https://www.clw.csiro.au/aclep/documents/McBratney%20et%20al.%202003.pdf

On digital soil mapping

Some developments in the mathematical analysis of resistivity well-logging measurements in anisotropic beds are presented. Treatment of the no-borehole case in which two thick, anisotropic beds meet at a plane interface for bedding planes parallel to the interface is extended to include arbitrary orientation of the bedding planes. Relations are derived for finding the potential distributions in the two media produced by a point current source in one of them. Numerically evaluated apparent-resistivity profiles across the boundary between two anisotropic beds are shown for a normal resistivity-logging device for various conditions of anisotropy and dip. For electrode devices using alternating current, solutions are derived in terms of the vector potential for the case of a borehole penetrating a thick anisotropic bed normal to the bedding planes and for the no-borehole case where the sonde axis is perpendicular to a sequence of beds with all bedding planes parallel to the bed boundaries. For induction-logging devices, the transmitter-coil sources of the electromagnetic (EM) field are treated as (alternating) magnetic dipoles. When the source- and receiver-coil axes both are oriented perpendicularly to the bedding planes, only the component of resistivity parallel to the bedding planes affects the responses. With the addition of coilsmore » oriented parallel to the bedding planes, it is theoreticallypossible to determine formation dip from the out-of-phase (reactive) voltages in the receiver coils. Analyses are outlined for a homogeneous medium, for a thin bed, and for borehole cases usually considered. Values of the horizontal and vertical conductivities (and coefficient of anisotropy) can, in principle, be derived from the measured values of the induction-logging conductivity signal and the out-of-phase signal from the formation. 21 figures, 4 tables.« less

Effects of formation anisotropy on resistivity‐logging measurements

Solutions to the problem of radiation of dipole antennas in the presence of a stratified anisotropic media are facilitated by decomposing a general wave field into transverse magnetic (TM) and transverse electric (TE) modes. Employing the propagation matrices, wave amplitudes in any region are related to those in any other regions. The reflection coefficients, which embed all the information about the geometrical configuration and the physical constituents of the medium, are obtained in closed form. In view of the general formulation, various special cases are discussed.

Electromagnetic fields due to dipole antennas over stratified anisotropic media.

SUMMARY

This paper presents a method for calculating the electromagnetic field from a dipole source in stratified media with general anisotropy. The formulation can be applied to geophysical applications such as ground-penetrating radar and marine controlled source electromagnetic (CSEM) methods. In stratified media, the propagation of fields can be considered in the frequency–wavenumber domain. The resulting set of ordinary differential equations consists of a field vector, a system matrix, and a source vector. In each piecewise homogeneous region, the system matrix is given by the material properties and the horizontal slownesses. The vertical slownesses are the eigenvalues of the system matrix. A diagonalization of the system matrix transforms the field vector into a mode-field that contains upgoing and downgoing field constituents. For system matrices that account for general anisotropy, it is shown how the electromagnetic field from any of the four basic dipole types can be calculated at any desired position in the stratified medium. It is furthermore shown how the reflection and transmission response from a stack can be calculated by a recursive scheme. Potential numerical instabilities due to using propagators are avoided by using this reflectivity method. Due to an energy-flux normalization of the eigenvector matrices, the reciprocity relations for reflection and transmission of electromagnetic fields in general anisotropic media can be derived. Several other useful relations between the reflection and transmission matrices are obtained as well. The propagator method is dependent on the ability to calculate eigenvalues and eigenvectors of the system matrix for all layers. In simple cases with isotropy or transversal isotropy in the direction of medium variation, the eigenvalue problem can be solved explicitly. These eigenvector matrices have useful properties, e.g. when processing data. The possibility to remove layers above or below the receiver layer follows from the decomposition of a field into upgoing and downgoing polarization modes. The propagator theory was implemented in order to model anisotropy in marine CSEM. A modelling study shows that responses are affected by horizontal, vertical, and dipping anisotropy in different manners. This suggests that when anisotropy is present at a survey site, careful planning and interpretation are required in order to correctly account for the responses.

/pdf/electromagnetic-fields-in-planarly-layered-anisotropic-media-54xoj95t38.pdf

Electromagnetic fields in planarly layered anisotropic media

This paper presents a tutorial review of electrical and electromagnetic(herein collectively called geoelectromagnetic) methods as applied in the search for natural resources. First, the paper discusses the technical problems and advances in geoelectromagnetic methods in the last decade. A scheme for integrating electrical and electromagnetic depth sounding data is suggested.Then, for natural resources exploration, it focuses on three themes: (1) understandinggeological models of resource targets, their physical properties, and the development of conceptual geoelectromagnetic exploration models, (2) overview of geoelectromagnetic case studies in resourceexploration, and (3) outstanding challenges in exploration. For brevity, model development is restricted to groundwater, geothermal and hydrocarbon resources, metallic ore-bodies (exemplified byvolcanogenic massive sulphides, porphyry coppers, and epithermal and Archaean greenstone belt gold deposits) and diamonds. In the treatment of resource exploration in this paper, the unifying themeis that geochemical processes of weathering and hydrothermal alteration form clayey products that may render natural resource targets directly or indirectly detectable by their resistivity characteristics.Since hydrated clays are an important feature of most resource types and are major causes of low resistivity anomalies in geoelectromagnetic exploration, they may be taken as providing detectable marker horizons or pathfinders and a basis for developing a consistent investigative approachfor natural resources. However, it is recognised that no single resource model or standard approach may be universally applicable. Natural resource systems are inherently 3D and require large numbers of depth soundings at high station densities to image adequately. Thus, developing methodsof increasing the productivity of data acquisition, the development of better 3D software tools and lowering costs are seen as the major challenges facing the use of geoelectromagnetic methods for naturalresource exploration.

https://link.springer.com/content/pdf/10.1023/a:1015052419222.pdf

Geoelectromagnetic exploration for natural resources: models, case studies and challenges

The electromagnetic fields of a low‐frequency horizontal electric dipole placed over a two‐layer earth have been derived. The overburden is considered to be transversely isotropic with respect to the conductivity. The unequal principal axis of the conductivity tensor is normal to the layers. The substratum is taken as isotropic. The vector potentials at the surface of the earth have been evaluated and expressed in such a way that the fields may be easily calculated. We have considered the special cases of a perfectly conducting, a perfectly insulating, and a substratum whose conductivity is very close to the longitudinal conductivity of the overburden. Asymptotic expressions for the fields have also been calculated. All the results are given in terms of known functions, and some numerical results have been included.

Electric Dipole Over AN Anisotropic and Inhomogeneous Earth

The problem of electromagnetic wave propagation from an oscillating magnetic dipole placed over a uniaxially anisotropic earth has been considered. Formal expressions for the vector potentials inside the earth have been derived. It has been shown that for a vertical magnetic dipole, the field components are identical to those in the case of an isotropic medium in which the conductivity is the “horizontal or longitudinal conductivity.” For a horizontal dipole, directed along the x axis, it has been shown that the vector potential inside the earth will have a y component as well as x and z components. Formal expressions for the vector potentials in air have been obtained for the case of a horizontal magnetic dipole. However when the conductivity of air is considered to be negligibly small, the field components are not affected by the anisotropy.

Electromagnetic fields of an oscillating magnetic dipole over an anisotropic earth

A detailed analysis has been made on the relative effectiveness of the four types of coil arrangements used in airborne electromagnetic surveying for the mapping of subsurface inhomogeneities. By comparing the theoretical responses for the four systems over known geologic sections, it has been established that the horizontal coplanar system is the most effective for detecting inhomogeneities in single‐frequency airborne surveys and produces the largest anomaly in multifrequency work. The next largest anomaly in both the cases is obtained in the vertical coplanar arrangement. The multilayer computer program used to derive the theoretical master curves for comparing the performance of the four systems is completely general except for our assumption of the quasi‐static conditions, which is justified in all geophysical induction problems. A study of the “hidden‐layer problem” to determine the best system and conditions for detection of a thin layer sandwiched between two thicker beds has been made with the he...

Comparison Of Airborne Em Coil Systems Placed Over A Multilayer Conducting Earth

Airborne electromagnetic mapping by wavetilt measurement is especially suitable for highly resistive strata like the permafrost terrains of northern Canada. A theoretical study has been made on the influence of the altitude of the aircraft and displacement currents on the measured wave tilt values over a range of frequency from VLF (very low frequency) to BCB (broadcast band). A computer modeling study has shown that the effects of displacement currents cannot be ignored over resistive ground if the frequency is greater than 100 kHz. The altitude effect is significant beyond 20 m for medium frequencies and resistive ground. The phase of the wavetilt is almost always more sensitive to these factors than the amplitude. When the top layer is thicker than three skin depths in that layer, the effects of lower layers on the wavetilt is negligible. It is also apparent that before attempting to interpret wavetilt data over a layered medium, one should carefully determine the nature of the source field. The result...

Ajit K. Sinha

Papers

Electric Dipole Over AN Anisotropic and Inhomogeneous Earth

Electromagnetic fields of an oscillating magnetic dipole over an anisotropic earth

Comparison Of Airborne Em Coil Systems Placed Over A Multilayer Conducting Earth

Influence of altitude and displacement currents on plane‐wave em fields

A study of topographic and misorientation effects in multifrequency electromagnetic soundings