DAMPED LEAST-SQUARES INVERSION OF TIME-DOMAIN AIRBORNE EM DATA BASED ON SINGULAR VALUE DECOMPOSITION1

Airborne electromagnetic (AEM) methods are increasingly being used as tools of geological mapping, groundwater exploration and prospecting for coal and lignite. In such applications, quantitative interpretation is commonly based on the layered-earth model. A new approach, a damped least-squares inversion with singular value decomposition, is proposed for interpretation of time-domain, towed-bird AEM data. Studies using theoretical and field AEM data indicate that inversion techniques are dependable and provide fast converging solutions. An analysis has been made of the accuracy of model parameter determination, which depends on resistivity and thickness distribution. In the common case of conductive overburden, upper-layer resistivity and thickness are usually well determined, although situations exist where their separation becomes difficult. In the case of a resistive layer overlying a conductive basement, the layer thickness is the best-determined parameter. In both cases, estimates of basement resistivity are the least reliable. Field data obtained with the Chinese-made M-l AEM system in Dongling, Anhui Province, China, were processed using the described inversion algorithm. The survey area comprised fluvial Cenozoic clays and weathered Mesozoic sediments. Inversion of AEM data resulted in accurate depth-to-bedrock sections and realistic estimates of the resistivities of overburden and bedrock which agree with the results of drilling and resistivity sounding.     

Vertical–vertical controlled-source electromagnetic instrumentation and acquisition

Vertical–vertical controlled-source electromagnetic is an alternative to other techniques for providing three-dimensional resistivity images of the subsurface. It utilizes a large and powerful vertical dipole transmitter and arrays of E-field receivers with vertical and horizontal dipole sensors. The necessary instrumentation and acquisition procedures which differ strongly from other controlled-source electromagnetic methods are described in the paper.     

Electrical resistivity tomography to investigate geological structures of the earth's upper crust

It is important to have detailed knowledge of the electrical properties of the earth's crust in order to recognize geological structures and to understand tectonic processes. In the area surrounding the German Continental Deep Drilling Project (KTB), we have used DC dipole–dipole soundings to investigate the electrical conductivity distribution down to a depth of several kilometres. We have adapted the electrical resistivity tomography (ERT) technique, a well-established near-surface method, to large-scale experiments. Independent transmitting and receiving units were used to realize the concept of simultaneous multichannel registration of the scalar electrical potential at 44 dipoles. The measured data yielded apparent resistivities which were inverted to a 2D resistivity model ranging from the surface down to a depth of 4 km. Two highly conductive structures with steep inclination were detected. They are expected to be major fault zones embedded in a metamorphic body. The rather low resistivity ( ρ  < 10 Ωm) can be explained by the existence of graphitic minerals and/or electrolytic fluids.     

时间域航空电磁扩散特征和成像深度研究

为了研究时间域航空电磁系统扩散特征,基于连续性边界条件将电磁场向下延拓得到地下介质中各点处的频率域响应,通过傅里叶变换将其变换到时间域.计算阶跃波形发射时垂直磁偶极子和水平磁偶极子在均匀半空间介质和两层介质中产生的电磁场,通过电流密度矢量图和随时间变化的电流密度等值线展示电磁场在地下介质中的扩散过程.电磁场在地下的扩散受电阻率结构的影响.在良导地区电磁场扩散慢、衰减快,而在高阻地区电磁场扩散快、衰减慢.垂直磁偶极子在地下产生的感应电流形成一个电流环随时间向下、向外扩散.水平磁偶极子在地下产生的感应电流形成两个互相叠加的电流环.时间域电磁场扩散代表着真正物理意义上的电磁扩散,因为它展示了地下电磁场空间分布随时间的变化和场强的衰减.基于对感应电流环的研究,我们探究了扩散深度和时间域航空电磁数据成像深度的关系.时间域电磁场扩散规律的研究不仅加深了对电磁扩散特征的理解,更有助于提高航空电磁数据解释水平.     

Use of magnetotelluric signals from 50 Hz power lines for resistivity mapping of geothermal fields in New Zealand

Electromagnetic (EM) fields radiated from the transmission lines of the New Zealand electricity grid have been digitally recorded at test sites near the Tokaanu geothermal field. Amplitudes and phases of the 50 Hz signals (and the odd harmonics up to 450 Hz) were determined using a software implementation of a phase-locked filter. These data were then analysed to determine the components of the magnetotelluric impedance tensor and the corresponding apparent resistivities and phases. At most sites, there was sufficient variation in the elliptical polarization of the EM fields to enable the impedance tensors to be determined in full. Sites where the EM data had been affected by near-source effects were identified by having large vertical magnetic field components and by being closer to a power line source than about 3–5 skin depths. With the test measurements, the north-eastern part of the Tokaanu geothermal field was successfully delineated giving low resistivities (< 5 Ωm) on the inside and higher resistivities on the outside, in agreement with the Schlumberger array DC apparent resistivities. The small size of the 50 Hz magnetotelluric equipment and its portable nature make this method of resistivity measurement suitable for reconnaissance resistivity mapping in places with difficult access.     

An assessment of inversion methods for AEM data applied to environmental studies

Airborne electromagnetic (AEM) surveys are currently being flown over populated areas and applied to detailed problems using high flight line densities. Interpretation information is supplied through a model of the subsurface resistivity distribution. Theoretical and survey data are used here to study the character and reliability of such models. Although the survey data were obtained using a fixed-wing system, the corresponding associations with helicopter, towed-bird systems are discussed. Both Fraser half-space and 1D inversion techniques are considered in relation to their ability to distinguish geological, cultural and environmental influences on the survey data. Fraser half-space modelling provides the dual interpretation parameters of apparent resistivity and apparent depth at each operational frequency. The apparent resistivity was found to be a remarkably stable parameter and appears robust to the presence of a variety of at-surface cultural features. Such features provide both incorrect altitude data and multidimensional influences. Their influences are observed most strongly in the joint estimate of apparent depth and this accounts for the stability of the apparent resistivity. Positive apparent depths, in the example data, result from underestimated altitude measurements. It is demonstrated that increasingly negative apparent depths are associated with increasing misfits between a 1D model and the data. Centroid depth calculations, which are a transform of the Fraser half-space parameters, provide an example of the detection of non-1D influences on data obtained above a populated area. 1D inversion of both theoretical and survey data is examined. The simplest use of the 1D inversion method is in providing an estimate of a half-space resistivity. This can be undertaken prior to multilayer inversion as an initial assessment. Underestimated altitude measurements also enter the problem and, in keeping with the Fraser pseudo-layer concept, an at-surface highly resistive layer of variable thickness can be usefully introduced as a constrained parameter. It is clearly difficult to ascribe levels of significance to a ‘measure’ of misfit contained in a negative apparent depth with the dimensions of metres. The reliability of 1D models is better assessed using a formal misfit parameter. With the misfit parameter in place, the example data suggest that the 1D inversion methods provide reliable apparent resistivity values with a higher resolution than the equivalent information from the Fraser half-space estimates.     

飞行高度同时反演的固定翼航空瞬变电磁-维反演

航空电磁测量记录中,不仅感生电动势测量数据有观测误差,而且高度计测量数据也有误差,直接进行常规反演往往导致反演结果不可靠,研究飞行高度数据有误差下的反演算法具有实际意义.本文以层状模型的固定翼时间域航空电磁多分量理论响应数据为例,提出了两种针对飞行高度计记录数据有误差时的正则化反演算法,一个是自适应正则化反演方法,另一...     

Stream bottom resistivity tomography to map ground water discharge

This study investigates the effectiveness of direct current electrical resistivity as a tool for assessing ground water/surface water interactions within streams. This research has shown that patterns of ground water discharge can be mapped at the meter scale, which is important for understanding stream water quality and ecosystem function. Underwater electrical resistivity surveys along a 107-m stream section within the Burd Run Watershed in South Central Pennsylvania identified three resistivity layers: a resistive (100 to 400 Ωm) surface layer corresponding to the streambed sediments, a conductive (20 to 100 Ωm) middle layer corresponding to residual clay sediments, and a resistive (100 to 450 Ωm) bottom layer corresponding to the carbonate bedrock. Tile probing to determine the depth to the bedrock and resistivity test box analysis of augered sediment samples confirmed these interpretations of the resistivity data. Ground water seeps occurred where the resistivity data showed that the residual clays were thinnest and bedrock was closest to the streambed. Plotting the difference in resistivity between two surveys, one conducted during low-stage and the other during high-stage stream conditions, showed changes in the conductivity of the pore fluids saturating the sediments. Under high-stream stage conditions, the top layer showed increased resistivity values for sections with surface water infiltration but showed nearly constant resistivity in sections with ground water seeps. This was expressed as difference values less than 50 Ωm in the area of the seeps and greater than 50 Ωm change for the streambed sediments saturated by surface water. Thus, electrical resistivity aided in characterizing ground water discharge zones by detecting variations in subsurface resistivity under high- and low-stream stage conditions as well as mapping subsurface heterogeneities that promote these exchanges.     

3D anisotropic modeling and identification for airborne EM systems based on the spectral-element method

The airborne electromagnetic (AEM) method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element (SE) method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell’s equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic geology.     

Airborne EM skin depths

Skin depth is an electromagnetic (EM) scale length that provides a measure of the degree of attenuation experienced by a particular frequency of an EM system. As has been discussed in the literature, skin depth is not a complete measure of the depth of investigation, but the two may be related. Frequency‐domain airborne EM systems employ pairs of transmitter and receiver coils that use a frequency range from several hundred hertz to over 100 kHz. For elevated dipoles, both geometrical and frequency‐dependent attenuation of the induced fields must be considered. For airborne EM systems it is possible to define a skin depth based only on the electric field induced by the transmitter. A vertical decay scale length, here defined from the at‐surface position of maximum electric field, enables the same skin‐depth estimate to be obtained for both cases of vertical and horizontal dipolar excitation. Such dipolar skin depths associated with towed‐bird and fixed‐wing airborne systems are studied in relation to frequency, conductivity and sensor elevation. Dipolar skin depths are found to be much smaller than their plane‐wave counterparts except at high frequency (>50 kHz) and in combination with high conductivity. For the majority of airborne systems the influence of altitude on skin depth is highly significant. Dipolar skin depths increase with increasing sensor elevation. Low frequencies display the greatest sensitivity. At low elevation (<40 m), geometrical attenuation dominates the behaviour of the skin depth. The study indicates that typical low‐altitude airborne surveys provide vertically compact assessments of subsurface conductivity, well suited to near‐surface, environmental applications.     

一维电阻率各向异性对海洋可控源电磁响应的影响研究

地下介质的电阻率常常表现为各向异性,海底裂隙地层和层状沉积序列可能形成宏观电阻率各向异性.在解释海洋电磁资料时,电阻率各向异性的影响不应该被忽略,否则可能会得到错误的海底地电模型.作者编写了电阻率任意各向异性一维层状介质海洋可控源电磁场计算程序,计算了电阻率各向异性层状模型的海洋可控源电磁响应,讨论了覆盖层和高阻储层分别具有电阻率各向异性时的电磁场响应特征.     

水平n层导电介质中时谐垂直电偶极子的电磁场

对于包含n层线性、均匀、各向同性的水平成层导电介质,本文应用汉克尔变换及其逆变换推导求得了位于顶层导电媒质中的时谐垂直电偶极子在该层产生的电磁场的表达通式．通过这些表达式能够很方便地求得包含任意多层导体半空间中的电磁场．文中最后计算了导电半体空间和二层导电介质中时谐垂直电偶极子产生的电磁场,验正了本文所得结果的正确性。     

基于异常线圈的时间域AEM系统测试和标定方法研究

为了检验和测试时间域航空电磁系统的测量精度和有效性,采用地面铺设闭合的异常线圈模拟地下有限导体的方法,将异常线圈的电磁响应理论值与系统实测数据进行拟合分析,来确定系统误差和飞行几何参数误差.在计算异常线圈电磁响应的基础上,研究了衰减曲线、剖面曲线与线圈的电性、几何参数关系,设计了野外测试实验方案.在长春市大鹅岛附近,采用吊车进行了系统测试,测试结果表明:单点实测数据的平均绝对误差为0.48 mV,系统相对误差小于1%,飞行高度误差为0.4 m、水平偏移误差为0.2 m.基于异常线圈进行时间域航空电磁系统的测试和标定,是一种准确、快速、经济可行的方法,具有野外施工便捷、参数调整灵活等特点,适用于任何时间域电磁测量系统的检测.     

均匀大地上空的时间域电磁响应

为了脉冲式航空电磁法的应用,本文介绍了均匀大地上空的时间域电磁响应。用傅里叶变换由频率域公式导出了时间域的响应公式。然后以国产脉冲式航电系统的参数计算了二次场的水平分量和垂直分量。根据时间域的计算结果,本文给出了一些解释的图件,可以用来解决两个主要问题。其一是解释在不同飞行高度测得的时间域航空电磁法资料,从而提供大地电阻率;其二是如果给出了大地电阻率,则可计算时间域的航空电磁响应,因此可以校正由飞行高度改变引起的假异常。     

Trans‐dimensional Bayesian inversion of controlled‐source electromagnetic data in the German North Sea

This paper presents the first controlled‐source electromagnetic survey carried out in the German North Sea with a recently developed seafloor‐towed electrical dipole–dipole system, i.e., HYDRA II. Controlled‐source electromagnetic data are measured, processed, and inverted in the time domain to estimate an electrical resistivity model of the sub‐seafloor. The controlled‐source electromagnetic survey targeted a shallow, phase‐reversed, seismic reflector, which potentially indicates free gas. To compare the resistivity model to reflection seismic data and draw a combined interpretation, we apply a trans‐dimensional Bayesian inversion that estimates model parameters and uncertainties, and samples probabilistically over the number of layers of the resistivity model. The controlled‐source electromagnetic data errors show time‐varying correlations, and we therefore apply a non‐Toeplitz data covariance matrix in the inversion that is estimated from residual analysis. The geological interpretation drawn from controlled‐source electromagnetic inversion results and borehole and reflection seismic data yield resistivities of ～1 Ωm at the seafloor, which are typical for fine‐grained marine deposits, whereas resistivities below ～20 mbsf increase to 2–4 Ωm and can be related to a transition from fine‐grained (Holocene age) to unsorted, coarse‐grained, and compacted glacial sediments (Pleistocene age). Interface depths from controlled‐source electromagnetic inversion generally match the seismic reflector related to the contrast between the different depositional environments. Resistivities decrease again at greater depths to ～1 Ωm with a minimum resistivity at ～300 mbsf where a seismic reflector (that marks a major flooding surface of late Miocene age) correlates with an increased gamma‐ray count, indicating an increased amount of fine‐grained sediments. We suggest that the grain size may have a major impact on the electrical resistivity of the sediment with lower resistivities for fine‐grained sediments. Concerning the phase‐reversed seismic reflector that was targeted by the survey, controlled‐source electromagnetic inversion results yield no indication for free gas below it as resistivities are generally elevated above the reflector. We suggest that the elevated resistivities are caused by an overall decrease in porosity in the glacial sediments and that the seismic reflector could be caused by an impedance contrast at a thin low‐velocity layer. Controlled‐source electromagnetic interface depths near the reflector are quite uncertain and variable. We conclude that the seismic interface cannot be resolved with the controlled‐source electromagnetic data, but the thickness of the corresponding resistive layer follows the trend of the reflector that is inclined towards the west.     

一维垂直各向异性介质频率域海洋可控源电磁资料反演方法

本文提出了一维垂直各向异性(VTI)介质倾斜偶极源频率域海洋可控源电磁(CSEM)资料高斯-牛顿反演方法.在电阻率各向异性介质水平偶极源和垂直偶极源海洋CSEM正演算法的基础上,利用欧拉旋转方法,实现了各向异性介质倾斜偶极源海洋CSEM正演算法.海洋可控源电磁场关于地下介质横向电阻率(ρ_h)和垂向电阻率(ρ_v)的偏导数(即灵敏度矩阵)是解析计算的,结合垂直各向异性介质横向电阻率与垂向电阻率的关系,将各向异性率融入到正则化因子选择中,实现了正则化因子的自适应选择.理论模型合成数据和实测资料反演算例表明,我们提出的反演方法能够较准确的重构海底围岩和基岩的各向异性电阻率以及高阻薄层的埋藏深度、厚度和垂向电阻率.     

Three-dimensional resistivity characterization of a coastal area: Application of Grounded Electrical-Source Airborne Transient Electromagnetic (GREATEM) survey data from Kujukuri Beach,Japan

An airborne electromagnetic (AEM) survey using the Grounded Electrical-Source Airborne Transient Electromagnetic (GREATEM) system was conducted over the Kujukuri coastal plain in southeast Japan to assess the system's ability to accurately describe the geological structure beneath shallow seawater. To obtain high-quality data with an optimized signal-to-noise ratio, a series of data processing techniques were used to obtain the final transient response curves from the field survey data. These steps included movement correction, coordinate transformation, the removal of local noise, data stacking, and signal portion extraction.We performed numerical forward modeling to generate a three-dimensional (3D) resistivity structure model from the GREATEM data. This model was developed from an initial one-dimensional (1D) resistivity structure that was also inverted from the GREATEM field survey data. We modified a 3D electromagnetic forward-modeling scheme based on a finite-difference staggered-grid method and used it to calculate the response of the 3D resistivity model along each survey line. We verified the model by examining the fit of the magnetic-transient responses between field data and the 3D forward-model computed data, the latter of which were convolved with the measured system responses of the corresponding data set.The inverted 3D resistivity structures showed that the GREATEM system has the capability to map resistivity structures as far as 800 m offshore and as deep as 300–350 m underground in coastal areas of relatively shallow seawater depth (5–10 m).     

INLINE AND BROADSIDE EM DIPOLE DIPOLE PROFILING OVER A THIN VERTICAL INFINITELY CONDUCTING VEIN *

Master diagrams for electromagnetic responses of nine dipole dipole systems are presented for various depths of a vertical infinitely conducting vein. The YY system gives the minimum anomaly for both the inline and broadside arrays. Among other inline systems, it is difficult to decide the clearcut superiority of one system over the other, whereas the XX system in broadside array gives maximum anomaly.     

Numerical modelling of airborne electromagnetic anomalies originating from low-conductivity 3D bodies1

Responses of a multifrequency, multicoil airborne electromagnetic (AEM) system were modelled numerically for 3D electrical conductors embedded in a resistive bedrock and overlain by an overburden of low to moderate conductivity. The results cover a horizontal coplanar coil configuration and two frequencies, 7837 Hz and 51 250 Hz. The models studied are single or multiple, poor conductors (conductance lower than 0.1 S) embedded in a host rock of high but finite resistivity (5000 Ωm) and overlain by a layer of overburden with finite thickness and low to moderate conductivity (conductance up to 2 S). On the basis of the modelling results, limits of detectability for poor conductors have been studied for the various model structures. The results indicate that the anomaly from a steeply dipping, plate-like conductor will decrease significantly when the conductor is embedded in a weakly conductive host rock and is overlain by a conductive overburden. However, an anomaly is obtained, and its magnitude can even increase with increasing overburden conductivity or frequency. The plate anomaly remains practically constant when only the overburden thickness is varied. Changes in overburden conductivity will cause the plate-anomaly values to change markedly. If the plate conductance is less than that of the overburden, a local anomaly opposite in sign to the normal type of anomaly will be recorded. Another major consequence is that conductors interpreted with free-space models will be heavily overestimated in depth or underestimated in conductance, if in reality induction and current channelling in the host rock and overburden make even a slight contribution to the anomalous EM field. The lateral resolution for the horizontal coplanar coil system was found to be about 1.7 times the sensor altitude. Similarly, the lateral extension of a horizontal conductive ribbon, required to reach the semi-infinite (half-space) behaviour, is more than three times the sensor altitude. Finally, screening of a steeply dipping plate, caused by a small, conductive horizontal ribbon, is much more severe than screening of the same plate by an extensive horizontal layer.