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

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.

Geophysics ◽  
1986 ◽  
Vol 51 (4) ◽  
pp. 984-987 ◽  
Author(s):  
R. N. Edwards ◽  
A. D. Chave

The electrical conductivity of the sea floor is usually much less than that of sea water, and not all electrical measurements made on the sea floor are particularly sensitive to the electrical conductivity value. The analytic impulse and step‐on transient responses of two conductive, adjoining half‐spaces (with a large conductivity contrast) to an in‐line electric dipole‐dipole electromagnetic system located on the interface are derived. The shape of the transient at relatively early time is seen to be independent of the conductivity of the more conductive half‐space and is indicative of the conductivity of the less conductive haft‐space. Based on this observation, a simple, practical system can be designed to measure sea floor conductivity.


Geophysics ◽  
1987 ◽  
Vol 52 (2) ◽  
pp. 204-217 ◽  
Author(s):  
S. J. Cheesman ◽  
R. N. Edwards ◽  
A. D. Chave

The electrical conductivity of the sea floor is usually much less than that of the seawater above it. A theoretical study of the transient step‐on responses of some common controlled‐source, electromagnetic systems to adjoining conductive half‐spaces shows that two systems, the horizontal, in‐line, electric dipole‐dipole and horizontal, coaxial, magnetic dipole‐dipole, are capable of accurately measuring the relatively low conductivity of the sea floor in the presence of seawater. For these systems, the position in time of the initial transient is indicative of the conductivity of the sea floor, while at distinctly later times, a second characteristic of the transient is a measure of the seawater conductivity. The diagnostic separation in time between the two parts of the transient response does not occur for many other systems, including several systems commonly used for exploration on land. A change in the conductivity of the sea floor produces a minor perturbation in what is essentially a seawater response. Some transient responses which could be observed with a practical, deep‐towed coaxial magnetic dipole‐dipole system located near the sea floor are those for half‐space, the layer over a conductive or resistive basement, and the half‐space with an intermediate resistive zone. The system response to two adjoining half‐spaces, representing seawater and sea floor, respectively, is derived analytically. The solution is valid for all time, provided the conductivity ratio is greater than about ten, or less than about one‐tenth. The analytic theory confirms the validity of numerical evaluations of closed‐form solutions to these layered‐earth models. A lateral conductor such as a vertical, infinite, conductive dike outcropping at the sea floor delays the arrival of the initial crustal transient response. The delay varies linearly with the conductance of the dike. This suggests that time delay could be inverted directly to give a measure of the anomalous integrated conductance of the sea floor both between and in the vicinity of the transmitter and the receiver dipoles.


Geophysics ◽  
1992 ◽  
Vol 57 (9) ◽  
pp. 1116-1126 ◽  
Author(s):  
James E. Hanneson

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.


Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 861-869 ◽  
Author(s):  
Perry A. Eaton ◽  
Gerald W. Hohmann

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.


Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 1027-1029 ◽  
Author(s):  
M. N. Nabighian ◽  
M. L. Oristaglio

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.


Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 63-74 ◽  
Author(s):  
R. Nigel Edwards

Methane hydrates are solid, nonstoichiometric mixtures of water and the gas methane. They occur worldwide in sediment beneath the sea floor, and estimates of the total mass available there exceed [Formula: see text]. Since each volume of hydrate can yield up to 164 volumes of gas, offshore methane hydrate is recognized as a very important natural energy resource. The depth extent and stability of the hydrate zone is governed by the phase diagram for mixtures of methane and hydrate and determined by ambient pressures and temperatures. In sea depths greater than about 300 m, the pressure is high enough and the temperature low enough for hydrate to occur at the seafloor. The fraction of hydrate in the sediment usually increases with increasing depth. The base of the hydrate zone is a phase boundary between solid hydrate and free gas and water. Its depth is determined principally by the value of the geothermal gradient. It stands out on seismic sections as a bright reflection. The diffuse upper boundary is not as well marked so that the total mass of hydrate is not determined easily by seismic alone. The addition of electrical data, collected with a seafloor transient electric dipole‐dipole system, can aid in the evaluation of the resource. Methane hydrate, like ice, is electrically insulating. Deposits of hydrate in porous sediment cause an increase in the formation resistivity. The data consist of measurements of the time taken for an electrical disturbance to diffuse from the transmitting dipole to the receiving dipole. The traveltime is related simply to the resistivity: the higher the resistivity, the shorter the traveltime. A sounding curve may be obtained by measuring traveltimes as a function of the separation between the dipoles and interpreted in terms of the variation of porosity with depth. Two exploration scenarios are investigated through numerical modeling. In the first, a very simple example illustrating some of the fundamental characteristics of the electrical response, most of the properties of the section including the probable, regional thickness of the hydrate zone (200 m) are assumed known from seismic and spot drilling. The amount of hydrate in the available pore space is the only free parameter. Hydrate content expressed as a percentage may be determined to about ±ε given a measurement of traveltime at just one separation (800 m) to ε%. The rule holds over the complete range of anticipated hydrate content values. In the second example, less information is assumed available a priori and the complementary electrical survey is required to find both the thickness and the hydrate content in a hydrate zone about 200 m thick beneath the sea floor containing 20 and 40% hydrate in the available pore space, respectively. A linear eigenfunction analysis reveals that for these two models, the total mass of hydrate, the product of hydrate content and thickness, may be estimated to an accuracy of about 3ε% given measurements of traveltime to an accuracy of ε% over a range of separations from 100 to 1300 m. The value of the electrical information depends directly on the accuracy to which transient arrivals can be measured on the sea floor in water depths exceeding 300 m over a separation of the order of a kilometer, the error parameter ε. While results of appropriate surveys, or even noise measurements, have not been published in the open literature, surveys on a smaller 100 m scale have been conducted by my group. Based on these data, I suggest that the value of ε may be of the order of 3%.


Geophysics ◽  
1963 ◽  
Vol 28 (4) ◽  
pp. 563-581 ◽  
Author(s):  
John W. Dunkin

The problem of transient wave propagation in a three‐layered, fluid or solid half‐plane is investigated with the point of view of determining the effect of refracting bed thickness on the character of the two‐dimensional head wave. The “ray‐theory” technique is used to obtain exact expressions for the vertical displacement at the surface caused by an impulsive line load. The impulsive solutions are convolved with a time function having the shape of one cycle of a sinusoid. The multiple reflections in the refracting bed are found to affect the head wave significantly. For thin refracting beds in the fluid half‐space the character of the head wave can be completely altered by the strong multiple reflections. In the solid half‐space the weaker multiple reflections affect both the rate of decay of the amplitude of the head wave with distance and the apparent velocity of the head wave by changing its shape. A comparison is made of the results for the solid half‐space with previously published results of model experiments.


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