Using a non-integer moment of the impulse response to estimate the half-space conductivity

The nth-order moments of the electromagnetic impulse response are useful for interpreting electromagnetic data. We have derived an analytic expression for the half-order moment of a conductive half-space. By inverting this expression, the measured half-order moment can be used to estimate an apparent conductivity of the ground. The first-order moment can also be used to estimate the half-space conductivity. A sensitivity analysis indicates that for an airborne EM configuration, the half-order moment will be most sensitive to material in the top 26–48 m, while the first-order moment will be sensitive to deeper material (down to depths between 66 and 127 m).     

均匀半空间表面大定源瞬变电磁响应的快速算法

大定源是地面瞬变电磁观测的主要方式之一, 该方式在大深度、高密度的面积测量时具有明显的优势. 但当接收点偏离发射框中心时, 由于场源的非对称性(即框边影响), 数据处理和解释比较困难, 特别是全程瞬变响应的精确计算相当耗时. 本文介绍一种数值算法, 它既能实现快速计算, 又能满足精度要求. 该算法通过对瞬变场垂直分量(b_z)及其时间变化率(b_z/t)的核函数Y(Z)和Y'(Z)表现特性的研究, 以参数Z把整个瞬变过程分为早期阶段(Z→0), 中期阶段和晚期阶段(Z→∞). 计算全程响应时, 早期和晚期阶段分别采用Y(Z)和Y'(Z)的渐近表达式;对中期阶段, 内层积分(即误差函数erf)采用有理Chebyshev渐近展开式, 外层积分采用Romberg数值积分法. 理论模型计算表明, 利用该算法可以快速计算空间任意点(除发射边框)的全程响应核函数Y(Z)和Y'(Z). 当测点到边框的距离大于边长的25%时, 计算速度比常规数值积分算法快7倍;其它测点处计算速度比常规数值积分算法快4倍. 全程时段的相对误差<0.0002%.     

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。     

基于PCA-RBF神经网络的航空飞行几何参数拟合

采用地面异常线圈对直升机时域航空电磁探测系统进行标定时,发射-接收线圈姿态的变化将导致实测数据产生误差,影响标定的精度.本文基于时间域航空电磁系统,计算了发射-接收线圈姿态任意变化时异常线圈的电磁响应,提出了主成分分析-径向基神经网络(PCA-RBF)的拟合算法,采用主成分分析法提取飞行几何参数的贡献率,利用径向基神经网络法对电磁响应进行了测线剖面的批量数据拟合,并对理论仿真和河南桐柏直升机飞行试验数据进行拟合分析,单一异常体理论数据的绝对误差平均值小于20nV·m-2,双异常体理论数据绝对误差平均值为160nV·m-2.野外实测数据在异常线圈中心位置的拟合相对误差小于1%,整条剖面测线的拟合相对误差小于±6%,平均值为2.5%.结果表明PCA-RBF拟合算法能够较好地实现航空电磁系统飞行参数的拟合,为航空电磁系统海量实测数据的快速处理提供了新方法.     

伪随机编码源激发下的时域电磁信号合成

将伪随机编码技术引入到人工源电磁法后,可以通过加大发射功率以及应用后续的相关处理技术来达到压制噪声、加大探测深度及提高分辨率的目的,因此引起了越来越多学者的关注及研究,但大多数研究集中在资料处理的相关技术上,对模拟电磁信号关注较少.然而,资料处理工作大多是从电磁信号出发的,模拟伪随机编码源激发下的电磁信号不但可以为资料处理环节提供理论数据,而且可以为检测资料处理的效果提供中间结果,因此,模拟电磁信号工作必不可少.本文根据获得接收信号的物理过程来实现伪随机编码源激发下的电磁信号合成.首先用解析公式获得特定地电结构的大地频率域响应,然后通过余弦变换得到时间域阶跃响应,接下来用阶跃响应的时间导数得到大地脉冲响应,通过将大地脉冲响应与伪随机编码源的褶积得到理想接收信号,最后,用低通滤波器来模拟发射设备和接收设备的频带限制,将之和噪声一起加到理想接收信号上,最终模拟出仿真的合成信号.通过和野外实际接收信号对比发现本文合成信号仿真度较高,可以服务于后续的数据处理环节.     

磁性层状介质的CSAMT电场分量响应特征

在传统的勘探电磁学理论中,往往把岩层磁导率近似看成空气中的磁导率,从而得到简化后的电磁场响应式,主要用于指导非磁性介质情况下的电磁探测.本文开展了磁性介质的电磁响应理论、数值模拟和特征分析等研究,以便实现对磁性矿体的电磁精细探测.首先推导出磁性层情况下的电磁响应表达式;然后,计算了几种典型磁性介质地质断面的响应曲线,并对其响应特征进行了分析;研究结果表明:当磁性层位于地表时,当表层相对磁导率μr1.2,磁性层对电磁测深曲线具体明显的影响;当岩层为中间层时,只要μr1.2,对H型、A型曲线中段会有影响.对H型曲线,主要表现在使极小值处的曲线抬高、变宽,以致使曲线形态发生变化;当磁性层处于最后一层时,不论岩层的磁导率是多少,对各类二、三层曲线来讲,不会影响曲线的形态,只是使渐近线前第一个极值点的位置右移,极值点至渐近线之间的线段变得较为陡峭.     

Calibrating a Salt Water Intrusion Model with Time‐Domain Electromagnetic Data

Salt water intrusion models are commonly used to support groundwater resource management in coastal aquifers. Concentration data used for model calibration are often sparse and limited in spatial extent. With airborne and ground‐based electromagnetic surveys, electrical resistivity models can be obtained to provide high‐resolution three‐dimensional models of subsurface resistivity variations that can be related to geology and salt concentrations on a regional scale. Several previous studies have calibrated salt water intrusion models with geophysical data, but are typically limited to the use of the inverted electrical resistivity models without considering the measured geophysical data directly. This induces a number of errors related to inconsistent scales between the geophysical and hydrologic models and the applied regularization constraints in the geophysical inversion. To overcome these errors, we perform a coupled hydrogeophysical inversion (CHI) in which we use a salt water intrusion model to interpret the geophysical data and guide the geophysical inversion. We refer to this methodology as a Coupled Hydrogeophysical Inversion‐State (CHI‐S), in which simulated salt concentrations are transformed to an electrical resistivity model, after which a geophysical forward response is calculated and compared with the measured geophysical data. This approach was applied for a field site in Santa Cruz County, California, where a time‐domain electromagnetic (TDEM) dataset was collected. For this location, a simple two‐dimensional cross‐sectional salt water intrusion model was developed, for which we estimated five uniform aquifer properties, incorporating the porosity that was also part of the employed petrophysical relationship. In addition, one geophysical parameter was estimated. The six parameters could be resolved well by fitting more than 300 apparent resistivities that were comprised by the TDEM dataset. Except for three sounding locations, all the TDEM data could be fitted close to a root‐mean‐square error of 1. Possible explanations for the poor fit of these soundings are the assumption of spatial uniformity, fixed boundary conditions and the neglecting of 3D effects in the groundwater model and the TDEM forward responses.     

Characterization of the subsurface architecture and identification of potential groundwater paths in a clay-rich floodplain using multi-electrode resistivity imaging

The interaction between surface water and groundwater in clay-rich fluvial environments can be complex and is generally poorly understood. Airborne electromagnetic surveys are often used for characterizing regional groundwater systems, but they are constrained by the resolution of the method. A resistivity imaging survey has been carried out in the Macquarie Marshes (New South Wales, Australia) in combination with water chemical sampling. The results have enabled the identification of buried palaeochannels and the location of potential recharge points. The data have been compared with previously published airborne electromagnetic data in the same area. Deeper less conductive features suggest that there is a potential connection between the Great Artesian Basin and groundwater contained within the shallow sand aquifer. Even though the chemistry of the groundwater samples does not indicate interaction with the Great Artesian Basin, the observed discontinuity in the saprolite implies potential for this to happen in other locations.     

瞬变电磁测深早期数据的修正

通过时间-频率转换关系,TEM数据可以转换成平面波场测深数据,从而可以对TEM资料进行拟平面波场处理解释.在对瞬变电磁视电阻率数据向平面波场测深视电阻率数据转换时,发现由于瞬变电磁使用晚期计算公式及装置问题,使测深曲线早期数据发生畸变.文中建立了视电阻率曲线进入晚期所满足的关系式,从理论上给出不同情况下瞬变电磁测深视电阻率曲线进入晚期的临界点.以瞬变电磁、大地电磁、CSAMT为例,对大量的模型进行正演计算,对计算结果进行对比分析,建立不同地表电性结构、不同时间延迟情况下,瞬变电磁早期数据误差的校正量板.     

Coil response inversion for very early time modelling of helicopter‐borne time‐domain electromagnetic data and mapping of near‐surface geological layers

Very early times in the order of 2–3 μs from the end of the turn‐off ramp for time‐domain electromagnetic systems are crucial for obtaining a detailed resolution of the near‐surface geology in the depth interval 0–20 m. For transient electromagnetic systems working in the off time, an electric current is abruptly turned off in a large transmitter loop causing a secondary electromagnetic field to be generated by the eddy currents induced in the ground. Often, however, there is still a residual primary field generated by remaining slowly decaying currents in the transmitter loop. The decay disturbs or biases the earth response data at the very early times. These biased data must be culled, or some specific processing must be applied in order to compensate or remove the residual primary field. As the bias response can be attributed to decaying currents with its time constantly controlled by the geometry of the transmitter loop, we denote it the ‘Coil Response’. The modelling of a helicopter‐borne time‐domain system by an equivalent electronic circuit shows that the time decay of the coil response remains identical whatever the position of the receiver loop, which is confirmed by field measurements. The modelling also shows that the coil response has a theoretical zero location and positioning the receiver coil at the zero location eliminates the coil response completely. However, spatial variations of the coil response around the zero location are not insignificant and even a few cm deformation of the carrier frame will introduce a small coil response. Here we present an approach for subtracting the coil response from the data by measuring it at high altitudes and then including an extra shift factor into the inversion scheme. The scheme is successfully applied to data from the SkyTEM system and enables the use of very early time gates, as early as 2–3 μs from the end of the ramp, or 5–6 μs from the beginning of the ramp. Applied to a large‐scale airborne electromagnetic survey, the coil response compensation provides airborne electromagnetic methods with a hitherto unseen good resolution of shallow geological layers in the depth interval 0–20 m. This is proved by comparing results from the airborne electromagnetic survey to more than 100 km of Electrical Resistivity Tomography measured with 5 m electrode spacing.     

全波形时间域航空电磁响应三维有限差分数值计算

全波形时域航空电磁测量具有解释精度高、分辨率高等优点,已成为新一代时域航空电磁探测发展的趋势.为此,本文基于无源有限差分法,将发射电流离散为若干梯形脉冲元,将脉冲元在时间上产生的电磁场转换为空间初始场,在差分迭代过程中分时引入差分方程,逐步将有源有限差分方程转换为无源有限差分方程,最终实现了发射电流为任意波形时,全波形时间域航空电磁响应的三维数值计算.计算结果表明:在梯形波发射时,对于典型地电模型的航空时间域电磁响应,计算稳定时间大于10 ms;与积分方程法相比,发射线圈中心点二次场响应平均误差小于1%.任意源三维全波形数值计算的实现为全波形三维反演和仪器设计奠定了基础.     

Frequency-domain modelling of airborne electromagnetic responses using staggered finite differences1

A 3D frequency-domain EM modelling code has been implemented for helicopter electromagnetic (HEM) simulations. A vector Helmholtz equation for the electric fields is employed to avoid convergence problems associated with the first-order Maxwell's equations when air is present. Additional stability is introduced by formulating the problem in terms of the scattered electric fields. With this formulation the impressed dipole source is replaced with an equivalent source, which for the airborne configuration possesses a smoother spatial dependence and is easier to model. In order to compute this equivalent source, a primary field arising from dipole sources of either a whole space or a layered half-space must be calculated at locations where the conductivity is different from that of the background. The Helmholtz equation is approximated using finite differences on a staggered grid. After finite-differencing, a complex-symmetric matrix system of equations is assembled and preconditioned using Jacobi scaling before it is solved using the quasi-minimum residual (QMR) method. The modelling code has been compared with other 1D and 3D numerical models and is found to produce results in good agreement. We have used the solution to simulate novel HEM responses that are computationally intractable using integral equation (IE) solutions. These simulations include a 2D conductor residing at a fault contact with and without topography. Our simulations show that the quadrature response is a very good indicator of the faulted background, while the in-phase response indicates the presence of the conductor. However when interpreting the in-phase response, it is possible erroneously to infer a dipping conductor due to the contribution of the faulted background.     

3D joint inversion of magnetotelluric and airborne tipper data: a case study from the Morrison porphyry Cu–Au–Mo deposit,British Columbia,Canada

Z‐axis tipper electromagnetic and broadband magnetotelluric data were used to determine three‐dimensional electrical resistivity models of the Morrison porphyry Cu–Au–Mo deposit in British Columbia. Z‐axis tipper electromagnetic data are collected with a helicopter, thus allowing rapid surveys with uniform spatial sampling. Ground‐based magnetotelluric surveys can achieve a greater exploration depth than Z‐axis tipper electromagnetic surveys, but data collection is slower and can be limited by difficult terrain. The airborne Z‐axis tipper electromagnetic tipper data and the ground magnetotelluric tipper data show good agreement at the Morrison deposit despite differences in the data collection method, spatial sampling, and collection date. Resistivity models derived from individual inversions of the Z‐axis tipper electromagnetic tipper data and magnetotelluric impedance data contain some similar features, but the Z‐axis tipper electromagnetic model appears to lack resolution below a depth of 1 km, and the magnetotelluric model suffers from non‐uniform and relatively sparse spatial sampling. The joint Z‐axis tipper electromagnetic inversion solves these issues by combining the dense spatial sampling of the airborne Z‐axis tipper electromagnetic technique and the deeper penetration of the lower frequency magnetotelluric data. The resulting joint resistivity model correlates well with the known geology and distribution of alteration at the Morrison deposit. Higher resistivity is associated with the potassic alteration zone and volcanic country rocks, whereas areas of lower resistivity agree with known faults and sedimentary units. The pyrite halo and ≥0.3% Cu zone have the moderate resistivity that is expected of disseminated sulphides. The joint Z‐axis tipper electromagnetic inversion provides an improved resistivity model by enhancing the lateral and depth resolution of resistivity features compared with the individual Z‐axis tipper electromagnetic and magnetotelluric inversions. This case study shows that a joint Z‐axis tipper electromagnetic–magnetotelluric approach effectively images the interpreted mineralised zone at the Morrison deposit and could be beneficial in exploration for disseminated sulphides at other porphyry deposits.     

Analysing two‐dimensional effects in central loop transient electromagnetic sounding data using a semi‐synthetic tipper approach

We present a simple and feasible approach to analyse and identify two‐dimensional effects in central loop transient electromagnetic sounding data and the correspondingly derived quasi two‐dimensional conductivity models. The proposed strategy is particularly useful in minimising interpretation errors. It is based on the calculation of a semi‐synthetic transient electromagnetic tipper at each sounding and for each observational transient time point. The semi‐synthetic transient electromagnetic tipper is derived from the measured vertical component of the induced voltage and the synthetically calculated horizontal component. The approach is computationally inexpensive and involves one two‐dimensional forward calculation of an obtained quasi two‐dimensional conductivity section. Based on a synthetic example, we demonstrate that the transient electromagnetic tipper approach is applicable in identifying which transient data points and which corresponding zones in a derived quasi two‐dimensional subsurface model are affected by two‐dimensional inhomogeneities. The one‐dimensional inversion of such data leads to false models. An application of the semi‐synthetic transient electromagnetic tipper to field data from the Azraq basin in Jordan reveals that, in total, eight of 80 investigated soundings are affected by two‐dimensional structures although the field data can be fitted optimally using one‐dimensional inversion techniques. The largest semi‐synthetic tipper response occurs in a 300 m‐wide region around a strong lateral resistivity contrast. The approach is useful for analysing structural features in derived quasi two‐dimensional sections and for qualitatively investigating how these features affect the transient response. To avoid misinterpretation, these identified zones corresponding to large tipper values are excluded from the interpretation of a quasi two‐dimensional conductivity model. Based on the semi‐synthetic study, we also demonstrate that a quantitative interpretation of the horizontal voltage response (e.g. by inversion) is usually not feasible as it requires the exact sensor position to be known. Although a tipper derived purely from field data is useful as a qualitative tool for identifying two‐dimensional distortion effects, it is only feasible if the sensor setup is sufficiently accurate. Our proposed semi‐synthetic transient electromagnetic tipper approach is particularly feasible as an a posteriori approach if no horizontal components are recorded or if the sensor setup in the field is not sufficiently accurate.     

2.5D forward modeling and inversion of frequency-domain airborne electromagnetic data

Frequency-domain airborne electromagnetics is a proven geophysical exploration method. Presently, the interpretation is mainly based on resistivity—depth imaging and one-dimensional layered inversion; nevertheless, it is difficult to obtain satisfactory results for two- or three-dimensional complex earth structures using 1D methods. 3D forward modeling and inversion can be used but are hampered by computational limitations because of the large number of data. Thus, we developed a 2.5D frequency-domain airborne electromagnetic forward modeling and inversion algorithm. To eliminate the source singularities in the numerical simulations, we split the fields into primary and secondary fields. The primary fields are calculated using homogeneous or layered models with analytical solutions, and the secondary (scattered) fields are solved by the finite-element method. The linear system of equations is solved by using the large-scale sparse matrix parallel direct solver, which greatly improves the computational efficiency. The inversion algorithm was based on damping least-squares and singular value decomposition and combined the pseudo forward modeling and reciprocity principle to compute the Jacobian matrix. Synthetic and field data were used to test the effectiveness of the proposed method.     

Turning off low and high currents in a transmitter loop used in the transient electromagnetic method

In near-surface transient electromagnetic studies, it is desirable to measure the transient response starting from the earliest possible time. This requires the current in the transmitter loop to be switched off quickly, which necessitates working with a low transmitter current. As for deep-target transient electromagnetic studies, the transmitter current is as high as possible. The transmitter current's turn-off waveform and total duration affect the transient voltage response, especially at early times, which is to be accounted for when interpreting transient electromagnetic data. This article discusses the difference in switching off low and high current in a horizontal loop used as the source of the primary magnetic field in the transient electromagnetic method. Low and high currents are turned off in fundamentally different ways. When the current to be switched off is low, the loop can be represented as a symmetric combination of two transmission lines grounded at the middle of the loop perimeter. Such a representation of a loop allows calculating the current turn-off waveform at any point of the loop. The waveform and total duration of switching off a low current does not depend on its magnitude, but is determined by the period of natural oscillations of the current in the loop and the resistance of a shunting resistor. Switching off a low current in a loop can be represented as the sum of stepped current waves travelling along the loop wire. As a consequence, the current at different points of the loop perimeter is turned off at different times. In contrast to a low current, a high current is switched off linearly in time and synchronously at all points of the loop perimeter. The wave phenomena appear only at the very beginning of the current shutdown for a time interval that is much less than the total current turn-off duration. Presentation of the loop using a simple lumped-circuit model predicts the waveform and duration of the high current turn-off that coincide with the measured ones. There are two reasons why the article may be of interest to those engaged in the theory and/or practice of electromagnetic geophysical methods. First, it contributes to a general understanding of how the current in the transmitter loop is turned off. Second, the article shows how the parameters of a transmitter loop determine the current turn-off duration and thus the minimum depth of the transient electromagnetic sounding method.     

多辐射源地空瞬变电磁响应三维数值模拟研究

地空瞬变电磁法结合地面和航空电磁法的优点,可实现探测深度和工作效率的平衡.当前地空瞬变电磁法采用单一线源激发电磁辐射场,仅能从一个侧面与地质体耦合,难以获得地质体的全息影像.采用多辐射源是解决这一问题的途径.本文采用三维矢量有限元法对两个不同地质体多个辐射源情况下的地空瞬变电磁响应开展了模拟研究,分析了多辐射源在不同辐...     

Advancing process‐based watershed hydrological research using near‐surface geophysics: a vision for,and review of,electrical and magnetic geophysical methods

We want to develop a dialogue between geophysicists and hydrologists interested in synergistically advancing process based watershed research. We identify recent advances in geophysical instrumentation, and provide a vision for the use of electrical and magnetic geophysical instrumentation in watershed scale hydrology. The focus of the paper is to identify instrumentation that could significantly advance this vision for geophysics and hydrology during the next 3–5 years. We acknowledge that this is one of a number of possible ways forward and seek only to offer a relatively narrow and achievable vision. The vision focuses on the measurement of geological structure and identification of flow paths using electrical and magnetic methods. The paper identifies instruments, provides examples of their use, and describes how synergy between measurement and modelling could be achieved. Of specific interest are the airborne systems that can cover large areas and are appropriate for watershed studies. Although airborne geophysics has been around for some time, only in the last few years have systems designed exclusively for hydrological applications begun to emerge. These systems, such as airborne electromagnetic (EM) and transient electromagnetic (TEM), could revolutionize hydrogeological interpretations. Our vision centers on developing nested and cross scale electrical and magnetic measurements that can be used to construct a three‐dimensional (3D) electrical or magnetic model of the subsurface in watersheds. The methodological framework assumes a ‘top down’ approach using airborne methods to identify the large scale, dominant architecture of the subsurface. We recognize that the integration of geophysical measurement methods, and data, into watershed process characterization and modelling can only be achieved through dialogue. Especially, through the development of partnerships between geophysicists and hydrologists, partnerships that explore how the application of geophysics can answer critical hydrological science questions, and conversely provide an understanding of the limitations of geophysical measurements and interpretation. Copyright © 2008 John Wiley & Sons, Ltd.     

无人飞艇长导线源时域地空电磁勘探系统及其应用

以无人飞艇作为载体的时域地空电磁探测系统,具有高效、低成本、勘探深度大和空间分辨率高等优点.本文基于二维有限差分方法,分析了长导线源地空电磁响应的特征和变化规律、以及飞行高度的影响;在此基础上,采用32位Cortex-M3内核处理器,以全差分模拟前端压制电磁干扰,实现了24位低噪声多通道海量电磁数据的同步采样及存储,研制了一套可搭载于无人飞艇的时域电磁接收系统,并基于Wi-Fi Mesh无线多跳网络实现了地面远程监控.通过分析飞艇发动机的电磁噪声特点,采用独立分量分析法进行实测数据的噪声去除.研制的地空电磁接收系统使用无人飞艇搭载,在江苏省南通市如东县和内蒙古巴彦宝力格地区进行了电磁探测实验,地空电磁勘探结果与地面瞬变电磁和大地电磁方法进行了对比,证明了地空电磁探测方法的有效性.无人飞艇时域地空电磁探测系统的成功飞行实验,为在我国草原沙漠地区、海陆交互地带、沼泽地带、无人山区等特殊景观地区开展矿产资源、水资源、地质灾害等电磁探测提供了新方法和新思路.     

A comparison of helicopter‐borne electromagnetic systems for hydrogeologic studies

The increased application of airborne electromagnetic surveys to hydrogeological studies is driving a demand for data that can consistently be inverted for accurate subsurface resistivity structure from the near surface to depths of several hundred metres. We present an evaluation of three commercial airborne electromagnetic systems over two test blocks in western Nebraska, USA. The selected test blocks are representative of shallow and deep alluvial aquifer systems with low groundwater salinity and an electrically conductive base of aquifer. The aquifer units show significant lithologic heterogeneity and include both modern and ancient river systems. We compared the various data sets to one another and inverted resistivity models to borehole lithology and to ground geophysical models. We find distinct differences among the airborne electromagnetic systems as regards the spatial resolution of models, the depth of investigation, and the ability to recover near‐surface resistivity variations. We further identify systematic biases in some data sets, which we attribute to incomplete or inexact calibration or compensation procedures.