Joint Inversion Method Research Articles

Joint Inversion of DC Resistivity and Gravity Data with Undulating Terrain Based on Deformed Hexahedral Mesh

In the field of mineral resource exploration, accurate imaging of subsurface structures is key to discovering and assessing potential mineral deposits. Traditional single geophysical methods, limited by terrain variations and their own constraints, can lead to divergent solutions and structural inconsistencies, affecting the reliability of exploration outcomes. To address these challenges, this paper presents a joint inversion method for three-dimensional direct current (DC) resistivity and gravity data based on a deformed hexahedral mesh. The article begins by outlining the current state of development of the method under study and proposes a research plan, followed by a detailed explanation of the theoretical basis and algorithmic implementation of the proposed method. Model tests confirm the advantages of the deformed hexahedral mesh in reducing terrain impacts and enhancing model resolution, demonstrating the optimization and complementarity of the resolution between the two methods after joint inversion. Finally, applying this method to actual data from the Huaniu Mountain area shows that joint inversion not only improves the consistency of the ore belt structure but also provides a more precise analysis for the quantitative interpretation of the distribution of underground mineral resources. This confirms the method’s effectiveness and potential in practical geological exploration.

Joint PP and PS AVA inversion using an acceleration algorithm and a multi-trace strategy

Abstract Exploration utilizing converted wave (PS) technology has garnered considerable interest in recent years owing to its ability to provide distinct insights into subsurface properties compared to compressional waves (PP). PS wave is particularly advantageous for accurately determining S-wave velocity (${V}_S$) and bulk density ($\rho $), whereas PP wave is better suited for assessing P-wave velocity (${V}_P$). Thus, theoretically, joint PP and PS AVA inversion can yield precise results for ${V}_P$, ${V}_S$, and $\rho $. However, a critical step before joint inversion is PP and PS registration, which is prone to causing lateral discontinuity in the inversion outcomes. To mitigate this issue, we present a simultaneous multi-trace joint inversion method. The method can improve the lateral consistency of inversion results by imposing lateral continuity constraints on the elastic parameters being inverted. Nevertheless, this simultaneous multi-trace inversion method inherently increases computational burden. To enhance algorithmic efficiency without sacrificing inversion precision, we implement an acceleration strategy. Synthetic and real data examples demonstrate that the proposed method offers remarkable performance in enhancing computational efficiency and lateral continuity compared to the conventional methods.

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.

High-resolution seismic inversion method based on joint data-driven in the time-frequency domain

Seismic inversion can be divided into time-domain inversion and frequency-domain inversion based on different transform domains. Time-domain inversion has stronger stability and noise resistance compared to frequency-domain inversion. Frequency domain inversion has stronger ability to identify small-scale bodies and higher inversion resolution. Therefore, the research on the joint inversion method in the time-frequency domain is of great significance for improving the inversion resolution, stability, and noise resistance. The introduction of prior information constraints can effectively reduce ambiguity in the inversion process. However, the existing model-driven time-frequency joint inversion assumes a specific prior distribution of the reservoir. These methods do not consider the original features of the data and are difficult to describe the relationship between time-domain features and frequency-domain features. Therefore, this paper proposes a high-resolution seismic inversion method based on joint data-driven in the time-frequency domain. The method is based on the impedance and reflectivity samples from logging, using joint dictionary learning to obtain adaptive feature information of the reservoir, and using sparse coefficients to capture the intrinsic relationship between impedance and reflectivity. The optimization result of the inversion is achieved through the regularization term of the joint dictionary sparse representation. We have finally achieved an inversion method that combines constraints on time-domain features and frequency features. By testing the model data and field data, the method has higher resolution in the inversion results and good noise resistance.

Crustal and uppermost mantle structures of the North American Midcontinent Rift revealed by joint full-waveform inversion of ambient-noise data and teleseismic P waves

The Midcontinent Rift (MCR), hosting several world-class ore deposits, is the fossil remnant of a massive Mesoproterozoic rifting event (1.1 Ga) that did not lead to the formation of an ocean basin. To better understand the lithospheric processes associated with the rifting stage and its subsequent failure, we developed a novel full-waveform joint inversion method using ambient noise data and teleseismic P waves for this seismically inactive region. We apply this approach to three years (2011-2013) of seismic recordings from the Superior Province Rifting EarthScope Experiment (SPREE) (~12 km average station spacing) and the USArray Transportable Array (~70 km average station spacing), and obtain a new 3D high-resolution Vs model down to 100 km depth, as well as Vp and density models down to 60 km depth. The model shows major velocity anomalies in agreement with previous seismic studies for the western arm of the MCR. In particular, we observe high density (2.8-3.0 g/cm3), Vp (6.3-6.5 km/s), and Vs (3.6-3.7 km/s) structures in the shallow upper crust within the rift, likely associated with volcanic rocks. Similar to a previously identified underplated layer, we also observe extensive normal-to-high Vs (3.8-4.2 km/s) along the whole rift axis and Vp (6.8-7.5 km/s) beneath the northern segment of the rift within the lower crust. However, the Vs and Vp values are lower than average for typical underplated materials. We suggest that this underplated layer may represent a combination of different intrusive rock types (e.g., gabbro, anorthosite) developed during magma differentiation processes, or contamination of the mafic magma by surrounding crustal material, or intrusions of sills.

A Joint Inversion Method Algorithm for T2-Pc two Dimensional NMR based on Logistic Functions

Data processing is a key step in the analysis of nuclear magnetic resonance (NMR) experimental data, and efficient and accurate computer inversion algorithms are the core of the T2-Pc two-dimensional NMR experiment. T2-Pc two-dimensional NMR experiment is an advanced experimental method that characterizes reservoir connectivity through two dimensions: relaxation time and capillary pressure, and can obtain irreducible water saturation under different pressure differences. However, the algorithm currently used for T2-Pc two-dimensional spectrum inversion uses a mutation kernel function, resulting in low accuracy of calculation results. This paper uses the Logistic function as the two-dimensional inversion kernel function, rewrites the inversion algorithm, and obtains more accurate inversion results. Numerical simulations have proven that the T2-Pc two-dimensional map obtained by this method not only has higher resolution, but also has greater applicability in the case of low signal-to-noise ratio and a small number of centrifugal echo groups. Practice has found that the proposed method can reduce the number of centrifugations during the experiment and significantly improve the efficiency of T2-Pc two-dimensional nuclear magnetic resonance experiments.

An empirical method for joint inversion of wave and wind parameters based on SAR and wave spectrometer data

An empirical method for joint inversion of wave and wind parameters based on SAR and wave spectrometer data

Joint Inversion of Gravity and Magnetic Data based on the Modified Structural Similarity Index for the Structural Consistency Constraint

Joint inversion is a crucial approach to mitigate the non-uniqueness problem in geophysical inversion. Nevertheless, existing joint inversion methods fall short of meeting the stringent requirements of high-precision exploration, necessitating the development of new techniques. In this paper, we introduce the Structural Similarity Index (SSIM) as a novel structural consistency constraint for the joint inversion of gravity and magnetic data. Compared with the results of cross-gradient inversion, our method demonstrates outstanding performance and stability. SSIM inversion not only introduces a new class of joint inversion with structural constraints but also enhances the consistency of inversion results in the distribution of physical attribute values. The structural constraints of SSIM inversion are more comprehensive and robust, significantly improving the reliability of the inversion. Both synthetic and real data applications demonstrate that the proposed method can effectively handle both synthetic and real data, yielding outstanding results.

Joint Inversion Method of Gravity and Magnetic Data with Adaptive Zoning Using Gramian in Both Petrophysical and Structural Domains

Joint Inversion Method of Gravity and Magnetic Data with Adaptive Zoning Using Gramian in Both Petrophysical and Structural Domains

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.

A simple weighting method for inverting earthquake source parameters using geodetic multisource data under Bayesian algorithm

SUMMARY More accurate inversion of source fault geometry and slip parameters under the constraint of the Bayesian algorithm has become a research hotspot in the field of geodetic inversion in recent years. In nonlinear inversion, the determination of the weight ratio of the joint inversion of multisource data is more complicated. In this context, this paper proposes a simple and easily generalized weighting method for inversion of source fault parameters by joint geodetic multisource data under the Bayesian framework. This method determines the relative weight ratio of multisource data by root mean square error (RMSE) value and can be extended to other nonlinear search algorithms. To verify the validity of the method in this paper, this paper first sets up four sets of simulated seismic experiment schemes. The inversion results show that the joint inversion weighting method proposed in this paper has a significant decrease in the large residual value compared with the equal weight joint inversion and the single data source joint inversion method. The east–west deformation RMSE is 0.1458 mm, the north–south deformation RMSE is 0.2119 mm and the vertical deformation RMSE is 0.2756 mm. The RMSEs of the three directions are lower than those of other schemes, indicating that the proposed method is suitable for the joint inversion of source parameters under Bayesian algorithm. To further verify the applicability of the proposed method in complex earthquakes, the source parameters of the Maduo earthquake were inverted using the method of this paper. The focal depth of the inversion results in this paper is closer to the focal depth released by the GCMT agency. In terms of strike angle and dip angle, the joint inversion in this paper is also more inclined to the GCMT results. The joint inversion results generally conform to the characteristics of left-lateral strike-slip, which shows the adaptability of this method in complex earthquakes.

Near-surface imaging by joint inversion of ERT and seismic traveltime data with guided FCM clustering

We present a novel joint inversion strategy for electrical resistivity tomography (ERT) and seismic first-arrival traveltime data with guided fuzzy c-means (GFCM) clustering coupling to increase the accuracy of inversion results and improve the characterization of heterogeneous near-surface materials. The physical parameter correlation between the resistivity and seismic velocity is enforced using a GFCM clustering coupling term in the objective function, which also includes misfit and regularization terms. The physical property models estimated by joint inversion are guided by the clustering centers of a priori petrophysical parameters. A limited-memory quasi-Newton approach is used to optimize the objective function. To validate the proposed approach and describe its implementation in detail, tests were first performed using two synthetic models. The stratigraphic structures recovered by joint inversion with GFCM clustering coupling are more consistent with the true model than those inverted by individual inversion, cross-gradient and fuzzy c-means (FCM) joint inversion. Furthermore, the physical parameters estimated using GFCM joint inversion are significantly more accurate than those estimated using individual inversion and the other two joint inversion methods. The joint inversion algorithm was applied to field data from the Liangzhu site in Hangzhou, China. The depth and shape of the stratigraphic interface imaged by GFCM joint inversion are consistent with the drilling results. However, when using individual inversion and the other two joint inversion methods, the recovered stratigraphic structures have some differences with the drilling data. Therefore, GFCM joint inversion is an effective and reliable method for near-surface fine imaging.

Joint inversion method of multipoint ambient noise horizontal-to-vertical spectral ratio for 3-D velocity structure of local site and its application

SUMMARY The diffusion field theory has been widely used to interpret ambient noise wave fields. Based on this theory, 1-D subsurface velocity structure inversion method is developed. However, few studies have referred to the noise horizontal to vertical (NHV) spectral ratio inversion of 3-D subsurface velocity structures, and almost no effective 3-D NHV inversion tools have been developed. To develop a useful tool for obtaining 3-D soil layer velocity structures, we combined the NHV forward calculation formula derived from diffusion field theory with the guided Monte Carlo algorithm and then extended the single-point NHV inversion to multipoint joint inversion through a joint objective function. Subsequently, a new 3-D soil layer velocity structure inversion method was proposed. Subsequently, a synthetic 2-D case was used to verify the proposed method. Finally, the proposed method was applied to the Xiangtang Array in Tangshan, China, to identify the 3-D velocity structures of the site based on noise observations. The results show that the proposed multipoint joint 3-D inversion method is effective for identifying 3-D underground velocity structures.

Joint Inversion Method of Rock Physics Based on Hunger Games Search Correction and Bidirectional Long-Short-Term Memory Network

Joint Inversion Method of Rock Physics Based on Hunger Games Search Correction and Bidirectional Long-Short-Term Memory Network

Deep Structure of Nanling-Xuancheng Ore District, Eastern China: Insights from Integrated Geophysical Exploration

As the depth of mineral exploration increases, integrated geophysical methods are increasingly playing a crucial role in prospecting deep structures at the district scale. The Nanling-Xuancheng ore district is the eighth ore district in the middle-lower Yangtze metallogenic belt in China. To reveal the deep structure of the mining district, this study mainly focuses on regional high-precision gravity and magnetic data and integrates the interpretation of magnetotelluric and reflection seismic data from a key area. By using a 2.5D joint inversion method with prior information constraints, new insights into the deep structures, tectonic deformation, and magmatic activity are obtained. Structurally, the Nanling-Xuancheng ore district presents a structural pattern of “two uplifts and two depressions” composed of multi-level thrust-overturned and folds formed by Mesozoic depressions, which has a three-layer structure in the vertical direction (shallower than 10 km). Tectonically, the main faults in the study area trend NW, which intersect with NE-trending and EW-trending faults to form a branching structure from deep to shallow. The fault intersections provide pathways for magma intrusion. The distribution of deep-seated concealed magmatic rocks shows the characteristic pattern of “a primary magma source spawning multiple subsidiary intrusion”.

Gradient optimization method for tunnel resistivity and chargeability joint inversion based on deep learning

The water inrush hazards have become one of the bottleneck problems that constrain tunnel construction. Ahead geological prospecting is the major tool to avoid geo-hazards and ensure safe, economical and efficient tunnelling. This work proposes a novel deep learning-based electrical method, which jointly inverses resistivity and chargeability to estimate water-bearing structures and water volume. Specifically, we design an encoder–decoder network, with one shared encoder to extract features from input data, two encoders to output resistivity and chargeability models, respectively, and an elaborate collinear regularization on the two outputs to reduce solution multiplicity. Moreover, our input is first transformed to the gradient domain to address the spatial incorrespondence issue between observation data and the electrical model. Compared with traditional linear inversion methods, our proposed method demonstrates superiority in locating and delineating anomalous bodies. The ablation study also shows that joint inversion of two parameters could benefit and outperform independent parameter inversion.

Joint inversion for facies and petrophysical properties based on a bi‐level optimization model

AbstractIn many subsurface studies, facies and petrophysical properties are two important reservoir parameters that are closely correlated. They are routinely used in well interpretation, hydrocarbon reserve calculation and production profile prediction. These two parameters have commonly been determined in two separate tasks because of their mathematical differences (facies are discrete, and petrophysical properties are continuous). However, this is incorrect because facies and petrophysical properties are often strongly correlated. Therefore, we propose a new joint inversion method of facies and petrophysical properties based on a bi‐level optimization model. In the bi‐level optimization model, the upper‐level problem is the petrophysical property inversion while the lower‐level problem can identify the facies and add a facies‐related constraint for the upper‐level optimization. We also develop a new genetic algorithm for the discrete‐continuous inversion problem based on the bi‐level optimization model because the inversion problem usually has multiple local solutions. In addition, rock physics and statistics are combined in the inversion process. A rock physics model is used to establish the basic relationships between the petrophysical and elastic parameters, and the statistical approach is used to describe the intrinsic connection among the multiple reservoir parameters based on well log data. The numerical experiments indicate that the traditional separate prediction method and the new joint inversion method can quickly obtain more accurate results. In the application examples of real data, the inversion results can be matched to the well log data within the limits of the input data resolution, which further verifies the reliability and application potential of this new method.

Joint Inversion of Saturation and Qv in Low-Permeability Sandstones Using Spontaneous Potential and Resistivity Logs

Hydrocarbon saturation is an important formation parameter and the basis for quantitative reservoir evaluation. However, the saturation models of shaly sandstones contain more parameters than clean sandstones; therefore, determining these parameters for shaly sandstone is difficult. In this study, based on the response of spontaneous potential (SP) logging, the membrane potential equations of shaly sandstone in water-saturated and oil-water states were derived, and an analytical equation of the anomaly amplitude of the SP in shaly sandstone was obtained. On this basis, the influencing factors of the SP anomaly were analyzed. Furthermore, a joint inversion of SP and resistivity was established to calculate oil saturation and cation exchange capacity per unit pore volume (Qv). The SP log was interpreted using the proposed analytical model, and the resistivity log was processed using the Waxman-Smits model. The particle swarm optimization method was used to resolve the objective function. Finally, the method was applied to the Chang 8 Reservoir in Yanchang, on the western edge of the Ordos Basin, China. The resistivity and SP log curves synthesized using the inverse parameters agree with the field logs. The inversion of the saturation and Qv is consistent with core data and oil testing, indicating that the joint inversion method is stable, reliable, and accurate.

Multi-scale data joint inversion of minerals and porosity in altered igneous reservoirs—A case study in the South China Sea

There are abundant igneous gas reservoirs in the South China Sea with significant value of research, and lithology classification, mineral analysis and porosity inversion are important links in reservoir evaluation. However, affected by the diverse lithology, complicated mineral and widespread alteration, conventional logging lithology classification and mineral inversion become considerably difficult. At the same time, owing to the limitation of the wireline log response equation, the quantity and accuracy of minerals can hardly meet the exploration requirements of igneous formations. To overcome those issues, this study takes the South China Sea as an example, and combines multi-scale data such as micro rock slices, petrophysical experiments, wireline log and element cutting log to establish a set of joint inversion methods for minerals and porosity of altered igneous rocks. Specifically, we define the lithology and mineral characteristics through core slices and mineral data, and establish an igneous multi-mineral volumetric model. Then we determine element cutting log correction method based on core element data, and combine wireline log and corrected element cutting log to perform the lithology classification and joint inversion of minerals and porosity. However, it is always difficult to determine the elemental eigenvalues of different minerals in inversion. This paper uses multiple linear regression methods to solve this problem. Finally, an integrated inversion technique for altered igneous formations was developed. The results show that the corrected element cutting log are in good agreement with the core element data, and the mineral and porosity results obtained from the joint inversion based on the wireline log and corrected element cutting log are also in good agreement with the core data from X-ray diffraction. The results demonstrate that the inversion technique is applicable and this study provides a new direction for the mineral inversion research of altered igneous formations.

Three-Dimensional Separate and Joint Inversions of Multi-Component Frequency-Domain Airborne Electromagnetic Data: Synthetic Model Studies.

Airborne electromagnetic (AEM) surveys using airborne mobile platforms enable rapid and efficient exploration of areas where groundwork is difficult. They have been widely used in fields such as shallow resource exploration and environmental engineering. Three-dimensional AEM inversion is the main technique used in fine structural interpretation. However, most current methods focus on separate component data inversions, which limit the kinds of structures that can be recovered in the inversion results. To address this issue, a method for the robust 3D joint inversion of multicomponent frequency-domain AEM data was developed in this study. First, a finite element method based on unstructured tetrahedral grids was used to solve the forward problem of frequency-domain AEM data for both isotropic and anisotropic media. During inversion, a limited-memory quasi-Newton (L-BFGS) method was used to reduce the memory requirements and enable the joint inversion of large-scale multicomponent AEM data. The effectiveness of our algorithm was demonstrated using synthetic models for both isotropic and anisotropic cases, with 5% Gaussian noise added to the modeling data to simulate the measured data for separate and joint inversions. The results of the synthetic models show that joint inversion has advantages over separate inversion in that it enables the recovery of finer underground structures and provides a novel approach for the fine interpretation of frequency-domain AEM data.