The influence of a conductive host on two‐dimensional borehole transient electromagnetic responses

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 861-869 ◽  
Author(s):  
Perry A. Eaton ◽  
Gerald W. Hohmann
Keyword(s):  
Electric Field ◽  
Half Space ◽  
Time Window ◽  
Time Derivative ◽  
Finite Width ◽  
Late Time ◽  
Time Behavior ◽  
Two Dimensional ◽  
Peak Response ◽  
Transient Electromagnetic

We have computed transient borehole electromagnetic (EM) responses of two‐dimensional (2-D) models using a direct and explicit finite‐difference algorithm. The program computes the secondary electric field which is defined as the difference between the total field and the primary (half‐space) field. The time derivative of the vertical magnetic field in a borehole is computed by numerical differentiation of the total electric field. These models consist of a thin horizontal conductor with a finite width, embedded in a conductive half‐space. Dual line sources energized by a step‐function current lie on the surface of the half‐space and simulate the long sides of a large rectangular loop. Numerical results substantiate several important features of the transient impulse response of such models. The peak response of the target is attenuated as the resistivity of the host decreases. A sign reversal in the secondary electric field occurs later in time as the resistivity of the host decreases. The peak response and the onset of late‐time behavior are delayed in time as well. Secondary responses for models with different host resistivities (10–1000 Ω-m) are approximately the same at late time. If the target is less conductive, the effects of the host, i.e., the attenuation and time delay, are less. It is readily apparent that there exists a time window within which the target’s response is at a maximum relative to the half‐space response. At late time the shape of the borehole anomaly due to a thin conductive 2-D target appears to be independent of the conductivity of the host. The late‐time secondary decay of the target is neither exponential nor power law, and a time constant computed from the slope of a log‐linear decay curve at late time may be much larger than the actual value for the same target in free space.

scholarly journals A parallel finite‐difference approach for 3D transient electromagnetic modeling with galvanic sources

Geophysics ◽  
2004 ◽  
Vol 69 (5) ◽  
pp. 1192-1202 ◽  
Author(s):  
Michael Commer ◽  
Gregory Newman
Keyword(s):  
Magnetic Field ◽  
Finite Difference ◽  
Electric Field ◽  
Electric Fields ◽  
Time Derivative ◽  
Stable Solution ◽  
Parallel Computer ◽  
Staggered Grid ◽  
Electromagnetic Modeling ◽  
Transient Electromagnetic

A parallel finite‐difference algorithm for the solution of diffusive, three‐dimensional (3D) transient electromagnetic field simulations is presented. The purpose of the scheme is the simulation of both electric fields and the time derivative of magnetic fields generated by galvanic sources (grounded wires) over arbitrarily complicated distributions of conductivity and magnetic permeability. Using a staggered grid and a modified DuFort‐Frankel method, the scheme steps Maxwell's equations in time. Electric field initialization is done by a conjugate‐gradient solution of a 3D Poisson problem, as is common in 3D resistivity modeling. Instead of calculating the initial magnetic field directly, its time derivative and curl are employed in order to advance the electric field in time. A divergence‐free condition is enforced for both the magnetic‐field time derivative and the total conduction‐current density, providing accurate results at late times. In order to simulate large realistic earth models, the algorithm has been designed to run on parallel computer platforms. The upward continuation boundary condition for a stable solution in the infinitely resistive air layer involves a two‐dimensional parallel fast Fourier transform. Example simulations are compared with analytical, integral‐equation and spectral Lanczos decomposition solutions and demonstrate the accuracy of the scheme.

Resistivity mapping using inductive sources

1989 ◽  
Vol 20 (2) ◽  
pp. 47 ◽  
Author(s):  
J. MacNae ◽  
P. McGowan ◽  
Y. Lamontagne
Keyword(s):  
Electric Field ◽  
Time Derivative ◽  
Constant Current ◽  
Magnetic Component ◽  
Late Time ◽  
Gold Mine ◽  
Practical Application ◽  
Electric Component ◽  
Resistive Zone

In electromagnetic (EM) exploration for conductive targets, measurements of the magnetic component or its time derivative have received more theoretical attention and practical application than have measurements of the electric component. However, the electric component can be shown to be particularly useful in the search for resistive zones not usually detected by the magnetic component. Normalized measurements of the surface voltage differences caused by the constant current induced at late time by the UTEM transmitter are called 'Inductive Source Resistivity' or ISR measurements.Data collected on a grid located just south of the Temora gold mine in N.S.W. clearly show the effectiveness of the ISR technique in detecting a resistive zone of silicification located unconformably under 10S of conductive cover. Due to the relatively slow falloff of the electric field from an inductive source, the technique is ideal for the rapid exploration of large areas.

The transient EM step response of a dipping plate in a conductive half‐space

Geophysics ◽  
1992 ◽  
Vol 57 (9) ◽  
pp. 1116-1126 ◽  
Author(s):  
James E. Hanneson
Keyword(s):  
Half Space ◽  
Free Space ◽  
Early Time ◽  
Step Response ◽  
Current Loop ◽  
Late Time ◽  
Electromagnetic System ◽  
University Of Toronto ◽  
Transient Electromagnetic ◽  
Induction Process

An algorithm for computing the transient electromagnetic (TEM) response of a dipping plate in a conductive half‐space has been developed. For a stationary [Formula: see text] current loop source, calculated profiles simulate the response of the University of Toronto electromagnetic system (UTEM) over a plate in a 1000 Ω ⋅ m half‐space. The objective is to add to knowledge of the galvanic process (causing poloidal plate currents) and the local induction process (causing toroidal currents) by studying host and plate currents with respect to surface profiles. Both processes can occur during TEM surveys. Plates are all [Formula: see text] thick with various depths, dips, and conductances. Calculated host and plate currents provide quantitative examples of several effects. For sufficiently conductive plates, the late time currents are toroidal as for a free‐space host. At earlier times, or at all times for poorly conducting plates, the plate currents are poloidal, and the transitions to toroidal currents, if they occur, are gradual. At very late times, poloidal currents again dominate any toroidal currents but this effect is rarely observed. Stripped, point‐normalized profiles, which reflect secondary fields caused by the anomalous plate currents, illustrate effects such as early time blanking (caused by noninstantaneous diffusion of fields into the target), mid‐time anomaly enhancement (caused by galvanic currents), and late time plate‐in‐free‐space asymptotic behavior.

Diffusion of electromagnetic fields into a two‐dimensional earth: A finite‐difference approach

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 870-894 ◽  
Author(s):  
M. L. Oristaglio ◽  
G. W. Hohmann
Keyword(s):  
Finite Difference ◽  
Half Space ◽  
Small Time ◽  
Two Dimensional ◽  
Time Step ◽  
Small Peak ◽  
Transient Electromagnetic ◽  
The Earth ◽  
Air Interface ◽  
Equation Boundary

We describe a numerical method for time‐stepping Maxwell’s equations in the two‐dimensional (2-D) TE‐mode, which in a conductive earth reduces to the diffusion equation. The method is based on the classical DuFort‐Frankel finite‐difference scheme, which is both explicit and stable for any size of the time step. With this method, small time steps can be used at early times to track the rapid variations of the field, and large steps can be used at late times, when the field becomes smooth and its rates of diffusion and decay slow down. The boundary condition at the earth‐air interface is handled explicitly by calculating the field in the air from its values at the earth’s surface with an upward continuation based on Laplace’s equation. Boundary conditions in the earth are imposed by using a large, graded grid and setting the values at the sides and bottom to those for a haft‐space. We use the 2-D model to simulate transient electromagnetic (TE) surveys over a thin vertical conductor embedded in a half‐space and in a half‐space with overburden. At early times (microseconds), the patterns of diffusion in the earth are controlled mainly by geometric features of the models and show a great deal of complexity. But at late times, the current concentrates at the center of the thin conductor and, with a large contrast (1000:1) between conductor and half‐space, produces the characteristic crossover and peaked anomalies in the surface profiles of the vertical and horizontal emfs. With a smaller contrast (100:1), however, the crossover in the vertical emf is obscured by the halfspace response, although the horizontal emf still shows a small peak directly above the target.

Two‐dimensional modeling of a towed in‐line electric dipole‐dipole sea‐floor electromagnetic system: The optimum time delay or frequency for target resolution

Geophysics ◽  
1988 ◽  
Vol 53 (6) ◽  
pp. 846-853 ◽  
Author(s):  
R. N. Edwards
Keyword(s):  
Time Delay ◽  
Half Space ◽  
Electric Dipole ◽  
Late Time ◽  
Crustal Material ◽  
Two Dimensional ◽  
Optimum Time ◽  
Electromagnetic System ◽  
Sea Floor ◽  
Dipole System

Towed in‐line transient electric dipole‐dipole systems are being used to map the electrical conductivity of the sea floor. The characteristic response of a double half‐space model representing conductive seawater and less conductive crustal material to a dipole‐dipole system located at the interface consists of two distinct parts. As time in the transient measurements progresses, two changes in field strength are observed. The first change is caused by the diffusion of the electromagnetic field through the resistive sea floor; the second is caused by diffusion through the seawater. The characteristic times at which the two events occur are measures of sea‐floor and seawater conductivity, respectively. Entirely equivalent responses are observed in a frequency‐domain measurement as frequency is swept from high to low. The simple double half‐space response is modified when the towed array crosses over a conductivity anomaly. I evaluate the magnitude of the anomalous response as a function of delay time and frequency using a two‐dimensional theory and a vertical, plate‐like target. If the ratio of the conductivity of the seawater to that of the sea floor is greater than unity, then an optimum time delay or frequency can be found which maximizes the response. For large conductivity contrasts, the optimum response is greater than the response at late time or zero frequency by a factor of the order of the conductivity ratio.

Three‐dimensional transient electromagnetic responses for a grounded source

Geophysics ◽  
1986 ◽  
Vol 51 (11) ◽  
pp. 2117-2130 ◽  
Author(s):  
Brian M. Gunderson ◽  
Gregory A. Newman ◽  
Gerald W. Hohmann
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Time Derivative ◽  
Three Dimensional ◽  
The Body ◽  
Vertical Magnetic Field ◽  
Horizontal Magnetic Field ◽  
One Dimensional ◽  
Transient Electromagnetic ◽  
Electromagnetic Responses

When the current in a grounded wire is terminated abruptly, currents immediately flow in the Earth to preserve the magnetic field. Initially the current is concentrated near the wire, with a broad zone of return currents below. The electric field maximum broadens and moves downward with time. Currents are channeled into a conductive three‐dimensional body, resulting in anomalous magnetic fields. At early times, when the return currents are channeled into the body, the vertical magnetic field is less than the half‐space field on the far side of the body but is greater than the half‐space field between the source and the body. Later the current in the body reverses; the vertical field is enhanced on the far side of the body and decreased between the source and the body. The horizontal magnetic field has a well‐defined maximum directly over the body at late times, and is a better indicator of the position of the body. The vertical magnetic field and its time derivative change sign with time at receiver locations near the source if a three‐dimensional body is present. These sign reversals present serious problems for one‐dimensional inversion, because decay curves for a layered earth do not change sign. At positions away from the source, the decay curves exhibit no sign reversals—only decreases and enhancements relative to one‐dimensional decay curves. In such cases one‐dimensional inversions may provide useful information, but they are likely to result in fictitious layers and erroneous interpretations.

On the approximation of finite loop sources by two‐dimensional line sources

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 1027-1029 ◽  
Author(s):  
M. N. Nabighian ◽  
M. L. Oristaglio
Keyword(s):  
Half Space ◽  
Line Source ◽  
Opposite Polarity ◽  
Closed Form Expression ◽  
Late Time ◽  
Two Dimensional ◽  
Form Expression ◽  
Time Domain Electromagnetics ◽  
Receiving Coil ◽  
Finite Loop

An appealing feature of time‐domain electromagnetics is that the transient response simplifies considerably at late time, usually tending to a power‐law or exponential decay. In this note, we point out an interesting discrepancy between the late‐time asymptotics of a finite loop source over a half‐space and its natural two‐dimensional (2-D) approximation, which is two line sources of opposite polarity lying on a half‐space. Expressions for the transient responses of both loop (Wait and Ott, 1972) and line sources (Oristaglio, 1982) have been derived before; they show that at late times the voltage induced in a horizontal receiving coil decays as [Formula: see text] for a loop source and [Formula: see text] for a line source. Here we show that the slower decay for the line source is inherently a 2-D effect. To do this, we derive a closed‐form expression for the transient voltage induced by a finite wire of length 2L on a half‐space—a new result, for which we can separately examine the limits [Formula: see text] and [Formula: see text] Surprisingly, these limits are not interchangeable. First taking L to be infinite and then doing the late‐time asymptotic expansion yields the [Formula: see text] decay of a line source; in contrast, first doing the late‐time expansion gives a decay of [Formula: see text] for the finite wire, which is formally unchanged as the length goes to infinity.

Effect of conductive host rock on borehole transient electromagnetic responses

Geophysics ◽  
1989 ◽  
Vol 54 (5) ◽  
pp. 598-608 ◽  
Author(s):  
Gregory A. Newman ◽  
Walter L. Anderson ◽  
Gerald W. Hohmann
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Time Derivative ◽  
The Body ◽  
Galvanic Current ◽  
Large Loop ◽  
Transient Electromagnetic ◽  
Electromagnetic Responses ◽  
Pass Through ◽  
The Magnetic Field

Transient electromagnetic (TEM) borehole responses of 3-D vertical and horizontal tabular bodies in a half‐space are calculated to assess the effect of a conductive host. The transmitter is a large loop at the surface of the earth, and the receiver measures the time derivative of the vertical magnetic field. When the host is conductive (100 Ω ⋅ m), the borehole response is due mainly to current channeled through the body. The observed magnetic‐field response can be visualized as due to galvanic currents that pass through the conductor and return in the half‐space. When the host resistivity is increased, the magnetic field of the conductor is influenced more by vortex currents that flow in closed loops inside the conductor. For a moderately resistive host (1000 Ω ⋅ m), the magnetic field of the body is caused by both vortex and galvanic currents. The galvanic response is observed at early times, followed by the vortex response at later times if the body is well coupled to the transmitter. If the host is very resistive, the galvanic response vanishes; and the response of the conductor is caused only by vortex currents. The shapes of the borehole profiles change considerably with changes in the host resistivity because vortex and galvanic current distributions are very different. When only the vortex response is observed, it is easy to distinguish vertical and horizontal conductors. However, in a conductive host where the galvanic response is dominant, it is difficult to interpret the geometry of the body; only the approximate location of the body can be determined easily. For a horizontal conductor and a single transmitting loop, only the galvanic response enables one to determine whether the conductor is between the transmitter and the borehole or beyond the borehole. A field example shows behavior similar to that of our theoretical results.

Two‐dimensional transient electromagnetic responses

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2849-2861 ◽  
Author(s):  
Jopie I. Adhidjaja ◽  
Gerald W. Hohmann ◽  
Michael L. Oristaglio
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Time Domain ◽  
The Body ◽  
Two Dimensional ◽  
Total Field ◽  
Secondary Field ◽  
Field Solution ◽  
Transient Electromagnetic ◽  
Simple Boundary

The time‐domain electromagnetic (TEM) modeling method of Oristaglio and Hohmann is reformulated here in terms of the secondary field. This finite‐difference method gives a direct, explicit time‐domain solution for a two‐dimensional body in a conductive earth by advancing the field in time with DuFort‐Frankel time‐differencing. As a result, solving for the secondary field, defined as the difference between the total field and field of a half‐space, is not only more efficient but is also simpler and eliminates several problems inherent in the solution for the total field. For example, because the secondary field varies slowly both in space and time, it can be modeled on a coarse grid with large time steps. In addition, for a simple body the field is local; therefore, because the field can be assumed to satisfy a simple boundary condition in the earth computation is greatly simplified. Our tests show that for the same accuracy, the secondary‐field solution is roughly five times faster than the total‐field solution. We compute and analyze the magnetic field impulse response for a suite of models, most of which consist of a thin body embedded in a conductive half‐space—with or without overburden. The results indicate the conductive half‐space will both delay and attenuate the response of the body and even obscure it if the conductivity contrast is small. The results also suggest that the conductive host can alter the decay rate of the response of the body from its free‐space counterpart. Our results for multiple bodies illustrate the importance of early‐time measurements to obtain resolution, particularly for measurements of the horizontal magnetic field. The vertical magnetic field, however, can be used to infer the dip direction of a dipping body by studying the migration of the crossover. The results for models which include overburden show that the effect of a conductive overburden, in addition to the half‐space effect, is to delay the response of the body, because the primary current initially tends to concentrate and slowly diffuse through the overburden, and does not reach the body until later time. This effect also complicates the early‐times profiles, becoming more severe as the conductivity of the overburden is increased.

Vertical and horizontal resistive limit formulas for a rectangular-loop source on a conductive half-space

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. E91-E99 ◽  
Author(s):  
Ralf Schaa ◽  
Peter K. Fullagar
Keyword(s):  
Least Squares ◽  
Half Space ◽  
Host Rock ◽  
Late Time ◽  
Definite Integrals ◽  
Apparent Conductivity ◽  
Transient Electromagnetic ◽  
Analytic Expressions ◽  
Fast Transient

We derived analytic expressions for the time integrals of vertical and horizontal transient B-field responses on a conductive half-space excited by a rectangular-loop source. These formulas were applied in two ways in a fast transient electromagnetic (TEM) inversion scheme. Indefinite integrals were used to extrapolate measured TEM decays to early and late time to convert the observed data to resistive limits. Definite integrals over all time provided estimates for the resistive limit response of host-rock. An apparent conductivity of the host was calculated from the resistive limits via a simple least-squares formulation. These applications of the formulas were tested on synthetic and real TEM data.

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