Journal articles on the topic 'Inversion uncertainty'
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Vantassel, Joseph P., and Brady R. Cox. "SWinvert: a workflow for performing rigorous 1-D surface wave inversions." Geophysical Journal International 224, no. 2 (September 9, 2020): 1141–56. http://dx.doi.org/10.1093/gji/ggaa426.
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SUMMARY SWinvert is a workflow developed at The University of Texas at Austin for the inversion of surface wave dispersion data. SWinvert encourages analysts to investigate inversion uncertainty and non-uniqueness in shear wave velocity (Vs) by providing a systematic procedure and specific actionable recommendations for surface wave inversion. In particular, the workflow encourages the use of multiple layering parametrizations to address the inversion's non-uniqueness, multiple global searches for each parametrization to address the inverse problem's non-linearity and quantification of Vs uncertainty in the resulting profiles. While the workflow uses the Dinver module of the popular open-source Geopsy software as its inversion engine, the principles presented are of relevance to analysts using other inversion programs. To illustrate the effectiveness of the SWinvert workflow and to develop a set of benchmarks for use in future surface wave inversion studies, synthetic experimental dispersion data for 12 subsurface models of varying complexity are inverted. While the effects of inversion uncertainty and non-uniqueness are shown to be minimal for simple subsurface models characterized by broad-band dispersion data, these effects cannot be ignored in the Vs profiles derived for more complex models with band-limited dispersion data. To encourage adoption of the SWinvert workflow, an open-source Python package (SWprepost), for pre- and post-processing of surface wave inversion data, and an application on the DesignSafe-Cyberinfrastructure (SWbatch), for performing batch-style surface wave inversions with Dinver using high-performance computing, have been developed and released in conjunction with this work. The SWinvert workflow is shown to provide a methodical procedure and a powerful set of tools for performing rigorous surface wave inversions and quantifying the uncertainty in the resulting Vs profiles.
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Scalzo, Richard, David Kohn, Hugo Olierook, Gregory Houseman, Rohitash Chandra, Mark Girolami, and Sally Cripps. "Efficiency and robustness in Monte Carlo sampling for 3-D geophysical inversions with Obsidian v0.1.2: setting up for success." Geoscientific Model Development 12, no. 7 (July 15, 2019): 2941–60. http://dx.doi.org/10.5194/gmd-12-2941-2019.
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Abstract. The rigorous quantification of uncertainty in geophysical inversions is a challenging problem. Inversions are often ill-posed and the likelihood surface may be multi-modal; properties of any single mode become inadequate uncertainty measures, and sampling methods become inefficient for irregular posteriors or high-dimensional parameter spaces. We explore the influences of different choices made by the practitioner on the efficiency and accuracy of Bayesian geophysical inversion methods that rely on Markov chain Monte Carlo sampling to assess uncertainty using a multi-sensor inversion of the three-dimensional structure and composition of a region in the Cooper Basin of South Australia as a case study. The inversion is performed using an updated version of the Obsidian distributed inversion software. We find that the posterior for this inversion has a complex local covariance structure, hindering the efficiency of adaptive sampling methods that adjust the proposal based on the chain history. Within the context of a parallel-tempered Markov chain Monte Carlo scheme for exploring high-dimensional multi-modal posteriors, a preconditioned Crank–Nicolson proposal outperforms more conventional forms of random walk. Aspects of the problem setup, such as priors on petrophysics and on 3-D geological structure, affect the shape and separation of posterior modes, influencing sampling performance as well as the inversion results. The use of uninformative priors on sensor noise enables optimal weighting among multiple sensors even if noise levels are uncertain.
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Hu, Xufei, and Yiren Fan. "Huber inversion for logging-while-drilling resistivity measurements in high angle and horizontal wells." GEOPHYSICS 83, no. 4 (July 1, 2018): D113—D125. http://dx.doi.org/10.1190/geo2017-0459.1.
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Logging-while-drilling (LWD) resistivity responses are inevitably contaminated by Gaussian and non-Gaussian noise. Noise contamination can influence the stability and accuracy of the inversion of the data. In addition, the uncertainty of the bed-boundary positions can complicate the inversion. We have developed a novel efficient nonlinear inversion algorithm, called Huber inversion, to accurately estimate the layer-by-layer resistivity when LWD measurements were affected by Gaussian and non-Gaussian noise. Huber inversion combines the advantages of the [Formula: see text]- and [Formula: see text]-norm inversions, which are more robust than the traditional least-squares inversion algorithm. We use a multiple initial bed-boundary positions method to reduce the inversion uncertainty caused by uncertain bed-boundary positions. The initial bed-boundary positions could be restricted into defined ranges based on the investigation depth of LWD instruments, the geologic environment, and log data from adjacent wells. The slipping inversion window technique is also adopted to satisfy the real-time requirements and ensure that the inversion parameters are the global optima. Numerical simulations under different conditions demonstrate the high stability and superiority of the proposed method. Reliable inversion results can be used for routine petrophysical interpretation, accurate geosteering, and quantitative formation evaluation.
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De Franco, Allan Peixoto, Sérgio Adriano Moura Oliveira, and Fernando Sergio Moraes. "Uncertainty Analysis of Multicomponent Elastic Inversion of Thin-Layers." Brazilian Journal of Geophysics 39, no. 4 (June 7, 2022): 535. http://dx.doi.org/10.22564/rbgf.v39i4.2111.
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ABSTRACT. We assessed the effectiveness of seismic inversion in estimating the elastic properties of layers whose thickness represents a fraction of the wavelength. We used an approach that integrates a quantitative study of inversion uncertainties based on the stochastic Bayesian method and sensitivity analysis, considering the full waveform seismic response of the layer model. Three inversion input data combinations PP, PS, and joint PP-PS reflections provide comprehensive information for the analysis. Estimates of Vp, Vs, and the density of thin layers are sensitive to the intensity of the elastic property contrasts and incidence angle coverage. Results show that the elastic parameters of layers as thin as 1/16 of the peak wavelength can be estimated with low uncertainty if the input data contain incidence angles up to 40 degrees for the PP-PS case and up to 55 degrees for the PP case, when the elastic property contrast is not small.Keywords: stochastic inversion; reflectivity method; sensitivity analysis. Análise de Incertezas da Inversão Elástica Multicomponente de Camadas FinasRESUMO. Nós avaliamos a eficácia da inversão sísmica na estimativa das propriedades elásticas de camadas cuja espessura representa uma fração do comprimento de onda. Utilizamos uma abordagem que integra um estudo quantitativo de incertezas de inversão baseado no método estocástico Bayesiano e análise de sensibilidade, considerando a resposta sísmica completa da forma de onda do modelo de camadas. As análises foram realizadas em três combinações de dados de entrada para inversão: PP, PS e reflexões PP-PS conjuntas. As estimativas de Vp, Vs e densidade de camadas finas são sensíveis à intensidade dos contrastes de propriedades elásticas e à cobertura do ângulo de incidência. Os resultados mostram que os parâmetros elásticos de camadas tão finas quanto 1/16 do comprimento de onda de pico podem ser estimados com baixa incerteza se os dados de entrada contiverem ângulos de incidência de até 40 graus para o caso PP-PS e até 55 graus para o caso PP, quando o contraste da propriedade elástica não é pequeno.Palavras-chave: inversão estocástica; método da refletividade; análise de sensibilidade.
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Zaroukian, Erin. "Expressing numerical uncertainty." LSA Annual Meeting Extended Abstracts 1 (May 2, 2010): 16. http://dx.doi.org/10.3765/exabs.v0i0.495.
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In Russian, numeral expressions can be made approximate through Approximative Inversion, whereby the noun and the numeral appear to exchange positions. Approximative Inversion has been analyzed as head movement, where a head containing the noun raises to the left of the numeral, but this leads to incorrect semantics. I propose that Approximative Inversion involves post-nominal generation of the numeral in a reduced relative structure, where it is associated with a feature marking speaker uncertainty. This feature triggers a round-number reading of the numeral, resulting in what appears to be number approximation due to speaker uncertainty.
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Wang, Yilong, Grégoire Broquet, Philippe Ciais, Frédéric Chevallier, Felix Vogel, Lin Wu, Yi Yin, Rong Wang, and Shu Tao. "Potential of European <sup>14</sup>CO<sub>2</sub> observation network to estimate the fossil fuel CO<sub>2</sub> emissions via atmospheric inversions." Atmospheric Chemistry and Physics 18, no. 6 (March 28, 2018): 4229–50. http://dx.doi.org/10.5194/acp-18-4229-2018.
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Abstract. Combining measurements of atmospheric CO2 and its radiocarbon (14CO2) fraction and transport modeling in atmospheric inversions offers a way to derive improved estimates of CO2 emitted from fossil fuel (FFCO2). In this study, we solve for the monthly FFCO2 emission budgets at regional scale (i.e., the size of a medium-sized country in Europe) and investigate the performance of different observation networks and sampling strategies across Europe. The inversion system is built on the LMDZv4 global transport model at 3.75∘ × 2.5∘ resolution. We conduct Observing System Simulation Experiments (OSSEs) and use two types of diagnostics to assess the potential of the observation and inverse modeling frameworks. The first one relies on the theoretical computation of the uncertainty in the estimate of emissions from the inversion, known as “posterior uncertainty”, and on the uncertainty reduction compared to the uncertainty in the inventories of these emissions, which are used as a prior knowledge by the inversion (called “prior uncertainty”). The second one is based on comparisons of prior and posterior estimates of the emission to synthetic “true” emissions when these true emissions are used beforehand to generate the synthetic fossil fuel CO2 mixing ratio measurements that are assimilated in the inversion. With 17 stations currently measuring 14CO2 across Europe using 2-week integrated sampling, the uncertainty reduction for monthly FFCO2 emissions in a country where the network is rather dense like Germany, is larger than 30 %. With the 43 14CO2 measurement stations planned in Europe, the uncertainty reduction for monthly FFCO2 emissions is increased for the UK, France, Italy, eastern Europe and the Balkans, depending on the configuration of prior uncertainty. Further increasing the number of stations or the sampling frequency improves the uncertainty reduction (up to 40 to 70 %) in high emitting regions, but the performance of the inversion remains limited over low-emitting regions, even assuming a dense observation network covering the whole of Europe. This study also shows that both the theoretical uncertainty reduction (and resulting posterior uncertainty) from the inversion and the posterior estimate of emissions itself, for a given prior and “true” estimate of the emissions, are highly sensitive to the choice between two configurations of the prior uncertainty derived from the general estimate by inventory compilers or computations on existing inventories. In particular, when the configuration of the prior uncertainty statistics in the inversion system does not match the difference between these prior and true estimates, the posterior estimate of emissions deviates significantly from the truth. This highlights the difficulty of filtering the targeted signal in the model–data misfit for this specific inversion framework, the need to strongly rely on the prior uncertainty characterization for this and, consequently, the need for improved estimates of the uncertainties in current emission inventories for real applications with actual data. We apply the posterior uncertainty in annual emissions to the problem of detecting a trend of FFCO2, showing that increasing the monitoring period (e.g., more than 20 years) is more efficient than reducing uncertainty in annual emissions by adding stations. The coarse spatial resolution of the atmospheric transport model used in this OSSE (typical of models used for global inversions of natural CO2 fluxes) leads to large representation errors (related to the inability of the transport model to capture the spatial variability of the actual fluxes and mixing ratios at subgrid scales), which is a key limitation of our OSSE setup to improve the accuracy of the monitoring of FFCO2 emissions in European regions. Using a high-resolution transport model should improve the potential to retrieve FFCO2 emissions, and this needs to be investigated.
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Sambridge, Malcolm, Rhys Hawkins, and Jan Dettmer. "Taming uncertainty in geophysical inversion." ASEG Extended Abstracts 2016, no. 1 (December 2016): 1–5. http://dx.doi.org/10.1071/aseg2016ab134.
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Jessell, M., L. Aillères, E. de Kemp, M. Lindsay, F. Wellmann, M. Hillier, G. Laurent, T. Carmichael, and R. Martin. "Geological uncertainty and geophysical inversion." Geotectonic Research 97, no. 1 (September 1, 2015): 141. http://dx.doi.org/10.1127/1864-5658/2015-62.
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Ren, Zhengyong, and Thomas Kalscheuer. "Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data." Surveys in Geophysics 41, no. 1 (September 24, 2019): 47–112. http://dx.doi.org/10.1007/s10712-019-09567-3.
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Abstract A meaningful solution to an inversion problem should be composed of the preferred inversion model and its uncertainty and resolution estimates. The model uncertainty estimate describes an equivalent model domain in which each model generates responses which fit the observed data to within a threshold value. The model resolution matrix measures to what extent the unknown true solution maps into the preferred solution. However, most current geophysical electromagnetic (also gravity, magnetic and seismic) inversion studies only offer the preferred inversion model and ignore model uncertainty and resolution estimates, which makes the reliability of the preferred inversion model questionable. This may be caused by the fact that the computation and analysis of an inversion model depend on multiple factors, such as the misfit or objective function, the accuracy of the forward solvers, data coverage and noise, values of trade-off parameters, the initial model, the reference model and the model constraints. Depending on the particular method selected, large computational costs ensue. In this review, we first try to cover linearised model analysis tools such as the sensitivity matrix, the model resolution matrix and the model covariance matrix also providing a partially nonlinear description of the equivalent model domain based on pseudo-hyperellipsoids. Linearised model analysis tools can offer quantitative measures. In particular, the model resolution and covariance matrices measure how far the preferred inversion model is from the true model and how uncertainty in the measurements maps into model uncertainty. We also cover nonlinear model analysis tools including changes to the preferred inversion model (nonlinear sensitivity tests), modifications of the data set (using bootstrap re-sampling and generalised cross-validation), modifications of data uncertainty, variations of model constraints (including changes to the trade-off parameter, reference model and matrix regularisation operator), the edgehog method, most-squares inversion and global searching algorithms. These nonlinear model analysis tools try to explore larger parts of the model domain than linearised model analysis and, hence, may assemble a more comprehensive equivalent model domain. Then, to overcome the bottleneck of computational cost in model analysis, we present several practical algorithms to accelerate the computation. Here, we emphasise linearised model analysis, as efficient computation of nonlinear model uncertainty and resolution estimates is mainly determined by fast forward and inversion solvers. In the last part of our review, we present applications of model analysis to models computed from individual and joint inversions of electromagnetic data; we also describe optimal survey design and inversion grid design as important applications of model analysis. The currently available model uncertainty and resolution analyses are mainly for 1D and 2D problems due to the limitations in computational cost. With significant enhancements of computing power, 3D model analyses are expected to be increasingly used and to help analyse and establish confidence in 3D inversion models.
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Buland, Arild, Odd Kolbjørnsen, and Andrew J. Carter. "Bayesian Dix inversion." GEOPHYSICS 76, no. 2 (March 2011): R15—R22. http://dx.doi.org/10.1190/1.3552596.
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We have developed a Bayesian method for Dix inversion and illustrated it with examples from the North Sea. The method is a constrained Dix inversion in which the uncertainty of the estimated interval velocities is an integral part of the solution. The method combines available geologic prior knowledge with the information in the picked rms velocities so that the prior model stabilizes and constrains the inversion. The definition of layers or intervals is flexible. One possibility is the classical layering whereby the top and bottom of the intervals are defined directly from the times of the picked rms velocities, but the intervals can be defined arbitrarily and independent of the picked velocities. Even a pseudocontinuous velocity profile with dense time sampling can be predicted with corresponding uncertainty. The Dix inversion is conventionally formulated as a 1D inversion problem in the locations with picked rms velocities. Under the assumption that Dix inversion is adequate, we have defined a method for spatial prediction at any position in a 3D model. This involves spatial smoothing and interpolation, and provides a method for building a velocity cube with the corresponding uncertainty on any grid. Explicit analytic expressions were found for both the optimal solution and the uncertainty. In general, the uncertainty of the estimated interval velocities increases with depth and with decreasing layer thickness. The uncertainty of the spatial prediction decreases with increasing spatial correlation. Because the solution is of an explicit analytic form, the Bayesian Dix inversion is computationally fast and does not require stochastic simulation.
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Grifka, Jasmin, Maximilian Weigand, Andreas Kemna, and Thomas Heinze. "Impact of an Uncertain Structural Constraint on Electrical Resistivity Tomography for Water Content Estimation in Landslides." Land 11, no. 8 (July 31, 2022): 1207. http://dx.doi.org/10.3390/land11081207.
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Geoelectrical methods can be part of early warning systems for landslide-prone hillslopes by giving estimates of the water content distribution. Structurally constrained inversions of geoelectrical data can improve the water content estimation by reducing the smoothness constraint along known lithological boundaries, which is especially important for landslides, as often layers with strongly divergent hydrological parameters and varying electrical signatures are present in landslides. However, any a priori information about those boundaries has an intrinsic uncertainty. A detailed synthetic study and a field investigation are combined to study the influence of misplaced structural constraints and the strength of the smoothness reduction via a coupling coefficient on inversion results of electrical resistivity data. While a well-known lithological boundary with a substantial reduction of the smoothness constraint can significantly improve the inversion result, a flawed constraint can cause strong divergences from the synthetic model. The divergence can even grow above the divergence of a fully smoothed inversion result. For correctly placed structural constraints, a coupling coefficient smaller than 10−4 uncovers previously unseen dynamics in the resistivity distribution compared to smoothed inversion results. Uncertain layer boundaries can be included in the inversion process with a larger coupling coefficient to avoid flawed results as long as the uncertainty of the layer thickness is below 20%. The application to field data confirms these findings but is less sensitive to a further reduction of the coupling coefficient, probably due to uncertainties in the structural information.
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Yang, Xiuwei, Ningbo Mao, Peimin Zhu, and Dan Xiao. "Two-level uncertainty assessment in stochastic seismic inversion based on the gradual deformation method." GEOPHYSICS 85, no. 4 (June 15, 2020): M33—M42. http://dx.doi.org/10.1190/geo2019-0492.1.
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Geostatistical seismic inversion can combine seismic data, well data, and spatial continuity of the property of interest to obtain high-resolution reservoir models and evaluate uncertainties. Some workflows estimate global geostatistical parameters, such as correlation length, and keep them fixed in all simulations and inversions. This can introduce biases due to the sparsity of available well data and underestimate the uncertainty of inversion. A better approach is to incorporate the uncertainty in these global parameters. Lateral correlation length is one of the most difficult parameters to estimate. We have developed a seismic inversion method based on local gradual deformation method, which incorporates the uncertainty of lateral correlation length and provides a two-level uncertainty evaluation. We first estimate a uniform prior distribution of lateral correlation length from well data and additional geologic expert knowledge. After using fast Fourier transform (FFT) moving average simulations and local gradual deformation optimization, we obtain multiple realizations from which we could extract the lateral correlation lengths and calculate their posterior distribution. The FFT moving average method generates reservoir models by a convolution between a filter operator and a random noise field. The filter operator does not change during inversion, and the correlation structure of the random noise field could be changed by the local gradual deformation method to match the seismic data. A synthetic model test shows that the correlation lengths and the global probability distribution of the inverted results tend to the true geostatistical characteristics. The posterior distribution of the lateral correlation length narrows after inversion. Compared with conventional geostatistical seismic inversion techniques, uncertainties in the results increase because we incorporate the uncertainty in the global parameters. A real case also demonstrated that by modifying the random noise field locally, thin layers in a thick formation are well restored, even if they are not interpreted in advance.
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Peng, Ronghua, Pritam Yogeshwar, Yajun Liu, and Xiangyun Hu. "Transdimensional Markov Chain Monte Carlo joint inversion of direct current resistivity and transient electromagnetic data." Geophysical Journal International 224, no. 2 (November 10, 2020): 1429–42. http://dx.doi.org/10.1093/gji/ggaa535.
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SUMMARY Joint inversion of multiple geophysical data sets with complementary information content can significantly reduce the non-uniqueness inherent to each individual data set and, therefore, can improve subsurface characterization. Gradient-based joint inversion methods depend on the choice of model regularization and usually produce one single optimal model, and rely on linearization to estimate model parameter uncertainty. However, a quantitative evaluation of the parameter uncertainty of the derived model parameters is crucial for reliable data interpretation. In this study, we present a transdimensional Markov Chain Monte Carlo (MCMC) method for the joint inversion of direct current resistivity and transient electromagnetic data, which provides a rigorous assessment of the uncertainty associated with the derived model. The transdimensional property of the algorithm allows the number of unknown model parameters to be determined adaptively by the data. This usually favours models with fewer parameters through the parsimony criterion of the Bayesian method by choosing suitable prior distributions. In this paper, we demonstrate that the transdimensional MCMC method combines complementary information contained in each data set and reduces the overall uncertainty using synthetic examples. Furthermore, we successfully applied the new joint inversion scheme to field data from Azraq, Jordan. The transdimensional MCMC inversion results are in good agreement with the results obtained by deterministic inversion techniques. From the MCMC inversion results we identified the thickness of a basalt formation and a conductive zone, which were uncertain and not interpreted in prior studies, adding to the geological interpretation.
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Giraud, Jeremie, Mark Lindsay, Vitaliy Ogarko, Mark Jessell, Roland Martin, and Evren Pakyuz-Charrier. "Integration of geoscientific uncertainty into geophysical inversion by means of local gradient regularization." Solid Earth 10, no. 1 (January 25, 2019): 193–210. http://dx.doi.org/10.5194/se-10-193-2019.
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Abstract. We introduce a workflow integrating geological modelling uncertainty information to constrain gravity inversions. We test and apply this approach to the Yerrida Basin (Western Australia), where we focus on prospective greenstone belts beneath sedimentary cover. Geological uncertainty information is extracted from the results of a probabilistic geological modelling process using geological field data and their inferred accuracy as inputs. The uncertainty information is utilized to locally adjust the weights of a minimum-structure gradient-based regularization function constraining geophysical inversion. Our results demonstrate that this technique allows geophysical inversion to update the model preferentially in geologically less certain areas. It also indicates that inverted models are consistent with both the probabilistic geological model and geophysical data of the area, reducing interpretation uncertainty. The interpretation of inverted models reveals that the recovered greenstone belts may be shallower and thinner than previously thought.
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Ardid, Alberto, David Dempsey, Edward Bertrand, Fabian Sepulveda, Pascal Tarits, Flora Solon, and Rosalind Archer. "Bayesian magnetotelluric inversion using methylene blue structural priors for imaging shallow conductors in geothermal fields." GEOPHYSICS 86, no. 3 (April 8, 2021): E171—E183. http://dx.doi.org/10.1190/geo2020-0226.1.
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In geothermal exploration, magnetotelluric (MT) data and inversion models are commonly used to image shallow conductors typically associated with the presence of an electrically conductive clay cap that overlies the main reservoir. However, these inversion models suffer from nonuniqueness and uncertainty, and the inclusion of useful geologic information is still limited. We have developed a Bayesian inversion method that integrates the electrical resistivity distribution from MT surveys with borehole methylene blue (MeB) data, an indicator of conductive clay content. The MeB data were used to inform structural priors for the MT Bayesian inversion that focus on inferring with uncertainty the shallow conductor boundary in geothermal fields. By incorporating borehole information, our inversion reduced nonuniqueness and then explicitly represented the irreducible uncertainty as estimated depth intervals for the conductor boundary. We used the Markov chain Monte Carlo and a 1D three-layer resistivity model to accelerate the Bayesian inversion of the MT signal beneath each station. Then, inferred conductor boundary distributions were interpolated to construct pseudo-2D/3D models of the uncertain conductor geometry. We compare our approach against deterministic MT inversion software on synthetic and field examples, and our approach has good performance in estimating the depth to the bottom of the conductor, a valuable target in geothermal reservoir exploration.
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Houck, Richard T., Adrian Ciucivara, and Scott Hornbostel. "Accuracy and effectiveness of three-dimensional controlled source electromagnetic data inversions." GEOPHYSICS 80, no. 2 (March 1, 2015): E83—E95. http://dx.doi.org/10.1190/geo2014-0142.1.
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Unconstrained 3D inversion of marine controlled source electromagnetic data (CSEM) data sets produces resistivity volumes that have an uncertain relationship to the true subsurface resistivity at the scale of typical hydrocarbon reservoirs. Furthermore, CSEM-scale resistivity is an ambiguous indicator of hydrocarbon presence; not all resistivity anomalies are caused by hydrocarbon reservoirs, and not all hydrocarbon reservoirs produce a distinct resistivity anomaly. We have developed a method for quantifying the effectiveness of resistivities from CSEM inversion in detecting hydrocarbon reservoirs. Our approach uses probabilistic rock-physics modeling to update information from a preexisting prospect assessment, based on uncertain resistivities from CSEM. The result is an estimate the probability of hydrocarbon presence that accounts for uncertainty in the resistivity and in rock properties. Examples using synthetic and real CSEM data sets demonstrate that the effectiveness of CSEM inversion in identifying hydrocarbon reservoirs depends on the interaction between the uncertainty associated with the inversion-derived resistivity and the range of rock and fluid properties that were expected for the targeted prospect. Resistivity uncertainty that has a small effect on hydrocarbon probability for one set of rock property distributions may have a large effect for a different set of rock properties. Depending on the consequences of this interaction, resistivities from CSEM inversion might reduce the risk associated with predictions of hydrocarbon presence, but they cannot be expected to guarantee a specific well outcome.
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Pereira, Pedro, Fernando Bordignon, Leonardo Azevedo, Ruben Nunes, and Amílcar Soares. "Strategies for integrating uncertainty in iterative geostatistical seismic inversion." GEOPHYSICS 84, no. 2 (March 1, 2019): R207—R219. http://dx.doi.org/10.1190/geo2017-0758.1.
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Iterative geostatistical seismic inversion integrates seismic and well data to infer the spatial distribution of subsurface elastic properties. These methods provide limited assessment to the spatial uncertainty of the inverted elastic properties, overlooking alternative sources of uncertainty such as those associated with poor well-log data, upscaling, and noise within the seismic data. We have expressed uncertain well-log samples, due to bad logging reads and upscaling, in terms of local probability distribution functions (PDFs). Local PDFs are used as conditioning data to a stochastic sequential simulation algorithm, included as the model perturbation within the inversion. The problem of noisy seismic and narrow exploration of the model parameter space, particularly in the early steps of the inversion, is tackled by the introduction of a cap on local correlation coefficients (CCs) responsible for the generation of the new set of models during the next iteration. We evaluate a single geostatistical framework with application to a real case study. When compared against a conventional iterative geostatistical seismic inversion, the integration of additional sources of uncertainty increases the match between real and inverted seismic traces and the variability within the ensemble of models inverted at the last iteration. The selection of the local PDFs plays a central role in the reliability of the inverted elastic models. Avoiding high local CCs at early stages of the inversion increases convergence in terms of global correlation between synthetic and real seismic reflection data at the end of the inversion.
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Palmer, Derecke. "Uncertainty in Near-Surface Refraction Inversion." ASEG Extended Abstracts 2012, no. 1 (December 2012): 1–4. http://dx.doi.org/10.1071/aseg2012ab410.
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Chapman, N. Ross. "Measures of uncertainty in geoacoustic inversion." Journal of the Acoustical Society of America 113, no. 4 (April 2003): 2190. http://dx.doi.org/10.1121/1.4780132.
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Imhof, Matthias G., and Arvind K. Sharma. "Seismostratigraphic inversion: Appraisal, ambiguity, and uncertainty." GEOPHYSICS 72, no. 4 (July 2007): R51—R66. http://dx.doi.org/10.1190/1.2720496.
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Geologic process models predict the geometry of geologic strata and their petrophysical properties, based on mathematical models of geological processes that affect the formation and evolution of geologic strata. Such processes include erosion, sediment transport, and deposition. The resulting forward model is typically nonlinear. Given observations and a misfit measure, one may attempt inversion of these models to estimate process parameters that yield compatible predictions. For seismostratigraphic inversion, seismic data are used as observations. We tested such an algorithm in a prograding-delta environment to examine the effect of using different seismic attributes as observations and, thus, different choices of misfit measures. The first measure,based on the degree of parallelism between seismic reflectors and modeled geologic strata, demonstrated a trade-off between geologic time and the sediment-influx rate used to parameterize the model. A second misfit measure used unwrapped seismic instantaneous phase as a crude proxy to relative geologic time, which regularized the model parameters. Then last, we combined the two measures to take advantage of their individual characteristics. For most of these inversion experiments, we obtained results that capture the geometry of the geologic strata as observed on the seismic data. With the exception of the depositional time-rate trade-off, where the same strata can be obtained in a shorter geologic interval when rates are increased, we found the inversion to be surprisingly stable, with a unique cluster of acceptable parameters, despite the nonlinearity of the geologic forward model.
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Fernández-Muñiz, Zulima, Hassan Khaniani, and Juan Luis Fernández-Martínez. "Data kit inversion and uncertainty analysis." Journal of Applied Geophysics 161 (February 2019): 228–38. http://dx.doi.org/10.1016/j.jappgeo.2018.12.022.
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Talarico, Erick Costa e. Silva, Dario Grana, Leandro Passos de Figueiredo, and Sinesio Pesco. "Uncertainty quantification in seismic facies inversion." GEOPHYSICS 85, no. 4 (June 24, 2020): M43—M56. http://dx.doi.org/10.1190/geo2019-0392.1.
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In seismic reservoir characterization, facies prediction from seismic data often is formulated as an inverse problem. However, the uncertainty in the parameters that control their spatial distributions usually is not investigated. In a probabilistic setting, the vertical distribution of facies often is described by statistical models, such as Markov chains. Assuming that the transition probabilities in the vertical direction are known, the most likely facies sequence and its uncertainty can be obtained by computing the posterior distribution of a Bayesian inverse problem conditioned by seismic data. Generally, the model hyperparameters such as the transition matrix are inferred from seismic data and nearby wells using a Bayesian inference framework. It is assumed that there is a unique set of hyperparameters that optimally fit the measurements. The novelty of the proposed work is to investigate the nonuniqueness of the transition matrix and show the multimodality of their distribution. We then generalize the Bayesian inversion approach based on Markov chain models by assuming that the hyperparameters, the facies prior proportions and transition matrix, are unknown and derive the full posterior distribution. Including all of the possible transition matrices in the inversion improves the uncertainty quantification of the predicted facies conditioned by seismic data. Our method is demonstrated on synthetic and real seismic data sets, and it has high relevance in exploration studies due to the limited number of well data and in geologic environments with rapid lateral variations of the facies vertical distribution.
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Simpson, Janelle, and Graham Heinson. "Estimating interpretation uncertainty from magnetotelluric inversion." ASEG Extended Abstracts 2019, no. 1 (November 11, 2019): 1–5. http://dx.doi.org/10.1080/22020586.2019.12073138.
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Keating, Scott D., and Kristopher A. Innanen. "Null-space shuttles for targeted uncertainty analysis in full-waveform inversion." GEOPHYSICS 86, no. 1 (January 1, 2021): R63—R76. http://dx.doi.org/10.1190/geo2020-0192.1.
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Full-waveform inversion (FWI) is an effective tool for recovering subsurface information, but many factors make this recovery subject to uncertainty. In particular, unwanted noise in measurements can bias results toward models that are not representative of the true subsurface and numerical optimization techniques used in the inversion only allow for approximate minimization of the objective function. Both factors contribute to the nonuniqueness of FWI solutions. Assessing the uncertainty that this nonuniqueness introduces can be difficult, due to the large dimensionality of the inversion problem. Fortunately, complete characterization of inversion uncertainty is seldom necessary for applications using an inversion result, meaning that the entire dimensionality of the problem may not be relevant for practical uncertainty quantification. Typically, it is only the uncertainty in a few specific aspects of the inversion that is important (for instance, confidence in a recovered anomaly). A targeted uncertainty quantification, characterizing only the confidence in a specific feature of the subsurface model, can greatly reduce the dimensionality of the uncertainty characterization problem, potentially making it tractable. We have adopted an approach for quantifying the confidence of the inversion in a chosen hypothesis about the recovered subsurface model. We tested each hypothesis through numerical optimization on the set of equal-objective model-space steps, called null-space shuttles. By approximating the null-space shuttle that maximally violates a given hypothesis about the inversion, this method establishes an effective approximation of the uncertainty in that hypothesis. We tested the use of this technique on several numerical examples for the case of viscoelastic inversion. These examples demonstrate that, at a reasonable computational cost, this method can generate estimates of the lower bound on the maximal uncertainty associated with incomplete numerical optimization. In the viscoelastic examples considered, the velocity variables are much better constrained than the [Formula: see text] and density variables according to this metric.
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Tan, Zeli, Qianlai Zhuang, Daven K. Henze, Christian Frankenberg, Ed Dlugokencky, Colm Sweeney, Alexander J. Turner, Motoki Sasakawa, and Toshinobu Machida. "Inverse modeling of pan-Arctic methane emissions at high spatial resolution: what can we learn from assimilating satellite retrievals and using different process-based wetland and lake biogeochemical models?" Atmospheric Chemistry and Physics 16, no. 19 (October 12, 2016): 12649–66. http://dx.doi.org/10.5194/acp-16-12649-2016.
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Abstract. Understanding methane emissions from the Arctic, a fast-warming carbon reservoir, is important for projecting future changes in the global methane cycle. Here we optimized methane emissions from north of 60° N (pan-Arctic) regions using a nested-grid high-resolution inverse model that assimilates both high-precision surface measurements and column-average SCanning Imaging Absorption spectroMeter for Atmospheric CHartogrphY (SCIAMACHY) satellite retrievals of methane mole fraction. For the first time, methane emissions from lakes were integrated into an atmospheric transport and inversion estimate, together with prior wetland emissions estimated with six biogeochemical models. In our estimates, in 2005, global methane emissions were in the range of 496.4–511.5 Tg yr−1, and pan-Arctic methane emissions were in the range of 11.9–28.5 Tg yr−1. Methane emissions from pan-Arctic wetlands and lakes were 5.5–14.2 and 2.4–14.2 Tg yr−1, respectively. Methane emissions from Siberian wetlands and lakes are the largest and also have the largest uncertainty. Our results indicate that the uncertainty introduced by different wetland models could be much larger than the uncertainty of each inversion. We also show that assimilating satellite retrievals can reduce the uncertainty of the nested-grid inversions. The significance of lake emissions cannot be identified across the pan-Arctic by high-resolution inversions, but it is possible to identify high lake emissions from some specific regions. In contrast to global inversions, high-resolution nested-grid inversions perform better in estimating near-surface methane concentrations.
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Sengupta, Madhumita, Houzhu Zhang, Yang Zhao, Mike Jervis, and Dario Grana. "Direct depth-domain Bayesian amplitude-variation-with-offset inversion." GEOPHYSICS 86, no. 5 (August 2, 2021): M167—M176. http://dx.doi.org/10.1190/geo2020-0219.1.
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We have developed a new approach to perform Bayesian linearized amplitude-variation-with-offset (AVO) inversion in the depth domain using nonstationary wavelets. Bayesian linearized AVO inversion, a hybrid approach combining physics-based models with statistical learning, has gained immense popularity because of its superior computational speed and ability to estimate uncertainties in inverted model parameters. Bayesian linearized AVO inversion is performed on time-domain seismic data; therefore, depth-imaged seismic cannot be inverted directly using this method and would require depth-to-time conversion before AVO inversion can be done. Subsequently, time-to-depth conversion of the inverted volumes would be required for reservoir modeling and well placement. Domain conversions introduce additional uncertainty in geophysical workflows. In conventional AVO inversion, the seismic wavelet is assumed to be stationary, and this assumption leads to a restriction in the length of the time window over which the inversion can be performed. Therefore, AVO inversion is usually restricted to a narrow time window around the target of interest, and if multiple targets are present at different depths, multiple inversions must be run on the same volume. Depth-domain amplitude inversion is a recent development and has been previously presented in an iterative formulation. Implementing linearized Bayesian inversion directly in the depth domain using nonstationary wavelets is a convenient new approach that takes advantage of superior computational speed and uncertainty quantification without compromising the accurate spatial location that depth imaging provides. Combining these two ideas creates a novel, unique, and powerful seismic inversion technique that can be useful for quantitative interpretation and reservoir characterization.
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Buland, Arild, and Youness El Ouair. "Bayesian time-lapse inversion." GEOPHYSICS 71, no. 3 (May 2006): R43—R48. http://dx.doi.org/10.1190/1.2196874.
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A new, fast inversion approach for time-lapse seismic data is developed where the uncertainty of the inversion results is an integral part of the solution. The inversion method estimates changes in the elastic material properties of a reservoir because of production of hydrocarbons, including uncertainty bounds on these estimates. The changes in elastic properties then can be related to changes in hydrocarbon saturation and reservoir pressure by using rock-physics relations. The inversion operates directly on the difference between a repeat survey and a baseline survey. This is advantageous with respect to the uncertainty calculation, because an estimate of the seismic uncertainty can be obtained directly from the difference data in zones not affected by production. The method is formulated in a Bayesian setting, and the solution is represented by explicit expressions for the posterior expectation and the covariance of the elastic parameter changes. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Results of the applied approach to a real data set from the Norne field are consistent with the expected effects of water flushing because of water injection.
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Chevallier, Frédéric, Marine Remaud, Christopher W. O'Dell, David Baker, Philippe Peylin, and Anne Cozic. "Objective evaluation of surface- and satellite-driven carbon dioxide atmospheric inversions." Atmospheric Chemistry and Physics 19, no. 22 (November 26, 2019): 14233–51. http://dx.doi.org/10.5194/acp-19-14233-2019.
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Abstract. We study an ensemble of six multi-year global Bayesian carbon dioxide (CO2) atmospheric inversions that vary in terms of assimilated observations (either column retrievals from one of two satellites or surface air sample measurements) and transport model. The time series of inferred annual fluxes are first compared with each other at various spatial scales. We then objectively evaluate the small inversion ensemble based on a large dataset of accurate aircraft measurements in the free troposphere over the globe, which are independent of all assimilated data. The measured variables are connected with the inferred fluxes through mass-conserving transport in the global atmosphere and are part of the inversion results. Large-scale annual fluxes estimated from the bias-corrected land retrievals of the second Orbiting Carbon Observatory (OCO-2) differ greatly from the prior fluxes, but are similar to the fluxes estimated from the surface network within the uncertainty of these surface-based estimates. The OCO-2-based and surface-based inversions have similar performance when projected in the space of the aircraft data, but the relative strengths and weaknesses of the two flux estimates vary within the northern and tropical parts of the continents. The verification data also suggest that the more complex and more recent transport model does not improve the inversion skill. In contrast, the inversion using bias-corrected retrievals from the Greenhouse Gases Observing Satellite (GOSAT) or, to a larger extent, a non-Bayesian inversion that simply adjusts a recent bottom-up flux estimate with the annual growth rate diagnosed from marine surface measurements both estimate much different fluxes and fit the aircraft data less. Our study highlights a way to rate global atmospheric inversions. Without any general claim regarding the usefulness of all OCO-2 retrieval datasets vs. all GOSAT retrieval datasets, it still suggests that some satellite retrievals can now provide inversion results that are, despite their uncertainty, comparable with respect to credibility to traditional inversions using the accurate but sparse surface network and that are therefore complementary for studies of the global carbon budget.
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Sinha, Supriya, Arthur Walmsley, Nigel Clegg, Brigido Vicuña, Hsu-Hsiang (Mark) Wu, Andrew McGill, Téo Paiva dos Reis, et al. "Past, Present, and Future Applications of Ultradeep Directional Resistivity Measurements: A Case History From the Norwegian Continental Shelf." Petrophysics – The SPWLA Journal of Formation Evaluation and Reservoir Description 63, no. 6 (December 1, 2022): 604–33. http://dx.doi.org/10.30632/pjv63n6-2022a3.
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With the introduction of ultradeep azimuthal resistivity (UDAR) logging-while-drilling (LWD) tools toward the beginning of the last decade, the oil and gas industry went from real-time mapping of formation boundaries a few meters from the wellbore to tens of meters away. This innovation allowed early identification of resistivity boundaries and promoted proactive geosteering, allowing for optimization of the wellbore position. Additionally, boundaries and secondary targets that may never be intersected are mapped, allowing for improved well planning for sidetracks, multilaterals, and future wells. Modern tool design and inversion algorithms allow mapping the reservoir in 3D and exploring the sensitivity of these tools to the electromagnetic field ahead of the measure point for look-ahead resistivity. Improvements in the technology over the past decade have changed the way wellbores are planned, drilled, and completed, and reservoir models are updated. This paper presents a case study summarizing the advances in UDAR measurements and inversions over the last decade. The case study presents the whole workflow from prejob planning, service design, and execution of one-dimensional (1D) and three-dimensional (3D) inversion in addition to the future potential of look ahead in horizontal wells. Prewell simulations provide a guide to expected real-time tool responses in highly heterogeneous formations. This identifies how far from the wellbore 1D inversions can map major boundaries above and below the well. A fault was expected toward the toe of the well, and UDAR was used as a safeguard to avoid exiting the reservoir. Standard 1D inversion approaches are too simplistic in this complex geologic setting. Thus, 3D inversion around the wellbore and ahead of the transmitter is also explored to demonstrate the improvements this understanding can bring regarding geostopping toward the fault and reservoir understanding in general. Successful geosteering requires personnel trained to handle complex scenarios. Geosteering training simulators (GTS) could be efficient tools for training to interpret inversions where the “truth” is known from realistic 3D model scenarios. The team can learn how to best exploit UDAR technology and inversion results within its limits and not extend the interpretation beyond acceptable uncertainty levels. It will also be addressed how the understanding of inversion uncertainty could be updated in real time in the future. The continued future success of UDAR technology and 1D to 3D inversion results for look-ahead and look-around applications will depend heavily on uncertainty management of the inversions to avoid wrong decisions and potentially reduced well economy.
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Azevedo, Leonardo, and Vasily Demyanov. "Multiscale uncertainty assessment in geostatistical seismic inversion." GEOPHYSICS 84, no. 3 (May 1, 2019): R355—R369. http://dx.doi.org/10.1190/geo2018-0329.1.
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Geostatistical seismic inversion is commonly used to infer the spatial distribution of the subsurface petroelastic properties by perturbing the model parameter space through iterative stochastic sequential simulations/co-simulations. The spatial uncertainty of the inferred petroelastic properties is represented with the updated a posteriori variance from an ensemble of the simulated realizations. Within this setting, petroelastic realizations are generated assuming stationary and known large-scale geologic parameters (metaparameters), such as the spatial correlation model and the global a priori distribution of the properties of interest, for the entire inversion domain. This assumption leads to underestimation of the uncertainty associated with the inverted models. We have developed a practical framework to quantify uncertainty of the large-scale geologic parameters in geostatistical seismic inversion. The framework couples geostatistical seismic inversion with a stochastic adaptive sampling and Bayesian inference of the metaparameters to provide a more accurate and realistic prediction of uncertainty not restricted by heavy assumptions on large-scale geologic parameters. The proposed framework is illustrated with synthetic and real case studies. The results indicate the ability to retrieve more reliable acoustic impedance models with a more adequate uncertainty spread when compared with conventional geostatistical seismic inversion techniques. The proposed approach accounts for geologic uncertainty at the large scale (metaparameters) and the local scale (trace-by-trace inversion).
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Trainor-Guitton, Whitney, and G. Michael Hoversten. "Stochastic inversion for electromagnetic geophysics: Practical challenges and improving convergence efficiency." GEOPHYSICS 76, no. 6 (November 2011): F373—F386. http://dx.doi.org/10.1190/geo2010-0223.1.
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Traditional deterministic geophysical inversion algorithms are not designed to provide a robust evaluation of uncertainty that reflects the limitations of the geophysical technique. Stochastic inversions, which do provide a sampling-based measure of uncertainty, are computationally expensive and not straightforward to implement for nonexperts (nonstatisticians). Our results include stochastic inversion for magnetotelluric and controlled source electromagnetic data. Two Markov Chain sampling algorithms (Metropolis-Hastings and Slice Sampler) can significantly decrease the computational expense compared to using either sampler alone. The statistics of the stochastic inversion allow for (1) variances that better reveal the measurement sensitivities of the two different electromagnetic techniques than traditional techniques and (2) models defined by the median and modes of parameter probability density functions, which produce amplitude and phase data that are consistent with the observed data. In general, parameter error estimates from the covariance matrix significantly underestimate the true parameter error, whereas the parameter variance derived from Markov chains accurately encompass the error.
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Zhu, Dehan, and Richard Gibson. "Seismic inversion and uncertainty quantification using transdimensional Markov chain Monte Carlo method." GEOPHYSICS 83, no. 4 (July 1, 2018): R321—R334. http://dx.doi.org/10.1190/geo2016-0594.1.
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We applied a transdimensional stochastic inversion algorithm, reversible jump Markov chain Monte Carlo (rjMCMC), to angle-stack seismic inversion for characterization of reservoir acoustic and shear impedance with uncertainty quantification. The rjMCMC is able to infer the number of parameters for the model as well as the parameter values. In our case, the number of parameters depends on the number of model layers for a given data set. We also use this method in uncertainty quantification because a transdimensional sampling helps prevent underparameterization or strong overparameterization. An ensemble of models with proper parameterization can improve parameter estimation and uncertainty quantification. Our new results in uncertainty analysis indicate that (1) the uncertainty in seismic inversion, including uncertainty in earth properties and their locations, is related to the discontinuity of property across an interface, and (2) there is a trade-off between property uncertainty and location uncertainty. A stronger discontinuity will induce more property uncertainty but less location uncertainty at the discontinuity interface. Therefore, we further use the inversion uncertainty as a novel seismic attribute to assist in delineation of subsurface discontinuity interfaces and quantify the magnitude of the discontinuities, which further facilitates quantitative interpretation and stratigraphic interpretation.
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Bredesen, Kenneth, Ian Herbert, Florian Smit, Ask Frode Jakobsen, Peter Frykman, and Anders Bruun. "Characterizing a Wedged Chalk Prospect in the Danish Central Graben Using Direct Probabilistic Inversion." Geosciences 12, no. 5 (April 29, 2022): 194. http://dx.doi.org/10.3390/geosciences12050194.
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A novel direct probabilistic inversion using seismic pre-stack data as input to characterize a wedged chalk reservoir prospect was demonstrated from the Upper Cretaceous unit, Danish North Sea. The objective was to better resolve the lateral extent and pinch-out of the chalk prospect in a frontier exploration setting and compare the results with a more traditional deterministic inversion and geostatistical reservoir modeling. The direct probabilistic inversion results provided additional reservoir insights that were challenging to obtain from the more traditional workflows and are also more flexible for associated uncertainty assessments. Hence, this study demonstrates the usefulness of such direct probabilistic inversions even with suboptimal data availability.
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Thore, Pierre. "Uncertainty in seismic inversion: What really matters?" Leading Edge 34, no. 9 (September 2015): 1000–1004. http://dx.doi.org/10.1190/tle34091000.1.
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Dosso, Stan E. "Matched‐field inversion for geoacoustic uncertainty distributions." Journal of the Acoustical Society of America 104, no. 3 (September 1998): 1740. http://dx.doi.org/10.1121/1.423622.
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Song, Yi-Qiao. "Resolution and uncertainty of Laplace inversion spectrum." Magnetic Resonance Imaging 25, no. 4 (May 2007): 445–48. http://dx.doi.org/10.1016/j.mri.2006.11.023.
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Du, Jing, and Norm R. Warpinski. "Uncertainty in FPSs from moment-tensor inversion." GEOPHYSICS 76, no. 6 (November 2011): WC65—WC75. http://dx.doi.org/10.1190/geo2011-0024.1.
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Although microseismic monitoring of hydraulic fractures has primarily been concerned with the dimensions, complexity, and growth of fractures or fracture systems, there is an ever-increasing desire to extract more information about the hydraulic-fracturing and/or natural fractures from microseismic data. Source mechanism analysis, which is concerned with deducing details of the failure process from the microseismic waveform data, is, therefore, attracting more attention. However, most of the studies focus more on the moment-tensor inversion than on extracting fault-plane solutions (FPSs) from inverted moment tensors. The FPSs can be extracted from the inverted moment-tensor, but there remains a question regarding how errors associated with the inversion of the moment-tensor affect the accuracy of the FPSs. We examine the uncertainties of FPS, given the uncertainties of the amplitude data, by looking into the uncertainty propagation from amplitude data into the moment-tensor and then into the resultant FPS. The uncertainty propagation method will be demonstrated using two synthetic examples.
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Nickless, Alecia, Peter J. Rayner, Robert J. Scholes, Francois Engelbrecht, and Birgit Erni. "An atmospheric inversion over the city of Cape Town: sensitivity analyses." Atmospheric Chemistry and Physics 19, no. 11 (June 12, 2019): 7789–816. http://dx.doi.org/10.5194/acp-19-7789-2019.
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Abstract. An atmospheric inversion was performed for the city of Cape Town for the period of March 2012 to June 2013, making use of in situ measurements of CO2 concentrations at temporary measurement sites located to the north-east and south-west of Cape Town. This paper presents results of sensitivity analyses that tested assumptions regarding the prior information and the uncertainty covariance matrices associated with the prior fluxes and with the observations. Alternative prior products were considered in the form of a carbon assessment analysis to provide biogenic fluxes and the ODIAC (Open-source Data Inventory for Anthropogenic CO2 product) fossil fuel product. These were used in place of the reference inversion's biogenic fluxes from CABLE (Community Atmosphere Biosphere Land Exchange model) and fossil fuel emissions from a bespoke inventory analysis carried out specifically for the Cape Town inversion. Our results confirmed that the inversion solution was strongly dependent on the prior information, but by using independent alternative prior products to run multiple inversions, we were able to infer limits for the true domain flux. Where the reference inversion had aggregated prior flux estimates that were made more positive by the inversion – suggesting that CABLE was overestimating the amount of CO2 biogenic uptake – the carbon assessment prior fluxes were made more negative by the inversion. As the posterior estimates tended towards the same point, we could infer that the best estimate was located somewhere between these two posterior fluxes. The inversion was shown to be sensitive to the spatial error correlation length in the biogenic fluxes – even a short correlation length – influencing the spatial distribution of the posterior fluxes, the size of the aggregated flux across the domain, and the uncertainty reduction achieved by the inversion. Taking advantage of expected spatial correlations in the fluxes is key to maximizing the use of a limited observation network. Changes to the temporal correlations in the observation errors had a very minor effect on the inversion. The control vector in the original version consisted of separate daytime and night-time weekly fluxes for fossil fuel and biogenic fluxes over a 4-week inversion period. When we considered solving for mean weekly fluxes over each 4-week period – i.e. assuming the flux remained constant over the month – larger changes to the prior fossil fuel and biogenic fluxes were possible, as well as further changes to the spatial distribution of the fluxes compared with the reference. The uncertainty reduction achieved in the estimation of the overall flux increased from 25.6 % for the reference inversion to 47.2 % for the mean weekly flux inversion. This demonstrates that if flux components that change slowly can be solved for separately in the inversion, where these fluxes are assumed to be constant over long periods of time, the posterior estimates of these fluxes substantially benefit from the additional observational constraint. In summary, estimates of Cape Town fluxes can be improved by using better and multiple prior information sources, and particularly on biogenic fluxes. Fossil fuel and biogenic fluxes should be broken down into components, building in knowledge of spatial and temporal consistency in these components into the control vector and uncertainties specified for the sources for the inversion. This would allow the limited observations to provide maximum constraint on the flux estimates.
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Kubo, Hisahiko, Wataru Suzuki, and Akemi Noda. "Effect of fault discretization on geodetic source inversion and usefulness of the trans-dimensional inversion approach." Geophysical Journal International 229, no. 2 (December 23, 2021): 1063–76. http://dx.doi.org/10.1093/gji/ggab515.
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SUMMARY Earthquake source inversion, which estimates the heterogeneous slip distribution on fault from geophysical data, is a fundamental technique for estimating earthquake rupture process and obtaining information about the physics of fault rupture. Source inversion requires the spatial discretization of fault, which can be performed uniformly and non-uniformly. Uniform fault discretization is a conventional approach that requires smoothing and/or non-negative constraints of slips as prior information to obtain a stable and reliable solution; however, the combination of uniform discretization and these prior constraints may distort a source-inversion solution. As a non-uniform discretization approach, source inversion using a trans-dimensional inversion approach has recently attracted attention. To study the effect of fault discretization on geodetic source inversion, through the analysis of geodetic data on the 2015 Gorkha, Nepal, earthquake and synthetic tests, we investigated what kind of solution the conventional source inversion with uniform discretization and the trans-dimensional source inversion provide and what kind of uncertainty their solutions have. We found that the combination of uniform discretization and non-negative constraint led to excessively smooth solutions with poor data fit. Even without using the non-negative constraint, the conventional inversion with uniform discretization provided distorted and sometimes overfitted solutions, which could not be identified based on uncertainty information. In contrast, the trans-dimensional source inversion provided reasonable solutions composed only of meaningful slips, which were required to explain the data. We also found that uncertainty information depends on the source-inversion method; consequently, the evaluation of method-induced uncertainty is difficult. This suggests that we look at earthquake ruptures through the lens of source inversion with inherent method-dependent bias.
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Rumpf, M., and J. Tronicke. "Assessing uncertainty in refraction seismic traveltime inversion using a global inversion strategy." Geophysical Prospecting 63, no. 5 (April 6, 2015): 1188–97. http://dx.doi.org/10.1111/1365-2478.12240.
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Bobe, Christin, Daan Hanssens, Thomas Hermans, and Ellen Van De Vijver. "Efficient Probabilistic Joint Inversion of Direct Current Resistivity and Small-Loop Electromagnetic Data." Algorithms 13, no. 6 (June 18, 2020): 144. http://dx.doi.org/10.3390/a13060144.
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Often, multiple geophysical measurements are sensitive to the same subsurface parameters. In this case, joint inversions are mostly preferred over two (or more) separate inversions of the geophysical data sets due to the expected reduction of the non-uniqueness in the joint inverse solution. This reduction can be quantified using Bayesian inversions. However, standard Markov chain Monte Carlo (MCMC) approaches are computationally expensive for most geophysical inverse problems. We present the Kalman ensemble generator (KEG) method as an efficient alternative to the standard MCMC inversion approaches. As proof of concept, we provide two synthetic studies of joint inversion of frequency domain electromagnetic (FDEM) and direct current (DC) resistivity data for a parameter model with vertical variation in electrical conductivity. For both studies, joint results show a considerable improvement for the joint framework over the separate inversions. This improvement consists of (1) an uncertainty reduction in the posterior probability density function and (2) an ensemble mean that is closer to the synthetic true electrical conductivities. Finally, we apply the KEG joint inversion to FDEM and DC resistivity field data. Joint field data inversions improve in the same way seen for the synthetic studies.
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Far, Mehdi E., Bob Hardage, and Don Wagner. "Fracture parameter inversion for Marcellus Shale." GEOPHYSICS 79, no. 3 (May 1, 2014): C55—C63. http://dx.doi.org/10.1190/geo2013-0236.1.
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We inverted P-wave amplitude variation with offset and azimuth (AVOAz) data from the Marcellus Shale to obtain fracture parameters that can fully describe the elastic behavior of fractured rocks with overall symmetry of orthorhombic or monoclinic. AVOAz data from two interfaces, (1) the upper interface between top Marcellus and Stafford limestone and (2) the lower interface between base Marcellus and Onondaga limestone, were used for inversion. To check the validity of our inversion results, fracture parameters for the Marcellus Shale were inverted for each interface using Monte Carlo simulation to include uncertainty in our a priori information, i.e., elastic properties of unfractured rocks that are assumed to be known from well logs. Inversion results appeared robust with respect to uncertainties and converge to the same values for the two inversions. Our results were also consistent with singular value decomposition analysis (resolution matrix).
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Lee, Jejung, Abdallah Sayyed-Ahmad, and Dong-Hoon Sheen. "Basin model inversion using information theory and seismic data." GEOPHYSICS 72, no. 6 (November 2007): R99—R108. http://dx.doi.org/10.1190/1.2757738.
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We present a new approach to basin-model inversion in which uncertain parameters in a basin model are estimated using information theory and seismic data. We derive a probability function from information theory to quantify uncertainties in the estimated parameters in basin modeling. The derivation requires two constraints: a normalization and a misfit constraint. The misfit constraint uses seismic information by minimizing the difference between calculated seismograms from a basin simulator and observed seismograms. The information-theory approach emphasizes the relative difference between the so-called expected and calculated minima of the misfit function. The synthetic-model application shows that the greater the difference between the expected and calculated minima of the misfit function, the larger the uncertainty in parameter estimation. Uncertainty analysis provides secondary information on how accurately the inversion process is performed in basin modeling.
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Hadavand Siri, Maryam, and Clayton V. Deutsch. "Multivariate stochastic seismic inversion with adaptive sampling." GEOPHYSICS 83, no. 5 (September 1, 2018): R429—R448. http://dx.doi.org/10.1190/geo2017-0025.1.
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We have developed a fully coupled categorical-multivariate continuous stochastic inversion with a combined petro-elastic model and convolution. The new multivariate stochastic seismic inversion approach simulates multiple reservoir properties simultaneously and conditions them to the well and seismic data at the same time through the close integration of multivariate geostatistical modeling and stochastic inversion. This approach combines a trace-by-trace (column-wise) adaptive sampling algorithm with multivariate geostatistical techniques to select reservoir properties that match the seismic data. The adaptive sampling method uses an acceptance-rejection approach to condition geostatistical models to the well and seismic data. The adaptive sampling algorithm defines a practical stopping criteria based on the inherent uncertainty due to modeling assumptions and the size of the uncertainty space. This technique samples the realizations inside the space of uncertainty; the number of realizations attempted increases with the size of the space of uncertainty. Characterizing multiple reservoir properties simultaneously through the close integration of seismic inversion and multivariate geostatistical techniques leads to improved high-resolution reservoir property models that reproduce the original seismic data. A case study is considered to compare the proposed stochastic inversion approach with the conventional methods. The case study represents multivariate stochastic inversion provides high-resolution facies and reservoir physical properties simultaneously that reproduce the original seismic data within quality of data better than the other approaches.
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Contreras, Arturo, Andre Gerhardt, Paul Spaans, and Matthew Docherty. "Characterization of fluvio-deltaic gas reservoirs through AVA deterministic, stochastic, and wave-equation-based seismic inversion: A case study from the Carnarvon Basin, Western Australia." Leading Edge 39, no. 2 (February 2020): 92–101. http://dx.doi.org/10.1190/tle39020092.1.
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Multiple state-of-the-art inversion methods have been implemented to integrate 3D seismic amplitude data, well logs, geologic information, and spatial variability to produce models of the subsurface. Amplitude variation with angle (AVA) deterministic, stochastic, and wave-equation-based amplitude variation with offset (WEB-AVO) inversion algorithms are used to describe Intra-Triassic Mungaroo gas reservoirs located in the Carnarvon Basin, Western Australia. The interpretation of inverted elastic properties in terms of lithology- and fluid-sensitive attributes from AVA deterministic inversion provides quantitative information about the geomorphology of fluvio-deltaic sediments as well as the delineation of gas reservoirs. AVA stochastic inversion delivers higher resolution realizations than those obtained from standard deterministic methods and allows for uncertainty analysis. Additionally, the cosimulation of petrophysical parameters from elastic properties provides precise 3D models of reservoir properties, such as volume of shale and water saturation, which can be used as part of the static model building process. Internal multiple scattering, transmission effects, and mode conversion (considered as noise in conventional linear inversion) become useful signals in WEB-AVO inversion. WEB-AVO compressibility shows increased sensitivity to residual/live gas discrimination compared to fluid-sensitive attributes obtained with conventional inversions.
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Lai, C. G., S. Foti, and G. J. Rix. "Propagation of Data Uncertainty in Surface Wave Inversion." Journal of Environmental & Engineering Geophysics 10, no. 2 (June 1, 2005): 219–28. http://dx.doi.org/10.2113/jeeg10.2.219.
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Athens, Noah D., and Jef K. Caers. "Gravity inversion for geothermal exploration with uncertainty quantification." Geothermics 97 (December 2021): 102230. http://dx.doi.org/10.1016/j.geothermics.2021.102230.
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Dosso, S. E., and M. J. Wilmut. "Data Uncertainty Estimation in Matched-Field Geoacoustic Inversion." IEEE Journal of Oceanic Engineering 31, no. 2 (April 2006): 470–79. http://dx.doi.org/10.1109/joe.2006.875099.
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Jessell, Mark. "Geological uncertainty and geophysical inversion Minerals keynote paper." ASEG Extended Abstracts 2015, no. 1 (December 2015): 1. http://dx.doi.org/10.1071/aseg2015ab108.
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Quijano, Jorge E., Stan Dosso, Jan Dettmer, Martin Siderius, and Lisa M. Zurk. "Bayesian ambient noise inversion for geoacoustic uncertainty estimation." Journal of the Acoustical Society of America 129, no. 4 (April 2011): 2459. http://dx.doi.org/10.1121/1.3588088.
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