Inversion Algorithm Research Articles

Formation density and photoelectric index calculation using an ultra-slim density tool

Measuring formation density accurately is challenging due to mud accumulated on wellbore and mudcake on the borehole wall, particularly for through-the-bit density tools, which are ultra-slim tools with smaller detector crystals. This work introduces a novel method that overcomes this challenge by utilizing detector response models based on gamma physics principles. These models include the effects of key parameters such as lithology and mudcake on density and Pe (Photoelectric index) measurements. Monte Carlo simulations are employed to create and calibrate the models, ensuring accurate responses for both short- and long-spaced detectors. Various logging scenarios are considered in the modelling process. High-precision forward models are designed to correct the reading of these smaller detectors. Inversion algorithms are then developed to minimize errors and obtain optimal solutions using a quasi-Newton method based on weighted regularization. The highlight of the method is that it allows simultaneous determination of formation density, formation photoelectric index, mudcake density, and mudcake photoelectric index. The method is validated using a recently introduced through-the-bit density tool. The average density error is less than 0.015 g/cm³, and the average formation Pe error is less than 0.2 b/e, proving the effectiveness of the method.

Simultaneous estimation of heat source strength of hot wire and thermal conductivity of material

The hot-wire (HW) technique is a widely used method for measuring the thermal conductivity (k) of insulation materials. However, there are some limitations to the applicability. For instance, inaccuracies may arise when the wire is assumed to be infinitely thin and long, or when the sample material is assumed to be an infinite medium. Additionally, the accuracy of k measurements relies on accurately specifying the heat source strength (QW ) generated by the HW. The modified conjugate gradient method (CGM) provides a solution to these limitations of the HW technique. In the modified CGM technique, a scaling factor based on the Levenberg-Marquardt method is utilized to address the low derivative and divergence issues of the traditional CGM. The current work simultaneously estimates QW generated by the HW and k of the sample materials by using modified CGM. The investigation looked into the effect of sensor positioning relative to the HW and the introduction of artificial Gaussian error (noise) with a standard deviation of 0.01 °C, 0.02 °C and 0.1 °C into the simulated temperature measurements. The modified CGM estimates the unknown parameters accurately compared to the traditional CGM. The measurement location should be closer to the HW to obtain accurate estimation results. The noise level of 0.1 °C results in low accuracy of estimation of k and QW for Plexiglas with one sensor, which can be enhanced by employing two sensors. Overall, the modified CGM algorithm proved to be a robust inverse algorithm that could be employed to estimate unknown parameters.

Multi‐mode non‐linear inversion of Rayleigh wave dispersion curves with grey wolf optimization and cuckoo search algorithm

AbstractDispersion curve inversion is one of the core contents of Rayleigh wave data processing. However, the dispersion curve inversion has the characteristics of multi‐parameter, multi‐extremum as well as nonlinearity. In the face of Rayleigh wave data processing under complex seismic‐geological conditions, it is difficult to reconstruct an underground structure quickly and accurately apply a single global‐searching non‐linear inversion algorithm. For this reason, we proposed a strategy to invert multi‐order mode Rayleigh wave dispersion curves by combining with grey wolf optimization (GWO) and cuckoo search (CS) algorithms. On the basis of introducing the mechanism of iterative chaotic map with infinite collapses (ICMIC) and the strategy of dimension learning–based hunting (DLH), an improved GWO was developed that was called IDGWO (ICMIC and DLH GWO). After searching the near‐optimal region through IDGWO, the CS with a variable step‐size Lévy flight search mechanism was switched adaptively to complete the final inversion. The correctness of our method was verified by the multi‐order mode dispersion curve inversion of a six‐layer high‐velocity interlayer model. Then it was further applied to the processing of real seismic datasets. The research results show that our method fully utilizes the advantages of each of the two global‐searching non‐linear algorithms after integrating IDGWO and CS, while effectively balancing the ability between global search and local exploitation, further improving the convergence speed and inversion accuracy and having good anti‐noise performance.

Design and Kinematics of a Novel Continuum Robot Connected by Unique Offset Cross Revolute Joints

Abstract Continuum robots have continuous structures and inherent compliance, which can be used for accessing unstructured and confined space in many fields, such as minimally invasive surgery and aero-engine in-situ inspection. A novel cable-driven continuum robot connected by unique offset cross revolute joints is proposed in this paper, which has excellent bending capacity and appropriate torsional stiffness compared with continuum robots connected by revolute joints and spherical joints, respectively. Furthermore, the kinematic modeling and analysis are carried out. The mappings among robot's actuator space, joint space and task space are established step by step. Particularly, an improved inverse kinematics algorithm is proposed by combining the constant curvature method with the numerical iterative method. This combined inverse kinematics algorithm can effectively reduce the error of approximate solution derived by the traditional constant curvature method. Numerical simulations are conducted to verify the proposed algorithm and analyze workspace of the continuum robot. Finally, experimental prototype of the robot is built to verify its excellent bending capacity and the correctness of the proposed kinematic model.

Schwartz Symmetry Condition for Coherent Diffraction Imaging Patterns

We demonstrate a symmetry condition for the mixed partial derivatives of measured data when performing a coherent diffraction imaging (CDI) experiment for differentiable samples under scientific investigation. The proposed condition can be used as a physical restriction to improve real data measurements and has been used within the most celebrated phase-retrieval inversion algorithms as an ad hoc constraint without proof. The symmetry relies on John’s ultrahyperbolic equation for the X-ray transform, which is also demonstrated to be valid in the imaging regime for CDI. The obtained conditions are easy to implement and can be used as a constraint by computational imaging methods.

A Comparison of Inversion Methods for Surrogate‐Based Groundwater Contamination Source Identification With Varying Degrees of Model Complexity

AbstractAccurate identification of groundwater contamination sources is important for designing efficacious site remediation strategies. Currently, the methods for identifying contamination sources mainly fall into three distinct categories: simulation optimization, Bayesian inference, and data assimilation. Each method has its own advantages and disadvantages under specific site conditions. To evaluate the applicability of these methods, we chose one representative inversion algorithm from each category, namely the Improved Butterfly Optimization Algorithm (IBOA) for simulation optimization, the Ensemble Smoother with Multiple Data Assimilation (ES‐MDA) for data assimilation, and the DiffeRential Evolution Adaptive Metropolis with a Snooker Update and Sampling from a Past Archive (DREAM(ZS)) for Bayesian inference. We conducted a comprehensive evaluation of these methods' performance under different model complexities, employing a surrogate model as a substitute for the complex forward model. By addressing two distinct problems involving conservative pollutant transport and Light Non‐Aqueous Phase Liquid (LNAPL) transport with biodegradation, we employed four criteria (elapsed time, result accuracy, posterior probability distribution, and noise resistance) for evaluation. The findings unequivocally indicate that DREAM(ZS) outperforms others in terms of result accuracy and posterior probability distribution. It also adeptly navigates the interrelations among disparate unknown variables. The strength of ES‐MDA lies in its efficiency. It achieves relatively satisfactory results with a reduced computational burden. In contrast, IBOA underperforms in both test problems. In terms of resistance to noise, both DREAM(ZS) and ES‐MDA perform better than IBOA does.

Symbolic position analysis for three 6-DOF parallel mechanisms and new insight

AbstractThe authors‘ previous research has demonstrated that parallel mechanisms (PMs) with hybrid branch chains (i.e., branch chains containing planar or spatial loops) can possess symbolic forward position (SFP) solutions and motion decoupling (MD). In order to further study the conditions of a three-chain six degrees of freedom (DOF) parallel mechanism with SFP and MD, this paper proposes one 6-DOF branch chain A and two 5-DOF branch chains B and C. Based on these, a class of four 6-DOF PMs with three branch chains is devised. The symbolic position analysis of three of four such PMs is performed consequently, featuring partial MD and SFPs, which reveals that if the position or orientation of a point on the moving platform can be determined by the position of the hybrid branch chain, the PM exhibits partial MD and SFP. Finally, the accuracy of the symbolized forward and inverse solution algorithms is verified through numerical examples. This research brings a new insight into the design and position analysis of 6-DOF PMs, particularly those with SFP and partial MD.

Identification of Wind Load Exerted on the Jacket Wind Turbines from Optimally Placed Strain Gauges Using C-Optimal Design and Mathematical Model Reduction

Wind turbine towers experience complex dynamic loads during actual operation, and these loads are difficult to accurately predict in advance, which may lead to inaccurate structural fatigue and strength assessment during the structural design phase, thereby posing safety risks to the wind turbine tower. However, online monitoring of wind loads has become possible with the development of load identification technology. Therefore, an identification method for wind load exerted on wind turbine towers was developed in this study to estimate the wind loads using structural strain, which can be used for online monitoring of wind loads. The wind loads exerted on the wind turbine tower were simplified into six equivalent concentrated forces on the topside of the tower, and the initial mathematical model for wind load identification was established based on dynamic load identification theory in the frequency domain, in which many candidate sensor locations and directions were considered. Then, the initial mathematical model was expressed as a linear system of equations. A numerical example was used to verify the accuracy and stability of the initial mathematical model for the wind load identification, and the identification results indicate that the initial mathematical model combined with the Moore–Penrose inverse algorithm can provide stable and accurate reconstruction results. However, the initial mathematical model uses too many sensors, which is not conducive to engineering applications. Therefore, D-optimal and C-optimal design methods were used to reduce the dimension of the initial mathematical model and determine the location and direction of strain gauges. The C-optimal design method adopts a direct optimisation search strategy, while the D-optimal design method adopts an indirect optimisation search strategy. Then, four numerical examples of wind load identification show that dimensionality reduction of the mathematical model leads to high accuracy, in which the C-optimal design algorithm provides more robust identification results. Moreover, the fatigue damage calculated based on the load identification wind loads closely approximates that derived from finite element simulation wind load, with a relative error within 6%. Therefore, the load identification method developed in this study offers a pragmatic solution for the accurate acquisition of the actual wind load of a wind turbine tower.

Accelerating finite-difference frequency-domain simulations of inverse designed structures in nanophotonics using deep learning

The inverse design of nanophotonic devices is becoming increasingly relevant for the development of complex photonic integrated circuits. Electromagnetic first-order simulations contribute to the overwhelming computational cost of the optimization routines in established inverse design algorithms, requiring more efficient methods for enabling improved and more complex design process flows. Here we present such a method to predict the electromagnetic field distribution for pixel-discrete planar inverse designed structures using deep learning. Our model is able to infer accurate predictions used to initialize a conventional finite-difference frequency-domain algorithm and thus lowers the average time required for simulating the electromagnetic response of nanophotonic device layouts by up to 53% in iterative design process flows. We demonstrate the applicability of our deep learning method for the inverse design of photonic integrated powersplitters and mode converters, and we highlight the possibility of exploiting previous learning results in subsequent design tasks of novel functionalities via fine-tuning reduced data sets, thus improving computational speed further.

Concrete quantum cryptanalysis of binary elliptic curves via addition chain

Thus far, several papers reported concrete resource estimates of Shor’s quantum algorithm for solving the elliptic curve discrete logarithm problem. In this paper, we study quantum FLT-based inversion algorithms over binary elliptic curves. There are two major algorithms proposed by Banegas et al. and Putranto et al., where the former and latter algorithms achieve fewer numbers of qubits and smaller depths of circuits, respectively. We propose two quantum FLT-based inversion algorithms that essentially outperform previous FLT-based algorithms and compare the performance for NIST curves of the degree n. Specifically, for all n, our first algorithm achieves fewer qubits than Putranto et al.’s one without sacrificing the number of Toffoli gates and the depth of circuits, while our second algorithm achieves smaller depths of circuits without sacrificing the number of qubits and Toffoli gates. For example, when n=571\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n = 571$$\\end{document}, the number of qubits of our first algorithm is 74 % of that of Putranto et al.’s one, while the depth of our second algorithm is 83 % of that of Banegas et al.’s one. The improvements stem from the fact that FLT-based inversions can be performed with arbitrary sequences of addition chains for n-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n - 1$$\\end{document} although both Banegas et al. and Putranto et al. follow fixed sequences that were introduced by Itoh and Tsujii’s classical FLT-based inversion. In particular, we analyze how several properties of addition chains, which do not affect the computational resources of classical FLT-based inversions, affect the computational resources of quantum FLT-based inversions and find appropriate sequences.

A reconstruction method for structural stress distribution of wind turbine tower using optimised mathematical model

Wind turbine towers experience complex dynamic loads during actual operation, and these loads are difficult to accurately predict in advance, which may lead to inaccurate structural strength assessment during the structural design phase, thereby posing safety risks to the wind turbine tower. Therefore, a reconstruction method for structural stress distribution of wind turbine tower was developed based on modal expansion and linear superposition theory to estimate the full-field stress distribution of a tower, which can be used for online monitoring of structural strength. The dynamic stress distribution of the tower is assumed to be the superposition of several structural modal stress distributions, in the reconstruction method for structural stress distribution developed in this study. The modes with the greatest contribution to the wind turbine structural response were selected based on the modal effective mass, and used for the base functions of an initial mathematical model for the reconstruction of structural stress distribution of the tower, in which many candidate strain gauge locations and directions were considered. Then, the initial mathematical model was expressed as a linear system of equations. Two numerical examples were used to verify the accuracy and stability of the initial mathematical model for the reconstruction of structural stress distribution of the tower, and the reconstruction results indicate that the initial mathematical model combined with the Moore–Penrose inverse algorithm can provide stable and accurate reconstruction results. However, the initial mathematical model uses too many sensors, which is not conducive to engineering applications. Therefore, D-optimal and C-optimal design methods were used to reduce the dimensions of the initial mathematical model, optimise the system of equations, and determine the location, direction and number of strain gauges. Finally, the numerical examples of stress distribution reconstruction show that dimensionality reduction of the mathematical model leads to higher accuracy, in which the C-optimal design algorithm providing a more robust reconstruction outcome.

Three-dimensional finite-memory quasi-Newton inversion of the magnetotelluric based on unstructured grids

Abstract Simulation optimization of complex geological bodies is a necessary means to improve inversion accuracy and computational efficiency; thus, inversion of magnetotelluric (MT) based on unstructured grids has become a research hotspot in recent years. This article realizes the three-dimensional (3D) finite element forward modeling of MT based on the magnetic vector potential-electric scalar potential method, using unstructured grids as the forward modeling grid, which improves computational efficiency. The inversion uses the limited-memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) method, and in the process of calculating the objective function gradient, the quasi-forward method is used to avoid solving the Jacobian matrix, which has the advantages of requiring small storage space and fast computational efficiency. Finally, the 3D LBFGS inversion algorithm of MT based on unstructured grids was realized, and the inversion studies of classic and complex models verified the effectiveness and the reliability of the algorithm proposed in this article.

A particle swarm optimization and prior knowledge fusion seismic damage prediction of concrete structures

A data-driven algorithm is developed to predict local seismic damage distribution of concrete structures based on the measured global structural response. Based on the algorithm, the signal of reaction force and displacement at one location is only necessary for seismic damage prediction. The algorithm is established based on the improved particle swarm optimization with two innovative strategies. One is the probabilistic mutation procedure, which can consider the prior knowledge of the positive correlation between the strain/stress level and damage level in the seismic damage optimization process. Another is the dynamic condition-based mutation and cross procedure, which can increase the diversity of the particle swarm in the optimization process to get rid of the possible local optimum. A representative example of a concrete column under cyclic load is designed and modeled to examine the performance of the algorithm. The prediction results based on the algorithm are compared with the traditional particle swarm optimization and the previous damage inversion algorithm based on ant colony optimization. The comparison results support that the local seismic damage distribution prediction based on the algorithm is closer to the corresponding experimental result. In addition, the error of the predicted macroscopic response in the final seismic stage based on the algorithm is 1.7%. The prediction error of the traditional particle swarm optimization algorithm is 12.6%, and the prediction error of the previous damage inversion algorithm based on ant colony optimization is 8.5%. The ability of the proposed algorithm is supported, which can be capable of seismic damage prediction of concrete structures subjected to earthquakes.

Forecasting the onset of volcanic eruptions using the increase in seismicity during magma ascent

The Failure Forecast Method (FFM) has been used to forecast the onset of volcanic eruptions with varying degrees of success. The method involves fitting its empirical equation to precursory observables, e.g., seismic data. Current models explaining the empirical equation assume that the seismic observables used (e.g., seismic event-rate, seismic moment-rate or seismic energy-rate) are related to accelerated fracture growth. In these models, such fracture growth results in an apparent increase in seismic activity. In this study, however, we propose an alternative explanation for the increase in seismicity culminating in volcanic eruptions. We suggest that the increase in seismicity, particularly in the seismic amplitudes, can result from ascending seismic sources towards the surface and that the increase can be used for eruption forecasts using the FFM. Our argument is based on the need for magma to migrate towards the surface to produce an eruption.To test our argument, we used synthetic and field/real data and fitted them with the FFM model. The synthetic data is generated using the body wave attenuation equation, and the real data is from the Piton de la Fournaise eruption on January 2nd, 2010. We used seismic amplitudes and seismic amplitude ratios as the precursory observables and used a combination of Simulated Annealing and Bayesian Inversion algorithms to obtain the best-fit parameters of the FFM model and their posterior distributions. For the synthetic cases, we found that the method gave reasonable estimates of failure or eruption time, suggesting that the seismic amplitudes and the seismic amplitude ratios can be used for forecasting using the FFM. For the field/real cases, the results gave information about the timing of magma chamber failure, magma propagation, and the eruption onset. Our results highlight an example of modelling volcano monitoring data with the FFM that gives reasonable estimates of eruption time even if the data may not fully represent failure processes. We suggest that the result may still be reasonable owing to the empirical and asymptotic nature of the FFM combined with the underlying physics of magma and seismic migrations.

Inverse Calculation and Regularization Process for the Solar Aspect System (SAS) of HXI Payload on ASO-S Spacecraft

For the ASO-S/HXI payload, the accuracy of the flare reconstruction is reliant on important factors such as the alignment of the dual grating and the precise measurement of observation orientation. To guarantee optimal functionality of the instrument throughout its life cycle, the Solar Aspect System (SAS) is imperative to ensure that measurements are accurate and reliable. This is achieved by capturing the target motion and utilizing a physical model-based inversion algorithm. However, the SAS optical system’s inversion model is a typical ill-posed inverse problem due to its optical parameters, which results in small target sampling errors triggering unacceptable shifts in the solution. To enhance inversion accuracy and make it more robust against observation errors, we suggest dividing the inversion operation into two stages based on the SAS spot motion model. First, the as-rigid-as-possible (ARAP) transformation algorithm calculates the relative rotations and an intermediate variable between the substrates. Second, we solve an inversion linear equation for the relative translation of the substrates, the offset of the optical axes, and the observation orientation. To address the ill-posed challenge, the Tikhonov method grounded on the discrepancy criterion and the maximum a posteriori (MAP) method founded on the Bayesian framework are utilized. The simulation results exhibit that the ARAP method achieves a solution with a rotational error of roughly ±3.″5 (1/2-quantile); both regularization techniques are successful in enhancing the stability of the solution, the variance of error in the MAP method is even smaller—it achieves a translational error of approximately ±18 μm (1/2-quantile) in comparison to the Tikhonov method’s error of around ±24 μm (1/2-quantile). Furthermore, the SAS practical application data indicates the method’s usability in this study. Lastly, this paper discusses the intrinsic interconnections between the regularization methods.

Snow Water Equivalent Monitoring—A Review of Large-Scale Remote Sensing Applications

Snow plays a crucial role in the global water cycle, providing water to over 20% of the world’s population and serving as a vital component for flora, fauna, and climate regulation. Changes in snow patterns due to global warming have far-reaching impacts on water management, agriculture, and other economic sectors such as winter tourism. Additionally, they have implications for environmental stability, prompting migration and cultural shifts in snow-dependent communities. Accurate information on snow and its variables is, thus, essential for both scientific understanding and societal planning. This review explores the potential of remote sensing in monitoring snow water equivalent (SWE) on a large scale, analyzing 164 selected publications from 2000 to 2023. Categorized by methodology and content, the analysis reveals a growing interest in the topic, with a concentration of research in North America and China. Methodologically, there is a shift from passive microwave (PMW) inversion algorithms to artificial intelligence (AI), particularly the Random Forest (RF) and neural network (NN) approaches. A majority of studies integrate PMW data with auxiliary information, focusing thematically on remote sensing and snow research, with limited incorporation into broader environmental contexts. Long-term studies (>30 years) suggest a general decrease in SWE in the Northern Hemisphere, though regional and seasonal variations exist. Finally, the review suggests potential future SWE research directions such as addressing PMW data issues, downsampling for detailed analyses, conducting interdisciplinary studies, and incorporating forecasting to enable more widespread applications.

Analysis and simulation of the effect of large optical range difference of common path coherent-dispersion spectrometer on the detection of exoplanet radial velocities

The Exoplanet Explorer common-path coherent-dispersion spectrometer (CODES) utilizes a unique combination of an asymmetric common path Sagnac interferometer and a low to medium resolution spectrometer. The ideal optical range difference (OPD) interval for CODES is OPD ∈ {15.06 mm, 19.45 mm}; however, the OPD of CODES is 64.3 mm to achieve better detection accuracy. Though they will increase the accuracy of detection, large OPDs outside of the ideal interval will also reduce the contrast of the interference fringes, making phase changes more hazy. This may also significantly affect the radial velocity inversion and reduce CODES's instrumental accuracy. This study creates an inverse tone mapping operator based on the photographic model and designs an inverse tone mapping algorithm called CODESCE. The outcomes of the experiments demonstrate that the tone mapping algorithm CODESCE in this work is appropriate for enhancing the contrast of interference fringe images with high OPD, and it can enhance the contrast of interference fringes by three orders of magnitude when OPD = 64.3 mm; the processed interference fringes are located in the range of interference fringe curves of the optimal OPD. By comparison with other current approaches, the suggested algorithm yields superior processing outcomes.

Fracture Height Quantification from Vertical and Horizontal Section Fiber Measurements: A Comprehensive Study Using LF-DAS Measurements from HFTS-2 Data Set

Summary Understanding fracture height growth is critical for optimizing hydraulic fracture treatments and field development. In recent years, low-frequency distributed acoustic sensing (LF-DAS) has become a popular tool for monitoring strain changes during hydraulic fracturing. While LF-DAS data from vertical monitoring wells (VMWs) can be used to determine fracture height, measurements from the vertical section of horizontal wells may have the potential to capture fracture height growth. The objectives of this study are (1) to apply three methods—(a) using the vertical section of horizontal fiber measurements, (b) using the vertical fiber measurements, and (c) using the horizontal section of horizontal fiber measurements—to determine the fracture height using the Hydraulic Fracturing Test Site 2 (HFTS-2) data set and (2) to demonstrate the reliability of using LF-DAS measurements from the vertical section of horizontal fibers for fracture height determination. In an effort to determine the fracture height from the HFTS-2 data set using the three methods, we demonstrate the reliability of the height prediction using strain measurements in the vertical section of the horizontal monitoring well (VS-HMW). First, we analyze the measurements from the vertical section of the horizontal fiber (B3H) during the stimulation of the heel-most stages of the horizontal wells (B1H, B2H, and B4H). Second, we analyze the measurements from the VMW (B5PH) during the stimulations of B1H, B2H, and B4H. Third, we use a geomechanical inversion algorithm to obtain height estimates from the horizontal section of the LF-DAS measurements at B3H during B1H, B2H, and B4H stimulations. The fracture height is determined based on the transition of the extension-compression zone in the LF-DAS measurements from the vertical sections. The height estimates obtained using the three methods are compared and found to be consistent in the six well pairs we analyzed. The LF-DAS measurements from the vertical well B5PH provide a complete height profile, while measurements from the vertical section capture fracture growth from the upper tip of the fracture to the landing depth of the horizontal well. The fracture height estimates obtained from our inversion algorithm represent the average height value of all fracture hits at the chosen stage. This study demonstrates the potential to determine fracture height growth using LF-DAS measurements in the vertical section of a horizontal well, thus avoiding the cost associated with drilling VMWs to obtain fracture heights.

3-D imaging of whole-space environments with electromagnetic induction sensors based on linear approximation

Accurate mapping of the periphery of tunnel has become an essential step in underground mining and engineering. Because of high sensitivity to electric conductivity and magnetic permeability, the whole-space electromagnetic (EM) method has played an important role in geological forecast of groundwater and exploration of mineral ore. However, obtaining a three-dimensional (3-D) image of the whole-space EM method by 3-D inversion is challenging due to the limited observation space and inefficiencies in 3-D forward modeling algorithms. While 1-D inversion algorithms have long been used to map the periphery of the tunnel, various 3-D inversion algorithms have been successfully applied in other scenarios. Recently, the portable frequency domain loop-loop EM induction (EMI) measurement has been considered as an active source magnetic method in near surface surveys, because of the dominance of magnetic permeability in the in-phase (IP) response. The 3-D linear forward modeling method is developed based on the location-specific magnetic sensitivity function, and the 3-D inversion algorithm has been effectively employed for mapping magnetic anomalies in large-scale area. In this study, we intend to demonstrate that the EMI measurement can give 3-D image of the periphery of the tunnel by theory and numerical experiments. The IP response of EMI in whole-space is separated into three parts, and the 3-D linear forward modeling method is examined by analytical solution. The 1-D Fourier transform is used to accelerate the 3-D forward modeling, and the 3-D inversion show a good performance of mapping the magnetic abnormal bodies in underground space.

A new automatic geo-electric self-potential imaging technique for diverse sustainable development scenarios

This study introduces a rapid and efficient inversion algorithm designed for the interpretation of self-potential responses originating from mineralized and ore sources and hydrothermal activity, specifically addressing spherical, vertical, and horizontal cylindrical structures. The algorithm leverages local wavenumber and correlation imaging techniques to enhance accuracy in modeling. The correlation factor (Cf value) is crucial in this approach, calculated as the correlation between the local wavenumber of the measured self-potential field and that of the computed field. The algorithm identifies the maximum correlation Cf value (CF-max) as indicative of the optimal true model parameters. To validate the proposed algorithm, it was applied to three theoretical examples—one with contamination from regional background and another with multiple sources with and without different types of noises (random Gaussian and white Gaussian noises). Additionally, the approach was tested on three distinct real field cases related to mining, ore investigation and hydrothermal activity in India, Germany and USA. Through a comprehensive analysis of results from theoretical and real-world scenarios, including comparisons with different available data and literature information, the study concludes that the method is effective, applicable to multiple sources, accurate, and does not necessitate prior knowledge of the source shape. This algorithm presents a promising advancement in the field of self-potential interpretation for mineral exploration and geothermal exploration.