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SUMMARY Airborne electromagnetic (AEM) exploration produces large amounts of data due to its high sampling rate, so that the 3-D inversions take extremely big computation and time consumption. We present a fast 3-D inversion framework for large-scale AEM explorations using a pre-conditioned stochastic gradient descent combined with Gauss–Newton (PSG-GN) method. We adopt a compressed sensing (CS) in the 3-D forward modelling, in which a random undersampling is used to reduce the calculation, while the responses for all survey stations are obtained via a reconstruction technique. For our 3-D AEM inversions, a method of combining the stochastic gradient descent with Gauss–Newton (SG-GN) that requires only a small data set in each iteration instead of the conventional full-batch data (complete original data) inversion have been investigated. To further speed up the 3-D inversion, we develop a pre-conditioner considering the random sampling rate and gradient noise to achieve a fast convergence. We use two synthetic models to test the accuracy, convergence and efficiency of our algorithm. The results show that the conventional inversion with full-batch data and the PSG-GN method can both converge quickly, but our method can enhance the inversion efficiency up to 78 per cent. Finally, we invert a field data set acquired from a massive sulfide deposit in Ireland and obtain the results that agree well with the known geologies.

SUMMARY The seismoelectric effect is a coupling phenomenon between the seismic wavefield and electromagnetic field caused by the electric double layer in a fluid-saturated porous medium. As seismoelectric signals are sensitive to porous medium properties, such as the water saturation, salinity, porosity and permeability, they have good potential for imaging the structure and estimating underground parameters. In this study, we proposed an inversion method for estimating the salinity using coseismic electric fields generated by electrokinetic effects. The method was established by waveform matching between synthetic and observed coseismic electric signals based on a horizontally layered model. We used an L1 norm measure to construct the regularization term and achieve a high-resolution layer interface. Subsequently, we applied the first-order Taylor expansion to estimate the sensitivity and used logarithm transformation to constrain the range of parameters and reduce the solution space. Finally, we used an iteratively reweighted least-squares method to solve the final Gauss–Newton-type inversion function in each iteration to obtain the model update until the inversion converged. Numerical experiments were conducted to test the resolution, anti-noise ability and stability of the inversion algorithm. These results demonstrate that the proposed method can effectively recover the salinity structure, which broadens the application of seismoelectric effects. We further applied the method to the Mw 6.5 Jiuzhaigou earthquake in 2017 and used the observed coseismic electric field to estimate the salinity and conductivity beneath the station.

Three dimensional gravity inversion is an effective way to extract subsurface density distribution from gravity data. Different from the conventional geophysics-based inversions, machine-learning-based inversion is a data-driven method mapping the observed data to a 3D model. We have developed a new machine-learning-based inversion method by establishing a decomposition network (DecNet). Unlike existing machine-learning-based inversion methods, the proposed DecNet method is a mapping from 2D to 2D, which requires less training time and memory space. Instead of learning the density information of each grid point, this network learns the boundary position, vertical center, thickness, and density distribution by 2D-to-2D mapping and reconstructs the 3D model by using these predicted parameters. Furthermore, by using the highly accurate boundary information learned from this network as supplement information, the DecNet method is optimized into a DecNetB method. By comparing the least-squares inversion and U-Net inversion on synthetic and real survey data, the DecNet and DecNetB methods have shown the advantage in dealing with inverse problems for targets with boundaries.

Summary Geomagnetic depth sounding (GDS) is a geophysical electromagnetic (EM) method that studies the deep structure and composition of the earth by using long-period EM signals from geomagnetic observatories and satellites. In this paper, a three-dimensional (3D) anisotropic GDS modeling algorithm is developed. The curl-curl equation is discretized using the edge-based finite-element (FE) method on unstructured tetrahedral grids. In order to solve the computationally demanding problem of EM modeling on a global scale, the complex linear system is first separated into the equivalent real linear systems, and then the real system is iteratively solved by the flexible generalized minimum residual (FGMRES) method with a block diagonal preconditioner. This will greatly reduce the condition number of the linear system and thus speed up the solution process. We verify the accuracy of the proposed algorithm by comparing our results with the existing methods. After that, we design a subduction zone model to simulate the EM responses under isotropic and anisotropic environments, respectively. The numerical results show the high efficiency of the proposed algorithm and the response differences between isotropic and anisotropic models. This research can provide theoretical and technical support for the high-accuracy and efficient inversion of GDS data for the geo-dynamic study.

Summary We propose a novel smoothing regularization scheme for three-dimensional (3D) magnetotelluric (MT) inversion based on unstructured tetrahedral discretization. Different from conventional methods that explicitly add smoothing constraints to model parameters, we choose to do the gradient filtering to smooth the model updates in an implicit way. By transforming the model into a constraint domain, the gradient of the objective function for the parameters in the new domain can be taken as a product of transpose of inverse transformation operator and the conventional gradient. Since the transpose of inverse transformation is designed to be an inverse distance interpolation operator for each tetrahedron, the data fitting term in the gradient can be smoothed in a filtering-like process. We compare our new strategy with the conventional explicit smoothing ones by testing on synthetic data for different noise levels, initial models, and regularization factors. The numerical results show that suffering from the unequal volume and random centroid location of adjacent tetrahedrons, the inversion results of conventional methods often demonstrate scattered structures in slices. In contrast, our new method recovers the model in a smooth way and the convergence speed is largely improved. Finally, we adopt the USArray data for further testing and find that comparing to conventional inversion methods, our new strategy can provide more reliable underground structures with better data fitting.

The topography has serious effects on time-domain airborne electromagnetic (AEM) signal, and the EM responses resulted from the topography frequently overwhelm those from the underground abnormal bodies. This brings big challenges to the traditional AEM interpretations based on a flat ground model. In this article, we develop a 3-D AEM inversion algorithm for a topographic earth model. The time-domain finite-element algorithm based on unstructured mesh is used to model the AEM responses. The tetrahedral grids provide the flexibility to fit the rugged topography. Furthermore, we adopt the Gauss-Newton method for our inversion of time-domain AEM data. In the forward modeling and the calculation of Jacobian matrix, we introduce an unstructured local mesh and decouple the meshes for forward modeling and inversion to improve the computational efficiency. For that purpose, we first set up an unstructured inversion mesh and then extract those cells corresponding to the sensitive area of AEM system for each survey station from the inversion mesh and construct a local forward mesh with the extracted cells as the core. After that, we take advantage of the spatial relationship between the local forward meshes and the inversion ones to set up the global sensitivity matrix for Gauss-Newton inversion. We test the effectiveness of our algorithm by applying our 3-D inversion code to both synthetic and survey data. The numerical experiments show that the Earth topography can have big influence on AEM inversions, and ignoring the topography can create serious distortion to AEM inversion results.

The conventional, L2-norm-based, regularization term in electromagnetic (EM) inversions implements smooth constraints on model complexity in the space domain, which can smoothen the boundaries of complex underground structures. To improve the resolution of 3-D frequency-domain airborne EM (AEM) inversions, we propose a new algorithm for sparse-regularized inversion based on the shearlet transform. Unlike traditional methods that invert the model parameters in the space domain, we first transform the 3-D resistivity model into the frequency domain and then invert the sparse coefficients using an L1-norm measure to ensure the sparseness of the solution. Finally, we transform the shearlet coefficients back to the space domain to update the model. The shearlet transform has inherent multiscale and multidirectional properties, making it capable of effectively extracting complex geometries such as curved boundaries. We adopt the finite-difference method and the iteratively reweighted least-squares scheme for our 3-D AEM modeling and inversions and apply the ``moving footprint'' technique to speed up the inversion. Tests using synthetic data show that sparse-regularized inversion based on the shearlet transform can obtain more-focused inversion results than conventional smoothness-constrained inversions based on the L2-norm. Tests using field survey data also reveal that the new method can achieve more realistic underground structures.

The hydrogel exhibited concurrently enhanced mechanical properties, freezing resistance, water retention ability and biocompatibility by introducing AMY, which could serve as a wearable sensor for monitoring human motions and physiological signals.

For the mineral exploration in complex terrain areas, the semi-airborne transient electromagnetic (SATEM) technology is one of the most powerful methods due to its high efficiency and low cost. However, since the mainstream SATEM systems only observe the component dBz/dt and the data are usually processed by simple interpretation or one-dimensional (1D) inversion, their resolutions are too low to accurately decipher the fine underground structures. To overcome these problems, we proposed a novel 3D forward and inversion method for the multi-component SATEM system. We applied unstructured tetrahedron grids to finely discretize the model with complex terrain, subsequently we used the vector finite element method to calculate the SATEM responses and sensitivity information, and finally we used the quasi-Newton method to achieve high-resolution underground structures. Numerical experiments showed that the 3D inversion could accurately recover the location and resistivities of the underground anomalous bodies under the complex terrain. Compared to a single component data, the inversion of the multi-component data was more accurate in describing the vertical boundary of the electrical structures, and preferable for high-resolution imaging of underground minerals.

Spontaneous coal combustion is a serious hazard that affects mining safety. Since the coal seams are thin and their resistivity dramatically changes during spontaneous combustion, locating the burned cavities or caving zones using electromagnetic (EM) methods is challenging. The conventional transient electromagnetic (TEM) method with a loop transmitter is ineffective, as the main targets are mostly horizontal and resistive. We propose in this paper to apply TEM with an electrical source to detect the resistive targets of spontaneous coal combustion. Considering that its areas generally have very complex geometry, we adopt the unstructured finite-element method for accurate EM forward modeling. For the time discretization, we choose the unconditionally stable backward Euler scheme. Numerical experiments for typical spontaneous combustion models show the high sensitivity of TEM for an electrical source to the burned cavities, and based on this we further use the limited-memory BFGS method to do 3D inversions. To obtain high-resolution imaging results, we bound the resistivity based on the measurements to the coal mine. The inversion results show that the 3D TEM inversions can effectively recover the locations and resistivities of the burned cavities, implying TEM is a valid tool for detecting spontaneous coal combustion.

Airborne electromagnetic (AEM) methods have been more and more widely used in mineral exploration, environmental and engineering studies, and ground water investigation. However, compared with ground-based electromagnetic (EM) methods, such as magnetotelluric or controlled-source EM, AEM methods generally produce large amounts of data, which leads to very costly 3D EM inversions. We have developed a new 3D AEM inversion scheme based on the finite-element method and unstructured tetrahedral local meshes. This is different from the traditional local mesh method in that the traditional method uses regular cuboids for 3D AEM inversions, whereas our scheme uses irregular tetrahedral meshes that can easily accommodate the topography and complex underground structure. Moreover, because we create our local mesh by extracting from part of the global model mesh, the relationship between the local and global meshes is straightforward, so we can easily create a projection of the Jacobian matrix between global and local meshes and rapidly construct the global Jacobian matrix for 3D EM inversions. After formulating the boundary value problem based on the finite-element method, we verify the accuracy of our modeling algorithm by checking against the semianalytical solution for a homogeneous half-space model, and we test our inversion algorithm by running inversions on synthetic and survey data collected over Vesterålen, Norway. The numerical experiments demonstrate that our method can model the AEM responses at high accuracy and recover the subsurface main resistivity structures from synthetic and field data.

Conductive hydrogels are potential materials for fabricating wearable strain sensors owing to their excellent mechanical properties and high conductivity. However, it is a challenge to simultaneously enhance the mechanical properties and conductivity of hydrogels. Herein, a simple strategy was proposed for concurrently enhancing the mechanical properties and conductivity of the wearable hydrogel sensors by introducing carboxymethyl starch sodium (CMS). The introduction of CMS not only dramatically enhanced the mechanical performance of the hydrogel due to hydrogen bonding and electrostatic interaction, but also improved the conductivity of the hydrogel owing to the existence of sodium ions. As a result, the hydrogel sensors with excellent durability and stability could repeatedly detect and distinguish various human activities, including walking, chewing and speaking. Meanwhile, multiple sensors are also assembled into a 3D sensor array for detecting the three-dimensional distribution of stress and strain. Moreover, the peaks of EMG signals and the waveforms of ECG signals could be recorded because the hydrogel sensor presented super sensitivity and fast response. Therefore, the multifunctional hydrogel presented remarkable potential for applications in human medical diagnosis, health monitoring and artificial intelligence.

With geophysical surveys evolving from traditional 2D to 3D models, the large volume of data adds challenges to inversion, especially when aiming to resolve complex 3D structures. An iterative forward solver for the controlled-source electromagnetic (CSEM) method requires less memory than that for a direct solver; however, it is not easy to iteratively solve an ill-conditioned linear system of equations arising from finite-element discretization of Maxwell’s equations. To solve this problem, we have developed efficient and robust iterative solvers for frequency- and time-domain CSEM modeling problems. For the frequency-domain problem, we first transform the linear system into its equivalent real-number format, and then introduce an optimal block-diagonal preconditioner. Because the condition number of the preconditioned linear equation system has an upper bound of [Formula: see text], we can achieve fast solution convergence when applying a flexible generalized minimum residual solver. Applying the block preconditioner further results in solving two smaller linear systems with the same coefficient matrix. For the time-domain problem, we first discretize the partial differential equation for the electric field in time using an unconditionally stable backward Euler scheme. We then solve the resulting linear equation system iteratively at each time step. After the spatial discretization in the frequency domain, or space-time discretization in the time domain, we exploit the conjugate-gradient solver with auxiliary-space preconditioners derived from the Hiptmair-Xu decomposition to solve these real linear systems. Finally, we check the efficiency and effectiveness of our iterative methods by simulating complex CSEM models. The most significant advantage of our approach is that the iterative solvers we adopt have almost the same accuracy and robustness as direct solvers but require much less memory, rendering them more suitable for large-scale 3D CSEM forward modeling and inversion.

Flexible and conductive hydrogels have been widely used in the field of flexible wearable sensors. However, the traditional carbon-based composite hydrogel sensors tend to present weak adhesion and mechanical strength, limiting the sensitivity and reliability of practical applications. Here, a gum arabic-tackified reduced graphene oxide composite hydrogel is successfully fabricated. The introduction of gum arabic endows the hydrogel with high mechanical strength, and fatigue resistance, as well as robust adhesion on metal, plastic, glass, rubber, and skin. Furthermore, the reduced graphene oxide would improve the conductivity of hydrogels. As a result, the skin-attached hydrogel sensors featuring high sensitivity, fast response, and wide detection range were demonstrated for monitoring various mechanical stimuli and human motions. It is anticipated that the gum arabic-tackified skin-attached hydrogel sensors hold prospective applications in electronic skin, human–machine interfaces, and soft robotics.

Currently, most hydrogel sensors require an isolation layer to prevent current from damaging the skin. However, the mismatch of mechanical property between the isolation layer and the hydrogel sens...

We propose a new 3D inversion scheme to invert the near- and transition-zone data of CSAMT with topography accurately. In this new method, the earth was discretized into unstructured tetrahedra to fit the ragged topography and the vector finite-element method was adopted to obtain precise responses and good sensitivity. To simulate the attitude and shape of the transmitter, we divided a long-grounded transmitter into dipoles and integrated these dipoles to obtain good responses in the near- and transition-field zones. Next, we designed an L2 norm-based objective functional and applied a standard quasi-Newton method as the optimization method to solve the inverse problem and guarantee steady convergence. We tested our 3D inversion method first on synthetic data and then on a field dataset acquired from select sites near Changbai Mountain, China. In both tests, the new inversion algorithm achieved excellent fitting between the predicted and observed data, even in near- and transition-field zones, and the inversion results agreed well with the true model. These findings reveal that the proposed algorithm is effective for 3D inversion of CSAMT data.

Due to the huge amount of data generated by time-domain airborne electromagnetic (AEM) systems, conductivity depth imaging methods are widely used to help in the interpretation of these data because they can be generated quickly and easily. We have introduced a new imaging method generated using a deep neural network. The network structure combines four convolutional neural networks with a long short-term memory technique and adopts an error back-propagation scheme to update the parameters. A deep hierarchical structure is used to extract and store the complex nonlinear relationship between the model and electromagnetic (EM) responses, creating results close to 1D inversions. To check the effectiveness, we have examined our algorithm on synthetic and survey AEM data. The imaging result shows that this method, when using reasonable network parameters, can not only image well at high speed, but the method also is not very sensitive to noise. Another advantage of this method is that once the training is completed on a well-distributed training set, the network can be used without any changes to process other data sets from an identically configured AEM system.

The electrical conductivity distribution within wide palaeochannels is usually well-mapped from airborne electromagnetic data using stitched 1D algorithms. Such stitched 1D solutions are, however, inappropriate for narrow valleys. An alternative option is to consider 2D or 3D models to allow for finite lateral extent of conductors. In airborne electromagnetic data within the Musgrave block near the well-studied Valen conductor, strong induced polarization (IP) and superparamagnetic (SPM) effects make physical property and structure estimation even more uncertain for deep channel clays, particularly those whose channel widths are comparable to their depth of burial. We developed a recursive data fitting algorithm based on dispersive thin sheet responses. The separate IP and SPM components of the fit provide near-surface chargeability and SPM distributions, and the associated electromagnetic (EM) fit provides stripped data with monotonic decays compatible with a simple nondispersive conductivity model. The validity of this stripped data prediction was tested through a comparison of 1D conductivity-depth imaging and 3D inversion applied to the original data and the stripped data. Due to the forked geometry of the deep conductivity structure in the region we investigated, we successfully used 3D rather than 2D inversion to predict the conductivity distribution related to the EM data. We recovered from the stripped data a continuous conductivity structure consistent with a branching, clay-filled palaeovalley under cover.

Recently, hydrogel-based sensors have been rapidly developed due to their excellent flexibility, stretchability and toughness. However, it is still necessary to develop a hydrogel sensor with shape memory and remolding performance for multi-field applications. Here, a dual physically cross-linked shape memory hydrogel sensor was fabricated via blending poly vinyl alcohol (PVA), cationic chitosan and graphene oxide in water and glycerol. The introduction of cationic chitosan endows the hydrogels with excellent electrical conductivity. Therefore, the hydrogel can be integrated as a strain sensor to repeatedly monitor human motions. Meanwhile, the hydrogel can be used as a thermo-responsive shape memory sensor by virtue of orientation of PVA molecular chains under force and disorientation after heating. Besides, the hydrogel possesses anti-freezing properties with mechanical flexibility at −20 °C. Due to the dual physical cross-linking, the hydrogels can effectively dissipate energy and reconstruct the network; thus, the hydrogels gain excellent strength and remolding properties. In a word, this strategy provides a feasible method to prepare multifunctional shape memory hydrogels applied as wearable strain sensors and shape memory sensors.

Flexible supercapacitors have attracted increasing attention due to their unique soft and capacitive properties. However, for a conductive polymer-based electrode material, the mechanical properties, conductivity and the interface bonding with the electrolyte are all challenging. Here, polypyrrole (PPy) hydrogel electrodes with high stretchability (over 700%), electrical conductivity (11.07 S m−1) and interfacial bonding properties were prepared by doping carboxymethyl cellulose (CMC). Due to the emulsification effect of CMC, PPy could form hydrophilic CMC/PPy fibers in aqueous solutions. Moreover, during the formation process of the PPy hydrogel, uniformly distributed CMC/PPy particles were obtained in situ, resulting in the unique visible light transmission and ultraviolet shielding characteristics of the PPy hydrogel. As a flexible electrode, the PPy hydrogels were assembled into an all-solid-state supercapacitor, which exhibited a specific capacitance of 126.38 F g−1 and excellent cyclic stability (capacitance retention of 82% after 1000 cycles). This facile method of preparing transparent PPy hydrogels can pave a new way for constructing capacitive electronic skins.

Breaking through the conventional way of conferring anti-icing ability on hydrogels with addition of organic solvents or inorganic salts, here a novel anti-icing hydrogel with toughness, adhesiveness and high transparency was successfully fabricated by introducing antifreeze protein (AFPS, inspired by fish) into a chemical crosslinking network copolymerized with acrylamide and 2-acrylamide-2-methylpropanesulfonic acid. The hydrogel exhibited surprising stretchability (up to 2400% tensile strain), high transparency (over 90% transmittance) and outstanding reversible adhesive performance bonding to different materials and even human skin. Meanwhile, the inhibition of ice crystal growth based on AFPS molecules also conferred anti-icing ability on the hydrogels, so that the toughness and adhesiveness of the hydrogels remained stable at −10 °C. Additionally, the existence of sulfonic groups also endowed the hydrogels with deformation sensitivity to act as strain or pressure sensors to accurately monitor human motions and even subtle physiological signals. Therefore, the novel anti-icing strategy would provide new insight for a new generation of hydrogel sensors.

Hydrogel strain sensors have attracted tremendous attention in medical monitoring, flexible wearable devices, and human-machine interfaces. However, traditional hydrogels exhibit isotropic sensing performance based on their isotropic structure. Therefore, it is challenging to fabricate a hydrogel with an anisotropic structure similar to human tissues for achieving anisotropic sensing characteristics. Herein, we proposed a simple and effective method for preparing anisotropic poly(vinyl alcohol) (PVA) conductive hydrogels, which demonstrated anisotropic mechanical properties and anisotropic ion conductivity. The anisotropic hydrogel was successfully constructed through first thermal stretching and then directional freezing. The mechanical strength of hydrogels along the parallel stretching direction (stress of 1596 kPa and toughness of 3.69 MJ/m

Gravity inversion is a typical geophysical inversion method that obtains the underground density distribution by analyzing the gravity anomaly. Normally, it can be divided into geophysics-based and deep learning based inversion. The 3D geophysics-based inversion is a time- and memory-consuming method, so 3D inversion is not routinely implemented in practical data interpretation. Here, we propose a deep learning method to transfer the 3D inversion problem to a multiple layers 2D mapping problem by decomposing the 3D target into four 2D images, including the horizontal location, vertical center, thickness and density distribution. This method is denoted as “decomposition network”. By implementing synthetic experiments with regular and complex models, and comparing with the 3D U-Net inversion, the proposed network has proved can reconstruct underground targets with high accuracy and high efficiency.