UAV-based transient electromagnetic 3D forward modeling and inversion and analysis of exploration capability

Unmanned aerial vehicle transient electromagnetic(UAV-TEM)is a novel airborne exploration method that offers advantages such as low cost,simple operation,high exploration efficiency and suitability for near-surface exploration in complex terrain areas.To improve the accuracy of data interpretation in this method,the authors conducted a systematic three-dimensional(3D)forward modeling and inversion of the UAV-TEM.This study utilized the finite element method based on unstructured tetrahedral elements and employed the second-order backward Euler method for time discretization.This allowed for accurate 3D modeling and accounted for the effects of complex terrain.Based on these,the influence characteristics of flight altitudes and the sizes,burial depths,and resistivities of anomalies are compared and analyzed to explore the UAV-TEM systems’exploration capability.Lastly,four typical geoelectrical models of landslides are designed,and the inversion method based on the Gauss-Newton optimization method is used to image the landslide models and analyze the imaging effect of the UAV-TEM method on landslide geohazards.Numerical results showed that UAV-TEM could have better exploration resolution and fine imaging of nearsurface structures,providing important technical support for monitoring,early warning,and preventing landslides and other geological hazards.

Contrast between 2D inversion and 3D inversion based on 2D high-density resistivity data

The 2D data processing adopted by the high-density resistivity method regards the geological structures as two degrees, which makes the results of the 2D data inversion only an approximate interpretation;the accuracy and effect can not meet the precise requirement of the inversion. Two typical models of the geological bodies were designed, and forward calculation was carried out using finite element method. The forward-modeled profiles were obtained. 1% Gaussian random error was added in the forward models and then 2D and 3D inversions using a high-density resistivity method were undertaken to realistically simulate field data and analyze the sensitivity of the 2D and 3D inversion algorithms to noise. Contrast between the 2D and 3D inversion results of least squares inversion shows that two inversion results of high-density resistivity method all can basically reflect the spatial position of an anomalous body. However, the 3D inversion can more effectively eliminate the influence of interference from Gaussian random error and better reflect the distribution of resistivity in the anomalous bodies. Overall, the 3D inversion was better than 2D inversion in terms of embodying anomalous body positions, morphology and resistivity properties.

Extrapolated Tikhonov method and inversion of 3D density images of gravity data

Tikhonov regularization（TR） method has played a very important role in the gravity data and magnetic data process. In this paper, the Tikhonov regularization method with respect to the inversion of gravity data is discussed. and the extrapolated TR method（EXTR） is introduced to improve the fitting error. Furthermore, the effect of the parameters in the EXTR method on the fitting error, number of iterations, and inversion results are discussed in details. The computation results using a synthetic model with the same and different densities indicated that. compared with the TR method, the EXTR method not only achieves the a priori fitting error level set by the interpreter but also increases the fitting precision, although it increases the computation time and number of iterations. And the EXTR inversion results are more compact than the TR inversion results, which are more divergent. The range of the inversion data is closer to the default range of the model parameters, and the model features and default model density distribution agree well.

3D inversion of audio-magnetotelluric data for mineral exploration:A case study of Layikeleke buried porphyry copper deposit,Xinjiang,China

Layikeleke copper deposit is a large-scale porphyry copper polymetallic buried deposit,which has been discovered recently in the eastern Junggar area of Xinjiang.Mineralization occurred in the Late Silurian and Early Devonian with the copper body mainly confined to tonalite.To find new ore bodies,it is necessary to map the 3D spatial distribution of the tonalite.For this reason,we deployed audio-magnetotelluric(AMT)sounding in the research area,collected 26 profi les and 1198 measuring points,carried out 3D inversion calculations of off-diagonal elements in the impedance tensor data using the nonlinear conjugate gradient method,and obtained a 3D electrical structure model.The electrical structure reveals two groups of NW-SE trending middle and middle low resistivity anomaly zones,which intersect the high resistivity bedrock area in the northwest of the study area.Based on the electrical data,it can be inferred that the medium low resistance tonalite in the northern part of the study area is the host rock of the porphyry copper polymetallic deposit,which has been verifi ed by borehole data.The results of 3D AMT inversion depict the spatial distribution and depth variation characteristics of the tonalite electrical structure model,providing a basis for further prospecting and exploration.Therefore,this method of identifying lithology by 3D inversion can provide an important basis for mineral exploration and mining of buried rock masses,and is an effective prospecting method.

3D inversion of borehole gravity data using cokriging

Borehole gravity has been used in mineral exploration recently with the advent of slim-hole gravimeters. It is logical to perform inversion to utilize the information in the newly acquired data. The inversions were carried out by using cokriging,which is a geostatistical method of estimation that minimizes the error variance by applying cross-correlation between several variables. In this study the estimated densities are derived by using boreholes gravity and known densities along the borehole. This method does not need iterative process and computes efficiently. The selection of examples demonstrates that this method has the ability to include physical property from borehole measurements in the inversion. The synthetic examples demonstrate the density variation along a borehole can be well determined without depth constraints in the inversion. The resolution of the recovered model can be further improved by including the densities along the borehole for inversion. However,this capability decreases dramatically with the increasing of distance between the anomalous body and the borehole.

Pseudo-Magnetotelluric 2D Inversion Technology of Magnetic-Source Transient Electromagnetics

Based on the fact that it is diffi cult to implement optimum inversion using 2D and 3D forward modeling with magnetic-source transient electromagnetics(TEM),this paper explores a novel approach to the implementation of 2D magnetic-source TEM inversion.In particular,we converted magnetic-source TEM data into magnetotelluric(MT)data and then used a 2D MT inversion method to implement a 2D magnetic-source TEM inversion interpretation.First,we studied the similarity between magnetic-source TEM waves and MT waves and between magnetic-source TEM all-time apparent resistivity and MT Cagniard apparent resistivity.Then,we selected an optimal time-frequency transformation coeffi cient to implement rapid time-frequency transformation of all-time TEM apparent resistivity to MT Cagniard apparent resistivity.Afterward,we conducted 1D pseudo-MT inversions of magnetic-source 1D TEM theoretical models.The 1D inversion results demonstrated that the diff erence between the inversion parameters and model parameters was small,while the MT 1D inversion method could be used to conduct magnetic 1D TEM inversion within a certain margin of error.We further conducted 2D pseudo-MT inversions of 3D magnetic-source TEM theoretical models,and the 2D inversion results indicated that selecting a joint 2D pseudo-MT transverse-electric(TE)and transverse-magnetic(TM)inversion method based on measuring the line above a 3D anomalous body can help to accurately implement a 2D inversion interpretation of the 3D TEM response.

Three-dimensional constrained gravity inversion of Moho depth and crustal structural characteristics at Mozambique continental margin

Mozambique's continental margin in East Africa was formed during the break-off stage of the east and west Gondwana lands. Studying the geological structure and division of continent-ocean boundary(COB) in Mozambique's continental margin is considered of great significance to rebuild Gondwana land and understand its movement mode. Along these lines, in this work, the initial Moho was fit using the known Moho depth from reflection seismic profiles, and a 3D multi-point constrained gravity inversion was carried out. Thus, highaccuracy Moho depth and crustal thickness in the study area were acquired. According to the crustal structure distribution based on the inversion results, the continental crust at the narrowest position of the Mozambique Channel was detected. According to the analysis of the crustal thickness, the Mozambique ridge is generally oceanic crust and the COB of the whole Mozambique continental margin is divided.

Three-Dimensional Density Distribution and Seismic Activity along the Guxiang–Tongmai Segment of the Jiali Fault,Tibet

The Guxiang-Tongmai segment of the Jiali fault is situated northeast of the Namche Barwa Syntaxis in northeastern Tibet.It is one of the most active strike-slip faults near the syntaxis and plays a pivotal role in the examination of seismic activity within the eastern Himalayan Syntaxis.New study in the research region has yielded a 1:200000 gravity dataset covering an area 1500 km^(2).Using wavelet transform multiscale decomposition,scratch analysis techniques,and 3D gravity inversion methods,gravity anomalies,fault distributions,and density structures were determined across various scales.Through the integration of our new gravity data with other geophysical and geological information,our findings demonstrate substantial variations in the overall crustal density within the region,with the fault distribution closely linked to these density fluctuations.Disparities in stratigraphic density are important causes of variations in the capacity of geological formations to endure regional tectonic stress.Earthquakes are predominantly concentrated within the density transition zone and are primarily situated in regions of elevated density.The hanging wall stress within the Guxiang-Tongmai segment of the Jiali fault exhibits a notable concentration,marked by pronounced anisotropy,and is positioned within the density differential zone,which is prone to earthquakes.

Intra-continental Orogeny:Insights from Magnetotelluric Data into the Mesozoic Uplift History of the Eastern Jiangnan Orogen in South China

Despite extensive efforts to understand the tectonic evolution of the Jiangnan Orogen in South China,the orogenic process and its mechanism remain a matter of dispute.Previous geodynamic studies have mostly focused on collisional orogeny,which is commonly invoked to explain the Jiangnan Orogen.However,it is difficult for such hypotheses to reconcile all the geological and geophysical data,especially the absence of ultrahigh-pressure metamorphic rocks.Based on the magnetotelluric data,we present a group of resistivity models produced through the combination of two-dimensional and three-dimensional inversions,revealing the geo-electrical structures of Jiangnan and a typical collisional orogen.In our models,the resistive crust is separated into three parts by a prominent conductive layer with opposite dipping directions on both sides.A special thrust-nappe system,which is different from that developed in a typical collisional process,is revealed in the Jiangnan Orogen.This structure suggests a process different from the simple collisional orogeny.To interpret our observations,an'intra-continental orogeny'is proposed to address the development of the Jiangnan Orogen in the Mesozoic.Furthermore,this'reworked'process may contain at least two stages caused by the decoupling of the lithosphere,which is revealed by an extra conductive layer beneath Jiangnan.

Fast inversion of array laterolog measurements in an axisymmetric medium

The array laterolog is an important tool for complex formation logging evaluation due to its high resolution and large detection depth.However,its logging responses are seriously affected by leakage events due to the surrounding rock and by mud invasion.These factors must be considered when inverting array lateral logging data,so that the inversion results reflect the true formation conditions as much as possible.The difficulties encountered in the inversion of array lateral logging data are:too many inversion parameters cause the calculation of the Jacobian matrix to be difficult and the time required to select the initial inversion values due to the slow forward-modeling speed.In this paper,we develop a fast processing method for array laterolog data.First,it is important to clearly define the main controlling factors for the array laterolog response,such as thickness,the surrounding rock,and invasion.Second,based on a depth-window technique,processing the array laterolog data for the entire well is transformed into multiple 2 D inversions of the layers using a series of continuous depth windows.For each formation in a depth window,combined with the1 D equivalent fast-forward algorithm,rapid extraction of the radial resistivity profile of the formation is achieved.Finally,the 1 D inversion result is used as the initial state to further eliminate the influence of surrounding rocks and layer thicknesses on the apparent resistivity response.Numerical simulation results show that the factors affecting the response of the array laterolog are the invasion properties,the layer thicknesses,and the surrounding rocks;the windowing technique greatly reduces the number of inversion parameters needed and improves the inversion speed.A real application of the method shows that 2 D inversion can rapidly reconstruct the actual resistivity distribution and improve the accuracy of reservoir saturation calculations.

Two-dimensional inversion of spectral induced polarization data using MPI parallel algorithm in data space

Traditional two-dimensional（2D） complex resistivity forward modeling is based on Poisson＇s equation but spectral induced polarization（SIP） data are the coproducts of the induced polarization（IP） and the electromagnetic induction（EMI） effects.This is especially true under high frequencies,where the EMI effect can exceed the IP effect.2D inversion that only considers the IP effect reduces the reliability of the inversion data.In this paper,we derive differential equations using Maxwell＇s equations.With the introduction of the Cole-Cole model,we use the finite-element method to conduct2 D SIP forward modeling that considers the EMI and IP effects simultaneously.The data-space Occam method,in which different constraints to the model smoothness and parametric boundaries are introduced,is then used to simultaneously obtain the four parameters of the Cole-Cole model using multi-array electric field data.This approach not only improves the stability of the inversion but also significantly reduces the solution ambiguity.To improve the computational efficiency,message passing interface programming was used to accelerate the 2D SIP forward modeling and inversion.Synthetic datasets were tested using both serial and parallel algorithms,and the tests suggest that the proposed parallel algorithm is robust and efficient.

Three-dimensional conjugate gradient inversion of magnetotelluric full information data

Based on the analysis of impedance tensor data, tipper data, and the conjugate gradient algorithm, we develop a three-dimensional （3D） conjugate gradient algorithm for inverting magnetotelluric full information data determined from five electric and magnetic field components and discuss the method to use the full information data for quantitative interpretation of 3D inversion results. Results from the 3D inversion of synthetic data indicate that the results from inverting full information data which combine the impedance tensor and tipper data are better than results from inverting only the impedance tensor data （or tipper data） in improving resolution and reliability. The synthetic examples also demonstrate the validity and stability of this 3D inversion algorithm.

Three-dimensional inversion of controlled-source audio-frequency magnetotelluric data based on unstructured fi nite-element method

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 fi nite-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-fi eld 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-fi eld zones,and the inversion results agreed well with the true model.These fi ndings reveal that the proposed algorithm is eff ective for 3D inversion of CSAMT data.

3D LBFGS inversion of controlled source extremely low frequency electromagnetic data

The controlled source extremely low frequency （CSELF） electromagnetic method is characterized by extremely long and powerful sources and a huge measurement range. Its electromagnetic field can therefore be affected by the ionosphere and displacement current. Research on 3D forward modeling and inversion of CSELF electromagnetic data is currently in its infancy. This paper makes exploratory attempts to firstly calculate the 1D extremely low frequency electromagnetic field under ionosphere-air-earth coupling circumstances, and secondly analyze the propagation characteristics of the background electromagnetic field. The 3D staggered-grid finite difference scheme for solving for the secondary electric field is adopted and incorporated with the 1D modeling algorithm to complete 3D forward modeling. Considering that surveys can be carried out in the near field and transition zone for lower frequencies, the 3D Limited-memory Broyden-Fletcher-Goldfarb-Shanno （LBFGS） inversion of CSELF electromagnetic data is presented （in which the sources, or primary fields, are included）, with the aim of directly inverting the impedance data, regardless of where it is acquired. Derivation of the objective functional gradient is the core component in the inversion. Synthetic tests indicate that the well-chosen approximation to the Hessian can significantly speed up the inversion. The model responses corresponding to the coexistence of conductive and resistive blocks show that the off-diagonal components of tensor impedance are much more sensitive to the resistivity variation than the diagonal components. In comparison with conventional scalar inversion, tensor inversion is superior in the recoveries of electric anomalies and background resistivity.

3D Step-by-step inversion strategy for audio magnetotellurics data based on unstructured mesh

A three-dimensional(3D)step-by-step inversion strategy for audio magnetotellurics(AMT)is investigated in this study.The objective function is minimized by iteratively solving the Gauss-Newton normal equation,and the inversion region is discretized with unstructured tetrahedral elements.The inversion proceeds step-by-step from a coarse mesh to a fine mesh.In the inversion iteration process,a mesh is adaptively optimized according to the spatial gradient information about the model resistivity to fine delineate the boundaries of abnormal bodies.In the early stage of inversion execution,a coarse mesh is used for inversion,and the inversion stability is improved by reducing the number of inversion elements.In addition,mesh refinement is performed in the iterative inversion process.The inversion results obtained from the previous mesh are used as the reference and initial models for the next mesh iterative inversion.The step-by-step inversion strategy can ensure that the inversion is performed in the correct direction,improving the inversion stability and results gradually.Synthetic results show that the step-by-step inversion strategy with a Gauss-Newton method for 3D AMT inversion is stable and reliable,which lays a foundation for further practical 3D AMT data inversion.

Optimization algorithm for rapid 3D gravity inversion

The practical application of 3D inversion of gravity data requires a lot of computation time and storage space.To solve this problem,we present an integrated optimization algorithm with the following components:(1)targeting high accuracy in the space domain and fast computation in the wavenumber domain,we design a fast 3D forward algorithm with high precision;and(2)taking advantage of the symmetry of the inversion matrix,the main calculation in gravity conjugate gradient inversion is decomposed into two forward calculations,thus optimizing the computational efficiency of 3D gravity inversion.We verify the calculation accuracy and efficiency of the optimization algorithm by testing various grid-number models through numerical simulation experiments.

Application of tensor CSAMT with high-power orthogonal signal sources in Jiama porphyry copper deposit,South Tibet

The Jiama porphyry copper deposit in Tibet is one of the proven supergiant copper deposits in the Qinghai-Tibet Plateau at present,with the reserves of geological resources equivalent to nearly 20×10^(6) t.However,it features wavy and steep terrain,leading to extremely difficult field operation and heavy interference.This study attempts to determine the effects of the tensor controlled-source audiomagnetotellurics(CSAMT)with high-power orthogonal signal sources(also referred to as the high-power tensor CSAMT)when it is applied to the deep geophysical exploration in plateaus with complex terrain and mining areas with strong interference.The test results show that the high current provided by the highpower tensor CSAMT not only greatly improved the signal-to-noise ratio but also guaranteed that effective signals were received in the case of a long transmitter-receiver distance.Meanwhile,the tensor data better described the anisotropy of deep geologic bodies.In addition,the tests also show that when the transmitting current reaches 60 A,it is still guaranteed that strong enough signals can be received in the case of the transmitter-receiver distance of about 25 km,sounding curves show no near field effect,and effective exploration depth can reach 3 km.The 2D inversion results are roughly consistent with drilling results,indicating that the high-power tensor CSAMT can be used to achieve nearly actual characteristics of underground electrical structures.Therefore,this method has great potential for application in deep geophysical exploration in plateaus and mining areas with complex terrain and strong interference,respectively.This study not only serves as important guidance on the prospecting in the Qinghai-Tibet Plateau but also can be used as positive references for deep mineral exploration in other areas.

Inversions for MT data in 2D symmetrical anisotropic media

In the paper, a 2D symmetrical anisotropic medium whose strike agrees with one of the horizontal principal axes is considered to develop a corresponding inversion technique. In the specified conditions, if we assume an equivalent conductivity anisotropy in both the vertical and dipping directions, i.e., σzz=σyy, the differential equations obtained are formally the same as that for TE and TM modes in the 2D isotropic geoelectrical media. The same inversion technique as that in the 2D isotropic media can be employed to obtain the anisotropic conductivities. It means that the TE and TM inversion results in the isotropic media can be respectively thought as the resistivities in the two principal directions of the symmetrically anisotropic media, which has offered a new approach and a theoretical guidance for interpreting magnetotelluric data. And the inversion technique developed here is used to test the magnetotelluric data in the area of Tianzhu and Yongdeng in Gansu Province, so that the crust anisotropic geoelectrical structures in this region can be obtained.

3D variable-grid full-waveform inversion on GPU

Full-waveform inversion(FWI)is a powerful tool to reconstruct subsurface geophysical parameters with high resolution.As3 D surveys become widely implemented,corresponding 3 D processing techniques are required to solve complex geological cases,while a large amount of computation is the most challenging problem.We propose an adaptive variable-grid 3 D FWI on graphics processing unit devices to improve computational efficiency without losing accuracy.The irregular-grid discretization strategy is based on a dispersion relation,and the grid size adapts to depth,velocity,and frequency automatically.According to the transformed grid coordinates,we derive a modified acoustic wave equation and apply it to full wavefield simulation.The 3 D variable-grid modeling is conducted on several 3 D models to validate its feasibility,accuracy and efficiency.Then we apply the proposed modeling method to full-waveform inversion for source and residual wavefield propagation.It is demonstrated that the adaptive variable-grid FWI is capable of decreasing computing time and memory requirements.From the inversion results of the 3 D SEG/EAGE overthrust model,our method retains inversion accuracy when recovering both thrust and channels.

A three-dimensional transient electromagnetic data inversion method based on a time–frequency transformation

Herein,a three-dimensional(3D)inversion method in the frequency domain based on a time–frequency transformation was developed to improve the efficiency of the 3D inversion of transient electromagnetic(TEM)data.The Fourier transform related to the electromagnetic response in the frequency and time domains becomes a sine or cosine transform under the excitation of downward-step current.We established a transformation matrix based on the digital fi ltering calculation for the sine transform,and then the frequency domain projection of the TEM data was determined from the linear transformation system using the smoothing constrained least squares inversion method,in which only the imaginary part was used to maintain the TEM data transformation equivalence in the bidirectional projection.Thus,the time-domain TEM inversion problem was indirectly and effectively solved in the frequency domain.In the 3D inversion of the transformed frequency-domain data,the limited-memory Broyden–Fletcher–Goldfarb–Shannoquasi–Newton(L-BFGS)method was used and modifi ed with a restart strategy to adjust the regularization parameter when the algorithm tended to a local minimum.Synthetic data tests showed that our domain transformation method can stably project the TEM data into the frequency domain with very high accuracy;furthe rmore,the 3D inversion of the transformed frequency-domain data is stable,can be used to recover the real resistivity model with an acceptable effi ciency.