In recent years, deep learning techniques have increasingly been applied to gravity inverse problems, and ResU-Net++ has demonstrated significant success in density-detail preservation during image segmentation and feature extraction. However, its large parameter space and high computational demand make it prone to overfitting. Diffusion models, conversely, excel at generating detailed samples and handling noisy data but generally underperform in segmentation tasks compared to ResU-Net++. To address these challenges, we propose ResDM-Net++, a novel framework that integrates the essential modules of ResU-Net++ into a diffusion model while embedding geophysical insights throughout. Specifically, we employ multi-channel gravity inputs obtained from physically forward-modeled density distributions to ensure that both localized and global subsurface features are learned. Moreover, rather than applying a generic denoising approach, the diffusion component is carefully adapted to retain the inherent spatial correlations of geophysical data, thus improving inversion stability and mitigating overfitting risks. Finally, ResDM-Net++ further embeds physics-based constraints into both the encoder-decoder path and the diffusion steps, forging a synergy between robust denoising and domain-focused feature extraction. Numerical study shows that ResDM-Net++ accurately recovers subsurface density anomalies, exhibiting clear model boundaries and minimal fitting errors. In field applications, it successfully delineates the F2 salt dome in Norway’s Nordkapp Basin with boundaries closely matching seismic interpretations, underscoring ResDM-Net++’s effectiveness in gravity data analysis, structural reconstruction, and inversion in both synthetic and real-world scenarios.

Salt domes are very important in hydrocarbon exploration and identification of potential drilling hazards. While seismic data is indispensable for detailed subsurface imaging, especially in delineating the geometry and properties of salt bodies and their boundaries, gravity inversion provides an additional layer of data by exploiting the density differential. However, traditional methodologies for tackling this problem are complicated by the ill-posedness of the inverse problems. The alternative approach to gravity image is based on machine learning algorithms. Despite the appealing attributes of Convolutional Neural Networks, they are not exempt from limitations, including diminished precision in pinpointing geological features, complications in managing the varying scales of geological structures, and inefficiencies in processing voluminous, high-dimensional data. These deficits can be mitigated by the proposed multi-scale functional MS-UNets network, which, through integration with Squeeze-and-Excitation and Strip Pooling modules, are designed to enhance the capture of detailed information about salt domes. These networks were subjected to rigorous testing using both synthetic and real gravity data, showcasing their robustness across diverse scenarios. This testing highlighted their significant potential for applications in geophysical data interpretation, structural modeling, and inversion processes.

The stark contrast in density between geological layers is a fundamental aspect in the examination of basic geological structures. The delineation between the crystalline basement and sedimentary layers, moreover, is pivotal in the pursuit of strategic energy resources, such as petroleum and natural gas. Traditional full space density inversion, however, is beleaguered by issues of stability and resolution, impeding the accurate characterization of the sharp density interface. To rectify these shortcomings, we introduce an innovative methodology for estimating 2-D depth-to-basement and overlying density distribution, employing a deep neural network with a leaky rectified linear unit as an activation function. Evaluation of the proposed method on simulated sedimentary basin models underscores its superior ability to discern complex geometries of basin boundaries and overlying density, despite the presence of various degrees of Gaussian noise. In practical application to the Poyang basin, the relief of the Cretaceous basement is proficiently recovered through vertical gravity field data, with validation provided by corresponding seismic sections and well-established stratigraphic markers.

Gravity interface inversion is a critical technique in delineating the substructure of basins, providing essential technological and data support for oil and gas exploration. Traditional gravity inversion approaches often encounter issues such as suboptimal local solutions and limited resolution. Moreover, conventional deep learning inversion methods typically require extensive time for empirical parameter adjustment, hindering the achievement of optimal training outcomes. By utilizing Bouguer gravity anomaly data, this research pioneers the application of the EfficientNetV2 network in predicting 3-D basement relief interfaces and variations in overburden density. The network employs a composite scaling technique to adaptively adjust its width, depth, and input resolution, thereby identifying the most effective network configuration. Concurrently, the innovative Fused-MBconv convolutional module efficiently achieves superior results with a reduced number of network parameters. Specifically, in the Poyang Lake Basin study in Jiangxi Province, China, the EfficientNetV2 model demonstrated enhanced accuracy in predicting density variations of the basement interface and overlying strata compared to traditional methodologies.

The study and assessment of the subsurface density distribution are vital for mining and oil & gas exploration. This can be achieved by the three-dimensional (3D) inversion of the observed gravity and gravity gradiometry (GG) data. Due to the ill-posedness of the geophysical inverse problem, the nonuniqueness and instability of solutions represent the main difficulties in inversion. In recent years, convolutional neural networks, especially U-net technology, have found wide applications in image processing, recognition, and reconstruction. This paper proposes using this method for fast reconstruction of the subsurface density models based on the ResUnet technology. The developed new method was examined on two 3D synthetic gravity and gravity gradiometry datasets inversion. The results show that the ResUnet network can reconstruct the density anomaly with sharp boundaries and is robust to the noise, making the solution stable.

Semi-airborne transient electromagnetic (SATEM) method has been efficiently used recently in geophysical exploration due to its relatively portability compared to the standard airborne surveys. However, the SATEM data are often complicated by induced polarization (IP) effects manifesting as abnormal decay and sign reversal in the responses. The IP information can be extracted from SATEM data by joint inversion of the electromagnetic data into the electrical resistivity and IP parameters described in Cole-Cole model. In this paper, we introduce a quasi-two-dimensional inversion scheme to recover the resistivity and IP parameters from SATEM responses by (1) a fast semi-analytical method for Jacobian matrix calculation; and (2) a staged inversion strategy with lateral constraints. The methodology is examined on two synthetic polarized models. Our study indicates that the proposed scheme can improve inversion stability and recover the underground resistivity and IP property distributions.

Towed streamer electromagnetic (TSEM) survey is an efficient data acquisition technique capable of collecting a large volume of electromagnetic (EM) data over extensive areas rapidly and economically. The TSEM survey is capable of detecting and characterizing marine hydrocarbon (HC) reservoirs. However, interpretation of the TSEM data is still a very challenging problem. We propose solving this problem by migrating the optimal synthetic aperture (OSA) data for the TSEM survey. We first represent the OSA data as a solution of Lippmann-Schwinger equation and then demonstrate that the migration of OSA data is just the inner product of the backward-propagated and forward-propagated EM fields. The migration problem is solved iteratively within the general framework of the reweighted, regularized, conjugate gradient (RRCG) method. The proposed method was tested with two synthetic models. We also applied this method to the TSEM data set collected in the Barents Sea and revealed a resistive layer at a depth of about 500 m.

The synthetic aperture (SA) method has recently found applications in the analysis of the low-frequency marine controlled-source electromagnetic (MCSEM) data. It has been shown that this method can enhance the response from an anomalous target. However, in a SA method, anomalous EM fields and the noise will be equally steered and focused, leading to amplifying the noise and introducing artifacts into the images. In addition, the current realizations of the SA method are very sensitive to the noise in the data and the parameters of the SA. In this article, we address these difficulties by introducing a robust SA (RSA) method. The RSA method consists of three steps, namely, robust smoothing of the background field, robust interpolation of EM fields from the real receiver positions to the virtual receiver positions, and estimating the SA weights with a robust optimization scheme. The synthetic model studies show that this method is stable to noise and has a relatively high spatial resolution. We have also applied this method to the towed streamer data collected in the Barents Sea. The generated pseudo-3-D images accurately reveal the locations of the salt domes and fault structures known from the seismic data.

It is well known that both gravity and magnetolluric (MT) methods can be used for the depth-to-basement estimation due to the density and conductivity contrast between the sedimentary basin and the underlaid basement rocks. In this case, the primary targets for both methods are the interface between the basement and sedimenary rocks as well as the physical properties of the rocks (density and conductivity). The solution of this inverse problem is typically nonunique and unstable, especially for gravity inversion. In order to overcome this difficulty and provide a more robust solution, we have developed a method of joint inversion to recover both the depth to the basement and the physical properties of the sediments and basement using gravity and MT data simultaneously. The joint inversion algorithm is based on the regularized conjugate gradient method. To speed up the inversion, we use an effective forward modeling method based on the surface Cauchy-type integrals for the gravity field and the surface integral equation representations for the MT field, respectively. We demonstrate the effectiveness of the developed method using several realistic model studies.

The mainstream approach to the interpretation of towed streamer electromagnetic (EM) data is based on 2.5-D and/or 3-D inversions of the observed data into the resistivity models of the subsurface formations. However, the rigorous 3-D and even 2.5-D inversions require large amounts of computational power and time. The synthetic aperture (SA) method is one of the key techniques in remote sensing using radio frequency signals. During recent years, this method was also applied to low-frequency EM fields used for geophysical exploration. This letter demonstrates that the concept of the SA EM method can be extended for rapid imaging of the large volumes of towed streamer EM data. We introduce a notion of virtual receivers, which complement the actual receivers in the construction of the SA for the towed streamer data. A numerical study demonstrates that this method increases the EM response from potential subsurface targets and opens a possibility for on-board real-time imaging of EM data during a survey. The method is illustrated by the imaging of towed streamer EM data acquired over the Troll oil and gas fields in the North Sea. Remarkably, the imaging of the entire towed streamer EM survey requires just a few seconds of computation time on a desktop PC. This result is significant, because it opens a possibility for real-time imaging of the towed streamer EM survey data.

Determining the sediment-basement interface is the major step in evaluating the mineral resource potential of a region. The magnetotelluric (MT) method can be effectively used for solving this problem because there exists a strong contrast in resistivity between a conductive sedimentary basin and a resistive basement. Conventional inversions of MT data are aimed at determining the volumetric distribution of the conductivity within the inversion domain. The recovered distribution of the subsurface conductivity is typically diffusive, which makes it difficult to select the sediment-basement interface. This letter develops a novel approach to 3-D MT inversion for the depth-to-basement estimate. The key to this approach is selection of the model parameterization, with the depth to basement being the major unknown parameter. In order to estimate the depth to the basement, the inversion algorithm recovers both the thickness and the conductivities of the sedimentary basin. The forward modeling is based on the integral equation approach. The inverse problem is solved using a regularized conjugate gradient method. The Fréchet derivative matrix is calculated based on quasi-Born approximation. The developed method and the algorithm for MT inversion for the depth-to-basement estimate are illustrated on several realistic geoelectrical models.

This letter introduces a new method for the modeling and inversion of magnetic anomalies caused by crystalline basements. The method is based on the 3-D Cauchy-type integral representation of the magnetic field. Traditional methods use volume integrals over the domains occupied by anomalous susceptibility and on the prismatic representation of the volumes with an anomalous susceptibility distribution. Such discretization is computationally expensive, particularly in 3-D cases. The technique of Cauchy-type integrals makes it possible to represent the magnetic field as surface integrals, which is particularly significant in solving problems of the modeling and inversion of magnetic data for the depth to the basement. In this letter, a novel method is proposed, which only requires discretizing the magnetic contrast surface for modeling and inversion. We demonstrate the method using several synthetic models. The results show that the new method is fast and capable of providing high-resolution depth estimation for the sediment-basement interface.

Modeling of induced polarization (IP) phenomena is important for developing effective methods for remote sensing of subsurface geology. However, the quantitative interpretation of IP data in a complex 3-D environment is still a challenging problem of applied geophysics. This letter develops a method of determining a 3-D distribution of the four parameters of the Cole-Cole model based on surface IP data. The method takes into account the nonlinear nature of both electromagnetic induction and IP phenomena. The solution of the 3-D IP inverse problem is based on the regularized conjugate gradient method. The method was tested on a synthetic model with variable dc conductivity, intrinsic chargeability, time constant, and relaxation parameters, and it was also applied to the actual 3-D IP survey data. We demonstrate that the four parameters of the Cole-Cole model, namely, dc electrical resistivity, chargeability, time constant, and the relaxation parameter, can be recovered from the observed IP data simultaneously.

This letter introduces a novel approach to the optimal design of the synthetic aperture method for marine controlled-source electromagnetic (MCSEM) surveys. We demonstrate that the sensitivity of the MCSEM survey to a specific geological target could be enhanced by selecting the appropriate amplitude and phase coefficients of the corresponding synthetic aperture. We have developed a general optimization technique to find the optimal parameters of the synthetic aperture method. This approach makes it possible to increase the corresponding ratio between total and background fields within the area of an expected reservoir anomaly and, in this way, improve the resolution of the EM data with respect to potential subsurface targets. We also demonstrate that this optimal synthetic aperture method can be used for a removal of the distorting airwave effect from the MCSEM data collected in shallow water.

We introduce multinary inversion to explicitly exploit the physical property contrasts between different objects and their host medium, e.g., between air-filled tunnels and their surrounding earth. Conceptually, multinary inversion is a generalization of binary inversion to multiple physical properties. However, unlike existing realizations of binary inversion which are solved using stochastic optimization methods, our realization of multinary inversion can be solved using deterministic optimization methods. This is significant as the method can be applied to both linear and nonlinear operators and easily extends to joint inversion of multimodal geophysical data. Using synthetic models of full-tensor gravity gradiometry data, multinary inversion is demonstrated to be robust for tunnel detection relative to the presence of significant geological noise.

We introduce a new approach to 3-D electromagnetic (EM) modeling for models with large conductivity contrast. It is based on the equations for integral current within the cells of the discretization grid, instead of the electric field or electric current themselves, which are used in the conventional integral-equation method. We obtain these integral currents by integrating the current density over each cell. The integral currents can be found accurately for the bodies with any conductivity. As a result, the method can be applied, in principle, for the models with high-conductivity contrast. At the same time, knowing the integral currents inside the anomalous domain allows us to compute the EM field components in the receivers using the standard integral representations of the Maxwell's equations. We call this technique an integral-electric-current method. The method is carefully tested by comparison with an analytical solution for a model of a sphere with large conductivity embedded in the homogenous whole space

Multitransmitter electromagnetic (EM) surveys are widely used in remote-sensing and geophysical exploration. The interpretation of the multitransmitter geophysical data requires numerous three-dimensional (3-D) modelings of the responses of the receivers for different geoelectrical models of complex geological formations. In this paper, we introduce a fast method for 3-D modeling of EM data, based on a modified version of quasilinear approximation, which uses a multigrid approach. This method significantly speeds up the modeling of multitransmitter-multireceiver surveys. The developed algorithm has been applied for the interpretation of marine controlled-source electromagnetic (MCSEM) data. We have tested our new method using synthetic problems and for the simulation of MCSEM data for a geoelectrical model of a Gemini salt body.