Series Expansion-Based Genetic Inversion of Wireline Logging Data

Szabó, Norbert Péter; Dobróka, Mihály

doi:10.1007/s11004-018-9768-4

Cited by 9 publications

(5 citation statements)

References 36 publications

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“…Combining Equations ( 6) and ( 7), the response function now depends on depth coordinates; therefore, the model parameters are interchanged by the series of expansion coefficients leading to a highly overdetermined inversion problem since the required number of expansion coefficients to describe the model parameters is smaller than the number of inverted data. For solving the inverse problem, we apply a genetic algorithmbased inversion approach, which assures to search for the global minimum of the deviation between the measured and calculated well logs and provides an initial-model independent solution [36]. In shale gas formations, the inversion method previously gave accurate estimation for kerogen volume (V k ), porosity (Φ), water saturation in invaded and virgin zone (S x0 and S w ), matrix (here quartz) volume (V ma ), clay content (V c ) and silt content (V s ), including their estimation errors in a joint inversion procedure [37].…”

Section: Application Of Interval Inversionmentioning

confidence: 99%

Factor Analysis of Well Logs for Total Organic Carbon Estimation in Unconventional Reservoirs

et al. 2021

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Several approaches have been applied for the evaluation of formation organic content. For further developments in the interpretation of organic richness, this research proposes a multivariate statistical method for exploring the interdependencies between the well logs and model parameters. A factor analysis-based approach is presented for the quantitative determination of total organic content of shale formations. Uncorrelated factors are extracted from well logging data using Jöreskog’s algorithm, and then the factor logs are correlated with estimated petrophysical properties. Whereas the first factor holds information on the amount of shaliness, the second is identified as an organic factor. The estimation method is applied both to synthetic and real datasets from different reservoir types and geologic basins, i.e., Derecske Trough in East Hungary (tight gas); Kingak formation in North Slope Alaska, United States of America (shale gas); and shale source rock formations in the Norwegian continental shelf. The estimated total organic content logs are verified by core data and/or results from other indirect estimation methods such as interval inversion, artificial neural networks and cluster analysis. The presented statistical method used for the interpretation of wireline logs offers an effective tool for the evaluation of organic matter content in unconventional reservoirs.

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Section: Application Of Interval Inversionmentioning

confidence: 99%

Factor Analysis of Well Logs for Total Organic Carbon Estimation in Unconventional Reservoirs

et al. 2021

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“…Another viable strategy to mitigate the curse of dimensionality and to reduce the computational complexity of high‐dimensional inverse problems is to compress the model space through appropriate reparameterization techniques (Fernández‐Martínez et al ., 2011; Azevedo et al ., 2016; Aleardi, 2019; Szabó and Dobróka, 2019; Numes et al ., 2019; Aleardi 2020b). However, it should be noted that the parameterization of an inverse problem must always constitute a compromise between model resolution and model uncertainty (Grana et al ., 2019).…”

Section: Introductionmentioning

confidence: 99%

Discrete cosine transform for parameter space reduction in Bayesian electrical resistivity tomography

Vinciguerra

Aleardi

Hojat

et al. 2021

Geophysical Prospecting

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Electrical resistivity tomography is a non‐linear and ill‐posed geophysical inverse problem that is usually solved through gradient‐descent methods. This strategy is computationally fast and easy to implement but impedes accurate uncertainty appraisals. We present a probabilistic approach to two‐dimensional electrical resistivity tomography in which a Markov chain Monte Carlo algorithm is used to numerically evaluate the posterior probability density function that fully quantifies the uncertainty affecting the recovered solution. The main drawback of Markov chain Monte Carlo approaches is related to the considerable number of sampled models needed to achieve accurate posterior assessments in high‐dimensional parameter spaces. Therefore, to reduce the computational burden of the inversion process, we employ the differential evolution Markov chain, a hybrid method between non‐linear optimization and Markov chain Monte Carlo sampling, which exploits multiple and interactive chains to speed up the probabilistic sampling. Moreover, the discrete cosine transform reparameterization is employed to reduce the dimensionality of the parameter space removing the high‐frequency components of the resistivity model which are not sensitive to data. In this framework, the unknown parameters become the series of coefficients associated with the retained discrete cosine transform basis functions. First, synthetic data inversions are used to validate the proposed method and to demonstrate the benefits provided by the discrete cosine transform compression. To this end, we compare the outcomes of the implemented approach with those provided by a differential evolution Markov chain algorithm running in the full, un‐reduced model space. Then, we apply the method to invert field data acquired along a river embankment. The results yielded by the implemented approach are also benchmarked against a standard local inversion algorithm. The proposed Bayesian inversion provides posterior mean models in agreement with the predictions achieved by the gradient‐based inversion, but it also provides model uncertainties, which can be used for penetration depth and resolution limit identification.

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“…These methods make use of different orthogonal basis functions (e.g., principal component analysis, wavelet transforms, Legendre polynomials, Discrete Cosine Transform) to reduce the dimensionality as well as the computational complexity of inverse problems. After such reparameterization, the unknown parameters become the numerical coefficients that multiply the basis functions (Dejtrakulwong et al, 2012;Lochbühler et al 2014;Fernández Martínez et al 2017;Aleardi 2019;Szabó and Dobróka, 2019). However, the compression should be applied keeping in mind that the model parameterization must always constitute a compromise between model resolution and model uncertainty (Grana et al 2019).…”

Section: Introductionmentioning

confidence: 99%