Time-domain Electromagnetic Response Research Articles

Three-dimensional forward calculation of time domain electromagnetic response stimulated by a pseudo-Gaussian pulse source

The calculation of three-dimensional (3D) electromagnetic responses using the controlled source time domain electromagnetic method suffers from low accuracy of the early response calculation and difficulty in the convergence of the later response for large-scale models. To address these problems, we propose a method of decomposing the time domain electromagnetic response into a primary field and a secondary field. This approach can easily address the above issues. In this paper, we use a time domain finite difference method based on a non-uniform step size and staggered grid and use an iterative algorithm with a non-uniform step size to calculate the late time domain electromagnetic response under high power pulse source excitation. Several example simulations were compared with analytical and spectral Lanczos decomposition solutions and demonstrate the correctness of the 3D forward modeling method. The response of a 3D anomaly excited by an electric dipole source pulse current was analyzed. The calculated time domain response revealed that the field excited by the high power pulse source diffused in the earth over time and exhibited a secondary diffusion process of the anomalous field generated by the 3D anomaly. The numerical simulation results showed that the time domain electromagnetic responses excited by the pulse source were stable and effective. The amplitude of the anomalous response was much greater than that of the step source, the signal-to-noise ratio was greater, and the detectability was better. The method may be used in inversion of the time domain electromagnetic response if the calculation speed can be further improved.

Forward modeling and 3D inversion of electromagnetic data collected over the McArthur River uranium deposit in the Athabasca Basin, Canada

Detection and assessment of the deeply buried high-grade uranium deposits in the Athabasca Basin rely on geophysical methods to map conductive rocks. Variable Quaternary surface cover can mask the anomalous signals from depth and affect the interpretation of inverted conductivity models. We present the analysis of several electromagnetic (EM) modeling studies and two field data sets to demonstrate the effects of varying Quaternary cover resistivity and thickness, on the ability to resolve the parameters of underlying sandstone, alteration, and basement conductors. Synthetic data, assuming a typical shallow EM sounding system and realistic resistivities found in the Athabasca Basin, indicate that resistivity and thickness parameters of the Quaternary cover can be separately recovered in cases in which this cover is more conductive than the underlying sandstone, but not when the cover is significantly more resistive. A 3D modeling study indicates that by using airborne EM data, it is possible to detect a basement conductor of 20 S at a depth of at least 600 m below the surface, even in the presence of Quaternary cover thickness variations of the up to 20% (40–60 m). Furthermore, although Quaternary cover variations and deeper sandstone alteration can produce comparable anomalous signal amplitudes in a time-domain EM response, their effects are most visible in distinctly separate time windows. Ground-penetrating radar and other data to characterize the Quaternary cover in the McArthur River area indicate that this cover consists mostly of sandy tills ranging in thickness from 0 to 117 m. Constrained 3D inversion of an airborne EM data set from the same area indicates basement conductors consistent with the depth and location of a known fault. Elevated conductivity in the sandstone by up to a factor of two over the background values could indicate possible alteration.

Three-dimensional finite-difference modeling of time-domain electromagnetic responses for a large-loop source

The time-domain/transient electromagnetic (TEM) method employs an alternating magnetic field that is established by passing a bidirectional pulsed current through a transmitter loop. A large wire loop on or above the earth is one of the most widely used sources in TEM survey systems. To simulate TEM responses of the large loop system, the effect of the loop size must be considered in a numerical modeling scheme. We have developed an efficient three-dimensional (3D) TEM modeling algorithm using a staggered-grid finite-difference time-domain (FDTD) method. In this paper, we first derive FDTD TEM equations using fictitious displacement currents based on an explicit mid-point method. Then, we employed a conversion method to efficiently obtain stepoff TEM responses from step-on responses. Further, following the concept of the conversion method, the charging and discharging processes of current waveform in loop does not need to be identical, implying we can apply the simulation scheme for more general source waveforms. The developed algorithm has been verified through comparison of numerical results for a homogeneous halfspace medium. Finally, we analyze TEM responses generated from a large loop source for a 3D conductive body buried in a homogeneous half space.

Closed-Form Expressions for the Analysis of Wave Propagation in Overhead Distribution Lines

The calculation of the influence of the imperfect earth on overhead conductors is an important issue in power system analysis. Rigorous solutions contain infinite integrals; thus, due to their complex form, different simplified closed-form expressions have been proposed in the literature. This paper presents a detailed analysis of the effect of different closed-form expressions on the investigation of the wave propagation of distribution overhead lines (OHLs). A sensitivity analysis is applied to determine the most important properties influencing the calculation of the OHL parameters. The accuracy of several closed-form earth impedance models is evaluated as well as the influence of the displacement current and imperfect earth on the shunt admittance, which are further employed in the calculation of the propagation characteristics of OHLs. The frequency-dependence of the soil electrical properties, as well as the application of different modal decomposition algorithms, are also investigated. Finally, results on the basis of frequency-domain signal scans and time-domain electromagnetic transient responses are also discussed.

3D Characterization of a Coastal Freshwater Aquifer in SE Malta (Mediterranean Sea) by Time-Domain Electromagnetics

Electromagnetic (EM) geophysical methods are well equipped to distinguish electrical resistivity contrasts between freshwater-saturated and seawater-saturated formations. Beneath the semi-arid, rapidly urbanizing island of Malta, offshore groundwater is an important potential resource but it is not known whether the regional mean sea-level aquifer (MSLA) extends offshore. To address this uncertainty, land-based alongshore and across-shore time-domain electromagnetic (TDEM) responses were acquired with the G-TEM instrument (Geonics Ltd., Mississauga, ON, Canada) and used to map the onshore structure of the aquifer. 1-D inversion results suggest that the onshore freshwater aquifer resides at 4–24 m depth, underlain by seawater-saturated formations. The freshwater aquifer thickens with distance from the coastline. We present 2D and 3D electromagnetic forward modeling based on finite-element (FE) analysis to further constrain the subsurface geometry of the onshore freshwater body. We interpret the high resistivity zones that as brackish water-saturated bodies are associated with the mean sea-level aquifer. Generally, time-domain electromagnetic (TDEM) results provide valuable onshore hydrogeological information, which can be augmented with marine and coastal transition-zone measurements to assess potential hydraulic continuity of terrestrial aquifers extending offshore.

Time-Domain Modeling of Thin High-Contrast Layers With Combined Dielectric and Magnetic Properties

Saltus-type boundary conditions for modeling the time-domain electromagnetic (EM) response of a thin layer with combined dielectric and magnetic properties are derived. Illustrative applications of the cross-layer conditions reveal potentialities of combined sheets to achieving the EM transparency for a causal pulsed EM-field excitation.

A Novel Semianalytic Algorithm for Cosine Transform in ATEM Measurement

First, we directly introduce the cosine transform to compute the time-domain electromagnetic (EM) response excited by cause step turnoff. Then, we advance a novel semianalytic algorithm based on integration, summation, and cube spline interpolation (ISCSI) method to efficiently accomplish the cosine transform. The ISCSI method divides the integral into a sum of partial integrals, which can be solved by cube spline interpolation combined with Newton-Leibniz formula. On the basis, we apply a known convolution method to further compute the time-domain response by arbitrarily waveform in airborne transient EM measurement. Finally, numerical tests valid the ISCSI method is easier to implement and more efficient than the traditional digital filter method because the ISCSI method only requires less frequency sampling amount to accomplish the cosine transform.

Heliborne Time Domain Electromagnetic Data Aiding Delineation of Carbonaceous Shale in Southwestern Part of Bijawar Basin and its Implication on Basinal Stratigraphy

Geophysical methods are tools to unravel concealed geological features that enhance knowledge. Heliborne time domain electromagnetic (TDEM) survey carried out over volcano-sedimentary sequence of Palaeoproterozoic Bijawar basin indicated presence of conductor in the western part of the basin. Subsequently boreholes drilled intercepted rhythmites made up of carbonaceous shale and dolomite within Bajno dolomite Formation. Measurement of conductivity on core samples established the high conductive carbonaceous shale as the contributor for TDEM response. TDEM signature indicate widespread presence of rhythmites in the western part of Bijawar basin reflecting different hydrodynamic condition from other parts of Bajno dolomite. Thus, Bajno dolomite Formation is classified into two members viz. Tigoda member and Sarwa member.

Time domain electromagnetic‐induced polarisation: extracting more induced polarisation information from grounded source time domain electromagnetic data

ABSTRACTElectrical induced polarisation surveys are used to detect chargeable materials in the earth. For interpretation of time domain electrical‐induced polarisation data a common procedure is to first invert the direct current data (electric current on time) to recover conductivity and then invert the induced polarisation data (current off‐time) to recover chargeability. This direct current‐induced polarisation inversion procedure assumes that the off time data are free of secondary electromagnetic induction effects. To comply with this, early time data are often discarded or not recorded. For mid‐time data, an electromagnetic decoupling technique, which removes electromagnetic induction in the observations, needs to be implemented. Usually, responses from a half‐space or a layered earth are subtracted. Recent capability in three‐dimensional time domain electromagnetic forward modelling and inversion allows to revisit these procedures. In a Time domain electromagnetic‐induced polarisation survey, a high sampling rate allows early time channels of the electromagnetic data to be recorded. The recovery of chargeability then follows a three‐step workflow: (i) invert early time channel time domain electromagnetic data to recover the three‐dimensional conductivity; (ii) use that conductivity to compute the time domain electromagnetic response at later time channels and subtract this fundamental response from the observations to extract the induced polarisation responses, and (iii) invert the induced polarisation responses to recover a three‐dimensional chargeability. This workflow effectively removes electromagnetic induction effects in the observations and produces better chargeability and conductivity models compared with conventional approaches. In a synthetic example involving a gradient array, we show that the conductivity structure obtained from the early time channel data, which are usually discarded, is superior to that obtained from the steady state direct current voltages. This adds a further reason to collect these electromagnetic data.

A New Imaging Approach for Dipole–Dipole Time-Domain Electromagnetic Data Based on the q-Transform

The inline dipole–dipole time-domain electromagnetic method is a useful supplementary tool for the exploration of a resistive target such as a hydrocarbon resource. Currently, the interpretation of the data from this configuration is based on the fitting of the modeled response and the recorded response in a least square sense. In the paper, we propose an imaging method based on a mathematical transformation named the q-transform, which could make the subsequent imaging of TEM data using the interpretation technique in seismic method possible. The imaging strategy is based on analytical derivation and analysis of the transformed wave-field from which pseudo-velocity and resistivity can be extracted. A numerical test is employed to get the transformed wave-field from the time-domain electromagnetic response with the selected regularization method. The proposed imaging method is tested on the synthetic data obtained from a homogeneous and layered half space models. The results reveal that it is a useful method to recover the resistivity of an underground medium and can provide an additional tool for fast and qualitative imaging of the subsurface resistivity.

3D inversion of total magnetic intensity data for time-domain EM at the Lalor massive sulphide deposit

The Lalor deposit is a massive sulphide that is characterised as a stack of conductive ore lenses buried more than 600 m deep. We invert helicopter sub-audio magnetics (HeliSAM) data from Lalor collected using a ground large transmitter loop and an airborne total magnetic intensity (TMI) magnetometer measuring the time-domain electromagnetic (EM) responses. The TMI data are modelled as a projection of the anomalous field onto the earth’s magnetic field. Inversion of these data is considered a significant case study because of two challenges. First, the early-time data are contaminated by the infrastructure on the surface. Second, inverting the data with a uniform half-space as the initial model results in a mathematically acceptable, but non-geologic, model. We create workflows to overcome these difficulties. For the contaminated data, we use a locally refined mesh and a constrained inversion to recover highly conductive cells near the surface that effectively represent the infrastructure. This allows us to safely extract geologic information from the early time data. The non-uniqueness in the inversion is reduced by warm-starting the voxel 3D inversion with a more reasonable initial guess, for example, a block model from geometric inversions. Those procedures greatly improve the inversion image from the surface to the bottom of the target at Lalor, and they can easily be incorporated into the industrial production workflows.

Central Loop Time Domain Electromagnetic Inversion Based on Born Approximation and Levenberg-Marquardt Algorithm

Time Domain Electromagnetic (TDEM) method uses electromagnetic wave to detect resistivity or conductivity difference of lithology in the subsurface, measured in the time domain. TDEM method has been developed in decades. There are forward modeling and inversion programs have been made. The purpose of making the forward modeling programs is to calculate TDEM response so that data acquisition parameters can be chosen correctly. The inversion program is for synthesizing geological model from measured TDEM data. Several TDEM programs have been made, but the procedures require heavy and complex computation, which need high computer specification and lot of calculation time. Nowadays program that used less complex computation and faster calculation is needed to match field data acquisition productivity. To achieve faster and more accurate process, we use Born Approximation of the apparent conductivity for the forward modeling program and Levenberg-Marquardt algorithm for the inversion program. We use many circumstances in testing our programs, from one layer to multi layers by varying the resistivity or thickness of lithology and compared with a validated program, EMUPLUS. At the end of the test, inversion of real data is taken as confirmation that the program can be used to process real TDEM data. Inversion results of both synthetic and real TDEM data show pleasant results. These test results indicate that our program can be used as daily forward modeling program for determining data field acquisition parameters and do the inversion procedure for synthetic and real TDEM data.

HELITEM detects the Lalor VMS deposit

CGG deployed HELITEM, a helicopter-borne time domain electromagnetic (TDEM) system over the Lalor Deposit and other proximal deep conductors of Hudbay Minerals in northern Canada. The Lalor Deposit is ~570 m deep and is a difficult target for airborne EM systems. The system was configured with a dipole moment of up to 1.9 MAm2 at base frequencies of 15 Hz and 30 Hz. The results of this survey have been used to characterise the TDEM response from deep volcanogenic massive sulphide (VMS) deposits within the region. HELITEM is the only airborne controlled source TDEM system to have detected the Lalor Deposit.

Transient electromagnetic fields of a buried horizontal magnetic dipole

Electromagnetic surveys using a vertical transmitter loop are common in land, marine, and airborne geophysical exploration. Most of these horizontal magnetic dipole (HMD) systems operate in the frequency domain, measuring the time derivative of the induced magnetic fields, and therefore a majority of studies have focused on this subset of field measurements. We examine the time-domain electromagnetic response of a HMD including the electric fields and corresponding smoke rings produced in a conductive half-space. Cases of a dipole at the surface and buried within the earth are considered. Results indicate that when the current in the transmitter is rapidly switched off, a single smoke ring is produced within the plane of the vertical transmitter loop, which is then distorted by the air-earth interface. In this situation, the circular smoke ring, which would normally diffuse symmetrically away from the source in a whole space, is approximately transformed into an ellipse, with a vertical major axis at an early time and a horizontal major axis at a late time. As measured from the location of the transmitter, the depth of investigation and lateral footprint of such a system increases with burial depth. It is also observed that the electric field measured in the direction of the magnetic dipole only contains a secondary response related to the charge accumulation on any horizontal conductivity boundaries because the primary field is always absent. This field component can be expressed analytically in terms of a static and time-varying field, the latter term adding spatial complexity to the total horizontal electric field at the earth surface at early times. Applications of this theoretical study include the design of time-domain induction-logging tools, crossborehole electromagnetic surveys, underground mine expansion work, mine rescue procedures, and novel marine electromagnetic experiments.

Representation of Electromagnetic Responses in Time Domain Using State-Space System Identification Method

This paper presents a control system methodology based on system identification (SI) to derive state matrices and system dynamics for the extrapolation of simulated time-domain electromagnetic (EM) responses using both input and output data. The method is applied to model transient responses for a dielectric resonator and a wideband slot antenna computed by the finite-integration method using non-Gaussian excitation pulses typically employed in digital signals. Using state-space SI formulation, a compact representation of the output time-domain signal is derived, including the early-time transient responses, and its numerical implementation depicts no instability in late-time responses plotted well beyond the steady state. Furthermore, all the system poles are found to lie within the unit circle in the complex plane. Excellent model corroboration is achieved with independently computed frequency domain data or measured results using modest computer resources.

Three effective inverse Laplace transform algorithms for computing time-domain electromagnetic responses

The inverse Laplace transform is one of the methods used to obtain time-domain electromagnetic (EM) responses in geophysics. The Gaver-Stehfest algorithm has so far been the most popular technique to compute the Laplace transform in the context of transient electromagnetics. However, the accuracy of the Gaver-Stehfest algorithm, even when using double-precision arithmetic, is relatively low at late times due to round-off errors. To overcome this issue, we have applied variable-precision arithmetic in the MATLAB computing environment to an implementation of the Gaver-Stehfest algorithm. This approach has proved to be effective in terms of improving accuracy, but it is computationally expensive. In addition, the Gaver-Stehfest algorithm is significantly problem dependent. Therefore, we have turned our attention to two other algorithms for computing inverse Laplace transforms, namely, the Euler and Talbot algorithms. Using as examples the responses for central-loop, fixed-loop, and horizontal electric dipole sources for homogeneous and layered mediums, these two algorithms, implemented using normal double-precision arithmetic, have been shown to provide more accurate results and to be less problem dependent than the standard Gaver-Stehfest algorithm. Furthermore, they have the capacity for yielding more accurate time-domain responses than the cosine and sine transforms for which the frequency-domain responses are obtained by interpolation between a limited number of explicitly computed frequency-domain responses. In addition, the Euler and Talbot algorithms have the potential of requiring fewer Laplace- or frequency-domain function evaluations than do the other transform methods commonly used to compute time-domain EM responses, and thus of providing a more efficient option.

Three-dimensional modeling of IP effects in time-domain electromagnetic data

Understanding the effects of induced-polarization (IP) effects on time-domain electromagnetic data requires the ability to simulate common survey techniques when taking chargeability into account. Most existing techniques preform this modeling in the frequency domain prior to transforming their results to the time domain. Even though this technique can allow for chargeable material to be easily incorporated, its application for some problems can be computationally limiting. We developed a new technique for forward modeling the time-domain electromagnetic response of chargeable materials in three dimensions. The frequency dependence of Ohms’ law translates to an ordinary differential equation when considered in the time domain. The system of ordinary-partial differential equations was then discretized using an implicit time-stepping algorithm, that yielded absolute stability. This approach allowed us to operate directly in the time domain and avoid frequency to time-domain transformations. Although this approach can be applied directly to materials exhibiting Debye dispersions, other Cole-Cole dispersions resulted in fractional derivatives in time. To overcome this difficulty, Padé approximations were used to represent the frequency dependence as a rational series of integer order terms. The resulting method was then simplified to generate a reduced time-domain model that can be used to forward model the IP decay curves in the absence of any electromagnetic coupling. We found numerical examples in which the method produced accurate results. The potential application of the method was demonstrated by modeling the full time-domain electromagnetic response of a gradient array IP survey, and the occurrence of negative transients in airborne time-domain electromagnetic data.

수평다층구조에 대한 시간영역 전자기장의 계산법

A computer program has been developed to estimate time-domain electromagnetic (EM) responses for a onedimensional model with multiple source and receiver dipoles that are finite in length. The time-domain solution can be obtained by applying an inverse fast Fourier transform (FFT) to frequency-domain fields for efficiency. Frequency-domain responses are first obtained for 10 logarithmically equidistant frequencies per decade, and then cubic spline interpolated to get the FFT input. In the case of phases, the phase curve must be made to be continuous prior to the spline interpolation. The spline interpolated data are convolved with a source current waveform prior to FFT. In this paper, only a step-off waveform is considered. This time-domain code is verified with an analytic solution and EM responses for a marine hydrocarbon reservoir model. Through these comparisons, we can confirm that the accuracy of the developed program is fairly high.

Influence of dispersive soil electromagnetic properties on hand‐held time domain electromagnetic sensors

ABSTRACTAlthough metal detectors remain the workhorses of humanitarian demining, it is well established that the performance of both continuous wave (frequency domain) and pulsed induction (time domain) detectors can be severely compromised by so‐called ‘soil‐effects’. Generally, problem soils reduce the signal‐to‐noise ratio and increase the false‐detection rate. In certain locations, the soil‐effect is so severe as to render the detector practically inoperable. The current study is part of an ongoing international effort to establish and quantify the influence of soil electromagnetic properties on the operation of metal detectors and related sensor technologies. In particular, we examine the relative influence of soil electrical conductivity, magnetic susceptibility and associated frequency dependence on the time domain electromagnetic (TDEM) response of pulsed induction metal detectors and related small‐scale TDEM sensors.

A weak approximation of stochastic time domain electromagnetic response of a conductive permeable sphere

Time domain electromagnetic (TDEM) response of a conductive permeable sphere is a main topic for good understanding and in developing past studies for detection and discrimination of buried metallic objects. Stochastic differential equation model is a valuable tool for stimulating real experience. In this paper, according to an Ito integral, we have obtained a weak approximation of stochastic TDEM response of permeable and nonpermeable sphere. We have used the deterministic solution of TDEM response of conductive permeable sphere by changing one of the variables that have been obtained from the boundary conditions of problem to random variable. By adding white noise to random variable and using stochastic integral, we have displayed stochastic time domain response of conductive permeable sphere. The Ito integral includes a factor that shows infirmity and intensity of noise which has been simply considered constant. Accordingly, we have showed the effect of noise for magnetic and nonmagnetic spheres. Numerical results from step and impulse response of TDEM have shown that the amount of this factor is different for the two types of spheres.