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.

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.

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.

TIME‐DEPENDENT ELECTROMAGNETIC FIELDS OF AN INFINITE, CONDUCTING CYLINDER EXCITED BY A LONG CURRENT‐CARRYING CABLE

Geophysics ◽  
1973 ◽  
Vol 38 (2) ◽  
pp. 369-379 ◽  
Author(s):  
Saurabh K. Verma
Keyword(s):  
Time Domain ◽  
Horizontal Cylinder ◽  
The Body ◽  
Time Dependent ◽  
Electromagnetic Response ◽  
Secondary Field ◽  
Function Type ◽  
Ore Body ◽  
Induced Field ◽  
Time Domain Electromagnetic

Theoretical and numerical computations have been made for the quasi‐static, time‐domain electromagnetic response of an infinite, conducting horizontal cylinder stimulated by long cable‐carrying step and ramp‐function type pulses. The effect of higher‐order induced multipoles on the secondary electric and magnetic field components is analyzed in detail, and the “threshold distances” at which individual multipoles become effective (contributing more than 5 percent of the secondary field) are presented. Also, the field fall‐off directly above the body and the variations in different induced‐field components along a traverse perpendicular to the strike of the ore body are examined.

The borehole transient electromagnetic response of a three‐dimensional fracture zone in a conductive half‐space

Geophysics ◽  
1988 ◽  
Vol 53 (11) ◽  
pp. 1469-1478 ◽  
Author(s):  
Richard C. West ◽  
Stanley H. Ward
Keyword(s):  
Half Space ◽  
Fracture Zone ◽  
Geophysical Methods ◽  
Practical Interest ◽  
The Body ◽  
Secondary Response ◽  
Direct Integral ◽  
Transient Electromagnetic ◽  
Integral Equation Formulation ◽  
Tem Method

Borehole geophysical methods can be useful in detecting subsurface fracture zones and mineral deposits which are nearby, but not intersected by boreholes. One electrical borehole technique which can be applied to this problem is the surface‐to‐borehole transient electromagnetic (TEM) method. In this method a transmitting loop is deployed on the surface while a receiving coil is moved down a borehole. A conductive, horizontal, tabular body in a homogeneous half space was chosen to simulate a 3-D fracture zone or mineral deposit within the earth. Theoretical borehole TEM responses for several models of practical interest were computed using a direct integral‐equation formulation. The anomalous TEM response (secondary response) is the result of a complex interaction between vortex and galvanic currents within the body. Distortion of the secondary response by the conductive host does not affect the estimate of the depth to the horizontal body but it does lead to erroneous estimates of the conductivity and size of the body. Increasing the resistivity of the host decreases the host effects and increases the peak response of the body. Decreasing the separation between the body and borehole or decreasing the depth of the body increases the secondary response. The decrease in the vortex response due to the decreased coupling when a transmitting loop is offset from the body is nearly countered by an increase in the galvanic response at late times; however, this phenomenon is model‐dependent. This study indicates promise for the borehole TEM method, but the application of the technique is limited by the hardware and modest modeling capabilities presently available.

scholarly journals A Two-Dimensional Generalized Electromagnetothermoelastic Diffusion Problem for a Rotating Half-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Jingrui Zhang ◽  
Yanyan Li
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Half Space ◽  
Chemical Potential ◽  
Diffusion Problem ◽  
Two Dimensional ◽  
Constant Intensity ◽  
Thermoelastic Wave ◽  
Thermoelastic Diffusion ◽  
Nondimensional Temperature

In the context of the theory of generalized thermoelastic diffusion, a two-dimensional generalized electromagnetothermoelastic problem with diffusion for a rotating half-space is investigated. The rotating half-space is placed in an external magnetic field with constant intensity and its bounding surface is subjected to a thermal shock and a chemical potential shock. The problem is formulated based on finite element method and the derived finite element equations are solved directly in time domain. The nondimensional temperature, displacement, stress, chemical potential, concentration, and induced magnetic field are obtained and illustrated graphically. The results show that all the considered variables have a nonzero value only in a bounded region and vanish identically outside this region, which fully demonstrates the nature of the finite speeds of thermoelastic wave and diffusive wave.

ELECTROMAGNETIC SCATTERING BY CONDUCTORS IN THE EARTH NEAR A LINE SOURCE OF CURRENT

Geophysics ◽  
1971 ◽  
Vol 36 (1) ◽  
pp. 101-131 ◽  
Author(s):  
Gerald W. Hohmann
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Line Source ◽  
Numerical Technique ◽  
The Body ◽  
Scale Model ◽  
Electromagnetic Response ◽  
Field Phase ◽  
Horizontal Magnetic Field ◽  
Depth Of Burial

A theoretical solution is developed for the electromagnetic response of a two‐dimensional inhomogeneity in a conductive half‐space, in the field of a line source of current. The solution is in the form of an integral equation, which is reduced to a matrix equation, and solved numerically for the electric field in the body. The electric and magnetic fields at the surface of the half‐space are found by integrating the half‐space Green’s functions over the scattering currents. One advantage of this particular numerical technique is that it is necessary to solve for scattering currents only in the conductor and not throughout the half‐space. The response of a thin, vertical conductor is studied in some detail. Because the only interpretational aids available previously were scale model results for conductors in free space, the results presented here should be useful in interpreting data and in designing new EM systems. As expected, anomalies decay rapidly as depth of burial is increased, due to attenuation in the conductive half‐space. Depth of exploration appears to be greatest for measurements of horizontal magnetic field phase, while vertical field phase is diagnostic of conductivity. Horizontal location and depth of burial are best determined through measurements of vertical or horizontal magnetic field amplitude.

The effect of a strong magnetic field on two-dimensional flows of a conducting fluid

1963 ◽  
Vol 15 (3) ◽  
pp. 429-441 ◽  
Author(s):  
Stephen Childress
Keyword(s):  
Magnetic Field ◽  
Perturbation Technique ◽  
The Body ◽  
Conducting Fluid ◽  
Order Effects ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Exterior Region ◽  
Electrically Conducting ◽  
Higher Order Effects

The motion of a viscous, electrically conducting fluid past a finite two-dimensional obstacle is investigated. The magnetic field is assumed to be uniform and parallel to the velocity at infinity. By means of a perturbation technique, approximations valid for large values of the Hartmann number M are derived. It is found that, over any finite region, the flow field is characterized by the presence of shear layers fore and aft of the body. The limit attained over the exterior region represents the two-dimensional counterpart of the axially symmetric solution given by Chester (1961). Attention is focused on a number of nominally ‘higher-order’ effects, including the presence of two distinct boundary layers. The results hold only when M [Gt ] Re; Re = Reynolds number. However, a generalization of the procedure, in which the last assumption is relaxed, is suggested.

Time-Domain Simulations of Radiation and Diffraction Forces

2010 ◽  
Vol 54 (02) ◽  
pp. 79-94 ◽  
Author(s):  
Xinshu Zhang ◽  
Piotr Bandyk ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Three Dimensional ◽  
The Body ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Forward Speed ◽  
Time Step ◽  
Surface Boundary Conditions ◽  
Strip Theory

Large-amplitude, time-domain, wave-body interactions are studied in this paper for problems with forward speed. Both two-dimensional strip theory and three-dimensional computation methods are shown and compared by a number of numerical simulations. In the present approach, an exact body boundary condition and linearized free surface boundary conditions are used. By distributing desingularized sources above the calm water surface and using constant-strength flat panels on the exact body surface, the boundary integral equations are solved numerically at each time step. The strip theory method implements Radial Basis Functions to approximate the longitudinal derivatives of the velocity potential on the body. Once the fluid velocities on the free surface are computed, the free surface elevation and potential are updated by integrating the free surface boundary conditions. After each time step, the body surface and free surface are regrided due to the instantaneous changing wetted body geometry. Extensive results are presented to validate the efficiency of the present methods. These results include the added mass and damping computations for a Wigley III hull and an S-175 hull with forward speed using both two-dimensional and three-dimensional approaches. Exciting forces acting on a Wigley III hull due to regular head seas are obtained and compared using both the fully three-dimensional method and the two-dimensional strip theory. All the computational results are compared with experiments or other numerical solutions.

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.

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