Linear Inversion Method Research Articles

Heat and mass transfer visualisation of an exothermic acid-base microfluidic reactor using infrared thermospectroscopy

ABSTRACT Here, a microfluidic reactor that is transparent in the mid-wave infrared spectrum with an effective path length of 38 µm is developed for characterisation via operando Fourier-transform Infrared (FTIR) thermospectroscopy. This imaging technique couples an infrared (IR) camera with an FTIR spectrometer to quantify heat and mass transfer in the exothermic acid-base reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH). The absorbance fields of the reaction are used to simultaneously derive the molar concentration fields of the reactants (HCl and NaOH) and products (sodium chloride [NaCl]) at the microscale through a linear inverse method. The heat generated at the reaction interface is visualised through a thermal field captured from the measured proper emission. Concentration and thermal fields are then compared to an advection-diffusion model for validation. The results proposed in this work present a refined contactless calorimetry process for characterising the heat and mass transport in an acid-base reaction. Further refinement of this work will enable accurate and non-invasive measurements for the enthalpy of reaction in chemical reactions.

Regional stress field in the SE margin of the Tibetan Plateau revealed by the focal mechanisms of small and moderate earthquakes

In this study, we investigate the stress field in the southeastern margin of the Tibetan Plateau. We first determine the focal mechanism solutions of 1537 small and moderate (3.2 ≤ MW ≤ 6.7) regional earthquakes from January 2009 to June 2021, and then use the focal mechanisms to invert for the spatial variation of crustal stress field by a damped linear inversion method. Our result suggests that in the southeastern margin of the Tibetan Plateau the seismogenic zone is in the upper crust above 15-km depth, and the stress field is predominantly strike-slip in the Sichuan-Yunnan Rhombic Block (SYRB). The maximum compressional stress axis is oriented in a fan-shaped pattern, rotating clockwise from nearly east-west in the Songpan-Ganzi Terrain in the north to northwest-southeast in the SYRB to nearly north-south across the Red River Fault in the Indo-China Block (ICB), consistent with the GPS-derived surface strain rate. The stress field around the border of the Tibetan Plateau with high elevation relief appears to be largely caused by gravitational effect with the maximum extensional axis perpendicular to the topography gradient. The stress field in the vicinity of the Longmenshan Fault Zone and in the Yangtze Craton is mainly thrust as a result of the eastward expansion of the Tibetan Plateau and the resistance of the Sichuan Basin. Near the epicenter of the 2008 Wenchuan earthquake and in the northeastern end of the Longmenshan Fault Zone, the thrust stress field shows spatial variations as a result of the perturbation by complex geometry and the post-seismic healing process. Our result provides multi-resolution images of the stress field for better understanding about the mechanisms of seismic activity and crustal deformation in the southeastern margin of Tibetan Plateau.

Estimating uncertainty of mean water table depth in the contiguous United States using highly parameterized linear inverse method

Because of spatiotemporal observation gaps and prohibitive computational cost, estimating uncertainty of mean water table depth in the continental scale is a challenging problem. Based on the groundwater flow of mean water table, we first analyzed uncertainty of the mean water table depth in the contiguous US using a highly parameterized linear inverse method with unknown boundary condition and source/sink terms. To estimate uncertainty of the mean heads, the total relative errors of temporal heads and mean heads for all observed wells with more than one head instead of the relative error of temporal heads and mean head for each observed well was proposed to obtain t Location-scale and Gaussian distributions of the total relative errors in the synthetic cases. The results indicate that uncertainties of the mean heads by t Location-scale distribution are more accurate than those by Gaussian distribution. Then, we applied the inverse method and t Location-scale distribution of the total relative errors in the contiguous US to estimate uncertainty of the mean water table depth during 1900–2016. The results demonstrate that uncertainty in the K values did not result in large uncertainty of the mean water table depth. Uncertainty of the mean water table depth in the contiguous US was first estimated based on variation of hydraulic conductivity and the observed mean water table, where 100 realizations of the mean water table depth were obtained by t Location-scale distribution. The results demonstrate both the feasibility and high precision of the inverse method.

Application of Neural Network in Seismic Risk Survey

The accuracy of inversion data is determined by the reliability of linear inversion method. Therefore, the study of nonlinear seismic inversion method is a meaningful work. This paper mainly aims at the application of nonlinear neural network inversion method in Fujian Risk Survey, the following work has been accomplished: (1) The theory and algorithm of the conventional multilayer feedforward neural network and some problems in the design of the model are analyzed and summarized. Aiming at the gradient descent function search algorithm in the BP algorithm, a method for global optimization is proposed by combining simulated annealing (global search algorithm) with Conjugate gradient method (local search algorithm) , the principle and implementation of simulated annealing and conjugate gradient algorithm are analyzed in detail. (2) Based on the analysis of conventional multilayer feedforward neural networks, the model structure and basic principle of probabilistic neural networks are studied. The object function search algorithm and its realization are analyzed. The method is applied to the risk elimination prediction for the first time, and the results are satisfactory. (3) The method and principle of inversion of reservoir parameters by using various seismic attribute information and neural network technology are discussed. In order to make full use of the effective information contained in seismic signal, the method of seismic attribute extraction and optimization is studied, the principle and implementation method of attribute optimal ranking by stepwise recursive method and selecting the most important attribute combination by interactive verification method are presented.

Comparison of Near-Surface Attenuation from Surface Array-Based Seismic Noise Data and Borehole Weak-Motion Recordings at the STIN Test Site in Northeastern Italy

Abstract Seismic wave attenuation and the related shear-wave quality factor (QS) in the near surface are crucial parameters for ground motion simulations and seismic hazard assessments. Although recent approaches developed to calculate QS from seismic noise acquired by surface arrays have been accepted for practice, additional testing and comparison of results estimated using various geophysical methods are still necessary to verify the reliability of such techniques. This work presents the results of an experiment conducted at the STIN site in northeastern Italy, which is equipped with a 100 m deep instrumented borehole. A seismic noise campaign was implemented by installing a temporary independent local surface array of seismological stations. The gathered data were used to initially estimate the shear-wave velocity (VS) profile and frequency-dependent Rayleigh-wave attenuation, and subsequently determine the QS factor via a linearized inversion method. The study compares these findings with the VS and QS values derived from analyzing weak-motion events recorded by two permanent seismic sensors positioned at the top and bottom of the well. The results confirm the potential of the inversion procedure used to obtain QS from local-scale seismic noise arrays as a promising approach for conducting attenuation studies at the local level in less geologically complex sites.

1087 Large Incidence and Risk Factors Meta-analysis of Dysphagia in Over 132,000 Anterior, Posterior, and Hybrid Surgeries for Cervical Spondylosis Myelopathy

INTRODUCTION: Surgical management of Cervical Spondylotic Myelopathy (CSM) is associated with complications with devastating impacts. Dysphagia is one of these major complications with the incidence rate being not completely known in different surgical approaches. METHODS: PubMed/MEDLINE, SCOPUS, and Cochrane were systematically searched until January 2023. Rates and risk of complications were assessed. Meta-analysis of rates and risks was performed with generalized linear mixed model (GLMM) and inverse variance method, respectively, and compared between techniques. RESULTS: 1196 citations were screened and 39 studies with 60 instances of dysphagia incidence/risk factors reports from over 132,442 patients were identified. Dysphagia’s overall incidence rate was 4.98%[95% confidence interval 3.23-7.61] and was significantly different between surgery groups (Chi2 p < 0.01). It was found in 7.97% [4.95–12.57] of anterior surgeries, 1.52% [0.94–2.45] of posterior ones, and 11.25% [3.38–31.44] of hybrid techniques (statistical comparison: P < A < H). Advanced age (>65) risked dysphagia significantly (OR 1.38 [95%CI 1.11-1.71]). CONCLUSIONS: Chances of posterior surgery being complicated with dysphagia is not negligible and should be discussed with patient before surgery, especially with older adults.

Seismic amplitude inversion based on a new PP-wave reflection coefficient approximation equation for vertical transversely isotropic media

We develop a method for the simultaneous amplitude-variation-with-offset or -angle inversion of anisotropic parameters for transversely isotropic media with vertical axis of symmetry (VTI media). First, we introduce a nonlinear PP-wave reflection coefficient approximation equation in terms of only P- and S-wave impedances for isotropic elastic media. Then, by replacing the isotropic part of Rüger’s equation with this equation, we obtain a new PP-wave reflection coefficient approximation equation called the ASI Rüger equation for VTI media. To invert the parameters for VTI media based on the ASI Rüger equation, we adopt the Bayesian generalized linear inversion (GLI) method, a combination of GLI and Bayesian linear inversion, in which the noise and model perturbation are assumed to conform to the zero-mean Gaussian distribution. Compared with Rüger’s equation, the ASI Rüger equation decreases the trade-off between the parameters and reduces the ill-posedness of the inverse problem. The synthetic and field data tests demonstrate the feasibility of our method for inverting VTI media parameters (the vertical P-wave impedance, the vertical S-wave impedance, and Thomsen’s parameters [Formula: see text] and [Formula: see text]).

Quantum Tomography: From Markovianity to Non-Markovianity

The engineering of quantum computers requires the reliable characterization of qubits, quantum operations, and even the entire hardware. Quantum tomography is an indispensable framework in quantum characterization, verification, and validation (QCVV), which has been widely accepted by researchers. According to the tomographic target, quantum tomography can be categorized into quantum state tomography (QST), quantum process tomography (QPT), gate set tomography (GST), process tensor tomography (PTT), and instrument set tomography (IST). Standard quantum tomography toolkits generally consist of basic linear inverse methods and statistical maximum likelihood estimation (MLE)-based methods. Furthermore, the performance of standard methods, including effectiveness and efficiency, has been further developed by exploiting Bayesian estimation, neural networks, matrix completion techniques, etc. In this review, we introduce the fundamental quantum tomography techniques, including QST, QPT, GST, PTT, and IST. We first introduce the details of basic linear inverse methods. Then, the framework of MLE methods with constraints is summarized. Finally, we briefly introduce recent further research in developing the performance of tomography, utilizing some symmetry properties of the target. This review provides a primary getting-start in developing quantum tomography, which promotes quantum computer development.

A method for constructing directional surface wave spectra from ICESat-2 altimetry

Abstract. Sea ice is important for Earth's energy budget as it influences surface albedo and air–sea fluxes in polar regions. On its margins, waves heavily impact sea ice. Routine and repeat observations of waves in sea ice are currently lacking, and therefore a comprehensive understanding of how waves interact with sea ice and are attenuated by it is elusive. In this paper, we develop methods to separate the two-dimensional (2D) surface wave spectra from sea-ice height observations made by the ICESat-2 (IS2) laser altimeter, a polar-orbiting satellite. A combination of a linear inverse method, called generalized Fourier transform (GFT), to estimate the wave spectra along each beam and a Metropolis–Hastings (MH) algorithm to estimate the dominant wave's incident angle was developed. It allows us to estimate the 2D wave signal and its uncertainty from the high-density, unstructured ATL03 ICESat-2 photon retrievals. The GFT is applied to re-binned photon retrievals on 25 km segments for all six beams and outperforms a discrete Fourier transform (DFT) in accuracy while having fewer constraints on the data structure. The MH algorithm infers wave direction from beam pairs every 25 km using coherent crests of the most energetic waves. Assuming a dominant incident angle, both methods together allow a decomposition into 2D surface wave spectra with the advantage that the residual surface heights can potentially be attributed to other sea-ice properties. The combined GFT–MH method shows promise in routinely isolating waves propagating through sea ice in ICESat-2 data. We demonstrate its ability on a set of example ICESat-2 tracks, suggesting a detailed comparison against in situ data is necessary to understand the quality of retrieved spectra.

Determination of the seismic structure of the Earth based on joint analysis of gravimetric and seismometric data – a case study

The evolution of the Earth’s surface is driven by external and internal forces, the latter of which can only be studied indirectly. Knowledge about the structure of the Earth’s interior is very important for modeling and predicting the processes occurring at the surface. This study presents a new concept of joint analysis of the gravimetric and seismometric recordings of earthquakes for determining the seismic structure of the Earth down to the depth of 1250 km. The proposed method allows the use of gravimetric data without the known full transfer function of the instrument. Group velocity dispersion curves of the fundamental mode of Rayleigh waves up to the period of 550 s are measured based on the joint analysis of the recordings of superconducting gravimeter and broadband seismometers operating at the same location in five testing sites in Europe, allowing for the exploration of a broader response for incoming seismic waves. Averaged dispersion curves for earthquakes around the world for each site are inverted by the weighted linear inversion and Monte Carlo methods to estimate the distribution of shear-wave seismic velocity in the Earth’s mantle. A comparison of the deterministic and probabilistic inversion methods can excellently demonstrate surface waves’ ability to determine the Earth’s mantle structure. The inversion results are compared with the global ak135 seismic model (Kennett et al. 1995) to verify the proposed method.

Adaptive linear inversion of Moho topography in the Tibetan Plateau by combining gravity and seismic data

The Tibetan Plateau is a region where the Indian and Asian-European plates collide. A high-precision Moho topography model is important for the study of plate motion and internal tectonics of the Tibetan Plateau. However, previous gravity-based models failed in representing adequately the Moho topography because crustal effects and biases in the inversion parameters were not fully considered. To address these issues, we extracted the gravity effect caused by the crust using wavelet multi-scale analysis, and used an adaptive linear inversion method with available gravity and seismic data to estimate more accurate inversion parameters. With these two improvements, we inverted for a high-precision Moho topography model of the Tibetan Plateau. The results show that the majority of the Tibetan Plateau has a Moho depth of 60–70 km. The Moho depth in the center of the Qaidam Basin is about 50 km, and the Moho topography between the east and west of the basin has obvious undulations. The Moho depth of the Tarim Basin ranges from 38–50 km. While the undulation of Moho is limited in the center of the basin, obvious uplifts are shown in northern and southern basin. The plate driving force between the Tibetan Plateau and the Tarim Basin may be the primary cause of this phenomenon. By comparing the difference with the seismic data, we found that the RMS of our model is 2.8 km smaller than that of the CRUST 1.0 model, which shows that our model is more accurate.

A New Highly Parameterized Linear Inversion of Water Table Change and Groundwater Depletion Rate Tested With the High Plains Aquifer, U.S.A.

AbstractUnderstanding groundwater resource dynamics is limited by the sparsity of observations of water levels, pumping rates, and hydraulic properties relative to their spatiotemporal heterogeneity. To address some of this complexity, we proposed a new highly parameterized linear inverse method to quantify water table change and groundwater depletion rate in unconfined aquifers that does not require initial or boundary conditions. The method requires linearization, and we tested the performance of six proposed water table functions with three coordinate systems with synthetic models, finding that water table functions by the dimensionless method achieve the lowest errors. Our inverted water table changes and depletion rates remained stable and accurate with head measurement error of 5%. However, inversions became less accurate when head observations contained large temporal gaps. Next, we applied the inversion for water table changes and depletion rates in the Texas High Plains Aquifer (HPA) and the HPA during 2000–2015. To address sparse water levels and uncertain hydraulic conductivity measurements, two modifications were made to improve data constraints for inversion: (a) calculating winter‐time water levels for wells with >1 head observation by linear interpolation and (b) using hydraulic conductivity geostatistical realizations. The inverted water table change and depletion rate expected mean values and uncertainties were reasonable compared to the known pumping records of the Texas HPA. With relatively minor data curation, the new inverse method can quantify spatiotemporally continuous water table change, depletion rates, and their uncertainty for heterogeneous aquifers with temporally sparse and noisy water level observations.

Scalable quantum measurement error mitigation via conditional independence and transfer learning

Mitigating measurement errors in quantum systems without relying on quantum error correction is of critical importance for the practical development of quantum technology. Deep learning-based quantum measurement error mitigation (QMEM) has exhibited advantages over the linear inversion method due to its capability to correct non-linear noise. However, scalability remains a challenge for both methods. In this study, we propose a scalable QMEM method that leverages the conditional independence (CI) of distant qubits and incorporates transfer learning (TL) techniques. By leveraging the CI assumption, we achieve an exponential reduction in the size of neural networks used for error mitigation. This enhancement also offers the benefit of reducing the number of training data needed for the machine learning model to successfully converge. Additionally, incorporating TL provides a constant speedup. We validate the effectiveness of our approach through experiments conducted on IBM quantum devices with 7 and 13 qubits, demonstrating excellent error mitigation performance and highlighting the efficiency of our method.

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.

Crustal structure in the Anyuan Coal Mine and its adjacent areas of Jiangxi Province by P-wave receiver functions

We collected high-quality teleseismic events recorded by 12 broadband seismographs deployed in the Anyuan Coal Mine and its adjacent areas in Pingxiang City, Jiangxi Province for nearly two years. The H-κ-c stacking method was employed to obtain the crustal thickness and Poisson's ratio distribution, then the characteristics of crustal structure below the stations were obtained by using the time-domain linear inversion method. The crustal thickness in the Anyuan Coal Mine and its adjacent areas ranges from approximately 32 ∼ 35 ​km, with an average thickness of 33 ​km, which is consistent with the crustal thickness results in South China from previous studies using the receiver function method. The average Poisson's ratio of the crustal bulk composition in the study area varies between 0.22 and 0.25, which is lower than the global value with a 0.27 average, indicating a predominantly intermediate-acidic or felsic crustal composition. There is a weak negative correlation between Poisson's ratio and crustal thickness estimates in the Anyuan Coal Mine and its adjacent areas, suggesting that the absence of mafic-ultramafic materials in the lower crust is associated with the process of crustal delamination. The velocity inversion results indicate that the crustal structure including three velocity discontinuity interfaces, with the first at a depth of approximately 1.5 ​km, the second at about 10 ∼ 15 ​km, and the third being the Moho. The study also indicates that the results obtained by the H-κ-c stacking method are significantly better than those obtained by the H-κ method, effectively reducing the standard deviation and dispersion of crustal thickness and vP/vS ratio.

2D magnetotelluric inversion based on ResNet

In this study, a deep learning algorithm was applied to two-dimensional magnetotelluric (MT) data inversion. Compared with the traditional linear iterative inversion methods, the MT inversion method based on convolutional neural networks (CNN) does not rely on the selection of the initial model parameters and does not fall into the local optima. Although the CNN inversion models can provide a clear electrical interface division, their inversion results may remain prone to abrupt electrical interfaces as opposed to the actual underground electrical situation. To solve this issue, a neural network with a residual network architecture (ResNet-50) was constructed in this study. With the apparent resistivity and phase pseudo-section data as the inputs and with the resistivity parameters of the geoelectric model as the training labels, the modified ResNet-50 model was trained end-to-end for producing samples according to the corresponding production strategy of the study area. Through experiments, the training of the ResNet-50 with the dice loss function effectively solved the issue of over-segmentation of the electrical interface by the cross-entropy function, avoided its abrupt inversion, and overcame the computational inefficiency of the traditional iterative methods. The proposed algorithm was validated against MT data measured from a geothermal field prospect in Huanggang, Hubei Province, which showed that the deep learning method has opened up broad prospects in the field of MT data inversion.

Density structure of the upper and middle crust in the northeast Dabie Orogen revealed by terrestrial gravity surveys

Moderate to strong earthquakes have occurred frequently in the northeast Dabie Orogen recently. From 2014 to 2017, the Guanmiao Earthquake Swarm (GES), with a maximum earthquake magnitude of M3.9, and the Quanjun Earthquake Swarm (QES), with a maximum earthquake magnitude of M3.7, occurred successively in the area near southeast Jinzhai County, where two main Mesozoic E–W‐striking boundary faults, including the Xiaotian–Mozitan and Xinyang–Shucheng faults, are cut by the Cenozoic NNE‐/NE‐trending dextral strike‐slip faulting system. These earthquake swarms occurred within areas of human activities and have the potential to cause more violent geological hazards. However, the tectonic geneses of the earthquake swarms are still unknown due to a lack of sufficient geophysical evidence. Based on terrestrial high‐resolution Bouguer gravity anomaly data, the density structure of the northeast Dabie Mountains is inverted using a 3D linear gravity inversion method. As a result, the occurrence and cutting depth of the reactivated faults near the earthquake swarms are defined, suggesting that the Shangloufang–Xialoufang Fault (F11) may be the seismogenic fault of the GES. The genesis of the QES is possibly associated with the fault termination of the Yingshan–Quanjun strike‐slip fault (F10). More broadly, F10 is one of the major synthetic faults of the NNE‐/NE‐trending dextral strike‐slip faulting system between the Tanlu and Shangcheng–Macheng (F2) faults, which bound the East Dabie Block together. The synthetic and antithetic faults fully cover the Beihuaiyang belt and North Dabie unit topography. These intraplate strike‐slip faults formed to accommodate vertical and lateral movements of the Dabie Mountains, driven by the oblique subduction of the Pacific Plate, were likely responsible for generating earthquakes in both Huoshan and Jinzhai.

Deep learning inversion method of tunnel resistivity synthetic data based on modelling data

AbstractDifferent water‐bearing geological structures in front of the tunnel face are the main cause of tunnel water inrush disasters, affecting tunnel constructionsafety. Due to the narrow tunnel space and the limited data that can be detected, the traditional linear inversion method for detecting them has multiple solutions. In this paper, we establish a database with complex models, including water‐bearing geological structures usually encountered during tunnel construction. Then we build a complex nonlinear relationship mapping between the tunnel face observation data and the resistivity model through the deep neural network algorithm (electrical resistivity inversion network tunnel, ERTInvNet‐T for short). ERTInvNet‐T first uses a fully connected network to extract the tunnel depth features from the observed data, from which a three‐dimensional geoelectric model of the tunnel is then generated by a three‐dimensional deconvolutional network. At the same time, there is a problem with the uneven spatial distribution of the sensitivity of the data to the model. Therefore, depth weighting information constraint based on the distance factor is added to the loss function, which improves the network algorithm's learning ability for different detection positions of the tunnel. The validity of the proposed method is verified by a large number of numerical simulation experiments.

Broadband Geoacoustic Inversions for Seabed Characterization of the New England Mud Patch

Geoacoustic inversions using broadband acoustic data acquired during the Seabed Characterization Experiment 2017 conducted in the New England Mud Patch area in March 2017 are presented in this article. The primary goal of the data inversions is to estimate the compressional wave speed and density profiles of the sediment layers. Both linear perturbative and nonlinear Bayesian inversion methods are utilized. These two inversion methods share the same principle of solution schemes, i.e., to minimize the difference between the signal acquired (or derived quantities) at the receiver and the prediction by the optimized bottom model. The differences between the two approaches are in the type of data utilized for inversion and on the inversion procedure used to determine the bottom geoacoustic properties. The linear inversion method uses the time difference of modal arrival, while the Bayesian inversion uses the bandpass-filtered sound pressure waveform. One of the study objectives is for the Bayesian inversion to provide a reference solution to the inverse problem and determine the ability of the linear inversion method to provide comparable results as compared with a more exhaustive search used in the Bayesian method. Another objective is to use the verified linear inversion method that is computationally faster to explore different models of sediment layering structure and to estimate the most appropriate bottom model for the experimental area.

Deep Learning Joint Inversion of Electrical Data for Ahead-Prospecting in Tunneling

Water inrush has become one of the bottlenecks restricting tunnel construction. Among various advanced forecasting techniques, the direct current method is more cost-effective and sensitive to water-bearing structures. It has been widely used in exploring water inrush disasters in practical engineering. Although traditional resistivity linear inversion methods are reasonably practical, they usually suffer from volume effects and cannot accurately locate the location and morphology of water-bearing bodies. Therefore, nonlinear techniques such as deep learning have recently become popular to directly approximate the inversion function by learning the mapping of apparent resistivity data to the geoelectric model. This work presents a novel deep learning-based electrical approach that combines resistivity and polarizability to estimate water-bearing location and morphology. Specifically, we design an encoder-decoder network. A shared encoder extracts features from the input data, two encoders output resistivity, and polarizability models, respectively, and fine-tuned collinear regularization for both outputs reduces solutions’ multiplicity. Compared with traditional linear inversion methods and independent parameter inversion, our proposed joint inversion method shows superiority in locating and delineating anomalous bodies.