Efficient trans-dimensional Bayesian inversion for geoacoustic profile estimation

Dosso, Stan E.; Dettmer, Jan; Steininger, Gavin; Holland, Charles W.

doi:10.1121/1.4899489

Cited by 8 publications

(15 citation statements)

References 38 publications

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“…Trans-dimensional inversion represents a powerful and general approach that has been applied for several geophysical problems (e.g., Malinverno 2002;Sambridge et al 2006;Bodin and Sambridge 2009;Dettmer et al 2010;Bodin et al 2012;Dosso et al 2014). Ray and Key (2012) implemented a trans-dimensional inversion for frequency-domain CSEM data to estimate the resolution of different field components of the electromagnetic response, and they illustrated the challenges of CSEM inversion when targeting deep-situated, thin hydrocarbon reservoirs in anisotropic environments.…”

Section: Inversionmentioning

confidence: 99%

“…Probabilistic sampling approaches, unlike linearized inversions, can provide rigorous estimates of model parameter uncertainties (e.g., Malinverno 2002). Trans-dimensional Bayesian inversion has recently been applied to invert various geophysical data sets (e.g., Bodin and Sambridge 2009;Dettmer, Dosso and Holland 2010;Ray et al 2013a;Dosso et al 2014).…”

Section: Introductionmentioning

confidence: 99%

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Trans‐dimensional Bayesian inversion of controlled‐source electromagnetic data in the German North Sea

Gehrmann

Dettmer

Schwalenberg

et al. 2015

Geophysical Prospecting

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This paper presents the first controlled‐source electromagnetic survey carried out in the German North Sea with a recently developed seafloor‐towed electrical dipole–dipole system, i.e., HYDRA II. Controlled‐source electromagnetic data are measured, processed, and inverted in the time domain to estimate an electrical resistivity model of the sub‐seafloor. The controlled‐source electromagnetic survey targeted a shallow, phase‐reversed, seismic reflector, which potentially indicates free gas. To compare the resistivity model to reflection seismic data and draw a combined interpretation, we apply a trans‐dimensional Bayesian inversion that estimates model parameters and uncertainties, and samples probabilistically over the number of layers of the resistivity model. The controlled‐source electromagnetic data errors show time‐varying correlations, and we therefore apply a non‐Toeplitz data covariance matrix in the inversion that is estimated from residual analysis. The geological interpretation drawn from controlled‐source electromagnetic inversion results and borehole and reflection seismic data yield resistivities of ∼1 Ωm at the seafloor, which are typical for fine‐grained marine deposits, whereas resistivities below ∼20 mbsf increase to 2–4 Ωm and can be related to a transition from fine‐grained (Holocene age) to unsorted, coarse‐grained, and compacted glacial sediments (Pleistocene age). Interface depths from controlled‐source electromagnetic inversion generally match the seismic reflector related to the contrast between the different depositional environments. Resistivities decrease again at greater depths to ∼1 Ωm with a minimum resistivity at ∼300 mbsf where a seismic reflector (that marks a major flooding surface of late Miocene age) correlates with an increased gamma‐ray count, indicating an increased amount of fine‐grained sediments. We suggest that the grain size may have a major impact on the electrical resistivity of the sediment with lower resistivities for fine‐grained sediments. Concerning the phase‐reversed seismic reflector that was targeted by the survey, controlled‐source electromagnetic inversion results yield no indication for free gas below it as resistivities are generally elevated above the reflector. We suggest that the elevated resistivities are caused by an overall decrease in porosity in the glacial sediments and that the seismic reflector could be caused by an impedance contrast at a thin low‐velocity layer. Controlled‐source electromagnetic interface depths near the reflector are quite uncertain and variable. We conclude that the seismic interface cannot be resolved with the controlled‐source electromagnetic data, but the thickness of the corresponding resistive layer follows the trend of the reflector that is inclined towards the west.

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Section: Inversionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Trans‐dimensional Bayesian inversion of controlled‐source electromagnetic data in the German North Sea

Gehrmann

Dettmer

Schwalenberg

et al. 2015

Geophysical Prospecting

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“…For this reason, the algorithm can be improved by sampling from an approximate posterior distribution rather than from the prior model. To this end, many strategies could be adopted, for example, implementing the adaptive Metropolis algorithm (Haario et al 2001), or sampling from an approximated estimate of the posterior covariance matrix computed from a local approximation of the Jacobian matrix (see Dosso et al 2014). In a 2D interval-oriented inversion of field seismic data we performed (not shown here for confidentiality reasons), we also found particularly useful deriving the starting model for the MCMC sampling from the results of a previous Bayesian linear inversion.…”

Section: Discussionmentioning

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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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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“…While this appears to improve the acceptance of resistivity and move steps, we find that the acceptance rates of transdimensional steps (birth and death) are normally very low (<10%). Hence, a natural extension of this study might include attempting to improve the acceptance rates of transdimensional steps by implementing a transdimensional delayed rejection scheme as developed by Green and Mira (2001), and/or by sampling the log(resistivity) value for newly generated Voronoi cells from the prior rather than using a Gaussian perturbation (equation (B16)) as suggested by Dosso et al (2014).…”

Section: Convergencementioning

confidence: 99%

“…Plots such as those shown in Figure 20 may therefore be used to choose an appropriate value for bd , such that the crossing point of the two curves is greater than 1 or 2 standard deviations from i , ensuring that natural parsimony will be achieved on average. Alternatively, the resistivity of a newly generated cell in a birth step may be sampled from the prior as suggested by Dosso et al (2014), which obviates the need for such tuning when prior ranges are narrow.…”

Section: Similar Tomentioning

confidence: 99%

Transdimensional Electrical Resistivity Tomography

Galetti

Curtis

2018

JGR Solid Earth

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This paper shows that imaging the interior of solid bodies with fully nonlinear physics can be highly beneficial compared to imaging with the equivalent linearized tomographic methods and that this is true for a variety of different types of physics. Including full nonlinearity provides interpretable uncertainties and far greater depth of image penetration into unknown targets such as the Earth's subsurface. We use an adaptively parameterized Monte Carlo method to invert electrical resistivity data for the conductivity structure of the Earth and demonstrate the method on two field data sets. Key results include the observation of directly interpretable uncertainty loops which define possible geometrical variations in the edges of isolated anomalies, hence quantifying the spatial resolution of these boundaries. These topologies of uncertainties are similar to those observed when performing fully nonlinear seismic traveltime tomography. This shows that loop‐like uncertainty topologies are expected in the solutions to a wide variety of tomographic problems, using a variety of data types and hence laws of physics (here the Laplace equation; in previous work the Eikonal or ray equations). We also show that the depth to which we can construct a tomographic image using electrical data is extended by up to a factor of 8 using nonlinear methods compared to linearized inversion using common standard linearized programs. These advantages come at the cost of significantly increased computation. All of these results are illustrated on both synthetic and real data examples.

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Efficient trans-dimensional Bayesian inversion for geoacoustic profile estimation

Cited by 8 publications

References 38 publications

Trans‐dimensional Bayesian inversion of controlled‐source electromagnetic data in the German North Sea

Trans‐dimensional Bayesian inversion of controlled‐source electromagnetic data in the German North Sea

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

Transdimensional Electrical Resistivity Tomography

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