The electromagnetic response of thin sheets buried in a uniformly conducting half‐space

Geophysics ◽  
1987 ◽  
Vol 52 (1) ◽  
pp. 108-117 ◽  
Author(s):  
R. Clark Robertson
Keyword(s):  
Thin Layer ◽  
Half Space ◽  
Thin Sheet ◽  
Three Dimensional ◽  
Horizontal Layer ◽  
Thin Layers ◽  
Electromagnetic Response ◽  
Thin Sheets ◽  
Magnetotelluric Data ◽  
The Earth

The interpretation of magnetotelluric data is hampered by the effect of three‐dimensional (3-D) conductivity variations within the earth. In particular, the effects of deep structures are masked by heterogeneities near the surface. In order to understand the effects of 3-D anomalies on magnetotelluric investigations, the electromagnetic response of 3-D models of the earth must be investigated. One technique used to model a 3-D earth is the thin‐sheet approximation. This technique confines all lateral changes in conductivity to a horizontal layer in a laterally homogeneous earth; however, the thin‐sheet technique can be applied only to anomalies that are electrically thin at the frequency of investigation. The thin‐sheet technique can be extended to include a greater variety of models by stacking heterogeneous thin layers. As a first step, the thin‐sheet technique is extended to model a buried, heterogeneous thin layer. Extension of the method to account for buried thin sheets is theoretically and computationally more involved than for a surface thin sheet, but the buried thin sheet still has computational advantages over other 3-D models.

To: “The electromagnetic response of thin sheets buried in a uniformly conducting half‐space,” by R. Clark Robertson in January 1987 GEOPHYSICS, p. 108–117

Geophysics ◽  
1987 ◽  
Vol 52 (4) ◽  
pp. 583-583
Keyword(s):  
Electric Field ◽  
Half Space ◽  
Thin Sheet ◽  
Skin Depth ◽  
Modeling Technique ◽  
Electromagnetic Response ◽  
Thin Sheets ◽  
Incident Electric Field

On p. 112, the caption of Figure 4 should read “The (a) magnitude and (b) phase in radians of the x component of the horizontal electric field obtained for a square thin sheet of integrated conductivity 1 S, 8 skin depths on a side, buried at a depth of 0.1 skin depth when the incident electric field is x polarized. Each segment is 1 skin depth on a side.” On p. 114, the last sentence of the first paragraph in the Discussion should read “It is easy to see why the surface thin sheet is a popular modeling technique for magnetotelluric applications.”

Crone pulse electromagnetic response of a conducting thin horizontal sheet—Theory and field application

Geophysics ◽  
1985 ◽  
Vol 50 (8) ◽  
pp. 1350-1354 ◽  
Author(s):  
S. S. Rai
Keyword(s):  
Thin Sheet ◽  
Horizontal Layer ◽  
Field Application ◽  
Step Response ◽  
Electromagnetic Response ◽  
Attractive Feature ◽  
Time Domain Response ◽  
The Time Domain ◽  
Interpretation Model ◽  
Response Formula

The horizontal, conducting thin‐sheet model represents a special interest in interpretation of electromagnetic field data since it is a suitable interpretation model for the surficial conductive layer, a common occurrence in many terrains. For small thicknesses of overburden layers [Formula: see text]separation) the resolution of layer thickness and conductivity is not possible and interpretation needs to be carried out in terms of the layer conductance. An attractive feature of the thin‐sheet model is the simplicity with which the time‐domain response [Formula: see text] can be calculated. The step response of an infinitely thin layer was derived by Maxwell (1891). In this paper I derive the Crone pulse electromagnetic (PEM) response of a conducting infinitely thin horizontal layer. Applicability of the study is demonstrated by means of a field example.

Estimating the parameters of simple models from two-component on-time airborne electromagnetic data

Geophysics ◽  
2021 ◽  
pp. 1-52
Author(s):  
Thomas Bagley ◽  
Richard S. Smith
Keyword(s):  
Half Space ◽  
Thin Sheet ◽  
Lower Half ◽  
Thick Sheet ◽  
Thin Sheets ◽  
Survey Area ◽  
Lower Half Space ◽  
Drill Holes ◽  
Airborne Electromagnetic Data ◽  
Simple Models

The horizontal and vertical components of the on-time electromagnetic (EM) response can be used to estimate the parameters of simple models like thin sheets, half-spaces, thin sheets over a lower half-space and a two-layer model. The formulae used in these methods are valid in areas where the on-time response is essentially proportional to the conductivity or conductance, the so called "resistive limit". The half-space and thin-sheet over a lower half-space models can be combined to give an estimate of the conductivity for a lower half-space below a thick sheet that might be reasonable for the whole of the survey area. With this estimation an equation solver can be used to estimate the thickness and conductivity of the overlying thick sheet over the whole survey area. This latter approach seemed most appropriate for the Russell South area in the Athabasca Basin, Canada, where GEOTEM data has been collected. The output of the algorithm was generally stable. Although it did not always reliably reproduce the overburden thicknesses as measured in a set of reference drill holes, it did give an estimate that was reasonable in the relatively conductive areas.

The effect of a conductive half‐space on the transient electromagnetic response of a three‐dimensional body

Geophysics ◽  
1985 ◽  
Vol 50 (7) ◽  
pp. 1144-1162 ◽  
Author(s):  
William A. SanFilipo ◽  
Perry A. Eaton ◽  
Gerald W. Hohmann
Keyword(s):  
Half Space ◽  
Free Space ◽  
Eddy Currents ◽  
Three Dimensional ◽  
Vertical Component ◽  
The Body ◽  
Electromagnetic Response ◽  
Loop Current ◽  
Transient Electromagnetic ◽  
Space Response

The transient electromagnetic (TEM) response of a three‐dimensional (3-D) prism in a conductive half‐space is not always approximated well by three‐dimensional free‐space or two‐dimensional (2-D) conductive host models. The 3-D conductive host model is characterized by a complex interaction between inductive and current channeling effects. We numerically computed 3-D TEM responses using a time‐domain integral‐equation solution. Models consist of a vertical or horizontal prismatic conductor in conductive half‐space, energized by a rapid linear turn‐off of current in a rectangular loop. Current channeling, characterized by currents that flow through the body, is produced by charges which accumulate on the surface of the 3-D body and results in response profiles that can be much different in amplitude and shape than the corresponding response for the same body in free space, even after subtracting the half‐space response. Responses characterized by inductive (vortex) currents circulating within the body are similar to the response of the body in free space after subtracting the half‐space contribution. The difference between responses dominated by either channeled or vortex currents is subtle for vertical bodies but dramatic for horizontal bodies. Changing the conductivity of the host effects the relative importance of current channeling, the velocity and rate of decay of the primary (half‐space) electric field, and the build‐up of eddy currents in the body. As host conductivity increases, current channeling enhances the amplitude of the response of a vertical body and broadens the anomaly along the profile. For a horizontal body the shape of the anomaly is distorted from the free‐space anomaly by current channeling and is highly sensitive to the resistivity of the host. In the latter case, a 2-D response is similar to the 3-D response only if current channeling effects dominate over inductive effects. For models that are not greatly elongated, TEM responses are more sensitive to the conductivity of the body than galvanic (dc) responses, which saturate at a moderate resistivity contrast. Multicomponent data are preferable to vertical component data because in some cases the presence and location of the target are more easily resolved in the horizontal response and because the horizontal half‐space response decays more quickly than does the corresponding vertical response.

To: “The electromagnetic response of thin sheets buried in a uniformly conducting half‐space,” which appeared in the January 1987 issue of GEOPHYSICS, p. 108–117

Geophysics ◽  
1987 ◽  
Vol 52 (10) ◽  
pp. 1455-1455
Keyword(s):  
Half Space ◽  
Electromagnetic Response ◽  
Thin Sheets ◽  
Left Hand

The term “4πσ” should be deleted from the left‐hand side of equations (16), (A-13), and (A-14).

On thin‐layer telluric modeling of magnetotelluric responses

Geophysics ◽  
1990 ◽  
Vol 55 (3) ◽  
pp. 372-375 ◽  
Author(s):  
Philip E. Wannamaker
Keyword(s):  
Thin Layer ◽  
Current Flow ◽  
Thin Sheet ◽  
Three Dimensional ◽  
Computational Effort ◽  
Response Functions ◽  
Plan View ◽  
Long Period ◽  
Period Limit ◽  
Zero Frequency

Modeling of three‐dimensional (3-D) thin‐sheet telluric anomalies has been a popular means of estimating the distortions of magnetotelluric (MT) response functions in the vicinity of an upper crustal resistivity inhomogeneity (Kaikkonen, 1986) because structures with an arbitrary 3-D shape in plan view can be simulated with modest computational effort. In the class of thin‐layer problems of this note, the sheet structure overlies an infinitely resistive basement; and anomalous fields are computed in the long‐period or zero‐frequency (dc) limit (e.g., Hermance, 1982). Under the assumption of no vertical current flow into the basement, this 3-D problem reduces to a two‐dimensional (2-D) dc solution across the sheet. Since only the long‐period limit is considered, however, the conclusions that can be drawn about the effects of general 3-D structures are restricted. The purpose of this note is to clarify restrictions on the use of 2-D MT interpretations in 3-D areas based on just thin‐sheet telluric modeling.

Thin-sheet EM modelling of the Tasman Sea

1989 ◽  
Vol 20 (2) ◽  
pp. 177 ◽  
Author(s):  
G.S. Heinson ◽  
F.E.M. Lilley
Keyword(s):  
Large Scale ◽  
Salt Water ◽  
Thin Sheet ◽  
Three Dimensional ◽  
One Dimensional ◽  
The Earth ◽  
Tasman Sea ◽  
Modelling Techniques ◽  
Tectonic Features ◽  
The University

The Tasman Project of Seafloor Magnetotelluric Exploration (TPSME) took place between December 1983 and April 1984 (Filloux et al., 1985; Ferguson et al., 1985; Lilley etal., 1989). Seven magnetotelluric and two (additional) magnetometer sites spanned a range of tectonic features across the Tasman Sea. Initial analysis by Ferguson (1988) indicated large-scale three-dimensional induction effects to be present in the data. It was concluded that the most probable causes were the continental margin effect and changes in bathymetry.In the present paper, a method is presented of modelling the salt water of the Tasman Sea and adjoining oceans as a thin sheet of variable lateral conductance, which overlies a series of uniform layers representing the solid Earth. The theory and a suitable computer algorithm were developed in a group led by J. T. Weaver at the University of Victoria, B.C., Canada. Many of the features present in the TPSME data are reproduced by this method, and with a greater understanding of induction processes in the ocean which is thus obtained, it is possible to remove three-dimensional effects from observed data. The TPSME data are then solely a measure of the response of the Earth directly beneath the observing sites, and one-dimensional modelling techniques may be used to determine the conductivity structures.

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