Bayesian seismic inversion based on rock-physics prior modeling for the joint estimation of acoustic impedance, porosity and lithofacies

Figueiredo, Leandro Passos de; Grana, Dario; Santos, M.; Figueiredo, W.; Roisenberg, Mauro; Neto, Guenther Schwedersky

doi:10.1016/j.jcp.2017.02.013

Cited by 66 publications

(22 citation statements)

References 26 publications

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“…Finally, the a posteriori mean elastic model can be derived as a weighted summation over the posterior Gaussian components (de Figueiredo et al . ):

{bolde}_{e s t} = \sum_{k = 1}^{K} λ_{i} {bold-italicμ}_{e | d}^{k} .

…”

Section: The Methodsmentioning

confidence: 99%

“…The coefficients λ i represent the point-wise posterior probability of facies, where point-wise means that the coefficients λ i at each spatial position are independent from those estimated at the neighbouring positions. Finally, the a posteriori mean elastic model can be derived as a weighted summation over the posterior Gaussian components (de Figueiredo et al 2017):…”

Section: Target-oriented Analytical Inversionmentioning

confidence: 99%

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Markov chain Monte Carlo algorithms for target‐oriented and interval‐oriented amplitude versus angle inversions with non‐parametric priors and non‐linear forward modellings

Aleardi

Salusti

2019

Geophysical Prospecting

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In geophysical inverse problems, the posterior model can be analytically assessed only in case of linear forward operators, Gaussian, Gaussian mixture, or generalized Gaussian prior models, continuous model properties, and Gaussian‐distributed noise contaminating the observed data. For this reason, one of the major challenges of seismic inversion is to derive reliable uncertainty appraisals in cases of complex prior models, non‐linear forward operators and mixed discrete‐continuous model parameters. We present two amplitude versus angle inversion strategies for the joint estimation of elastic properties and litho‐fluid facies from pre‐stack seismic data in case of non‐parametric mixture prior distributions and non‐linear forward modellings. The first strategy is a two‐dimensional target‐oriented inversion that inverts the amplitude versus angle responses of the target reflections by adopting the single‐interface full Zoeppritz equations. The second is an interval‐oriented approach that inverts the pre‐stack seismic responses along a given time interval using a one‐dimensional convolutional forward modelling still based on the Zoeppritz equations. In both approaches, the model vector includes the facies sequence and the elastic properties of P‐wave velocity, S‐wave velocity and density. The distribution of the elastic properties at each common‐mid‐point location (for the target‐oriented approach) or at each time‐sample position (for the time‐interval approach) is assumed to be multimodal with as many modes as the number of litho‐fluid facies considered. In this context, an analytical expression of the posterior model is no more available. For this reason, we adopt a Markov chain Monte Carlo algorithm to numerically evaluate the posterior uncertainties. With the aim of speeding up the convergence of the probabilistic sampling, we adopt a specific recipe that includes multiple chains, a parallel tempering strategy, a delayed rejection updating scheme and hybridizes the standard Metropolis–Hasting algorithm with the more advanced differential evolution Markov chain method. For the lack of available field seismic data, we validate the two implemented algorithms by inverting synthetic seismic data derived on the basis of realistic subsurface models and actual well log data. The two approaches are also benchmarked against two analytical inversion approaches that assume Gaussian‐mixture‐distributed elastic parameters. The final predictions and the convergence analysis of the two implemented methods proved that our approaches retrieve reliable estimations and accurate uncertainties quantifications with a reasonable computational effort.

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“…Finally, the a posteriori mean elastic model can be derived as a weighted summation over the posterior Gaussian components (de Figueiredo et al . ):

{bolde}_{e s t} = \sum_{k = 1}^{K} λ_{i} {bold-italicμ}_{e | d}^{k} .

…”

Section: The Methodsmentioning

confidence: 99%

Section: Target-oriented Analytical Inversionmentioning

confidence: 99%

Markov chain Monte Carlo algorithms for target‐oriented and interval‐oriented amplitude versus angle inversions with non‐parametric priors and non‐linear forward modellings

Aleardi

Salusti

2019

Geophysical Prospecting

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“…To circumvent this issue the estimation process is often solved through a multi-step procedure: first, litho-fluid facies are inferred from the available data (seismic or well log data), then the petrophysical properties are distributed within each facies. Alternatively, over the last years some approaches have been proposed to jointly estimate petrophysical or elastic parameters and litho-fluid facies from the observed data [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…The former neglects the facies dependency of porosity and acoustic impedance values, whereas the mixture models relate each component of the mixture to a specific litho-fluid facies. In the context of seismic inversion, the Gaussian or Gaussian-mixture models are often employed because of their many appealing properties; for example, they allow for an analytical computation of the posterior uncertainty and also make the inclusion of additional constraints (i.e., geostatistical constraints) into the inversion kernel possible [18,24]. On the other hand, a non-parametric distribution is not restricted by any statistical assumption about the underlying statistical model, but it impedes an analytical derivation of the posterior model and also complicates the inclusion of additional regularization operators or geostatistical constraints into the inversion framework.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Different Statistical Models in Probabilistic Joint Estimation of Porosity and Litho-Fluid Facies from Acoustic Impedance Values

Aleardi

2018

Geosciences

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We discuss the influence of different statistical models in the prediction of porosity and litho-fluid facies from logged and inverted acoustic impedance (Ip) values. We compare the inversion and classification results that were obtained under three different statistical a-priori assumptions: an analytical Gaussian distribution, an analytical Gaussian-mixture model, and a non-parametric mixtu re distribution. The first model assumes Gaussian distributed porosity and Ip values, thus neglecting their facies-dependent behaviour related to different lithologic and saturation conditions. Differently, the other two statistical models relate each component of the mixture to a specific litho-fluid facies, so that the facies-dependency of porosity and Ip values is taken into account. Blind well tests are used to validate the final predictions, whereas the analysis of the maximum-a-posteriori (MAP) solutions, the coverage ratio, and the contingency analysis tools are used to quantitatively compare the inversion outcomes. This work points out that the correct choice of the statistical petrophysical model could be crucial in reservoir characterization studies. Indeed, for the investigated zone, it turns out that the simple Gaussian model constitutes an oversimplified assumption, while the two mixture models provide more accurate estimates, although the non-parametric one yields slightly superior predictions with respect to the Gaussian-mixture assumption.

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“…Finally, some authors even joint invert seismic reflection data to facies, elastic properties, and petrophysical properties (23,24,25). (2), comparing direct seismic to facies inversion, and sequential inversion, from seismic to elastic properties, and then to facies.…”

Section: Quantitative Interpretationmentioning

confidence: 99%

Seismic to Facies Inversion Using Convolved Hidden Markov Model

TALARICO¹

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Bayesian seismic inversion based on rock-physics prior modeling for the joint estimation of acoustic impedance, porosity and lithofacies

Cited by 66 publications

References 26 publications

Markov chain Monte Carlo algorithms for target‐oriented and interval‐oriented amplitude versus angle inversions with non‐parametric priors and non‐linear forward modellings

Markov chain Monte Carlo algorithms for target‐oriented and interval‐oriented amplitude versus angle inversions with non‐parametric priors and non‐linear forward modellings

Analysis of Different Statistical Models in Probabilistic Joint Estimation of Porosity and Litho-Fluid Facies from Acoustic Impedance Values

Seismic to Facies Inversion Using Convolved Hidden Markov Model

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