Transient electromagnetic forward-modeling method based on a 3D anisotropic resistivity model constrained by well-logging and seismic data

Reservoir characterization (RC) is a process of finding petrophysical properties of the subsurface mainly from the seismic and well-log data. The nonlinear and heterogeneous nature of the subsurface is the major bottleneck in estimating the reservoir properties. In the past two decades, the RC has eventually turned out to be an interdisciplinary field of research involving computational science, signal processing, geostatistics, and geophysics. This article provides the interdisciplinary perspective in RC focusing on the applications of signal processing and machine learning (ML). We provide an account of various state-of-the-art algorithms while categorizing them into three stages in an RC framework: preprocessing, prediction, and postprocessing. RC has been known to be a highly data-driven problem. Huge volumes of seismic and well-log data are cleverly integrated by experts to decipher the subsurface properties. Some of the anomalies may lead to the existence of a potential reservoir. The signal processing tools are primarily required for information matching, preprocessing for noise and artifacts, and postprocessing for removing irregularities in the prediction, whereas the ML tools are required to map the seismic data to well logs. This article provides a comprehensive study on the recent advances in RC involving seismic volumes and well logs.

The elastic properties of subsurface media, such as density and P- and S-wave velocity, are essential for understanding the mechanical behavior of the subsurface as they reflect its physical and structural characteristics. Accurate elastic properties are increasingly critical for safety assessment, geological risk analysis, and reservoir characterization in subsurface applications. However, current data acquisition methods present complementary limitations: well-log data provide high-resolution and accurate elastic properties but offers only localized information due to spatial constraints, while seismic data covers regional areas but has lower resolution and accuracy. To address these limitations, this study develops a machine learning (ML) framework that integrates seismic and well-log data to improve the prediction accuracy of subsurface elastic properties. This study introduces a novel approach that integrates ML with Gaussian processes (GP), which allows not only elastic property prediction but also quantification of predictive uncertainty. The proposed approach was validated using well-log and post-stack seismic data from the Volve dataset. Five ML models were trained to predict density and P- and S-wave velocities, with the long short-term memory+GP model achieving superior performance among all tested models. The 3-D prediction capabilities were further validated by applying the trained model to a 3-D seismic cube from the Volve field, successfully estimating 3-D elastic properties and quantifying prediction uncertainty. While the approach improves uncertainty assessment, it should be noted that uncertainty quantification is often limited in highly heterogeneous zones, as prediction reliability is inherently dataset-dependent.

Quick clay, which is the main cause of landslides that occur in the northern countries, liquefies easily, and its presence implies an increased risk of landslide. Geophysical methods have been increasingly used in landslide investigations. Three-dimensional electric resistivity tomography, radio magnetotelluric (RMT), controlled-source RMT (CSRMT), and high-resolution reflection seismic data were acquired at a quick-clay landslide site in the southwest of Sweden. The main objectives were to evaluate the capability of each method in delineating different subsurface geologic structures that controlled a peculiar and hazardous retrogressive-type landslide in the study area. A 3D resistivity model from the inversion of CSRMT data showed the best correlation with the reflection seismic data and borehole information, thanks to the broad frequency range of the data set. It better imaged the resistive crystalline bedrock underlying the marine conductive clays and showed considerable correlations with the 3D reflection seismic data in resolving a coarse-grained layer that was interpreted to act as a conduit directing freshwater into the clays under a confined pressure, leaching their salt and forming quick clays. The 3D CSRMT resistivity model and 3D reflection seismic data showed that the coarse-grained layer has a varying thickness. At some locations, it was too thin to be resolved by the methods used here. Combination of the CSRMT model, reflection seismic data, and the borehole data suggested that a layer with thickness of approximately 5 m and resistivity between [Formula: see text] was potentially quick clay, which probably extended laterally in the entire study area. These observations suggested that future developments should focus on joint inversion of such 3D data sets incorporating sharp boundaries as constraints in the inversion and particularly when quick clays were studied.

In this work we present an approach to determine geologically plausible reservoir models that are consistent with well-log data and multimodal observations (e.g., production and seismic data). The methodology is based on optimization techniques that are not invasive to the simulators used to reproduce observations. The geologically plausible reservoir models obtained facilitate reliable probabilistic production forecasts and lead to more robust optimization and decision-making support tools. The methodology approaches model inversion as an optimization problem where the cost function is a measure of the discrepancy between simulated responses and measurement data. Reservoir model uncertainty quantification is addressed by means of multi-start optimization, i.e., the use of local optimization methods with multiple initial guesses. Parameter reduction techniques allow a more effective and efficient global exploration of the optimization space. Geological realism is incorporated in the approach through multiple-point statistics. The set of reservoir models, determined as the output of the multi-start optimization, is thereafter included in a framework for robust optimization under uncertainty (e.g., to determine the drilling location of a new well). The optimization algorithms used are noninvasive with respect to the simulators used in the workflow and are implemented on a distributed- computing cluster. Different aspects of this approach are illustrated by means of a comprehensive case example that uses well-log and production data. It is important to note that the use of simulator-noninvasive (black box, derivative-free) optimization algorithms reduces significantly the dependence of the methodology on the simulators. The optimization methods tested include Generalized Pattern Search, Mesh Adaptive Direct Search, Sequential Quadratic Programming (with numerical derivatives) and Particle Swarm Optimization, a population-based procedure. These algorithms may yield efficient performance in terms of wall-clock time when they are combined with parameter reduction techniques and distributed computing (as is the case in this work). When parallel computing resources are scarce or nonexistent one may resort to methods suited to serial implementations (examples of these simulator-noninvasive algorithms are Hooke-Jeeves Direct Search and model-based approaches). The parameter reduction techniques studied here are based on Principal Component Analysis. In particular, the recently introduced Optimization-based Principal Component Analysis has been observed to deal with complex geological models satisfactorily. Uncertainty in future production is then incorporated in the robust optimization of well placement and of reactive well controls. The Ensemble Kalman Filter is widely used in industry for reservoir model uncertainty quantification. This method fails in some occasions (e.g., the ensemble collapses) for reasons that are not yet well understood. The multistart methodology proposed in this work can be an alternative to the Ensemble Kalman Filter in these problematic situations. Seismic data could be included in this methodology to mitigate uncertainty in probabilistic forecasts.

Characterizing complex fluvial-deltaic deposits is a challenging task for finding hydrocarbon discoveries. We described a methodology for predicting the hydrocarbon zones from complex well-log and prestack seismic data. In this current study, data analysis involves an integrated framework based on Simultaneous prestack seismic inversion (SPSI), target correlation coefficient analysis (TCCA), Poisson impedance inversion, and non-parametric statistical analysis, and Bayesian classification. First, seismic elastic attributes from prestack seismic data were estimated. They can provide the spatial distribution of petrophysical properties of seismic data. Then target correlation coefficient analysis (TCCA) was estimated roration factor “c” from well-log data. Using the seismic elastic attributes and rotation factor “c”, Poisson impedance inversion was performed to predict the Poisson impedance volume. Finally, Bayesian classification integrated the Poisson impedance volume with non-parametric probabilistic density functions (PDFs) to estimate the spatial distribution of lithofacies. Despite complex characteristics in the elastic properties, the current study successfully delineated the complex fluvial-details deposits. These results were verified with conventional findings through numerical analysis.

Numerical 3D high-resolution models of subsurface petroelastic properties are key tools for exploration and production stages. Stochastic seismic inversion techniques are often used to infer the spatial distribution of the properties of interest by integrating simultaneously seismic reflection and well-log data also allowing accessing the spatial uncertainty of the retrieved models. In frontier exploration areas, the available data set is often composed exclusively of seismic reflection data due to the lack of drilled wells and are therefore of high uncertainty. In these cases, subsurface models are usually retrieved by deterministic seismic inversion methodologies based exclusively on the existing seismic reflection data and an a priori elastic model. The resulting models are smooth representations of the real complex geology and do not allow assessing the uncertainty. To overcome these limitations, we have developed a geostatistical framework that allows inverting seismic reflection data without the need of experimental data (i.e., well-log data) within the inversion area. This iterative geostatistical seismic inversion methodology simultaneously integrates the available seismic reflection data and information from geologic analogs (nearby wells and/or analog fields) allowing retrieving acoustic impedance models. The model parameter space is perturbed by a stochastic sequential simulation methodology that handles the nonstationary probability distribution function. Convergence from iteration to iteration is ensured by a genetic algorithm driven by the trace-by-trace mismatch between real and synthetic seismic reflection data. The method was successfully applied to a frontier basin offshore southwest Europe, where no well has been drilled yet. Geologic information about the expected impedance distribution was retrieved from nearby wells and integrated within the inversion procedure. The resulting acoustic impedance models are geologically consistent with the available information and data, and the match between the inverted and the real seismic data ranges from 85% to 90% in some regions.

Seismic deconvolution is a typical ill-posed inverse problem. The regularization technique in terms of different prior information is used for a unique and stable solution. Due to the difference between prior information and the actual subsurface situation, it is hard to obtain a solution with satisfactory accuracy and resolution. This letter presents the dictionary learning as an efficient adaptive deconvolution method for the reflectivity reconstruction problem. Considering the curse of dimensionality of conventional dictionary learning and the suboptimal solution of the patch-based dictionary learning, we take the convolutional sparse coding (CSC) model as the dictionary learning method. In this method, the prior information can be obtained from the well-log data in the form of sparse CSC dictionary of reflectivity. On the assumption that the deposition of the subsurface layers is stable, the CSC dictionary extracted from the well-log data can also be applied in the whole work area. The CSC-based deconvolution can be seen as the adaptive deconvolution due to the independence of the assumption made about the reflectivity and seismic data. The process of the adaptive CSC-based deconvolution is divided into three parts. First, the CSC dictionary is learned from the well-log data. Then, the objective function is formulated by combining the CSC dictionary and the single-channel seismic record misfit term for the reconstruction of reflectivity. Finally, the objective function is efficiently solved with the coordinate descent approach. We illustrate the performance of our adaptive deconvolution with synthetic and field seismic data.

The Arabian–Nubian Shield (ANS) hosts numerous volcanogenic massive sulphide (VMS) deposits formed in submarine volcanic settings and enriched by hydrothermal processes, making it a critical region for mineral exploration due to the types of deposits it hosts and its geological complexity. The Wadi Bidah Mineral Belt (WBMB), located within the Arabian Shield, contains over 30 polymetallic VMS occurrences associated with an island arc system active between 950 and 800 million years ago. Despite its mineral potential, the WBMB still needs to be explored, with limited geophysical studies to support resource evaluation. This study focuses on the Hawiah area, a prominent VMS site within the WBMB, to delineate subsurface mineralization using transient electromagnetic (TEM) methods. TEM surveys were conducted to characterize the conductivity structure and identify potential zones of sulphide mineralization. Data were processed and inverted to generate 1D, 2D, and 3D resistivity models, providing critical insights into the depth, geometry, and continuity of the mineralized zones based on the final 3D resistivity distribution. The results revealed distinct conductive (very low resistivity) anomalies, correlating with known surface gossans and inferred sulphide-rich layers, and extended these features into the subsurface. The integration of TEM results with geological and geochemical data highlights the effectiveness of this approach in detecting and mapping concealed mineral deposits in complex geological environments. This study advances the understanding of VMS systems in the WBMB and demonstrates the potential of TEM surveys as a key tool for mineral exploration in the Arabian Shield.

Reservoir heterogeneity understanding is critical to predict gas-water contact (GWC) movement in order to take early preventative measures to delay water breakthrough in wells and hence improve Well, Reservoir and Facilities Management (WRFM). This maximizes ultimate recovery of a gas brownfield. The carbonate gas field investigated in this paper (called Delta Field) is located in Central Luconia, with 20 years of production history. It is a platform type carbonate build-up, penetrated by eight production wells and a water disposal well. The contact movement of the reservoir was monitored using well surveillance logs. After 5 years of production, a horizontal well (Delta-110S1) was drilled in the southern part of the field. The well targeted attic gas at the top of the reservoir and was designed with a horizontal drainage bore to avoid early water breakthrough. However, it encountered water breakthrough in Feb 2004 after 1.5 years of production. By 2007, all Delta Field wells were producing water. This indicated that the gas-water contact (GWC) rose non-uniformly with water encroachment faster in the southern area of the field compared to the north, resulting in a tilted GWC. Hence, a ‘back-to-basics' reservoir characterization was required to understand the reservoir architecture and heterogeneities. Reservoir characterization was carried out to identify and map out the distribution of low porosity zones within the carbonate reservoir, based on seismic and well-log data as well as regional understanding. In the Central Luconia carbonate fields two types of tight layers with very different dynamic behaviours are encountered: (1) Tight layers that formed by floodings events with a large lateral extent and continuity, acting as baffles to gas and water flow, and (2) tight layers related to exposure-events with a more patchy distribution, which can act as minor, local baffles but can also function as conduits for water when they are related to karsts and/or fractures. To distinguish the nature of the tight layers and predict their dynamic behaviour, they were mapped out within and between platforms and calibrated with core and seismic data, to understand their depositional origins that control their properties impacting flow and their continuity. Subsurface reservoir models focusing on the key reservoir heterogeneities that matter for flow were built by incorporating core, well log, drilling and seismic data. Integrating this static understanding with completion data (perforation intervals, water shut offs) and dynamic data (GWC-rise history, production and water-cut rates) provided valuable insights into the evolution of the GWC movement and allowed more accurate prediction of production rates and identification of suitable infill well locations. Through this study, an infill well opportunity was identified to target remaining attic gas in the northern part of the field. In 2013, Delta-111S1 was abandoned and side-tracked to target remaining attic gas in the north of the field. Delta-111S2 achieved the first gas in December 2013 and has produced very successfully.

Seismic impedance inversion is a geophysical technique that transforms seismic data into quantitative subsurface properties, primarily acoustic impedance. This process enables the identification of rock boundaries, hydrocarbon reservoirs, and lithological variations, thus supporting informed drilling decisions and reducing exploration risks. However, conventional inversion methods face limitations such as noise sensitivity, low resolution, and reduced effectiveness in geologically complex areas, often resulting in oversimplified subsurface models. This study addresses these challenges by employing deep learning approaches, specifically LeNet, AlexNet, and conventional CNN architectures, to improve seismic resolution and synthetic seismogram generation. The methodology involves preprocessing seismic and well-log data, calculating acoustic impedance and reflection coefficients, and applying Continuous Wavelet Transform (CWT) for feature extraction. The models are trained using synthetic seismograms and validated against real seismic data. Among the models evaluated, AlexNet demonstrates superior performance in seismic data reconstruction, achieving the lowest MSE (0.0031), RMSE (0.0557), and MAE (0.052), along with the highest R2 score (0.993). The proposed technique demonstrates superior predictive accuracy, refined subsurface characterization, and reduced geological risk, thereby establishing a robust benchmark for advanced geophysical data analysis.

Summary The seismic data spectral inversion method, arisen in recent years, can improve the resolution of seismic data for obtaining reservoir characteristics. It does not rely on prior information such as well-logging data. By using partial spectrum information from the input seismic trace data, a sparse reflectivity series can be inverted. The inverted reflectivity series can be used to improve the resolution and impedance inversion for thin layer reservoir prediction. In this paper, we implement seismic spectral inversion based on a compressed sensing algorithm, which can solve the ill-posed problem of the inversion process. In the process of inversion, we introduce a quadratic spectrum method to calculate the spectrum of seismic wavelet in the frequency domain, which can stabilize the inversion and handle real field data. Synthetic and real field seismic data examples show that the proposed spectral inversion based on compressed sensing algorithm is stable and effective. Moreover, the real field data inversion results show a good signal-to-noise ratio (SNR) and lateral continuity.

Improved reservoir reservoir management and production optimisation demands require accurate characterisation of reservoir properties and their changes through time. Advances in geophysical data acquisition and interpretation have led to significant improvements in the remote imaging of earth structure and properties. However, when only a single data type is considered, ambiguities in the interpretation can remain. Here we will concentrate on three contrasting methods: surface seismic, marine controlled source electromagnetic (CSEM) and well-log data. It is clear that a careful combination of all three data types can supply information that is not available, or is unreliable from any one data type alone. By integrating complementary sources of information and exploiting the strengths of each, estimates of rock and fluid properties such as gas saturation and porosity can be obtained with greater confidence than from any one data type alone. We illustrate this using an example based on the Luva discovery in the Norwegian sea. Introduction There are a range of physical parameters we can use to investigate the earth and properties of fluids within it. Well logs provide a high resolution measurement of the properties of a reservoir and the surrounding strata, however properties can only be determined in a small area local to the well. Often a measurement of reservoir properties across the extent of a field are desirable for reservoir management or production optimization and for this we must turn to remote sensing methods. In the well logging industry both electric and acoustic properties are routinely collected and analysed to study lithology, reservoir properties and the properties of fluids within them: it would be almost unthinkable to collect one data type without collecting the other, since this would result in an incomplete dataset that left gaps in our understanding of the reservoir and surrounding strata. Until recently the same logic has not been applied in geophysical surveying and data analysis. Seismic methods, sensitive to acoustic properties only, have been the primary tools used in exploration, reservoir appraisal and monitoring. These methods are extremely powerful. Seismic data are commonly used to provide images of the sub-surface, and develop high resolution geological models of structure and stratigraphy. Amplitude variation with offset (AVO) and inversion for acoustic and elastic impedance may also be used to constrain properties such as elastic moduli and density. However seismic data alone in many situations cannot give a complete picture of the reservoir.

ABSTRACTAn accurate and efficient 3D finite‐difference (FD) forward algorithm for DC resistivity modelling is developed. In general, the most time‐consuming part of FD calculation is to solve large sets of linear equations: Ax=b, where A is a large sparse band symmetric matrix. The direct method using complete Choleski decomposition is quite slow and requires much more computer storage. We have introduced a row‐indexed sparse storage mode to store the coefficient matrix A and an incomplete Choleski conjugate‐gradient (ICCG) method to solve the large linear systems. By taking advantage of the matrix symmetry and sparsity, the ICCG method converges much more quickly and requires much less computer storage. It takes approximately 15 s on a 533 MHz Pentium computer for a grid with 46 020 nodes, which is approximately 700 times faster than the direct method and 2.5 times faster than the symmetric successive over‐relaxation (SSOR) conjugate‐gradient method. Compared with 3D finite‐element resistivity modelling with the improved ICCG solver, our algorithm is more efficient in terms of number of iterations and computer time. In addition, we solve for the secondary potential in 3D DC resistivity modelling by a simple manipulation of the FD equations. Two numerical examples of a two‐layered model and a vertical contact show that the method can achieve much higher accuracy than solving for the total potential directly with the same grid nodes. In addition, a 3D cubic body is simulated, for which the dipole–dipole apparent resistivities agree well with the results obtained with the finite‐element and integral‐equation methods. In conclusion, the combination of several techniques provides a rapid and accurate 3D FD forward modelling method which is fundamental to 3D resistivity inversion.

In seismic reservoir characterization one aims to derive petrophysical properties of hydrocarbon reservoir conditioned to both available well-log and seismic reflection data. In this paper we present a new global pre-stack seismic AVO inversion methodology that inverts pre-stack seismic data directly for density, p-wave velocity, s-wave velocity and facies models. The retrieved subsurface models are able to reproduce the high vertical resolution of the well-log data with the spatial coverage of the seismic data. This new approach is based on an iterative genetic algorithm where the perturbation is done recurring to geostatistical simulation and co-simulation. The inverted facies model is an intrinsic part of the solution and represents the link between the elastic models (observed seismic) and the subsurface geology.KeywordsGeostatistical inversionAVO inversionPre-stack seismic inversionElastic models.

Although the High Folded Zone in the Kurdistan Region of Iraq forms part of the Zagros-Taurus Folds and Thrust belt considered one of the potential hydrocarbon provinces, the oil fields within the zone are still lacking in geophysical exploration and scientific research. So, the rationale behind this study is the prospecting and evaluation of one of the Tertiary carbonate reservoirs at the “WN” oil field in the Duhok area by integrating the 3D seismic and well-log data. The methodology covered seismic interpretation, well logs and their relevant petrophysical analysis, attribute computation, and 3D static property modeling. The constructed reservoir maps revealed a double-plunging rollover anticlinal structure trending in the East-West direction parallel to the Taurus Mountain series. A total of nineteen minor reversal faults trending E-W to ENE-WSW dissecting the northern limb of the anticline were manually interpreted. The isopach map shows various thicknesses ranging from 160 to 330 m, averaging 245 m. The property models show the limited values of their parameters as the effective porosity is limited (0.97-23%), the secondary porosity (0.43-11.7%), permeability (0.00-238.8 mD), the water saturation (12.44-99.8%), and the clay volume (0.00-9.8%). The results of this research indicate that the horizon is a promising reservoir characteristic.