Propagation of Electromagnetic Waves into Anisotropic Media From an External Point-Dipole Source

Radio Science ◽  
1967 ◽  
Vol 2 (6) ◽  
pp. 607-618 ◽  
Author(s):  
Gary H. Price
Keyword(s):  
Electromagnetic Waves ◽  
Anisotropic Media ◽  
Dipole Source ◽  
Point Dipole ◽  
External Point

Euler’s differential equation and the identification of the magnetic point‐pole and point‐dipole sources

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1549-1553 ◽  
Author(s):  
J. O. Barongo
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Magnetic Anomalies ◽  
Field Vector ◽  
Magnetic Data ◽  
Dipole Source ◽  
Point Dipole ◽  
Main Subject ◽  
Depth Extent ◽  
Dipole Sources

The concept of point‐pole and point‐dipole in interpretation of magnetic data is often employed in the analysis of magnetic anomalies (or their derivatives) caused by geologic bodies whose geometric shapes approach those of (1) narrow prisms of infinite depth extent aligned, more or less, in the direction of the inducing earth’s magnetic field, and (2) spheres, respectively. The two geologic bodies are assumed to be magnetically polarized in the direction of the Earth’s total magnetic field vector (Figure 1). One problem that perhaps is not realized when interpretations are carried out on such anomalies, especially in regions of high magnetic latitudes (45–90 degrees), is that of being unable to differentiate an anomaly due to a point‐pole from that due to a point‐dipole source. The two anomalies look more or less alike at those latitudes (Figure 2). Hood (1971) presented a graphical procedure of determining depth to the top/center of the point pole/dipole in which he assumed prior knowledge of the anomaly type. While it is essential and mandatory to make an assumption such as this, it is very important to go a step further and carry out a test on the anomaly to check whether the assumption made is correct. The procedure to do this is the main subject of this note. I start off by first using some method that does not involve Euler’s differential equation to determine depth to the top/center of the suspected causative body. Then I employ the determined depth to identify the causative body from the graphical diagram of Hood (1971, Figure 26).

Ground‐penetrating radar velocity tomography in heterogeneous and anisotropic media

Geophysics ◽  
1997 ◽  
Vol 62 (6) ◽  
pp. 1758-1773 ◽  
Author(s):  
Don W. Vasco ◽  
John E. Peterson ◽  
Ki Ha Lee
Keyword(s):  
Ground Penetrating Radar ◽  
Electromagnetic Waves ◽  
Numerical Technique ◽  
Anisotropic Media ◽  
Perturbation Approach ◽  
Low Velocity ◽  
Weak Anisotropy ◽  
Geological Features ◽  
Velocity Anomalies ◽  
Ground Penetrating

A ray series solution for Maxwell's equations provides an efficient numerical technique for calculating wavefronts and raypaths associated with electromagnetic waves in anisotropic media. Using this methodology and assuming weak anisotropy, we show that a perturbation of the anisotropic structure may be related linearly to a variation in the traveltime of an electromagnetic wave. Thus, it is possible to infer lateral variations in the dielectric permittivity and magnetic permeability matrices. The perturbation approach is used to analyze a series of crosswell ground‐penetrating radar surveys conducted at the Idaho National Engineering Laboratory. Several important geological features are imaged, including a rubble zone at the interface between two basalt flows. Linear low‐velocity anomalies are imaged clearly and are continuous across well pairs.

Method for depth estimation on aeromagnetic vertical gradient anomalies

Geophysics ◽  
1985 ◽  
Vol 50 (6) ◽  
pp. 963-968 ◽  
Author(s):  
J. O. Barongo
Keyword(s):  
Geometric Model ◽  
Depth Estimation ◽  
Vertical Gradient ◽  
Dipole Source ◽  
Point Dipole ◽  
Horizontal Projection ◽  
Lake Region ◽  
Dip Angle ◽  
Pole Point ◽  
Study Application

The straight‐slope technique introduced some years ago by Vacquier et al. (1951) is employed to develop simple empirical procedures that can be used to determine depth to the top/center of anomalous sources on measured aeromagnetic vertical gradient profiles. Five geologic bodies/structures in the form of their magnetic/geometric model equivalents, namely, point pole, point dipole, finite dipole, dipping dike, and dipping contact are considered. From analysis of the normalized theoretical curves due to those models it is observed that the horizontal projection of the straight part of the steepest sections of each curve is insensitive to changes in the inclination of the Earth’s magnetic field and also to the dip angle of dipping models. Further analysis of the curves using this observation leads to the conclusion that, when dealing with the interpretation of observed vertical gradient profiles, the length of the horizontal projection on a given profile must be doubled to obtain depth to the point‐pole, point‐dipole, or finite‐dipole source. For a geologic contact and a wide but shallow (i.e., the width more than twice the depth) dike, the length of the projection gives the depth for either source. However, a thin but deeply buried (i.e., the width less than twice the depth) dike, requires use of characteristic curves such as those developed in this study. Application of the procedures to observed vertical gradient results from the White Lake region of Ontario, Canada, has proven quite successful.

Exact solutions for vertically polarized electromaǵnetic waves in a horizontally stratified maǵneto-plasma

1970 ◽  
Vol 67 (2) ◽  
pp. 491-501 ◽  
Author(s):  
B. S. Westcott
Keyword(s):  
Magnetic Field ◽  
Refractive Index ◽  
Wave Propagation ◽  
Exact Solutions ◽  
Radio Wave ◽  
Static Magnetic Field ◽  
Electromagnetic Waves ◽  
Anisotropic Media ◽  
Radio Wave Propagation ◽  
Isotropic Media

AbstractIn a previous paper (11) refractive index profiles capable of yielding exact solutions for vertically polarized electromagnetic waves propagating in horizontally stratified isotropic media were derived systematically. The present work extends the method to deal with anisotropic media in which propagation is transverse to a horizontally applied static magnetic field. The relevance to ELF radio wave propagation in the terrestrial ionosphere is noted.

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