by a reduction of data and model spaces through a discrete cosine transform reparameterization. This reparameterization acts as a regularization operator in the model space, while also preserving the spatial and temporal continuity of the elastic properties in the sampled models. We test the implemented algorithm on synthetic pre‐stack inversions under different signal‐to‐noise ratios in the observed data. We also compare the results provided by the presented method when a computationally expensive (but accurate) finite‐difference scheme is used for the Jacobian computation, with those obtained when the Jacobian is derived from the linearization of the exact Zoeppritz equations. The outcomes of the proposed approach are also compared against those yielded by a gradient‐free Monte Carlo sampling and by a deterministic least‐squares inversion. Our tests demonstrate that the gradient‐based sampling reaches accurate uncertainty estimations with a much lower computational effort than the gradient‐free approach.

show abstract

Using kernel principal component analysis to interpret seismic signatures of thin shaly-sand reservoirs

Cited by 10 publications

References 6 publications

The Attribute Optimization Method Based on the Probability Kernel Principal Component Analysis and Its Application

The Attribute Optimization Method Based on the Probability Kernel Principal Component Analysis and Its Application

Ensemble-Based Electrical Resistivity Tomography with Data and Model Space Compression

A gradient‐based Markov chain Monte Carlo algorithm for elastic pre‐stack inversion with data and model space reduction

Contact Info

Product

Resources

About