The electromagnetic response of a horizontal electric dipole buried in a multi‐layered earth

The electromagnetic response of a horizontal electric dipole transmitter in the presence of a conductive, layered earth is important in a number of geophysical applications, ranging from controlled‐source audio‐frequency magnetotellurics to borehole geophysics to marine electromagnetics. The problem has been thoroughly studied for more than a century, starting from a dipole resting on the surface of a half‐space and subsequently advancing all the way to a transmitter buried within a stack of anisotropic layers. The solution is still relevant today. For example, it is useful for one‐dimensional modelling and interpretation, as well as to provide background fields for two‐ and three‐dimensional modelling methods such as integral equation or primary–secondary field formulations. This tutorial borrows elements from the many texts and papers on the topic and combines them into what we believe is a helpful guide to performing layered earth electromagnetic field calculations. It is not intended to replace any of the existing work on the subject. However, we have found that this combination of elements is particularly effective in teaching electromagnetic theory and providing a basis for algorithmic development. Readers will be able to calculate electric and magnetic fields at any point in or above the earth, produced by a transmitter at any location. As an illustrative example, we calculate the fields of a dipole buried in a multi‐layered anisotropic earth to demonstrate how the theory that developed in this tutorial can be implemented in practice; we then use the example to examine the diffusion of volume charge density within anisotropic media—a rarely visualised process. The algorithm is internally validated by comparing the response of many thin layers with alternating high and low conductivity values to the theoretically equivalent (yet algorithmically simpler) anisotropic solution, as well as externally validated against an independent algorithm.     

Step-on versus step-off signals in time-domain controlled source electromagnetic methods using a grounded electric dipole

The time-domain controlled source electromagnetic method is a geophysical prospecting tool applied to image the subsurface resistivity distribution on land and in the marine environment. In its most general set-up, a square-wave current is fed into a grounded horizontal electric dipole, and several electric and magnetic field receivers at defined offsets to the imposed current measure the electromagnetic response of the Earth. In the marine environment, the application often uses only inline electric field receivers that, for a 50% duty-cycle current waveform, include both step-on and step-off signals. Here, forward and inverse 1D modelling is used to demonstrate limited sensitivity towards shallow resistive layers in the step-off electric field when transmitter and receivers are surrounded by conductive seawater. This observation is explained by a masking effect of the direct current signal that flows through the seawater and primarily affects step-off data. During a step-off measurement, this direct current is orders of magnitude larger than the inductive response at early and intermediate times, limiting the step-off sensitivity towards shallow resistive layers in the seafloor. Step-on data measure the resistive layer at times preceding the arrival of the direct current signal leading to higher sensitivity compared to step-off data. Such dichotomous behaviour between step-on and step-off data is less obvious in onshore experiments due to the lack of a strong overlying conductive zone and corresponding masking effect from direct current flow. Supported by synthetic 1D inversion studies, we conclude that time-domain controlled source electromagnetic measurements on land should apply both step-on and step-off data in a combined inversion approach to maximize signal-to-noise ratios and utilize the sensitivity characteristics of each signal. In an isotropic marine environment, step-off electric fields have inferior sensitivity towards shallow resistive layers compared to step-on data, resulting in an increase of non-uniqueness when interpreting step-off data in a single or combined inversion.     

Effects of metallic system components on marine electromagnetic loop data

Electromagnetic loop systems rely on the use of non-conductive materials near the sensor to minimize bias effects superimposed on measured data. For marine sensors, rigidity, compactness and ease of platform handling are essential. Thus, commonly a compromise between rigid, cost-effective and non-conductive materials (e.g. stainless steel versus fibreglass composites) needs to be found. For systems dedicated to controlled-source electromagnetic measurements, a spatial separation between critical system components and sensors may be feasible, whereas compact multi-sensor platforms, remotely operated vehicles and autonomous unmanned vehicles require the use of electrically conductive components near the sensor. While data analysis and geological interpretations benefit vastly from each added instrument and multidisciplinary approaches, this introduces a systematic and platform-immanent bias in the measured electromagnetic data. In this scope, we present two comparable case studies targeting loop-source electromagnetic applications in both time and frequency domains: the time-domain system trades the compact design for a clear separation of 15 m between an upper fibreglass frame, holding most critical titanium system components, and a lower frame with its coil and receivers. In case of the frequency-domain profiler, the compact and rigid design is achieved by a circular fibreglass platform, carrying the transmitting and receiving coils, as well as several titanium housings and instruments. In this study, we analyse and quantify the quasi-static influence of conductive objects on time- and frequency-domain coil systems by applying an analytically and experimentally verified 3D finite element model. Moreover, we present calibration and optimization procedures to minimize bias inherent in the measured data. The numerical experiments do not only show the significance of the bias on the inversion results, but also the efficiency of a system calibration against the analytically calculated response of a known environment. The remaining bias after calibration is a time/frequency-dependent function of seafloor conductivity, which doubles the commonly estimated noise floor from 1% to 2%, decreasing the sensitivity and resolution of the devices. By optimizing size and position of critical conductive system components (e.g. titanium housings) and/or modifying the transmitter/receiver geometry, we significantly reduce the effect of this residual bias on the inversion results as demonstrated by 3D modelling. These procedures motivate the opportunity to design dedicated, compact, low-bias platforms and provide a solution for autonomous and remotely steered designs by minimizing their effect on the sensitivity of the controlled-source electromagnetic sensor.     

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.     

The marine controlled source electromagnetic response of a steel borehole casing: applications for the NEPTUNE Canada gas hydrate observatory

Gas hydrates are a potential energy resource, a possible factor in climate change and an exploration geohazard. The University of Toronto has deployed a permanent seafloor time‐domain controlled source electromagnetic (CSEM) system offshore Vancouver Island, within the framework of the NEPTUNE Canada underwater cabled observatory. Hydrates are known to be present in the area and due to their electrically resistive nature can be monitored by 5 permanent electric field receivers. However, two cased boreholes may be drilled near the CSEM site in the near future. To understand any potential distortions of the electric fields due to the metal, we model the marine electromagnetic response of a conductive steel borehole casing. First, we consider the commonly used canonical model consisting of a 100 Ωm, 100 m thick resistive hydrocarbon layer embedded at a depth of 1000 m in a 1 Ωm conductive host medium, with the addition of a typical steel production casing extending from the seafloor to the resistive zone. Results show that in both the frequency and time domains the distortion produced by the casing occurs at smaller transmitter‐receiver offsets than the offsets required to detect the resistive layer. Second, we consider the experimentally determined model of the offshore Vancouver Island hydrate zone, consisting of a 5.5 Ωm, 36 m thick hydrate layer overlying a 0.7 Ωm sedimentary half‐space, with the addition of two borehole casings extending 300 m into the seafloor. In this case, results show that the distortion produced by casings located within a 100 m safety zone of the CSEM system will be measured at 4 of the 5 receivers. We conclude that the boreholes must be positioned at least 200 m away from the CSEM array so as to minimize the effects of the casings.     

A first application of a marine inductive source electromagnetic configuration with remote electric dipole receivers: Palinuro Seamount,Tyrrhenian Sea

We study a new marine electromagnetic configuration that consists of a ship‐towed inductive source transmitter and a series of remote electric dipole receivers placed on the seafloor. The approach was tested at the Palinuro Seamount in the southern Tyrrhenian Sea, at a site where massive sulphide mineralization has been previously identified by shallow drilling. A 3D model of the Palinuro study area was created using bathymetry data, and forward modelling of the electric field diffusion was carried out using a finite volume method. These numerical results suggest that the remote receivers can theoretically detect a block of shallowly buried conductive material at up to ～100 m away when the transmitter is located directly above the target. We also compared the sensitivity of the method using either a horizontal loop transmitter or a vertical loop transmitter and found that when either transmitter is located directly above the mineralized zone, the vertical loop transmitter has sensitivity to the target at a farther distance than the horizontal loop transmitter in the broadside direction by a few tens of metres. Furthermore, the vertical loop transmitter is more effective at distinguishing the seafloor conductivity structure when the vertical separation between transmitter and receiver is large due to the bathymetry. As a horizontal transmitter is logistically easier to deploy, we conducted a first test of the method with a horizontal transmitter. Apparent conductivities are calculated from the electric field transients recorded at the remote receivers. The analysis indicates higher apparent seafloor conductivities when the transmitter is located near the mineralized zone. Forward modelling suggests that the best match to the apparent conductivity data is obtained when the mineralized zone is extended southward by 40 m beyond the zone of previous drilling. Our results demonstrate that the method adds value to the exploration and characterization of seafloor massive sulphide deposits.     

An improved interpolation scheme at receiver positions for 2.5D frequency-domain marine controlled-source electromagnetic forward modelling

An improved interpolation scheme is presented for 2.5-dimensional marine controlled-source electromagnetic forward modelling. For the marine controlled-source electromagnetic method, due to the resistivity contrast between the seawater and seafloor sedimentary layers, it is difficult to compute the electromagnetic fields accurately at receivers, which are usually located at the seafloor. In this study, the 2.5-dimensional controlled-source electromagnetic responses are simulated by the staggered finite-difference method. The secondary-field approach is used to avoid the source singularities, and the one-dimensional layered background model is used for calculating the primary fields excited by the source quasi-analytically. The interpolation of electromagnetic fields at the cell nodes for the whole computational domain to the receiver locations is discussed in detail. Numerical tests indicate that the improved interpolation developed is more accurate for simulating the electromagnetic responses at receivers located at the seafloor, compared with the linear or rigorous interpolation.     

Wavenumber of the guided wave supported by a thin resistive layer in marine controlled‐source electromagnetics

This paper discusses the asymptotic behaviour of the electromagnetic fields received on the sea‐bed (target response), as well as the fields distributed inside a thin resistive target, generated by a horizontal electric dipole above the sea‐bed in marine controlled‐source electromagnetics for hydrocarbon exploration. It is found that the guided wave supported by a thin resistive target can be expressed as a single‐mode exponential function. A simple closed‐form expression is derived to relate the single‐mode wavenumber of the guided wave to the model parameters: the resistivity and thickness of the target layer, the sea‐bed resistivity and the frequency. When the air‐wave is removed, the guided wave is dominant among the fields received on the sea‐bed at far offset. Hence the wavenumber of the guided wave can be calculated from the fields measured on the sea‐bed. The closed‐form expression can then be used to invert the target property from the calculated wavenumber and hence, can be considered as a hydrocarbon indicator.     

Electromagnetic fields generated by finite‐length wire sources: comparison with point dipole solutions

In present‐day land and marine controlled‐source electromagnetic (CSEM) surveys, electromagnetic fields are commonly generated using wires that are hundreds of metres long. Nevertheless, simulations of CSEM data often approximate these sources as point dipoles. Although this is justified for sufficiently large source‐receiver distances, many real surveys include frequencies and distances at which the dipole approximation is inaccurate. For 1D layered media, electromagnetic (EM) fields for point dipole sources can be computed using well‐known quasi‐analytical solutions and fields for sources of finite length can be synthesized by superposing point dipole fields. However, the calculation of numerous point dipole fields is computationally expensive, requiring a large number of numerical integral evaluations. We combine a more efficient representation of finite‐length sources in terms of components related to the wire and its end points with very general expressions for EM fields in 1D layered media. We thus obtain a formulation that requires fewer numerical integrations than the superposition of dipole fields, permits source and receiver placement at any depth within the layer stack and can also easily be integrated into 3D modelling algorithms. Complex source geometries, such as wires bent due to surface obstructions, can be simulated by segmenting the wire and computing the responses for each segment separately. We first describe our finite‐length wire expressions and then present 1D and 3D examples of EM fields due to finite‐length sources for typical land and marine survey geometries and discuss differences to point dipole fields.     

Electric field data in inductive source electromagnetic surveys

Measurement of the electric field data due to an inductive loop source in a controlled source electromagnetic survey is not common, because electric field data, usually involving grounded electrodes, are expensive to acquire and difficult to interpret. With the recently developed capability of versatile three‐dimensional inversion, we revisit the idea of measuring electric field in a large ground loop survey for mineral exploration. The three‐dimensional modelling and inversion approach helps us quantitatively understand the detectability and recoverability of the proposed survey configuration. Our detectability study using forward modelling shows that the relative anomaly (percentage difference) in electric field does not decay with a lower induction number, but the conventional magnetic field data (dB/dt) does. Our recoverability study examines how much and what kind of information can be extracted from electric field data for the reconstruction of a three‐dimensional model. Synthetic inversions show the following observations. (i) Electric field data are good at locating lateral discontinuity, whereas dB/dt has better depth resolution. (ii) Electric field is less sensitive to the background conductivity and, thus, is prone to misinterpretation because of a bad initial model in inversion. We recommend warm‐starting the electric field inversion with an initial model from a separate dB/dt inversion. (iii) Electric field data may be severely contaminated by near‐surface heterogeneity, but an inversion can recover the deep target concealed by the geologic noise. (iv) Even one line of single‐component electric field data can greatly improve the horizontal resolution in a dB/dt inversion. Finally, we investigate a field dataset of both electric field and dB/dt measurements at a uranium deposit. The field example confirms that the electric field and magnetic field data contain independent information that is crucial in the accurate recovery of subsurface conductivity. Our synthetic and field examples demonstrate the benefit of acquiring electric field data along with magnetic field data in an inductive source survey.     

Two types of marine controlled source electromagnetic transmitters

Marine controlled source electromagnetic methods are used to derive the electrical properties of a wide range of sub‐seafloor targets, including gas hydrate reservoirs. In most marine controlled source electromagnetic surveys, the deep‐tow transmitter is used with a long horizontal electric dipole being towed above the seafloor, which is capable of transmitting dipole moments in the order of up to several thousand ampere‐metres. The newly developed deployed transmitter uses two horizontal orthogonal electrical dipoles and can land on the seafloor. It can transmit higher frequency electromagnetic signals, can provide accurate transmission orientation, and can obtain higher signal stacking, which compensates for the shorter source dipole length. In this paper, we present the study, key technologies, and implementation details of two new marine controlled source electromagnetic transmitters (the deep‐tow transmitter and the deployed transmitter). We also present the results of a marine controlled source electromagnetic experiment conducted from April to May 2014 in the South China Sea using both the deep‐tow transmitter and the deployed transmitter, which show that the two types of marine transmitters can be used as effective source for gas hydrate exploration.     

Controlled‐source electromagnetic monitoring of reservoir oil saturation using a novel borehole‐to‐surface configuration

To advance and optimize secondary and tertiary oil recovery techniques, it is essential to know the areal propagation and distribution of the injected fluids in the subsurface. We investigate the applicability of controlled‐source electromagnetic methods to monitor fluid movements in a German oilfield (Bockstedt, onshore Northwest Germany) as injected brines (highly saline formation water) have much lower electrical resistivity than the oil within the reservoir. The main focus of this study is on controlled‐source electromagnetic simulations to test the sensitivity of various source–receiver configurations. The background model for the simulations is based on two‐dimensional inversion of magnetotelluric data gathered across the oil field and calibrated with resistivity logs. Three‐dimensional modelling results suggest that controlled‐source electromagnetic methods are sensitive to resistivity changes at reservoir depths, but the effect is difficult to resolve with surface measurements only. Resolution increases significantly if sensors or transmitters can be placed in observation wells closer to the reservoir. In particular, observation of the vertical electric field component in shallow boreholes and/or use of source configurations consisting of combinations of vertical and horizontal dipoles are promising. Preliminary results from a borehole‐to‐surface controlled‐source electromagnetic field survey carried out in spring 2014 are in good agreement with the modelling studies.     

Elongated horizontal and vertical receivers in three-dimensional electromagnetic modelling and inversion

Electromagnetic geophysical methods often rely on measurements of naturally occurring or artificially impressed electric fields. It is technically impossible, however, to measure the electric field directly. Instead, the electric field is approximated by recording the voltage difference between two electrodes and dividing the obtained voltage by the distance between the electrodes. Typically, modelling and inversion algorithms assume that the electric fields are obtained over infinitely short point-dipoles and thus measured fields are assigned to a single point between the electrodes. Such procedures imply several assumptions: (1) The electric field between the two electrodes is regarded as constant or being a potential field and (2) the receiver dimensions are negligible compared to the dimensions of the underlying modelling grid. While these conditions are often fulfilled for horizontal electric fields, borehole sensors for recordings of the vertical electric field have dimensions in the order of ≈100 m and span several modelling grid cells. Observations from such elongated borehole sensors can therefore only be interpreted properly if true receiver dimensions and variations of electrical conductivity along the receiver are considered. Here, we introduce a numerical solution to include the true receiver geometry into electromagnetic modelling schemes, which does not rely on such simplifying assumptions. The algorithm is flexible, independent of the chosen numerical method to solve Maxwell's equations and can easily be implemented in other electromagnetic modelling and inversion codes. We present conceptual modelling results for land-based controlled source electromagnetic scenarios and discuss consideration of true receiver geometries for a series of examples of horizontal and vertical electric field measurements. Comparison with Ez data measured in an observation borehole in a producing oil field shows the importance of both considering the true length of the receiver and also its orientation. We show that misalignment from the vertical axis as small as 0.1° may seriously distort the measured signal, as horizontal electric field components are mapped into the desired vertical component. Adequate inclusion of elongated receivers in modelling and inversion can also help reducing effects of static shift when interpreting (natural source) magnetotelluric data.     

A parallel computing thin‐sheet inversion algorithm for airborne time‐domain data utilising a variable overburden

Accurate modelling of the conductivity structure of mineralisations can often be difficult. In order to remedy this, a parametric approach is often used. We have developed a parametric thin‐sheet code, with a variable overburden. The code is capable of performing inversions of time‐domain airborne electromagnetic data, and it has been tested successfully on both synthetic data and field data. The code implements an integral solution containing one or more conductive sheets, buried in a half‐space with a laterally varying conductive overburden. This implementation increases the area of applicability compared to, for example, codes operating in free space, but it comes with a significant increase in computational cost. To minimise the cost, the code is parallelised using OpenMP and heavily optimised, which means that inversions of field data can be performed in hours on multiprocessor desktop computers. The code models the full system transfer function of the electromagnetic system, including variable flight height. The code is demonstrated with a synthetic example imitating a mineralisation buried underneath a conductive meadow. As a field example, the Valen mineral deposit, which is a graphite mineral deposit located in a variable overburden, is successfully inverted. Our results match well with previous models of the deposit; however, our predicted sheet remains inconclusive. These examples collectively demonstrate the effectiveness of our thin‐sheet code.     

Transient electromagnetic field in magneto-viscous medium

When using Transient Geo-Electromagnetics (TEM) unusually slow decaying transients are sometimes observed in the absence of well-conductive objects. Many researchers explain this phenomenon by presence of material with magneto-viscous or superparamagnetic (SPM) properties. The analysis of electromagnetic (EM) field equations in conductive SPM medium is suggested in the present paper. It is shown that in a simplest case of small size single-domain magnetic particles with relative higher potential barrier energy, the SPM-medium is characterized by a very slow decaying exponential transient magnetic field, the level of which is much more as compared to that of due to non-magnetic medium of the same conductivity. This situation is traced up to the late transient time like 0.1 s and more. SPM and Induction fields are in the near zone additive. They depend in a different way on the superparamagnetic and electric properties of the SPM-medium. They also depend in different ways on the transient time and on the size of the transmitter–receiver configuration. These characteristics make it possible to recognize the presence of SPM-effect and to separate these fields.     

Enhancing imaging of the Sub-Andean Foothills geology using magnetotellurics: A case history of a 3D survey in southern Bolivia

A magnetotelluric acquisition and modelling campaign, comprising 400 full tensor soundings, was carried out in the Sub-Andean Foothills in the area located south of Santa Cruz de la Sierra, Bolivia. The objective of the survey was to improve the imaging of the Paleozoic section and provide insight to the overall structure of the Devonian Silurian complex. The acquired data were inverted assuming both two-dimensional and three-dimensional dimensionality of the subsurface structure, adopting a multi-step iterative workflow, which began applying unconstrained inversion and introduced increasing constraints determined at each following step based on the interpretation of the latest inversion results. The geological interpretation of the final inversion results allowed to better image the expected complexity in the structures, particularly highlighting several different levels of detachment, mainly in the area of Kirusillas Formation. Furthermore, an oblique sense was identified of the main tendency of N-S deformation, related to a dextral transgressional movement that generates discrete dislocations, at a length scale of the order of a few kilometres.     

Artificial neural networks for removal of couplings in airborne transient electromagnetic data

Modern airborne transient electromagnetic surveys typically produce datasets of thousands of line kilometres, requiring careful data processing in order to extract as much and as reliable information as possible. When surveys are flown in populated areas, data processing becomes particularly time consuming since the acquired data are contaminated by couplings to man‐made conductors (power lines, fences, pipes, etc.). Coupled soundings must be removed from the dataset prior to inversion, and this is a process that is difficult to automate. The signature of couplings can be both subtle and difficult to describe in mathematical terms, rendering removal of couplings mostly an expensive manual task for an experienced geophysicist. Here, we try to automate the process of removing couplings by means of an artificial neural network. We train an artificial neural network to recognize coupled soundings in manually processed reference data, and we use this network to identify couplings in other data. The approach provides a significant reduction in the time required for data processing since one can directly apply the network to the raw data. We describe the neural network put to use and present the inputs and normalizations required for maximizing its effectiveness. We further demonstrate and assess the training state and performance of the network before finally comparing inversions based on unprocessed data, manually processed data, and artificial neural network automatically processed data. The results show that a well‐trained network can produce high‐quality processing of airborne transient electromagnetic data, which is either ready for inversion or in need of minimal manual processing. We conclude that the use of artificial neural network scan significantly reduce the processing time and its costs by as much as 50%.     

A numerical comparison of time and frequency‐domain marine electromagnetic methods for hydrocarbon exploration in shallow water

In shallow water the frequency domain controlled source electromagnetic method is subject to airwave saturation that strongly limits the sensitivity to resistive hydrocarbon targets at depth. It has been suggested that time‐domain CSEM may offer an improved sensitivity and resolution of these deep targets in the presence of the airwave. In order to examine and test these claims, this work presents a side‐by‐side investigation of both methods with a main focus on practical considerations, and how these effect the resolution of a hydrocarbon reservoir. Synthetic noisy data for both time‐domain and frequency domain methods are simulated using a realistic frequency dependent noise model and frequency dependent scaling for representative source waveforms. The synthetic data studied here include the frequency domain response from a compact broadband waveform, the time‐domain step‐response from a low‐frequency square wave and the time‐domain impulse response obtained from pseudo‐random binary sequences. These data are used in a systematic resolution study of each method as a function of water‐depth, relative noise and stacking length. The results indicate that the broadband frequency domain data have the best resolution for a given stacking time, whereas the time‐domain data require prohibitively longer stacking times to achieve similar resolution.     

Two‐dimensional controlled‐source electromagnetic interferometry by multidimensional deconvolution: spatial sampling aspects

We use numerically modelled data sets to investigate the sensitivity of electromagnetic interferometry by multidimensional deconvolution to spatial receiver sampling. Interferometry by multidimensional deconvolution retrieves the reflection response below the receivers after decomposition of the fields into upward and downward decaying fields and deconvolving the upward decaying field by the downward decaying field. Thereby the medium above the receiver level is replaced with a homogeneous half‐space, the sources are redatumed to the receiver level and the direct field is removed. Consequently, in a marine setting the retrieved reflection response is independent of any effect of the water layer and the air above. A drawback of interferometry by multidimensional deconvolution is a possibly unstable matrix inversion, which is necessary to retrieve the reflection response. Additionally, in order to correctly separate the upward and the downward decaying fields, the electromagnetic fields need to be sampled properly. We show that the largest possible receiver spacing depends on two parameters: the vertical distance between the source and the receivers and the length of the source. The receiver spacing should not exceed the larger of these two parameters. Besides these two parameters, the presence of inhomogeneities close to the receivers may also require a dense receiver sampling. We show that by using the synthetic aperture concept, an elongated source can be created from conventionally acquired data in order to overcome these strict sampling criteria. Finally, we show that interferometry may work under real‐world conditions with random noise and receiver orientation and positioning errors.     

正交水平磁偶源的电磁场分布规律

正交水平磁偶源是模拟天然场源的较好人工源,可以方便地实现可控源高频大地电磁张量测量.正交水平磁偶源的电磁场分布规律是野外工作布置的理论基础,为此计算了均匀大地模型正交水平磁偶源的电磁场.计算结果表明:电磁场水平分量在各个象限都有一相对低值带,对应的标量视电阻率形成了畸变带,但张量视电阻率畸变带消失;张量视电阻率曲线形态显示出近区的低阻、过渡区的高阻隆起和远区趋于真值的规律.通过野外试验验证理论计算结果,在无法准确确定地下介质电阻率参数的情况下,以天然电磁场计算的电阻率为参照对比研究了正交水平磁偶源电磁场的分布规律.试验结果表明:正交水平磁偶源与电偶源的电磁场同样的存在近区、过渡区和远区;在远区,正交水平磁偶源与测点的相对位置对张量测量结果几乎没有影响,即在远区可以在任何方位测量;正交水平磁偶源的布置要考虑收发距的影响,保证测量在远区进行.