Deterministic Inversion Research Articles

Defect characterization from magnetic field leakage signals in petroleum and natural gas pipelines

Pipelines transport invaluable energy resources such as crude oil and natural gas over long distances. The integrity of the piping system in terms of safety of the process is then of high importance. However, pipes are prone by time to defects that may degrade their properties and lead to failures. In this paper, we study the effect of defect parameters on the magnetic field leakage captured by Hall sensors operating along the pipe. In fact, the obtained results show that the defect parameters influence directly the MFL amplitude and shape. For this reason, the inversion problem allowing us to reconstruct the defect from the MFL signals became fast and easier in comparison to the deterministic and probabilistic algorithm inversion procedure. However, the simplified system cannot describe the real defects and the three-dimensional numerical study became necessary. In tank floor inspection domain, as our recent published work, we have studied the performance of defect shape reconstruction from MFL array sensor imaging and depth estimation while using an iterative inversion method. Indeed, the first stage consists of determining the defect width and length from magnetic flux leakage mapping reconstructed from the recorded signals of the micro-integrated magnetic sensors. Then, after coupling Comsol and Matlab software, the defect depth is obtained by coupling the 3D finite elements method and a fast iterative algorithm recently developed. Consequently, the defect shape and size are obtained after a few iterations with high precision. Furthermore, this method of defect reconstruction and seizing can be extended for irregular defect shapes encountered in pipeline such as cracks and corrosion.

Collaborative Seismic Impedance Inversion under Bayesian Parameter Estimation

Abstract At present, the industry mainly divides seismic inversion methods into deterministic inversion and deterministic inversion based on the methods and principles used in inversion. There are two types of geostatistical inversion. Deterministic inversion is the process of directly modifying the model quantity through optimization algorithms under given initial constraint conditions to obtain a definite solution; Geostatistical inversion uses random simulation methods to obtain inversion results through simulation and selection. The seismic data did not participate in the direct modification of the model, but rather served as a matching optimization constraint for the random model. Starting from the Bayesian formula, this article unifies deterministic inversion and geostatistical inversion within the Bayesian parameter estimation framework. From a theoretical framework, it analyzes the similarities and differences between deterministic inversion and geostatistical inversion, and proposes a method that combines deterministic inversion and geostatistical inversion - seismic wave impedance co inversion. Sequential Gaussian simulation and model constrained inversion are used as examples of the two major methods, The correctness of the research results and the feasibility and effectiveness of the proposed new inversion method and process have been verified through the application of the Marmousi theoretical model and actual data from Fudong, Fukang Depression, Xinjiang. It has been proven that the proposed method can improve the accuracy and precision of inversion. The inversion method and process used in this study obtained high-resolution and high-precision inversion results, which have good application prospects.

Joint Physics and Data Driven Geometrical Factors of Array Laterolog in Layered Formations

Numerical geometrical factors (GFs) are developed for array laterolog measurements in one-dimensional (1D) cylindrically and planarly layered formations. The kernel of GFs assumes that laterolog responses can be expressed in terms of linear superposition of formation resistivities at different units. Two techniques, namely physics-driven modeling and data-driven approximation, have been employed to ensure both computational accuracy and efficiency of GFs. Physics-driven modeling utilizes a three-dimensional finite element algorithm to generate high-precision and fully labeled GFs data and library. Subsequently, these predetermined data are trained offline using classical neural network algorithm to establish an implicit relationship between formation parameters and GFs. The joint physics and data-driven GFs presents three main advantages. Firstly, it enables the direct representation of the spatial sensitivity of layered formations both laterally and horizontally in vertical and horizontal wells. Secondly, GFs can be used to rapidly calculate the array laterolog responses. The computation speed can be enhanced by thousands of times in comparison with traditional physic-driven modeling, allowing for real-time data processing. Another noteworthy aspect is that GFs forward modeling can handle formations with arbitrary layers, thereby resolving the fixed-layer modeling issue inherent in traditional data-driven methods. Thirdly, the GFs can be employed to approximate the derivative of logging response with respect to formation resistivity, significantly reducing the complexity of Jacobian matrix calculation for deterministic inversion. These numerical GFs not only serve as an excellent alternative simulator for array laterolog, but also will be helpful to accelerate the modeling and inversion of other logging measurement in layered structures.

Analysis on stable imaging and inverse algorithm for artificial source EM data

Abstract The inversion of artificial source electromagnetic (EM) method data fundamentally involves constructing a mathematical relationship between observable data and geological structures. The aim of imaging and inversion is to construct a geophysical model that matches the observable results, thereby realizing the identification of subsurface targets. The results of EM data inversion, due to the simplicity of geophysical models, limit inversion computing efficiency. Moreover, complexity of actual geological structures, and lack of onsite observable data, are often hindered by non-uniqueness. The challenge in the interpretation of artificial source EM data is in enhancing both the precision and expeditiousness of the inversion process. It can be classified into three main types for EM data inversion: direct imaging inversion, deterministic inversion, and stochastic inversion. To enhance computational efficiency and reduce non-uniqueness in the results, effective inversion methods, prior geological information, geophysical data, and comprehensive analysis can help mitigate the issue of non-uniqueness in EM data inversion, thereby leading to more rational geophysical interpretation results. With the progress of technology such as computing centers and the development of artificial intelligence methods, future inversion techniques will become faster, more efficient, and more intelligent, and will be applied to the interpretation of artificial source EM data.

Geostatistical Inversion for Subsurface Characterization Using Stein Variational Gradient Descent With Autoencoder Neural Network: An Application to Geologic Carbon Sequestration

AbstractGeophysical subsurface characterization plays a key role in the success of geologic carbon sequestration (GCS). While deterministic inversion methods are commonly used due to their computational efficiency, they often fail to adequately quantify the model uncertainty, which is essential for informed decision‐making and risk mitigation in GCS projects. In this study, we propose the SVGD‐AE method, a novel geostatistical inversion approach that integrates geophysical data with prior geological knowledge to estimate subsurface properties. SVGD‐AE combines Stein Variational Gradient Descent (SVGD) for sampling high‐dimensional distributions with an autoencoder (AE) neural network for re‐parameterizing reservoir models, aiming to accurately preserve geologic characteristics of reservoir models derived from prior knowledge. Through a synthetic example of pre‐stack seismic inversion, we demonstrate that the SVGD‐AE method outperforms traditional probabilistic methods, particularly in inverse problems with complex posterior distributions. Then, we apply the SVGD‐AE method to the Illinois Basin—Decatur Project (IBDP), a large‐scale CO2 storage initiative in Decatur, Illinois, USA. The resulting petrophysical models with quantified uncertainty enhance our understanding of subsurface properties and have broad implications for the feasibility, decision making, and long‐term safety of CO2 storage at the IBDP.

Seismic net-to-gross estimation for a geologic model update: A case study from a turbidite lobe reservoir in the deepwater of the Niger Delta

Geologic model updates are routinely performed in mature fields to obtain improved descriptions of facies distributions and reservoir properties such as volume of shale, net to gross (NTG), and porosity, for better understanding of the static and dynamic behaviors of reservoirs for effective well placement, improved production, and monitoring. A simple but integrated seismic NTG estimation approach, using detuned seismic amplitudes is used in guiding NTG modeling during the geologic model update of a thin turbidite lobe reservoir in a mature oil field in the deep offshore Niger Delta. The objective is to address NTG overestimation and gross rock volume (GRV) uncertainty in a previous model arising from seismic amplitude tuning effects. A seismic NTG approach is chosen relative to sophisticated deterministic or stochastic inversion techniques to avoid tuning effects, which usually bias NTG estimates in thin turbidite reservoirs. The primary data set is a 2019 reprocessed prestack depth-migrated (PSDM) seismic data vintage, which had better resolution, higher signal-to-noise ratio, and more appropriate angle-stack apertures for amplitude variation with angle fidelity, than the older 2011 PSDM seismic data that are used in the previous geologic model. The methodology involved rock-physics analysis, seismic data quality checks (QCs), tuned area determination, detuning of composite seismic amplitudes of the top and base reservoir, and their direct calibration to NTG at wells. Good correlations are obtained between the detuned composite seismic amplitudes and NTG at wells. The seismic NTG map shows good calibrations at wells and provides a robust trend for net sand modeling in the oil pool and aquifer. Static model QCs and dynamic simulations prove that the seismic NTG attribute addressed the GRV uncertainty in the earlier model, thus giving confidence for using the updated model for the planning and geosteering of infill wells, sand completions, reservoir monitoring, and production.

Pre-stack seismic inversion based on model-constrained generative adversarial network

Pre-stack seismic inversion usually uses various traditional algorithms to estimate elastic parameters such as P-wave velocity, S-wave velocity, and density. It is hard to derive accurate elastic parameters due to their non-uniqueness and high dimensionality between elastic parameters and seismic data, the calculation of elastic parameters is inaccurate. Convolutional Neural Networks (CNNs) have high-dimensional feature space mapping capabilities, which are utilized to establish mapping relationships between seismic data and elasticity parameters. However, their effectiveness is greatly affected by label data, and at the same time, due to the lack of enough label data, resulting in a low degree of fitting between prediction results and real data. In addition, conventional seismic inversion methods based on CNNs lack physical model constraints, resulting in low accuracy and poor interpretability of prediction results. We propose a Cycle-consistent Generative Adversarial Network based on a geophysical mechanism (SeisInv-CycleGAN). Deterministic inversion results and labeled data are combined into hybrid geophysical data as a training set of SeisInv-CycleGAN with geophysical constraints. At the same time, the residual (seismic loss) between the seismic data synthesized by forward modeling and the actual data is used as part of the loss function. The SeisInv-CycleGAN does not require building an initial model, and it can achieve higher accuracy in prediction results with a small amount of labeled data.

Bayesian linearized amplitude variation with offset and azimuth inversion and uncertainty analysis in horizontal transversely isotropic media

AbstractThe stratum can be modelled as a horizontal transversely isotropic medium when a single set of vertically parallel fractures embedded in an isotropic background medium, which facilitates efficient study for fractured reservoirs. Elastic parameters and fracture weaknesses are important parameters to describe the characteristics of fractured reservoirs, and seismic inversion plays a significant role in parameters estimation. The commonly used deterministic inversion methods do not fully utilize the prior information and fails to present the uncertainty analysis of inversion results. To address these shortcomings, we propose a Bayesian linearized amplitude variation with offset and azimuth inversion method tailored for horizontal transversely isotropic media, enabling a more robust analysis of uncertainty. Within the framework of Bayesian inversion, the proposed method successfully derives analytical expressions for the posterior mean and covariance of both elastic parameters and fracture weaknesses. The response characteristics of the anisotropic reflection coefficient are analysed, and it is found that the perturbations of elastic parameters have a greater effect on reflection coefficient compared to fracture weaknesses. Synthetic data examples confirm that the accuracy of estimated P‐ and S‐wave velocities and density surpasses that of fracture weaknesses, and the proposed method still performs well for the case of moderate noise. A field data example demonstrates that the inverted profiles agree well with the logging curve, and the estimated fracture weaknesses display significantly high values in the reservoir area. The estimated reservoir parameters not only contribute to a more accurate representation of the fractured gas‐bearing reservoir but also provide insights into the target gas reservoir through its posterior distribution. Both synthetic and field data examples demonstrate the stability and reliability of the proposed method in characterizing fractured reservoirs. We determine that the proposed method provides an available tool for nuanced evaluation of uncertainty for the inversion results, and it is helpful for the fine description of fractured hydrocarbon‐bearing reservoirs.

Novel approaches to uncertainty estimation in seismic subsurface characterization

Uncertainty estimation in subsurface characterization workflows is an important input to decision-making in earth science-related problems. We present three methods to characterize seismic-related uncertainty, each of which includes a real data case study. Two of these methods are designed to characterize depth uncertainty in positioning of migrated reflectors. Such estimates may be used in derisking well depth prognoses, analysis of well misties, and for estimating ranges on resource volume. The first method derives rapid and robust estimates of depth uncertainty around an existing velocity model using traditional velocity analysis to constrain the solution space while limiting a-priori constraints, consistent with a frequentist approach to uncertainty characterization. The second method characterizes depth uncertainty more rigorously in respect to the physics and prior information available by performing full-waveform inversion in a Bayesian framework. This method produces similar uncertainty estimates to the first in the case of simple velocity models but is more accurate where the overburden is complex; however, it requires significantly greater computational expense, thus limiting current practical applications. The third method is an amplitude variation with angle (AVA) inversion for reservoir properties designed to output uncertainty products for interpreters, utilizing the Bayesian framework and Zoeppritz equations to define the forward physics. Application to an offshore Egypt field demonstrates that it can generate reliable estimates of reservoir properties (e.g., lithofluid type or shale volume) including uncertainty, useful in various parts of subsurface characterization. These results also show that the method could provide improved point estimates of reservoir properties compared to conventional deterministic AVA inversion approaches. There is usually a trade-off between increasing the accuracy of subsurface characterization versus creating faster, less expensive, and more readily understood workflows for practitioners. We discuss how the relative importance of these competing factors should be considered within the context of how the outputs will be used.

Inversion of 2D Magnetotelluric (MT) Data with Axial Anisotropy using Adaptive Particle Swarm Optimization (PSO)

In the presence of anisotropic resistivity structures, Magnetotelluric (MT) data inversion based on an isotropic resistivity model will be insufficient. Recent work on anisotropic MT inversions is primarily conducted using gradient-based, deterministic methods which may converge towards local minima and in general, suffer from ill-posedness of the inversion problem. Alternatively, meta-heuristical methods, such as Particle Swarm Optimization (PSO), are able to find the global minima of cost function. At the same time, they are easy to implement and do not require access to the dense Jacobian (and Hessian) matrix as needed by deterministic inversion methods. In this paper we propose PSO inversion for the anisotropic MT inversion problem using an adaptive inertia weights control strategy to balance exploration and exploitation during the PSO search. Higher order differential regularization is introduced with a Gaussian filter, where the conventional first order, Occam-like regularization term is replaced by a variance term. We investigate the performance of the proposed PSO inversion for an isotropic as well as an axial anisotropic synthetic case to demonstrate improvements over an Occam-like regularization. For the COPROD2 benchmark data set, the proposed PSO inversion can not only reproduce the extend of the North American Central Plains (NACP) conductive anomaly, but also to predict an anisotropy ratio of two orders of magnitude, which is in accordance with laboratory findings.

Deep basin conductor characterization using machine learning-assisted magnetotelluric Bayesian inversion in the SW Barents Sea

SUMMARY In this paper, we use a new workflow to substantiate the characterization of a prominent, deep sediment conductor in the hyperextended Bjørnøya Basin (SW Barents Sea) previously identified in smooth resistivity models from 3-D deterministic inversion of magnetotelluric data. In low-dimensionality environments like layered sedimentary basin, 1-D Bayesian inversion can be advantageous for a thorough exploration of the solution space, but the violation of the 1-D assumption has to be efficiently handled. The primary geological objectives of this work is therefore preceded by a secondary task: the application of a new machine learning approach for handling the 1-D violation assumption for 21 MT field stations in the Barents Sea. We find that a decision tree can adequately learn the relationship between MT dimensionality parameters and the 1-D–3-D residual response for a training set of synthetic models, mimicking typical resistivity structures of the SW Barents Sea. The machine learning model is then used to predict the dimensionality compensation error for MT signal periods ranging of 1–3000 s for 21 receivers located over the Bjørnøya Basin and Veslemøy High. After running 1-D Bayesian inversion, we generated a posterior resistivity distribution for an ensemble of 6000 1-D models fitting the compensated MT data for each 21 field stations. The proportion of 1-D models showing ρ < 1 Ω·m is consistently beyond 80 per cent and systemically reaches a maximum of 100 per cent in the Early Aptian–Albian interval in the Bjørnøya Basin. In hyperextended basins of the SW Barents Sea, the dimensionality compensation workflow has permitted to refine the characterization of the deep basin conductor by leveraging the increased vertical resolution and optimal used of MT data. In comparison, the smooth 3-D deterministic models only poorly constrained depth and lateral extent of the basin anomaly. The highest probability of finding ρ < 1 Ω·m is robustly assigned to the syn-tectonic Early Aptian–Albian marine shales, now buried at 6–8 km depth. Based on a theoretical two phase fluid-rock model, we show that the pore fluid of these marine shales must have a higher salinity than seawater to explain the anomaly ρ < 1 Ω·m. Therefore, the primary pore fluid underwent mixing with a secondary brine during rifting. Using analogue rift systems in palaeomargins, we argue that two possible secondary brine reservoir may contribute to deep saline fluid circulation in the hyperextended basin: (1) Permian salt-derived fluid and, (2) mantle-reacted fluid from serpentinization.

Bayesian joint inversion of seismic and electromagnetic data for reservoir lithofluid facies, including geophysical and petrophysical rock properties

A Bayesian approach is developed to estimate lithofluid facies and other rock properties conditioned on seismic and electromagnetic data for reservoir characterization. Prior distributions are assumed to be facies-related Gaussian modes of geophysical rock properties directly acquired or converted from petrophysical properties by calibrated rock-physics modeling. An original generalization includes two distributions in the same marginalization integral, analytically solved under a linearized Gaussian assumption to provide a facies model likelihood conditioned on geophysical data. Because computing this probability for all possible facies configurations may be impractical, a Markov chain Monte Carlo algorithm efficiently samples models to provide a full posterior distribution. The linearized Gaussian approach allows the computation of the conditional distributions of geophysical and petrophysical rock properties by applying local deterministic inversions over the many sampled facies models. The inversion uses simulated geophysical data from a 1D synthetic model based on the geologic scenario and a well from a selected marine oil field. Two other wells from the same reservoir are used to gather prior distributions. Data from the well, calibration of the rock-physics modeling, and facies matching between the priors and the synthetic model are presented and discussed. Numerical tests validate nonlinear forward-modeling adaptations based on the assumed linearized Gaussian approach. The simulated stand-alone and joint geophysical data sets are then inverted for lithofluid facies models under different prior inputs. Two challenging geoelectric scenarios also are tested, one with lower resistivity contrasts and another with a misguided background model. All results demonstrate a gain in precision and accuracy when associating these geophysical signals to estimate the oil column. Facies-conditioned inversions for the rock properties also indicate potential for quantitative reservoir interpretations.

2-D probabilistic inversion of MT data and uncertainty quantification using the Hamiltonian Monte Carlo method

SUMMARY Bayesian methods provide a valuable framework for rigorously quantifying the model uncertainty arising from the inherent non-uniqueness in the magnetotelluric (MT) inversion. However, widely used Markov chain Monte Carlo (MCMC) sampling approaches usually require a significant number of model samples for accurate uncertainty estimates, making their applications computationally challenging for 2-D or 3-D MT problems. In this study, we explore the applicability of the Hamiltonian Monte Carlo (HMC) method for 2-D probabilistic MT inversion. The HMC provides a mechanism for efficient exploration in high-dimensional model space by making use of gradient information of the posterior probability distribution, resulting in a substantial reduction in the number of samples needed for reliable uncertainty quantification compared to the conventional MCMC methods. Numerical examples with synthetic data demonstrate that the HMC method achieves rapid convergence to the posterior probability distribution of model parameters with a limited number of model samples, indicating the computational advantages of the HMC in high-dimensional model space. Finally, we applied the developed approach to the COPROD2 field data set. The statistical models derived from the HMC approach agree well with previous results obtained by 2-D deterministic inversions. Most importantly, the probabilistic inversion provides valuable quantitative model uncertainty information associated with the resistivity structures derived from the observed data, which facilitates model interpretation.

Assessing and Improving the Robustness of Bayesian Evidential Learning in One Dimension for Inverting Time-Domain Electromagnetic Data: Introducing a New Threshold Procedure

Understanding the subsurface is of prime importance for many geological and hydrogeological applications. Geophysical methods offer an economical alternative for investigating the subsurface compared to costly borehole investigations. However, geophysical results are commonly obtained through deterministic inversion of data whose solution is non-unique. Alternatively, stochastic inversions investigate the full uncertainty range of the obtained models, yet are computationally more expensive. In this research, we investigate the robustness of the recently introduced Bayesian evidential learning in one dimension (BEL1D) for the stochastic inversion of time-domain electromagnetic data (TDEM). First, we analyse the impact of the accuracy of the numerical forward solver on the posterior distribution, and derive a compromise between accuracy and computational time. We also introduce a threshold-rejection method based on the data misfit after the first iteration, circumventing the need for further BEL1D iterations. Moreover, we analyse the impact of the prior-model space on the results. We apply the new BEL1D with a threshold approach on field data collected in the Luy River catchment (Vietnam) to delineate saltwater intrusions. Our results show that the proper selection of time and space discretization is essential for limiting the computational cost while maintaining the accuracy of the posterior estimation. The selection of the prior distribution has a direct impact on fitting the observed data and is crucial for a realistic uncertainty quantification. The application of BEL1D for stochastic TDEM inversion is an efficient approach, as it allows us to estimate the uncertainty at a limited cost.

Deterministic and Stochastic Modeling in Prediction of Petrophysical Properties of an Albian Carbonate Reservoir in the Campos Basin (Southeastern Brazil)

Abstract —Permeability is one of the most significant and challenging parameters to estimate when characterizing an oil reservoir. Several empirical methods with geophysical borehole logs have been employed to estimate it indirectly. They include the Timur model, which uses conventional logs, and the Timur–Coates model, which uses the nuclear magnetic resonance log. The first goal of this study was to evaluate porosity, because it directly impacts permeability estimates. Deterministic and stochastic inversions were then carried out, as the main objective of this work was to estimate the permeability in a carbonate reservoir of the Campos Basin, Southeastern Brazil. The ridge regression scheme was used to invert the Timur and Timur–Coates equations deterministically. The stochastic inversion was later solved using fuzzy logic as the forward problem, and the Monte Carlo method was utilized to assess uncertainty. The goodness of fit for the estimations was all checked with porosity and permeability laboratory data using the Pearson correlation coefficient (R), root mean square error (RMSE), mean absolute error (MAE), and Willmott’s agreement index (d). The results for the Timur model were R = 0.41; RMSE = 333.28; MAE = 95.56; and d = 0.55. These values were worse for the Timur–Coates model, with R = 0.39; RMSE = 355.28; MAE = 79.35; and d = 0.51. The Timur model with flow zones had R = 0.55; RMSE = 210.88; MAE = 116.66; and d = 0.84, which outperformed the other two models. The deterministic inversion showed, thus, little ability to adapt to the significant variations of the permeability values along the well, as can be seen from comparing these three approaches. However, the stochastic inversion using three bins had R = 0.35; RMSE = 320.27; MAE = 190.93; and d = 0.73, looking worse than the deterministic inversion. In the meantime, the stochastic inversion with six bins successfully adjusted the set of laboratory observations, because it provides R = 0.87; RMSE = 156.81; MAE = 74.60; and d = 0.92. This way, the last approach has proven it can produce a reliable solution with consistent parameters and an accurate permeability estimation.

Characterizing Offshore Freshened Groundwater Salinity Patterns Using Trans‐Dimensional Bayesian Inversion of Controlled Source Electromagnetic Data: A Case Study From the Canterbury Bight, New Zealand

AbstractThe study of offshore freshened groundwater (OFG) is gaining importance due to population growth and environmental pressure on coastal water resources. Marine controlled source electromagnetic (CSEM) methods can effectively map the spatial extent of OFG systems using electrical resistivity as a proxy. Integrating these resistivity models with sub‐surface properties, such as host‐rock porosity, allows for estimates of pore‐water salinity. However, evaluating the uncertainty in pore‐water salinity using resistivity models obtained from deterministic inversion approaches presents challenges, as they provide only one best‐fit model, with no associated estimate of uncertainty. To address this limitation, we employ trans‐dimensional Markov‐Chain Monte‐Carlo inversion on marine time‐domain CSEM data, acquired in the Canterbury Bight, New Zealand. We integrate resistivity posterior probability distributions with borehole and seismic reflection data to estimate pore‐water salinity with corresponding uncertainty estimates. The results highlight a low‐salinity groundwater body in the center of the survey area, hosted by consecutive silty‐ and fine‐sand layers approximately 20–60 km from the coast. The posterior probability distribution of resistivity models indicates freshening of the OFG body toward the shoreline within a permeable, coarse‐sand layer 40–150 m beneath the seafloor, suggesting an active connection between the OFG body and the terrestrial groundwater system. The approach demonstrates how Bayesian inversion constrains the uncertainties in resistivity models and subsequently in pore‐water salinity estimates. Our findings highlight the potential of Bayesian inversion to enhance our understanding of OFG systems and provide uncertainty constraints for hydrogeological modeling, thereby contributing to sustainable water resource development.

Cohesive approach for determining porosity and P-impedance in carbonate rocks using seismic attributes and inversion analysis

AbstractThe assessment of hydrocarbon flow through seismic and well-log data presents a persistent challenge in determining porosity. The acoustic impedance section provides a visual representation of the layers, while the raw seismic data showcase the subsurface reflectors that exist within the rock layers. The accuracy of acoustic impedance is widely acknowledged to surpass that of seismic data as a representation of reality. The primary objective of this study is to convert seismic reflector data into acoustic impedance values, which provide insights into the layer properties based on lithology. This approach enhances the accuracy of seismic inversion results by aligning them more closely with actual geological conditions. Seismic inversion is employed to ascertain the physical characteristics of the rock, including acoustic impedance and porosity. Carbonate reservoirs are recognised for their complex pore structures and heterogeneity, which present difficulties in their characterisation. The objective of this research is to predict the porosity and identify the reservoir within the dense carbonate reservoirs in Central Luconia, Sarawak. These objectives are achieved by employing a porosity and acoustic impedance cross-plot and improved precision and predictability through the integration of seismic attribute interpretation and deterministic seismic inversions. The uniqueness of our approach stems from the incorporation of various geophysical techniques to detect reservoirs that have hydrocarbon deposits. A correlation is observed between seismic inversion acoustic impedance and porosity within the zone of interest, indicating an estimated porosity range of 10–35%. The analysed area demonstrates the possibility of containing a hydrocarbon based on the observed relationship between porosity and impedance, as well as the outcomes of the inversion analysis.

Large-scale spatial reconstitution of groundwater fluxes in a karst aquifer on the basis of hydrodynamic and hydrodispersive measurements

This article presents a multiphysics-based approach for a large-scale spatial reconstitution of head and tracer tests responses measured in a regional scale karst aquifer in Southern France. The main dataset consists in hydraulic heads measured in 11 wells during 6 weeks and 4 tracer tests. A pump station withdraws groundwater from this aquifer at varying flow rates during days and nights to supply water to Montpellier agglomeration, generating a periodic signal which propagates in the whole aquifer. Some of the measurements show a periodic response, some others not. As a first step, this specificity is exploited to localize spatially the preferential flow paths network with a structural deterministic inversion approach. Then, inversions of the weekly averaged head variations are performed on the first and the last weeks of the dataset (showing different drawdown trends) to assess the hydraulic diffusivity field. Finally, the tracer restitutions at the spring are inverted in order to optimize the conduits diameters associated to the fastest flow paths.The proposed approach permits a satisfying reproduction of the hydraulic heads and tracer measurements. Simulations with the optimized model on a week of the dataset not used in the inversion allows to validate the inversion result. The inverted model suggests that daily periodic responses represent efficient constraints for the localization of the preferential flows, while the integration of weekly head variations provides a characterization of the hydraulic properties between each well and the closest preferential flow paths, and tracer restitutions permit to characterize the velocities in the preferential paths.

Posterior sampling with convolutional neural network-based plug-and-play regularization with applications to poststack seismic inversion

Uncertainty quantification is a crucial component in any geophysical inverse problem, as it provides decision makers with valuable information about the inversion results. Seismic inversion is a notoriously ill-posed inverse problem, due to the band-limited and noisy nature of seismic data; as such, quantifying the uncertainties associated with the ill-posed nature of this inversion process is essential for qualifying the subsequent interpretation and decision-making processes. Selecting appropriate prior information is a crucial — yet nontrivial — step in probabilistic inversion because it influences the ability of sampling-based inference algorithms to provide geologically plausible posterior samples. However, the necessity to encapsulate prior knowledge into a probability distribution can greatly limit our ability to define expressive priors. To address this limitation and following in the footsteps of the plug-and-play (PnP) methodology for deterministic inversion, we develop a regularized variational inference framework that performs posterior inference by implicitly regularizing the Kullback-Leibler divergence loss — a measure of the distance between the approximated and target probabilistic distributions — with a convolutional neural network-based denoiser. We call this new algorithm PnP Stein variational gradient descent and determine its ability to produce high-resolution trustworthy samples that realistically represent subsurface structures. Our method is validated on synthetic and field poststack seismic data.

Fast Initial Model Design for Electrical Resistivity Inversion by Using Broad Learning Framework

The electrical resistivity method is widely used in near-surface mineral exploration. At present, the deterministic algorithm is commonly employed in three-dimensional (3-D) electrical resistivity inversion to obtain subsurface electrical structures. However, the accuracy and efficiency of deterministic inversion rely on the initial model. In practice, obtaining an initial model that approximates the true subsurface electrical structures remains challenging. To address this issue, we introduce a broad learning (BL) network to determine the initial model and utilize the limited memory quasi-Newton (L-BFGS) algorithm to conduct the 3-D electrical resistivity inversion task. The powerful mapping capability of the BL network enables one to find the model that elucidates the actual observed data. The single-layer BL network makes it efficient and easy to realize, leading to much faster network training compared to that using the deep learning network. Both the synthetic and field experiments suggest that the BL framework could effectively obtain the initial model based on observed data. Furthermore, in comparison to using a homogeneous medium as the initial model, the L-BFGS inversion with the BL framework-designed initial model improves the inversion accuracy of subsurface electrical structures and expedites the convergence speed of the iteration. This study provides an effective approach for fast initial model design in a data-driven manner when the prior information is unavailable. The proposed method can be useful in high-precision imaging of near-surface mineral electrical structures.