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.

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.

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.

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.

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.

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.

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.

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.

Two-dimensional NMR inversion based on fast norm smoothing method

Two-dimensional(2D)nuclear magnetic resonance(NMR)inversion operates with massive echo train data and is an ill-posed problem.It is very important to select a suitable inversion method for the 2D NMR data processing.In this study,we propose a fast,robust,and effective method for 2D NMR inversion that improves the computational efficiency of the inversion process by avoiding estimation of some unneeded regularization parameters.Firstly,a method that combines window averaging(WA)and singular value decomposition(SVD)is used to compress the echo train data and obtain the singular values of the kernel matrix.Subsequently,an optimum regularization parameter in a fast manner using the signal-to-noise ratio(SNR)of the echo train data and the maximum singular value of the kernel matrix are determined.Finally,we use the Butler-Reeds-Dawson(BRD)method and the selected optimum regularization parameter to invert the compressed data to achieve a fast 2D NMR inversion.The numerical simulation results indicate that the proposed method not only achieves satisfactory 2D NMR spectra rapidly from the echo train data of different SNRs but also is insensitive to the number of the final compressed data points.

Application effect of high-density electrical method on detecting artificial filling layer: A case study of Chengjiangshan area of Huaibei City

High-density electrical method has been proved to be an effective method for probing shallow sedimentary layers.It is principally used to identify the boundary between the Quaternary soil layer and bedrock according to the vertical change of apparent resistivity.However,the artificial filling layer has the characteristics of heterogeneity and high porosity,which makes it challenging to detect the artificial filling layer by high-density electrical method.The key to solve this problem is to detect the difference of conductivity between the filling layer and the underlying bedrock.This paper takes the land in Chengjiangshan area of Huaibei City,Anhui Province as the detection target.On the basis of fully analyzing the physical properties of the artificial filling layer,two-dimensional high-density electrical survey and inversion are used to define the thickness of the artificial filling layer.The research shows that the highdensity resistivity method has obvious advantages in delineating the distribution of bedrock and the thickness of the filling layer,and the reliability of the high-density electrical method in the detection of the artificial filling layer,and delineates the scope of the filling layer is verified by the borehole data.

Concepts in the Direct Waveform Inversion(DWI)Using Explicit Time-Space Causality

The Direct Waveform Inversion(DWI)is a recently proposed waveform inversion idea that has the potential to simultaneously address several existing challenges in many full waveform inversion(FWI)schemes.A key ingredient in DWI is the explicit use of the time-space causality property of the wavefield in the inversion which allows us to convert the global nonlinear optimization problem in FWI,without information loss,into local linear inversions that can be readily solved.DWI is a recursive scheme which sequentially inverts for the subsurface model in a shallow-to-deep fashion.Therefore,there is no need for a global initial velocity model to implement DWI.DWI is unconditionally convergent when the reflection traveltime from the boundary of inverted model is beyond the finite recording time in seismic data.In order for DWI to work,DWI must use the full seismic wavefield including interbed and free surface multiples and it combines seismic migration and velocity model inversion into one process.We illustrate the concepts in DWI using 1D and 2D models.

Semi-discretization Difference Approximation for a Cauchy Problem of Heat Equation in Two-dimensional Space

In this paper we consider a semi-descretization difference scheme for solving a Cauchy problem of heat equation in two-dimensional setting. Some error estimates are proved for the semi-descretization difference regularization method which cannot be fitted into the framework of regularization theory presented by Engl, Hanke and Neubauer. Numerical results show that the proposed method works well.