Three-dimensional inversion of the single-profile magnetotelluric data

It is preferable to use the three-dimensional (3D) magnetotelluric inversion, which provides volumetric geoelectric models, to handle the array input data. However, the soundings are frequently conducted on the single profiles or on the profiles that are considerably spaced apart from each other. We explore the possibilities of the 3D inversion of such data by the example of a three-layer model containing three local inhomogeneities. We previously showed that the simple processing of the data and their 1D or 2D inversion enable reconstructing the background cross section and locating all the three inhomogeneities. In the present paper, we use this information for constructing several versions of the starting model and carrying out the smoothing 3D inversion of the data. The experiments show that if the background cross section is incorporated into the starting model, the final model provided by the inversion closely reproduces the real distribution of all geoelectric parameters. At the same time, if the starting model that hosts the inhomogeneities has the form of a homogeneous half-space, the inversion is not able to reconstruct an adequate final model.

     

Three-dimensional inversion of the single-profile magnetotelluric data

It is preferable to use the three-dimensional (3D) magnetotelluric inversion, which provides volumetric geoelectric models, to handle the array input data. However, the soundings are frequently conducted on the single profiles or on the profiles that are considerably spaced apart from each other. We explore the possibilities of the 3D inversion of such data by the example of a three-layer model containing three local inhomogeneities. We previously showed that the simple processing of the data and their 1D or 2D inversion enable reconstructing the background cross section and locating all the three inhomogeneities. In the present paper, we use this information for constructing several versions of the starting model and carrying out the smoothing 3D inversion of the data. The experiments show that if the background cross section is incorporated into the starting model, the final model provided by the inversion closely reproduces the real distribution of all geoelectric parameters. At the same time, if the starting model that hosts the inhomogeneities has the form of a homogeneous half-space, the inversion is not able to reconstruct an adequate final model.     

Generalised Series Expansion (GSE) used in DC geoelectric–seismic joint inversion

Horizontally layered (1D) earth models are often assumed as a model estimate for the interpretation of geophysical data measured along 2D geological structures. In this process, the individual data sets are usually inverted independently, and it is considered only in a later phase of interpretation that these local (1D) models have common characteristic features. Taking account of these common attributes, instead of the successive independent interpretations, the lateral variations of geometrical and petrophysical parameters can be efficiently determined for the whole 2D structure by applying a series expansion. Using global basis functions, two advantages can be achieved: (i) choosing an appropriate number of basis functions helps us to restrict the complexity of the model; (ii) the integration of all the data sets measured along the profile gives rise to the application of simultaneous or joint inversion methods. This results in a decrease of the number of independent unknowns, a higher stability during the inversion and a more accurate and reliable parameter estimation.In this paper, a joint inversion algorithm is presented using DC geoelectric apparent resistivities and refraction seismic travel times measured along various layouts above a 2D geological model. To describe lateral variations series, expansions are used, and furthermore, to improve the often used approximation of a (locally) 1D forward modelling, the integral mean value of the horizontally changing model parameters (calculated along an appropriately defined interval) is introduced. We call the inversion procedure that combines series expansions and the concept of integral mean Generalised Series Expansion (GSE) inversion. The method was developed and tested for both the simultaneous (integrating data sets of one method or methods on the same physical basis) and the joint inversion (where data sets of methods on different physical bases are joined together), using synthetic and field data sets. It is also demonstrated that the equivalence problem inherent in the independent inversion of DC geoelectric data can efficiently be resolved by the use of the joint GSE inversion method in the cases of conductive and resistive equivalent geological models.     

Joint 3D inversion of multiple electromagnetic datasets

Electromagnetic methods are routinely applied to image the subsurface from shallow to regional structures. Individual electromagnetic methods differ in their sensitivities towards resistive and conductive structures and in their exploration depths. If a good balance between different electromagnetic data can be be found, joint 3D inversion of multiple electromagnetic datasets can result in significantly better resolution of subsurface structures than the individual inversions. We present a weighting algorithm to combine magnetotelluric, controlled source electromagnetic, and geoelectric data. Magnetotelluric data are generally more sensitive to regional conductive structures, whereas controlled source electromagnetic and geoelectric data are better suited to recover more shallow and resistive structures. Our new scheme is based on weighting individual components of the total data gradient after each model update. Norms of individual data residuals are used to assess how much of the total data gradient must be assigned to each method to achieve a balanced contribution of all datasets for the joint inverse model. Synthetic inversion tests demonstrate advantages of joint inversion in general and also the influence of the weighting. In our tests, the controlled source electromagnetic data gradients are larger than those of the magnetotelluric and geoelectric datasets. Consequently, direct joint inversion of controlled source electromagnetic, magnetotelluric, and geoelectric data results in models that are mostly dominated by structures required by the controlled source electromagnetic data. Applying the new adaptive weighting scheme results in an inversion model that fits the data better and resembles more the original model. We used the modular system electromagnetic as a framework to implement the new joint inversion and briefly describe the new modules for forward modelling and their interfaces to the modular system electromagnetic package.     

On the Locality of Transient Electromagnetic Soundings with a Single-Loop Configuration

The possibilities of reconstructing two-dimensional (2D) cross sections based on the data of the profile soundings by the transient electromagnetic method (TEM) with a single ungrounded loop are illustrated on three-dimensional (3D) models. The process of reconstruction includes three main steps: transformation of the responses in the depth dependence of resistivity ρ(h) measured along the profile, with their subsequent stitching into the 2D pseudo section; point-by-point one-dimensional (1D) inversion of the responses with the starting model constructed based on the transformations; and correction of the 2D cross section with the use of 2.5-dimensional (2.5D) block inversion. It is shown that single-loop TEM soundings allow studying the geological media within a local domain the lateral dimensions of which are commensurate with the depth of the investigation. The structure of the medium beyond this domain insignificantly affects the sounding results. This locality enables the TEM to reconstruct the geoelectrical structure of the medium from the 2D cross sections with the minimal distortions caused by the lack of information beyond the profile of the transient response measurements.     

Quasi-2D hybrid joint inversion of seismic and geoelectric data

Many joint inversion schemes use 1D forward modelling in the integrated interpretation of various geophysical data. In extending the joint inversion approach to the investigation of 2D structures, the discretization of the model parameters and the appropriate choice of the forward‐modelling procedure play a very important role. In this paper, a hybrid seismic–geoelectric joint inversion method is proposed for the investigation of 2D near‐surface geological structures. The electric and seismic models are coupled together through the use of common boundaries between the adjacent layers. Assuming a 2D model composed of homogeneous layers with curved boundaries, a fast ray‐tracing algorithm is used for the calculation of refraction seismic traveltime data. In the geoelectric forward modelling, a locally 1D approximation is used. The boundary surfaces are written in the form of series expansion; the inversion algorithms are formulated for the expansion coefficients and the petrophysical parameters as unknowns. Two versions of the inversion method are proposed: in versions A and B, interval‐wise constant functions and Chebyshev polynomials are, respectively, used as basis functions of the series expansion. The versions are tested by means of synthetic and in situ measured data. The tests show that both methods are stable and accurate.     

一种反演不均匀介质大地电磁测深资料的方法

通过反演受近地表不均匀介质影响的大地电磁测深资料的新方法,可获得较准确的一维地电断面参数、不均匀体埋藏深度及其电性特征。本方法计算速度快,单测ρxy,ρyx可独立反演并相互验证结果的准确性     

APPLYING 3D INVERSION OF SINGLE-PROFILE MAGNETOTELLURIC DATA TO IDENTIFY THE SHADE AND YUNONGXI FAULTS

Many synthetic model studies suggested that the best way to obtain good 3D interpretation results is to distribute the MT sites at a 2D grid array with regular site spacing over the target area. However, MT 3D inversion was very difficult about 10 years ago. A lot of MT data were collected along one profile and then interpreted with 2D inversion. How to apply the state-of-the-art 3D inversion technique to interpret the accumulated mass MT profiles data is an important topic. Some studies on 3D inversion of measured MT profile data suggested that 2D inversions usually had higher resolution for the subsurface than 3D inversions. Meanwhile, they often made their interpretation based on 2D inversion results, and 3D inversion results were only used to evaluate whether the overall resistivity structures were correct. Some researchers thought that 3D inversions could not resolute the local structure well, while 2D inversion results could agree with the surface geologic features much well and interpret the geologic structures easily. But in the present paper, we find that the result of 3D inversion is better than that of 2D inversion in identifying the location of the two local faults, the Shade Fault(SDF)and the Yunongxi Fault(YNXF), and the deep structures. In this paper, we first studied the electrical structure of SDF and YNXF based on a measured magnetotelluric(MT) profile data. Besides, from the point of identifying active faults, we compared the capacity of identifying deep existing faults between 2D inversion models and 3D models with different inversion parameters. The results show that both 2D and 3D inversion of the single-profile data could obtain reasonable and reliable electrical structures on a regional scale. Combining 2D and 3D models, and according to our present data, we find that both SDF and YNXF probably have cut completely the high resistivity layer in the upper crust and extended to the high conductivity layer in the middle crust. In terms of the deep geometry of the faults, at the profile's location, the SDF dips nearly vertically or dips southeast with high dip angle, and the YNXF dips southeast at depth. In addition, according to the results from our measured MT profile, we find that the 3D inversion of single-profile MT data has the capacity of identifying the location and deep geometry of local faults under present computing ability. Finally, this research suggests that appropriate cell size and reasonable smoothing parameters are important factors for the 3D inversion of single-profile MT data, more specifically, too coarse meshes or too large smoothing parameters on horizontal direction of 3D inversion may result in low resolution of 3D inversions that cannot identify the structure of faults. While, for vertical mesh size and data error thresholds, they have limited effect on identifying shallow tectonics as long as their changes are within a reasonable range. 3D inversion results also indicate that, to some extent, adding tippers to the 3D inversion of a MT profile can improve the model's constraint on the deep geometry of the outcropped faults.     

利用大地电磁三维反演方法获得二维剖面附近三维电阻率结构的可行性

大地电磁野外实测数据月前大多为二维剖面数据.如何反演这些二维剖面数据获得较为接近实际地电情况的结果,是多数大地电磁工作者关心的问题.我们通过对理论模型的三维响应进行分析和对合成数据及实测资料的反演结果进行对比研究,讨论了利用三维反演的方法来获得大地电磁二维剖面附近三维电阻率结构的可行性.结果表明:可用三维反演的方法来解...     

A joint inversion algorithm to process geoelectric and surface wave seismic data. Part II: applications

Seismic and geoelectric methods are often used in the exploration of near-surface structures. Generally, these two methods give, independently of one other, a sufficiently exact model of the geological structure. However, sometimes the inversion of the seismic or geoelectric data fails. These failures can be avoided by combining various methods in one joint inversion which leads to much better parameter estimations of the near-surface underground than the independent inversions. In the companion paper (Part I: basic ideas), it was demonstrated theoretically that a joint inversion, using dispersive Rayleigh and Love waves in combination with the well-known methods of DC resistivity sounding, such as Schlumberger, radial dipole-dipole and pole-pole arrays, provides a better parameter estimation. Two applications are shown: a five layer structure in Borsod County, Hungary, and a three-layer structure in Thüringen, Germany. Layer thicknesses, wave velocities and resistivities are determined. Of course, the field data sets obtained from the ‘real world’ are not as complete and as good as the synthetic data sets in the theoretical Part I. In both applications, relative model distances, in percentages, serve as quality control factors for the different inversions; the lower the relative distance, the better the inversion result. In the Borsod field case, Love wave group slowness data and Schlumberger, radial dipole-dipole and pole-pole (i.e two-electrode) data sets are processed. The independent inversion performed using the Love wave data leads to a relative model distance of 155%. An independent Schlumberger inversion results in 41%, a joint geoelectric inversion of all data sets in 15%, a joint inversion of Love wave data and all geoelectric data sets in 15% and the robust joint inversion of Love wave data and the three geoelectric data sets in 10%. In the Thüringen field case, only Rayleigh wave group slowness data and Schlumberger data were available. The independent inversion using Rayleigh wave data results in a relative model distance of 19%. The independent inversion performed using Schlumberger data leads to 34%, the joint and robust joint inversion of Rayleigh wave and Schlumberger data gave results of 18% and 20%, respectively.     

基于卡尔曼滤波的自然电场数据时序反演

自然电场法常用于环境与工程等领域的监测作业,但各时刻观测数据往往单独反演解释.为了充分利用时序数据间的关联信息,提高监测数据的反演解释可靠性,提出基于卡尔曼滤波的自然电场监测数据时序反演方法.根据达西定律和阿尔奇公式建立污染物在孔隙介质中的运动扩散的动态地电模型,作为用于构建卡尔曼滤波的状态模型.而卡尔曼滤波的观测模型则通过常规的自然电场法正演获得.在建立状态模型和观测模型的基础上,构建起卡尔曼滤波递归,将地电模型演化信息与自然电场观测数据进行信息融合,实现自然电场监测数据的时序反演.加入噪声的自然电场模拟数据测试表明时序反演算法具有较好的鲁棒性,对噪声不敏感.沙槽物理实验监测数据的计算测试也同样证明时序反演能有效处理监测数据,实现对动态模型的准确重构.     

Analysis of magnetovariational response functions

Advances in magnetovariational sounding are stimulating further development of this area of deep geoelectrics. The paper contains a review of magnetovariational response functions revealing their main properties and proposing new methods of their analysis. The theory of magnetic perturbation ellipses having a higher resolution is set forth and methods of the decomposition of magnetovariational functions are discussed that allow one to reduce 3D magnetovariational interpretation to two or three independent 2D inversions and eliminate the effect of 2D regional structures of the geoelectric background.     

Parameter optimization of gravity density inversion based on correlation searching and the golden section algorithm

For density inversion of gravity anomaly data, once the inversion method is determined, the main factors affecting the inversion result are the inversion parameters and subdivision scheme. A set of reasonable inversion parameters and subdivision scheme can, not only improve the inversion process efficiency, but also ensure inversion result accuracy. The gravity inversion method based on correlation searching and the golden section algorithm is an effective potential field inversion method. It can be used to invert 2D and 3D physical properties with potential data observed on flat or rough surfaces. In this paper, we introduce in detail the density inversion principles based on correlation searching and the golden section algorithm. Considering that the gold section algorithm is not globally optimized, we present a heuristic method to ensure the inversion result is globally optimized. With a series of model tests, we systematically compare and analyze the inversion result efficiency and accuracy with different parameters. Based on the model test results, we conclude the selection principles for each inversion parameter with which the inversion accuracy can be obviously improved.     

Geoelectric Characterization of Thermal Water Aquifers Using 2.5D Inversion of VES Measurements

This paper presents a short theoretical summary of the series expansion-based 2.5D combined geoelectric weighted inversion (CGWI) method and highlights the advantageous way with which the number of unknowns can be decreased due to the simultaneous characteristic of this inversion. 2.5D CGWI is an approximate inversion method for the determination of 3D structures, which uses the joint 2D forward modeling of dip and strike direction data. In the inversion procedure, the Steiner’s most frequent value method is applied to the automatic separation of dip and strike direction data and outliers. The workflow of inversion and its practical application are presented in the study. For conventional vertical electrical sounding (VES) measurements, this method can determine the parameters of complex structures more accurately than the single inversion method. Field data show that the 2.5D CGWI which was developed can determine the optimal location for drilling an exploratory thermal water prospecting well. The novelty of this research is that the measured VES data in dip and strike direction are jointly inverted by the 2.5D CGWI method.     

基于矢量有限元的带地形大地电磁三维反演研究

研究了基于矢量有限元方法的大地电磁带地形三维反演算法并开发了三维反演计算程序代码.在大地电磁场正演数值模拟方面,采用并行直接稀疏求解器PARDISO且无需进行散度校正的快速正演方案,对典型地形模型,在中等规模计算条件下,与双共轭梯度法(BICG)计算结果比较,发现PARDISO比BICG快10倍以上;通过理论模型试算,并与前人的有限元法计算结果对比,验证了带地形三维正演计算程序的正确性.在反演方面,本研究基于共轭梯度方法编写了大地电磁带地形三维反演代码,为了避免直接求取雅可比矩阵,将反演中的雅可比矩阵计算问题转为求解两次“拟正演”问题,进而将PARDISO的快速正演方案应用于“拟正演”问题的求解,以提高反演计算效率.利用开发的反演算法对多个带地形地电模型的合成数据进行了三维反演,反演结果能很好地重现理论模型的电性结构,验证了本文开发的三维反演算法的正确性和可靠性.最后,利用该算法反演了某矿区大地电磁实测数据,反演得到的三维电性结构清晰地反映了研究区的地电特征,将反演结果与该区已有地质资料结合进行解释,应用效果明显,进一步验证了本文算法的有效性.     

Field test of sub‐basalt hydrocarbon exploration with marine controlled source electromagnetic and magnetotelluric data

The recent use of marine electromagnetic technology for exploration geophysics has primarily focused on applying the controlled source electromagnetic method for hydrocarbon mapping. However, this technology also has potential for structural mapping applications, particularly when the relative higher frequency controlled source electromagnetic data are combined with the lower frequencies of naturally occurring magnetotelluric data. This paper reports on an extensive test using data from 84 marine controlled source electromagnetic and magnetotelluric stations for imaging volcanic sections and underlying sediments on a 128‐km‐long profile. The profile extends across the trough between the Faroe and Shetland Islands in the North Sea. Here, we focus on how 2.5D inversion can best recover the volcanic and sedimentary sections. A synthetic test carried out with 3D anisotropic model responses shows that vertically transverse isotropy 2.5D inversion using controlled source electromagnetic and magnetotelluric data provides the most accurate prediction of the resistivity in both volcanic and sedimentary sections. We find the 2.5D inversion works well despite moderate 3D structure in the synthetic model. Triaxial inversion using the combination of controlled source electromagnetic and magnetotelluric data provided a constant resistivity contour that most closely matched the true base of the volcanic flows. For the field survey data, triaxial inversion of controlled source electromagnetic and magnetotelluric data provides the best overall tie to well logs with vertically transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data a close second. Vertical transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data provided the best interpreted base of the volcanic horizon when compared with our best seismic interpretation. The structural boundaries estimated by the 20‐Ω·m contour of the vertical resistivity obtained by vertical transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data gives a maximum geometric location error of 11% with a mean error of 1.2% compared with the interpreted base of the volcanic horizon. Both the model study and field data interpretation indicate that marine electromagnetic technology has the potential to discriminate between low‐resistivity prospective siliciclastic sediments and higher resistivity non‐prospective volcaniclastic sediments beneath the volcanic section.     

A joint inversion algorithm to process geoelectric and sutface wave seismic data. Part I: basic ideas1

For the exploration of near-surface structures, seismic and geoelectric methods are often applied. Usually, these two types of method give, independently of each other, a sufficiently exact model of the geological structure. However, sometimes the inversion of the seismic or geoelectric data fails. These failures can be avoided by combining various methods in one joint inversion which feads to much better parameter estimations of the model than the independent inversions. A suitable seismic method for exploring near-surface structures is the use of dispersive surface waves: the dispersive characteristics of Rayleigh and Love surface waves depend strongly on the structural and petrophysical (seismic velocities) features of the near-surface Underground. Geoelectric exploration of the structure Underground may be carried out with the well-known methods of DC resistivity sounding, such as the Schlumberger, the radial-dipole and the two-electrode arrays. The joint inversion algorithm is tested by means of synthetic data. It is demonstrated that the geoelectric joint inversion of Schlumberger, radial-dipole and two-electrode sounding data yields more reliable results than the single inversion of a single set of these data. The same holds for the seismic joint inversion of Love and Rayleigh group slowness data. The best inversion result is achieved by performing a joint inversion of both geoelectric and surface-wave data. The effect of noise on the accuracy of the solution for both Gaussian and non-Gaussian (sparsely distributed large) errors is analysed. After a comparison between least-square (LSQ) and least absolute deviation (LAD) inversion results, the LAD joint inversion is found to be an accurate and robust method.     

Neural network inversion of data in classes of parametrized geoelectric sections

A method of approximate magnetotelluric sounding (MTS) data inversion is developed on the basis of the representation of the inverse operator by an artificial neural network in classes of geoelectric structures. A methodology of the neural network inversion of magnetotelluric data is proposed for a family of classes of geoelectric structures and the uncertainty of the inferred results is estimated. A neural network algorithm of MTS data inversion is tested using synthetic 2-D data.     

航空电磁拟三维模型空间约束反演

为了克服时间域航空电磁数据单点反演结果中常见的电阻率或层厚度横向突变造成数据难以解释的问题,通过引入双向约束实现航空电磁拟三维空间约束反演.除考虑沿测线方向相邻测点之间的横向约束外,同时还考虑了垂直测线方向测点在空间上的相互约束.为此,首先设计拟三维模型中固定层厚和可变层厚两种空间约束反演方案,然后通过在目标函数中引入沿测线和垂直测线方向上的模型参数约束矩阵,并使用L-BFGS算法使目标函数最小化,获得最优拟三维模型空间反演解.基于理论模型和实测数据反演,对单点反演与两种空间约束反演方案的有效性进行比较,证明本文空间约束反演算法对于噪声的压制效果好,反演的界面连续光滑,同时内存需求和反演时间少,是一种快速有效的反演策略.     

Results of electromagnetic sounding with JASC submarine cable

We present the results of long-term deep geoelectric studies using the JASC (Japan Sea Cable) submarine communication cable in the region of the Sea of Japan. In the 2D inversion of the amplitude and phase’s apparent resistivity curves and the frequency dependences of the tipper, we invoked the geological and geophysical information about the region and on-shore electromagnetic observations to fit the model to the observations. The resulting geoelectrical cross section of the region of the Sea of Japan along the JASC cable obtained in this way agrees well with the experimental data. The upper part of the section contains a conductive block beneath the bottom of the Central basin of the Sea of Japan at a depth of 10–40 km, a fault submerging below the continent in the marginal part and a deep fault in the continental region. In the lower portions of the cross section, the high-resistivity block interrupts the continuity of the horizontal conductive layers beneath the Yamato Uplift, and the conductive bottom part of the geoelectric cross section submerges under the continent. In the continental segment of the cross section, there is a large block with reduced electric resistivity, which is located between the conductive layers at a depth interval of 200–560 km. We analyze the characteristic features of the geoelectric cross section and the deep section imaged by seismic tomography in the region of the Sea of Japan.