Electromagnetic induction of a three-dimensional conductivity inhomogeneity in a two-layer earth

Summary The results of numerical computations of the electromagnetic field induced in a two-layer model of the Earth with a three-dimensional inhomogeneity (a block) in the subsurface layer are given. Several recommendations are given which have enabled the solution of a complicated system of integral equations and the computation of the field at the Earth's surface in an effective way. The analysis of the obtained solution has proved that, in an anomalous electromagnetic field, the field of the horizontal electric dipole, oriented in the direction of the exciting field, is predominant. A number of practically usable diagrams and approximative formulae is given.     

Electromagnetic induction in a half-space with a cylindrical inhomogeneity

Summary The problem of electromagnetic induction in a half-space with a cylindrical inhomogeneity is treated. Solutions for TE and TM polarization of the exciting electromagnetic field are given, which can be used for computing sounding and profiling curves. The anisotropy of the surface impedance is pointed out, as well as a whole series of other interesting properties of the magnetotelluric field in this model; some of them are also demonstrated on the computed theoretical curves.     

Electromagnetic induction in a spherical model of the earth with a real distribution of near-surface conductivity

The current functions calculated for a spherical Earth model with real near-surface conductivity distribution are presented. The system is excited by a uniform external field of three different polarizations.     

Electromagnetic induction in a spherical earth with a circular bulge in the upper mantle

Summary Results of computing the anomalies of the variable magnetic field, generated by a harmonically variable field of the H_1,0-type in the model of a spherical Earth with an expressive bulge in the well-conducting part of the mantle, are presented. It was found that not only the radial, but also the tangential component of the magnetic field is disturbed above the bulge. The largest amplitudes of these changes can be observed over the area of the largest slope of the conductivity boundary if the exciting magnetic field is perpendicular to the surface of the interface.     

Electromagnetic induction in the earth due to stationary and moving sources

A new approach to the theory of electromagnetic induction is developed that is applicable to moving as well as stationary sources. The source field is considered to be a standing wave generated by two waves travelling in opposite directions along the surface of the earth. For a stationary source the incident waves have velocities of the same magnitude, however for a moving source the velocities of the two incident waves are respectively increased and decreased by the velocity of the source. Electromagnetic induction in the earth is then considered as refraction of these waves and gives, for both stationary and moving sources, the magnetotelluric relation: $$\frac{{ - E_y }}{{H_x }} = \left( {\frac{{i\omega \mu }}{\sigma }} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {1 - i\frac{{v^2 }}{{\omega \mu \sigma }}} \right)^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $$ where ν is the wavenumber of the source, μ is the permeability (4π·10^?7) and σ is the conductivity of the earth. ω is the angular frequency of the variation observed on the earth. For a stationary source the observed frequency is the same as the source frequency, however the effect of moving a time-varying source is to make the observed frequency different from the frequency of the source. Failure to recognise this in previous studies led to some erroneous conclusions. This study shows that a moving source isnot “electromagnetically broader” than a stationary source as had been suggested.     

Electromagnetic induction in the oceans and inferences on the constitution of the earth

This review concentrates on the uncertainties surrounding interpretation of sea floor impedance measurements. Oceanic motionally induced signals prove to be noise generators which limit the low frequency range of usable signals. At high frequencies the screening by a thick ocean and by the sediments and rocks of layer two present insuperable barriers to detection of poorly conducting rocks in the depth range 2 to 30 km below the sea bottom by usual methods. The conductivity of this layer is important for the interpretation of all ocean impedance measurements because it determines the width of a boundary zone at the continental margins of the ocean. If the conductivity is as low as 10^–5 S/m the bounding zone begins to fill the whole ocean. It is suggested that use of an active, manmade EM source can provide signals at the sea bottom capable of resolving the uncertainty.     

Electrical conductivity anomalies in the earth

Anomalies of short-period geomagnetic variations have been found in various regions over the world. It is known that such anomalies arise from electromagnetic induction within an electrical conductivity anomaly or from local perturbation of induced electric currents by a conductivity anomaly. In order to investigate a regional electric state in the Earth, conductivity anomaly (CA) studies based on anomalous behaviors of geomagnetic variations have been extensively undertaken, as well as studies based on magnetotelluries in which induced currents are directly used.Some of the geomagnetic variation anomalies, however, turned out to be caused by surface conductors, such as sea water and sediments. Anomalies of this sort have been intensively studied and classified into coast, island, peninsula, and strait effects in the case of sea effects. Three-dimensional conduction or channelling of induced electric currents is sometimes observed in the cases of sediments and some crustal conductivity anomalies. However, anomalies of such surface origins often provide some information of the underground conductivity structure.Electrical conductivity anomalies can be classified into two types: anomalies originating in the crust and in the upper mantle. Many of crustal anomalies are well correlated with metamorphic belts, fracture zones, and hydrated layers, and magnetic and gravity anomalies are also often found over the conductivity anomalies. Most of mantle anomalies have been interpreted mainly in terms of high temperature and partial melting, since conductivity anomalies coincide well with anomalies in heat flow and seismic wave velocities.     

Global electrical conductivity of the earth

The Banks (1969, 1972) and Parker (1970) models of the electrical conductivity distribution are critically reviewed along with classical models by Chapman (1919), Lahiri and Price (1939), Rikitake (1950a, b, c) and others. The modern models do not seem to account for the geomagnetic variations having a continuum spectrum and S_q at the same time. A large difference in response between the 1-day and 0.5-day period components of S_q is suspected to be caused by a resonance-like induction in the superficial layer of the earth. Dufficulties in determining the conductivity of the earth's top layer are also emphasized.An overall distribution of conductivity within the earth which seems to be the most reliable at present, is drawn mostly on the basis of Banks' model.     

The calculation of perturbation and induction arrows for a three-dimensional conductivity model and dipole source fields

A numerical method is used to calculate the electromagnetic fields associated with a three-dimensional conductivity anomaly. The source field is due to horizontal magnetic dipoles placed at two different positions with respect to the conductivity anomaly. The transfer functions and related perturbation and induction arrows associated with the fields are calculated and compared with the arrows obtained from a uniform source calculation. The results show the source effect on the induction arrows and indicate that the perturbation arrows provide a method of outlining the spatial extent of the anomaly. The transfer function calculations are made for both exact and approximate normal fields. In the transfer function calculation the anomalous fields are correlated with a normal field as suggested by Schmucker (1970) and Cochrane and Hyndman (1970).     

Electromagnetic induction in the World Ocean

The general state of global investigations of electromagnetic induction in the oceans and also some new results obtained in the past few years in the U.S.S.R. are considered.     

Detection of crustal inhomogeneity in the Nojima Fault zone using earth current noise

Abstract A resistivity survey method using artificial telluric noise was examined and applied to a field of a fault zone. The electric earth current was measured at 50 sites in the Nojima Fault zone, which is in the northwestern part of Awaji Island, southwestern Japan. The dominant component of the observed electric field is supposed to be leakage currents from DC electric railways running outside the island. Amplitude and polarization of the stray current were systematically investigated and were revealed to represent the subsurface electrical structure of the study area. Some features on the fault zone's electrical structure have been pointed out, including: (i) an electrical boundary that corresponds to a geological one between granite (resistive) and sediments (conductive); and (ii) a low resistivity spot on the surface rupture of the earthquake fault. The structure estimated in the present study is both qualitatively and quantitatively consistent with previous resistivity surveys done using other methods pursued in the same area. It shows the validity of the 'stray current method' as one that is easy and uses low-cost resistivity exploration tools in a region where the effect of artificial noise caused mainly by leakage currents from electrical railways cannot be ignored.     

Properties of the lithosphere-asthenosphere system in Europe with a view toward earth conductivity

Over the past 20 years the study ofP- andS-wave velocities in the upper mantle of the Mediterranean area and continental Europe has been the subject of intensive research work. We present a summary of results based on the inversion of available surface-wave dispersion data andP-wave trave time observations. For areas characterized by different tectonic settings and very large lateral variations, a discussion is made about structural models based on seismological, geothermal and electrical conductivity data.     

Constraints to the three-dimensional non-hydrostatic density distribution in the earth

Summary The paper is concerned with the properties of a density distribution within the Earth. A system of density parameter constraints involving Stokes' coefficients of the gravity field and the parameters describing the Earth's figure is derived. A density model, whose parameters fit these constraints, accounts for the fine structure of the gravity field and Earth's figure. Additional condition imposed on the average spherical density model are derived; they guarantee that the average spherical model is compatible with the 3-D density model.

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Matrix approach to the solution of electromagnetic induction in a spherically layered earth

Summary Matrix formulae for the intensities of the M- and E-fields have been derived. They have been applied to express the apparent resistivity, the transfer function, as well as the frequency equation determining the frequencies of free motion of the M- and E-waves. A fast algorithm for computing the transfer function and the apparent resistivity has been suggested.

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Electromagnetic transient response of a small wire loop buried in a homogeneous conducting earth

Summary The analysis extends previously obtained results for the transient magnetic fields of small loops in the presence of a homogeneous conducting half-space. Here, the secondary scattering of pulses by a buried target loop is examined for the case where both the source and receiver loops are located at the surface. While the response of the buried or target loop is orders of magnitude below the primary response, there is a significant difference in the respective transient waveforms. Thus, the results have possible application to mine rescue using a passive detection technique.     

Integral equation of relationship on the apparent conductivity and true conductivity in induction logging

This paper investigates the relation between the induced electromotive force measured by induction logging tool and the apparent conductivity, and the relation between the apparent conductivity and the formation true conductivity. Assuming the conductivity in Green’s function to be the function of the field point coordinate, the apparent conductivity expression of electric-field intensity is derived using Green’s formula, and the integral equation has been established representing the relationship of the apparent conductivity with the true conductivity under this condition. The integral equation is analyzed and then leads to the conclusion that the equivalent conductivity is the apparent conductivity and the values of the apparent conductivity function contain the true conductivity, and the method derived the true conductivity from the apparent conductivity around the well axis is put forward. The validity of the approach given in this paper is verified through numerical calculation. On the basis of above means, the transmitter coil produces an electric-field distribution in formation at every point where the induction logging tool moves along a wellbore, and a number of the receiving coils obtain an apparent conductivity distribution; this is what induction electric-field logging is.