Inversion Of Field Data Research Articles

3-D parallel anisotropic inversion of controlled-source electromagnetic data using nested tetrahedral grids

SUMMARY Geophysicists today face the challenge of quickly and reliably interpreting extensive controlled-source electromagnetic (CSEM) data sets to map subsurface conductivity structures within realistic geological environments. An ideal 3-D CSEM inversion algorithm using tetrahedral grids should be capable of distinguishing different resolution requirements between forward modelling and inversion grids, have an optimal parallel strategy that fully exploits the inherent independence of CSEM data sets while also possessing the capability to handle large-scale geo-electrical models, and incorporate conductivity anisotropy which should be a common characteristic in realistic subsurface environments. However, existing tools in the geo-electromagnetic community often fall short of these three demands. Addressing this gap, our study introduces a scalable and parallel anisotropic inversion technique for CSEM data, capitalizing on the potential of unstructured tetrahedral grids. We first apply the tetrahedral longest-edge bisection method to create a refined dense, heterogeneous forward modelling grid from a coarse inversion grid. This refinement, focused on areas around transmitters and receivers, is seamlessly integrated within the coarser inversion grid’s topology, enabling precise conductivity mapping and preserving electromagnetic response accuracy during model updates. We further innovate with a source-mesh double-level parallel strategy, utilizing the message passing interface technique for parallel handling of independent CSEM data sets and large-scale geo-electrical models. Externally, we dedicate a processor for inversion model updates employing the Limited-memory Broyden–Fletcher–Goldfarb–Shanno optimization algorithm and divide other processors into groups, each associated with specific transmitting sources and frequencies. Internally, in each group, we employ a domain-decomposition-based scalable and robust iterative solvers using the Auxiliary-Space Maxwell pre-conditioner to parallel quickly calculate the electromagnetic responses from its assigned source-frequency set. Additionally, recognizing the potential for electrical conductivity anisotropy in field data, we incorporate the case of vertical transverse isotropy. We validate the effectiveness of our method through examples, including an isotropic land model with undulating topography, an anisotropic marine model and a real-field data case. Results from both synthetic and field data inversions underscore our method’s significant advancements in efficiency and practicality, particularly in addressing large-scale 3-D CSEM data sets inversion challenges in realistic geological environments.

High‐Dimensional Covariance Estimation From a Small Number of Samples

AbstractWe synthesize knowledge from numerical weather prediction, inverse theory, and statistics to address the problem of estimating a high‐dimensional covariance matrix from a small number of samples. This problem is fundamental in statistics, machine learning/artificial intelligence, and in modern Earth science. We create several new adaptive methods for high‐dimensional covariance estimation, but one method, which we call Noise‐Informed Covariance Estimation (NICE), stands out because it has three important properties: (a) NICE is conceptually simple and computationally efficient; (b) NICE guarantees symmetric positive semi‐definite covariance estimates; and (c) NICE is largely tuning‐free. We illustrate the use of NICE on a large set of Earth science–inspired numerical examples, including cycling data assimilation, inversion of geophysical field data, and training of feed‐forward neural networks with time‐averaged data from a chaotic dynamical system. Our theory, heuristics and numerical tests suggest that NICE may indeed be a viable option for high‐dimensional covariance estimation in many Earth science problems.

Innovative imaging of iron deposits using cross‐gradient joint inversion of potential field data with petrophysical correlation

AbstractThis study demonstrates the application of the cross‐gradient joint inversion method to investigate iron mineralization zones within a volcano‐sedimentary environment. The presence of minerals with intense contrasts in density or magnetic susceptibility, such as hematite or magnetite, facilitates modelling the distribution of ore bodies with depth. Our approach involves establishing a unified interpretation of reconstructed density and susceptibility models through both independent and joint inversion with sparsity regularization in conjunction with a petrophysical model resulting from core data. This approach provides an ideal strategy to uncover the realistic geologic setting of iron ore deposits. We initially simulated a synthetic model closely resembling real‐case scenarios to assess the efficacy of the cross‐gradient joint inversion algorithm in comparison to independent inversion. Subsequently, the inversion algorithms were implemented on gravity and magnetic data, collected over an area of 500 × 600 m2 in Shavaz iron‐bearing deposits located in the central Iranian block. The primary iron oxide–apatite type mineralization in the study area is associated with the Nain–Dehshir–Baft fault as a NW–SE trending strike‐slip fault. Although both inversion methods yield satisfactory models, incorporating the cross‐gradient constraint in joint inversion resulted in a more constrained delineation of iron–oxide ore deposits in the fault system. This improvement facilitates the differentiation between hematite and a small percentage of magnetite, providing a more accurate estimation of ore depth. Inversion results suggest that the magnetite mineralization is coated with extensive hematite mineralization and both are positioned relatively within the same depth interval, covered by approximately a 15–25 m sequence of sediments.

Joint inversion of potential field data with adaptive unstructured tetrahedral mesh

Inverting potential field data presents a significant challenge due to its ill-posed nature, often leading to nonunique model solutions. Addressing this, our work focuses on developing a robust joint inversion method for potential field data, aiming to achieve more accurate density and magnetic susceptibility distributions. Unlike most previous work that used regular meshes, our approach adopts an adaptive, unstructured tetrahedral mesh, offering enhanced capabilities in handling the inverse problem of potential field methods. During inversion, the tetrahedral mesh is refined in response to the model update rate. We integrate a Gramian constraint into the objective function, allowing the enforcement of model similarity in terms of either the model parameters or their spatial gradients on an unstructured mesh. In addition, we use the moving least-squares method for gradient operator computation, which is essential for model regularization. Our model studies indicate that this method effectively inverts potential field data, yielding reliable subsurface density and magnetic susceptibility distributions. The joint inversion approach, compared with individual data set inversion, produces coherent geophysical models with enhanced correlations. Notably, it significantly mitigates the nonuniqueness problem, with the recovered anomaly locations aligning more closely with actual ground truths. Applying our methodology and algorithm to field data from the Ring of Fire area in Canada, the joint inversion process has generated comprehensive geophysical models with robust correlations, offering potential benefits for mineral exploration in the region.

Tomofast-x 2.0: an open-source parallel code for inversion of potential field data with topography using wavelet compression

Abstract. We present a major release of the Tomofast-x open-source gravity and magnetic inversion code that incorporates several functionalities enhancing its performance and applicability for both industrial and academic studies. The code has been re-designed with a focus on real-world mineral exploration scenarios, while offering flexibility for applications at regional scale or for crustal studies. This new version includes several major improvements: magnetisation vector inversion, inversion of multi-component magnetic data, wavelet compression, improved handling of topography with support for non-uniform grids, a new and efficient parallelisation scheme, a flexible parameter file, and optimised input–output operations. Extensive testing has been conducted on a large synthetic dataset and field data from a prospective area of the Eastern Goldfields (Western Australia) to explore new functionalities with a focus on inversion for magnetisation vectors and magnetic susceptibility, respectively. Results demonstrate the effectiveness of Tomofast-x 2.0 in real-world studies in terms of both the recovery of subsurface features and performances on shared and distributed memory machines. Overall, with its updated features, improved capabilities, and performances, the new version of Tomofast-x provides a free open-source, validated advanced and versatile tool for constrained gravity and magnetic inversion.

Indirect joint petrophysical inversion of shallow-seismic and multi-offset ground-penetrating radar field data

SUMMARY In near-surface surveys, shallow-seismic and ground-penetrating radar (GPR) full-waveform inversions (FWIs) have received increasing attention because of their ability to reconstruct high-resolution subsurface models. However, they have different sensitivities to the same targets and thus may yield conflicting geophysical parameter models. To solve this issue, we have developed an indirect joint petrophysical inversion (JPI) integrating shallow-seismic and multi-offset GPR data. These data are used to reconstruct porosity and saturation whereby we use only strong sensitivities between petrophysical and geophysical parameters. To promote its field application, we proposed an input strategy to avoid measuring rock matrix parameters and make indirect JPI more robust. We apply indirect JPI to the field data acquired in Rheinstetten, Germany and find that it reveals the mechanical, electrical and petrophysical properties more reliably than individual inversions. The reconstructed models are assessed by direct-push technology, borehole sample measurements and migrated GPR image. Indirect JPI can fit seismic and GPR observed data simultaneously and provide consistent multiparameter models, which are hard to achieve by FWIs and individual petrophysical inversions. We also find that the method is robust when there are uncertainties in petrophysical a priori information. Overall, the field example proves the great potential of using indirect JPI to solve real-world problems.

Coherence-enhancing anisotropic diffusion filter for 3D high-resolution reconstruction of P-wave velocity and density using full-waveform inversion: Application to a North Sea ocean bottom cable data set

Regularization is a central topic in the study of the solutions of ill-posed inverse problems. High-resolution seismic imaging using full-waveform inversion (FWI) belongs to this category of problems. Regularization through anisotropic diffusion, a technique that emerged in the field of image processing, is an interesting alternative to conventional regularization strategies. Exploiting the structural information of a given image, it has the capability to smooth this image along its main structures. The main difficulty is how to design the anisotropic diffusion operator. The concept of coherence enhancing proposed in 2D is extended in 3D and applied so as to filter and enhance the structural coherence of the model updates within an FWI algorithm. The benefits of this strategy are investigated on a 2D synthetic experiment before considering the multiparameter inversion of a 3D field data set from the North Sea up to 10 Hz. From this data, the vertical velocity and the density are simultaneously reconstructed. Compared with a conventional nonstationary Gaussian regularization strategy, the models obtained using the coherence-enhancing anisotropic diffusion strategy indicate an enhanced resolution, especially for the density model. The high-resolution reflectivity image computed from the impedance volume clearly illustrates the benefit this filtering approach can deliver in terms of structural interpretation.

Electrical resistivity tomography through reinforced concrete floor

AbstractThe electrical resistivity tomography (ERT) method is often challenged by the presence of reinforced concrete (RC) in urban and industrial environments, because the embedded metallic wire mesh can severely distort the distribution of subsurface currents. We investigate one typical scenario in real applications, in which an RC floor overlays the natural topsoil or rock. Our synthetic forward simulations show that the embedded wire mesh behaves like a local good conductor in data of small source‐receiver separations and acts like an equal‐potential object that keeps the potential from decaying at large source‐receiver separations. Routine ERT inversions that ignore the RC cannot work properly because the thin and highly conductive wire mesh may be manifested as large uninterpretable low‐resistivity anomalies in the imaging results. Two remedies are adopted to improve the ERT resolution in such cases. First, we find a top layer with high conductivity in our model to adequately represent the wire mesh; then, we initiate the inversion with the top‐layer model as the starting and reference model. This warm‐start approach overcomes the difficulty of recovering the large conductivity contrast between metallic objects and regular earth materials. Second, underground electrodes are added to the survey array, so more information from depth can be obtained to fight against the dominance of current channelling in the wire mesh. Finally, our strategies are used to invert a real ERT dataset from an indoor manufacturing plant, where RC covers the entire floor of the building and electrodes are in contact with the soil through open holes in the floor. Our simulation and field data inversion verify our findings and demonstrate the effectiveness of our solutions in improving the resolution of ERT when the survey is carried out over RC floor in urban and industrial environments.

Application of sensitivity patterns to inversion of magnetotelluric field data in Utah for selecting optimal input

AbstractMany different magnetotelluric response functions such as the impedance and tipper which are converted from measured electromagnetic fields to remove the effects of natural sources have been proposed and studied. To obtain good inversion results, it is important to know that the inversion results depend on the sensitivity patterns of the magnetotelluric response functions used as the input, indicating parts to which the magnetotelluric responses are sensitive. We introduce how to use the sensitivity patterns to determine optimal input magnetotelluric response functions for interpreting field data. For magnetotelluric field data, we use the data acquired at the Utah Frontier Observatory for Research in Geothermal Energy survey area. The target structure in the Utah Frontier Observatory for Research in Geothermal Energy survey area is associated with geothermal energy, and most of the sites are located to the left of the target structure. Examining the sensitivity patterns of the major magnetotelluric response functions, that is the components of the impedance tensor and tipper vector, for the target anomaly, the pattern of y‐component of the tipper vector () covers the areas where most of the sites are distributed. This means information about the target structure is mainly contained in . To investigate the impact of on inversion of the target anomalous body, we compare the inversion results for four cases that (1) the xy‐ and yx‐components of the impedance tensor ( and ) are used; (2) , and are used; (3) , and x‐component of the tipper vector () are applied; and (4) the all components of the impedance tensor (, , and ) are used as the input. This comparison shows that selected as the optimal input from the sensitivity patterns for this case study contributes to retrieving the target anomaly. Through the case study for the Utah Frontier Observatory for Research in Geothermal Energy site, we show how to design a strategy of selecting optimal magnetotelluric response functions based on the sensitivity patterns to effectively image target structures. Our experiment supports that the sensitivity patterns can be used to increase the reliability of magnetotelluric inversion.

The Charnwood Terrane revisited: an integrated petrogenetic and petrophysical model for crustal structure in southern Britain

We based an integrated petrological and petrophysical model for the Ediacaran crust of southern Britain on a review of the c. 570–550 Ma Charnian volcano-sedimentary complex. The latter was emplaced in a magmatic rift wedge within the juvenile continental crust of the c. 720–600 Ma Marches Terrane, a subduction magmatic domain formed at the margin of the Gondwana palaeocontinent. The Charnian magmatic arc is characterized by primitive island arc tholeiite to more evolved calc-alkaline compositions. The inversion of aeromagnetic potential field data and petrophysical modelling reveals details of the internal structure of the Charnian Domain, including a median rift, superimposed annular structures and partitioning lineaments. The modelling suggests that the arc foundation could incorporate magnetite-rich cumulates, which may explain the anomalous geophysical properties, including crustal thickness, rigidity and buoyancy. There is no evidence for significant tectonic displacement between the Charnian Domain and its Marches Terrane host. Instead, the domain likely occupies a wedge-shaped arc/marginal rift basin complex, propagated from a neighbouring ocean into the Gondwana margin. Contemporaneous volcanic rift successions in the Welsh Borderland and Wales of the 570–550 Ma Charnian magmatic phase developed in coeval ensialic rifts within less strongly extended Marches Terrane lithosphere. A comparable diversity of subduction-related magmatism is found in the Neogene–recent Hikurangi destructive margin of New Zealand, providing a plausible analogue for Charnian magmatism. Supplementary material: Supplementary Publication 1 (borehole geophysical log correlation; petrophysical data table; unannotated geophysical maps and sections) and Supplementary Publication 2 (geochemistry analytical conditions and data table) are available at https://doi.org/10.6084/m9.figshare.c.6805248

Cavity detection using a pseudo-3D electric resistivity tomography at the Palaeolithic/Neolithic site of Scaloria Cave, Apulia, Italy: integrated assessment of synthetic and field data sets

A pseudo-3D electrical resistivity tomography (ERT) survey has been carried out to detect cavities at the Neolithic/Palaeolithic site of Grotta Scaloria, close to Manfredonia, Apulia, Italy. Scaloria Cave has a rich history of archaeological research of more than 80 years and is one of the most important Neolithic complexes in the Mediterranean. Synthetic data modelling allowed to check the adequacy of the geophysical method and to develop a proper experimental setup at the survey design stage. Indeed, the results of the field data inversion revealed high resistivity anomalies which can be related to cavities and provided a good definition of the main geological structures and boundaries. Moreover, the results suggest that unknown and speleological unexplored cavities are still present at the Scaloria Cave study site. These findings may provide further insights on pseudo-3D ERT applicability, particularly for cavity detection. Furthermore, the approach used in this study yields fruitful information for further archaeological survey design and for the interpretation of ERT investigations targeting similar geological features and structures.

A novel approach to address source overprint and shadow effects in controlled-source audio-frequency magnetotelluric exploration

Source overprint and shadow effects can significantly affect controlled-source audio-frequency magnetotelluric (CSAMT) data and mask subsurface geologic structures; however, few solutions have been presented. Based on the traditional observation approach, we develop a new approach to solve this problem. An additional transmitter and measurement zone are introduced in the novel approach to constrain the anomalous body causing source overprint or shadow effects in the inversion. To test this approach, six experimental models are designed. Three-dimensional CSAMT responses on the six synthetic models have been simulated, and the results indicate that source overprint and shadow effects have a strong influence on the data. Strong source overprint and shadow effects are found at low frequencies. The distribution of the source overprint or shadow distortions is affected by the shape of the anomalies below the transmitter or between the transmitter and receiver. We evaluate our approach by comparing the inversion results obtained with the new and traditional approaches based on the six synthetic data sets. The results indicate that the new approach not only effectively resolves the anomalies causing source overprint or shadow distortions but also yields more accurate target results in terms of resistivity value, structure geometry, and position than the conventional scheme. The inversion of field data from Yanqing, China, further verifies the effectiveness of our approach. Compared with the traditional inversion, the new scheme inversion obtains results that are more consistent with the rock type revealed by a drillhole.

Feature-based magnetotelluric inversion by variational autoencoder using a subdomain encoding scheme

Magnetotelluric (MT) data inversion aims to reconstruct a subsurface resistivity model that minimizes the discrepancy between inverted and measured electromagnetic data. Conventional pixel-based minimum-structure inversion often yields a smoothed-out reconstruction with a relatively low resolution. A priori geophysical knowledge can be embedded into inversion and improve the reconstruction resolution through proper reparameterization. However, existing reparameterization approaches, such as model-based and parametric transform-based inversion, have limited ability to incorporate various a priori information. The effectiveness of existing deep generative model-based inversion algorithms is still debatable when applied to scenarios with complex backgrounds. We develop a feature-based MT data inversion method based on a variational autoencoder (VAE) with a subdomain encoding scheme. Instead of encoding the entire domain of an investigation, we adopt a 1D subdomain encoding scheme to encode the 1D resistivity-depth models using a single VAE. The latent variables for the 2D model are a combination of the latent variables for 1D models, and the encoded region of interest (ROI) can be flexibly determined. The latent variables of ROI and the pixels outside the ROI are simultaneously inverted using the gradient-descent method. Our 1D subdomain encoding scheme reduces the complexity and diversity of the data set, and it can flexibly embed a priori knowledge with various uncertainties. Synthetic data inversion and inversion of the Southern African Magnetotelluric Experiment field data validate our method’s ability to effectively improve inversion accuracy and resolution.

A Multi-Objective Geoacoustic Inversion of Modal-Dispersion and Waveform Envelope Data Based on Wasserstein Metric

The inversion of acoustic field data to estimate geoacoustic parameters has been a prominent research focus in the field of underwater acoustics for several decades. Modal-dispersion curves have been used to inverse seabed sound speed and density profiles, but such techniques do not account for attenuation inversion. In this study, a new approach where modal-dispersion and waveform envelope data are simultaneously inversed under a multi-objective framework is proposed. The inversion is performed using the Multi-Objective Bayesian Optimization (MOBO) method. The posterior probability densities (PPD) of the estimation results are obtained by resampling from the exploited state space using the Gibbs Sampler. In this study, the implemented MOBO approach is compared with individual inversions both from modal-dispersion curves and the waveform data. In addition, the effective use of the Wasserstein metric from optimal transport theory is explored. Then the MOBO performance is tested against two different cost functions based on the L2 norm and the Wasserstein metric, respectively. Numerical experiments are employed to evaluate the effect of different cost functions on inversion performance. It is found that the MOBO approach may have more profound advantages when applied to Wasserstein metrics. Results obtained from our study reveal that the MOBO approach exhibits reduced uncertainty in the inverse results when compared to individual inversion methods, such as modal-dispersion inversion or waveform inversion. However, it is important to note that this enhanced uncertainty reduction comes at the cost of sacrificing accuracy in certain parameters other than the sediment sound speed and attenuation.

Marine CSEM synthetic study to assess the detection of CO2 escape and saturation changes within a submarine chimney connected to a CO2 storage site

SUMMARY Carbon capture and storage (CCS) within sealed geological formations is an essential strategy to reduce global greenhouse gas emissions, the primary goal of the 2015 United Nations Paris Agreement. Large-scale commercial development of geological CO2 storage requires high-resolution remote sensing methods to monitor CO2 migration during/after injection. A geological formation containing a CO2 phase in its pore space commonly exhibits higher electrical resistivity than brine-saturated (background) sediments. Here, we explore the added value of the marine controlled-source electromagnetic (CSEM) method as an additional and relevant geophysical tool to monitor moderate to significant changes in CO2 saturation within a fluid conduit breaking through the seal of a CCS injection reservoir, using a suite of synthetic studies. Our 2-D CSEM synthetic models simulate various geological scenarios incorporating the main structural features and stratigraphy of two North Sea sites, the Scanner Pockmark and the Sleipner CCS site. Our results show significant differentiation of leakage through the seal with CO2 saturation ($S_{{\rm CO}_2}$) ranging between 20 and 50 per cent, while our rock physics model predicts that detection below 20 per cent would be challenging for CSEM alone. However, we are able to detect with our 2-D inversion models the effects of saturation with 10 and 20 per cent CO2 within a chimney with 10 per cent porosity. We demonstrate that simultaneous inversion of Ey and Ez synthetic electric field data facilitates a sharper delineation of a CO2 saturated chimney structure within the seal, whereas Ez synthetic data present higher sensitivity than Ey to $S_{{\rm CO}_2}$ variation, demonstrating the importance of acquiring the full 3-D electric field. This study illustrates the value of incorporating CSEM into measurement, monitoring and verification strategies for optimal operation of marine CCS sites.

HMCLab: a framework for solving diverse geophysical inverse problems using the Hamiltonian Monte Carlo method

SUMMARY The use of the probabilistic approach to solve inverse problems is becoming more popular in the geophysical community, thanks to its ability to address nonlinear forward problems and to provide uncertainty quantification. However, such strategy is often tailored to specific applications and therefore there is a need for common platforms to solve different geophysical inverse problems and showing potential and pitfalls of the methodology. In this work, we demonstrate a common framework within which it is possible to solve such inverse problems ranging from, for example, earthquake source location to potential field data inversion and seismic tomography. This allows us to fully address nonlinear problems and to derive useful information about the subsurface, including uncertainty estimation. This approach can, in fact, provide probabilities related to certain properties or structures of the subsurface, such as histograms of the value of some physical property, the expected volume of buried geological bodies or the probability of having boundaries defining different layers. Thanks to its ability to address high-dimensional problems, the Hamiltonian Monte Carlo (HMC) algorithm has emerged as the state-of-the-art tool for solving geophysical inverse problems within the probabilistic framework. HMC requires the computation of gradients, which can be obtained by adjoint methods. This unique combination of HMC and adjoint methods is what makes the solution of tomographic problems ultimately feasible. These results can be obtained with ‘HMCLab’, a numerical laboratory for solving a range of different geophysical inverse problems using sampling methods, focusing in particular on the HMC algorithm. HMCLab consists of a set of samplers (HMC and others) and a set of geophysical forward problems. For each problem its misfit function and gradient computation are provided and, in addition, a set of prior models can be combined to inject additional information into the inverse problem. This allows users to experiment with probabilistic inverse problems and also address real-world studies. We show how to solve a selected set of problems within this framework using variants of the HMC algorithm and analyse the results. HMCLab is provided as an open source package written both in Python and Julia, welcoming contributions from the community.

Influence and remedial measures of missing test data on magnetic field source location of underwater vehicle

Due to the incomplete data collected, it will increase the difficulty of inversion location in the field source inversion of the static magnetic field data of underwater vehicles. Therefore, it is very necessary to study the influence of data loss on the static magnetic source location of underwater vehicles and the field source location for timely remedy of missing data. In this paper, the static magnetic equivalent source model of underwater vehicle was established. Then the inversion positioning algorithm was used to locate the magnetic field source of the underwater vehicle obtained from the test, and the influence of the location result under the incomplete data information was analyzed. We used deleting method, linear interpolation method and sliding filling method to populate the data to fill the remedy of missing data. Using the localization algorithm to carried out the inversion location of source, then we took the location of source inversion and the size of the magnetic dipole moment to the ellipsoid model to get fitting curve of magnetic field. The simulation curve of contrast verification test data with experimental data and the lack of remedial method was feasible. The results show that the missing data can not be ignored for the location of the underwater vehicle’s magnetic field source, and the data pairs filled with missing data can be effectively located for the equivalent static magnetic field source of the underwater vehicle through using deletion method, linear interpolation method and sliding filling method.

Geometric 2.5D inversion of marine time domain electromagnetic data with application to hydrocarbon deposits prospecting

To solve the problem of detection and delineation of marine hydrocarbon deposits located at different depths in an inhomogeneous medium, we propose an approach to 2.5D inversion of electromagnetic (EM) data measured in the time domain (TD) using a differentially normalized method of electrical prospecting. The approach is based on geometric inversion, in which block structures are used to parameterize the geological medium. The sizes of blocks in the initial model are set depending on the depth. Bathymetry is taken into account as a 3D surface. As a result of inversion, the coordinates of block boundaries and conductivity inside blocks and layers are determined. The minimized functional is represented as a sum of weighted residuals between computed and practical data and regularizing terms. Adaptive regularization is used to satisfy parameter constraints. To solve a 3D forward problem and calculate derivatives with respect to parameters, the finite element method (FEM) is used. We propose to use a priori data on the depth of the target layers and use various options of block structures with an analysis of possible uncertainties in detecting target bodies and determining their boundaries. We present the results of a 2.5D inversion of field data obtained in one of the areas in the North Sea. Target bodies discovered as a result of inversion are confirmed by well data. Coincidences were obtained both for productive wells and for dry ones. Using synthetic data for various geoelectric models and options of block structures, we justify the proposed approach to the inversion of marine TD EM data and make recommendations for its use.

Spherical Planting Inversion of GRAIL Data

In large-scale potential field data inversion, constructing the kernel matrix is a time-consuming problem with large memory requirements. Therefore, a spherical planting inversion of Gravity Recovery and Interior Laboratory (GRAIL) data is proposed using the L1-norm in conjunction with tesseroids. Spherical planting inversion, however, is strongly dependent on the correct seeds’ density contrast, location, and number; otherwise, it can cause mutual intrusion of anomalous sources produced by different seeds. Hence, a weighting function was introduced to limit the influence area of the seeds for yielding robust solutions; moreover, it is challenging to set customized parameters for each seed, especially for the large number of seeds used or complex gravity anomalies data. Hence, we employed the “shape-of-anomaly” data-misfit function in conjunction with a new seed weighting function to improve the spherical planting inversion. The proposed seed weighting function is constructed based on the covariance matrix for given gravity data and can avoid manually setting customized parameters for each seed. The results of synthetic tests and field data show that spherical planting inversion requires less computer memory than traditional inversion. Furthermore, the proposed seed weighting function can effectively limit the seed influence area. The result of spherical planting inversion indicates that the crustal thickness of Mare Crisium is about 0 km because the Crisium impact may have removed all crust from parts of the basin.

3D trajectory inversion of an adjacent well using scattered P-wave

In oil and gas exploitation, cluster well technology can significantly reduce costs and improve efficiency. An effective adjacent well detection method can greatly reduce the risk of collision between adjacent wells. This study proposes a method to invert the 3D trajectory of an adjacent well using a scattered P-wave obtained by borehole azimuthal acoustic reflection imaging. After obtaining the scattered P-wave from the raw data of the target well using the wave field separation technology, the waveform data in an imaging profile can be obtained by the downhole acoustic directional reception technology. Migration imaging technology is then used to obtain the image of the formation in the imaging profile. Subsequently, by analyzing the images of the formation in the imaging profile of the different azimuths, the well spacing and azimuth of the target well can be determined. Finally, the 3D trajectory of the target well can be obtained by solving the inversion equation. This method was validated by processing the field data from a deviated well in a deep formation. The comparison of the inversion and actual trajectories of the target well demonstrated that the maximum deviation of the inversion trajectory is 0.9 m in the north-south direction, 0.78 m in the east-west direction, 1.45 m in the well spacing, and 2.48° in the azimuth. The field data inversion result demonstrated that the method can effectively use the azimuth reflection acoustic data to invert the 3D trajectory of an adjacent well, which indicates that the borehole azimuthal acoustic reflection imaging technology has great potential within the context of adjacent well detection.