Comparison between moving and stationary transmitter systems in induction logging

In a general treatment of the theory of induction logging, an exact integral representation has been obtained for the mutual impedance between a vertical dipole transmitter and a coaxial dipole receiver in a three layered earth. Based on this representation, a computer model has been devised using the traditional Slingram system of induction logging and the comparatively new Turam system, ignoring borehole effects. The model results indicate that due to its much larger response, the Turam system is in general preferable to the Slingram in mineral and groundwater investigations where formation conductivity much less than 1 S/m is generally encountered. However, if the surrounding media are conductive (more than 0.1 S/m), the Turam system suffers from large amplitude attenuation and phase rotation of the primary field caused by the conductive surrounding, and is less useful than the Slingram system which does not so suffer, unless the target bed is shallow. Because it is a more complex function of system parameters than the corresponding Slingram log, a Turam log can be conveniently interpreted only by the modern inverse method using a fast algorithm for the forward solution and a high speed digital computer.     

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.     

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

Summary The calculation of the elements of Green's tensor function is presented for solving the problem of the electromagnetic induction by means of a vector integral equation. A two-layered Earth is considered as the medium, the surface layer including a three-dimensional conductivity inhomogeneity. Use is made of the boundary condition requiring the vertical component of the electric current to be zero at the Earth's surface which partly simplifies the theoretical computation. Long-period asymptotics of the individual complicated functions, occurring in Green's tensor function as well as in the tensor function required to calculate the components of the anomalous magnetic field at the surface of the halfspace, were effected. With the aid of these asymptotics one can obtain estimates of the functions occurring in the theoretical analysis of the problem.     

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 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 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 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.     

Analytical solutions to global and local problems of electromagnetic induction in the earth

This review of analytic solutions is divided into two parts. The first part reviews electromagnetic induction in radially symmetric distributions of conductivity, and is appropriate to the study of global problems. In the second part, local problems of a specific nature are considered, the model being a half-space conductor with at least one lateral discontinuity separating regions of different uniform conductivities. In some problems, an approximate surface-boundary condition is used, and it is shown that the accuracy of the solutions has yet to be determined satisfactorily.     

Buried moving sources in an elastic halfspace

Summary The surface displacements ofP andS V types of motion produced in an homogeneous isotropic elastic halfspace by line- and couple-sources moving after creation parallel to the free surface with arbitrary speeds are obtained approximately by the method of steepest descent.     

Temperature production in the continental crust due to radioactive heat sources

Summary The purpose of this paper is to present a method for computing the temperature distribution in the continental crust as a function of depth and time. Computed results indicate that the rise of the temperature due to the decay of long half-life radioactive elements K⁴⁰, U²³⁵, U²³⁸, and Th²³² will reach its maximum 90 m.y. after heat sources and temperature are redistributed in the upper part of the earth. This suggests that the lower part of the crust and upper mantle were periodically remelted before the present stage of the crust was reached. At the present time the decay of the radioactive elements U²³⁸ and Th²³² still significantly influences the crustal temperature. The present near-surface thermal gradient due to the radioactive heat sources alone may reach 20°C/km in a high radioactive heat source province.     

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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On the generation of capillary-gravity waves due to two-dimensional sources

Summary With the aid of the generalized function method, a study is made of the linearized theory of transient development of capillary-gravity waves in an inviscid, incompressible and homogeneous liquid of finite and infinite depth due to an arbitrary oscillating source situated at a finite depth below the undisturbed free surface of the liquid. The initial value problem is solved by using Laplace-Fourier transforms combined with asymptotic methods. The asymptotic solution is found to consist of the steady state and the transient components which are independently modified by surface tension. The latter decays more rapidly as timet due to the presence of surface tension than in the case where surface tension is neglected. It is predicted that the principal effect of surface tension is to increase both the phase and group velocity of the waves and make the energy more readily available among the rapidly travelling progressive surface waves. In addition to the effects of surface tension on the physical properties of the wave motions, our method of solution provides an interesting illustration of the applicability of generalized functions in water wave phenomena.     

Electromagnetic induction in geothermal fields and volcanic belts

This review covers electromagnetic studies in geothermal and volcanic regions presented in the literature since 1983. It has been arranged by geographical areas, emphasizing where possible the data gathering, the interpretation techniques and the results of each study. The main conclusions of this review are: In all the surveys, people are measuring the complete MT impedance tensor. However, in general, this information is not being used in the interpretation mainly because of the poor quality of the data. This unfortunate situation originates by the presence of strong noise in the surveyed area and generally, by the lack of use of the remote reference technique. Crews with equipment and techniques that can gather data of very good quality, generally perform very detailed interpretations using most of the gathered information. Other groups that collect noisy data oversimplify the interpretation by using only one mode or averaging the resistivity of both modes and interpreting the results using simplified 1-D interpretations. At the interpretation stage, most of the mid-crustal conductors identified are being associated to the presence of trapped water of magmatic origin. In general, magma chambers are not being detected, probably because either they are absent or because there is a lack or resolution of the electromagnetic methods to detect them.     

Attenuation of ground vibrations due to different technical sources

The attenuation of technically induced surface waves is studied theoretically and experimentally.In this paper, nineteen measurements of ground vibrations induced by eight different technical sources including road and rail traffic, vibratory and impulsive construction work or pile driving, explosions, hammer impulses and mass drops are described, and it is shown that the technically induced ground vibrations exhibit a power-law attenuation v～r-q where the exponents q are in the range of 0.5 to 2.0 and depend on the source types.Comparisons performed demonstrate that the measured exponents are considerably higher than theoretically expected.Some potential effects on ground vibration attenuation are theoretically analyzed.The most important effect is due to the material or scattering damping.Each frequency component is attenuated exponentially as exp(-kr), but for a broad-band excitation, the sum of the exponential laws also yields a power law but with a high exponent.Additional effects are discussed, for example the dispersion of the Rayleigh wave due to soil layering, which yields an additional exponent of 0.5 in cases of impulsive loading.     

Propagation of waves in a visco-elastic half-space due to internal sources

Summary The nature of waves and disturbances generated by a time-periodic concentrated force acting inside a visco-elastic half-space has been studied. Interpretations have been given to the various terms in the expressions for the displacement components.     

Stresses and displacements due to a stationary point source of heat in an elastic halfspace

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Formation of cracks due to moving source over a thick crust

Summary In this paper the problem of a point source of stress moving over the surface of a thick aelotropic plate resting of a rigid foundation has been considered. Following the method ofAleksandrov & Vorovich (1960) the stress componentsZ _x andZ _z have been expanded in series of ascending powers of 1/h when the source velocity is less than (c ₄₄/)^1/2. When the velocity exceeds (c ₄₄/)^1/2 it has been shown that two cracks are produced in different directions and their successive reflections at the upper and lower surface are also obtained.     

Electromagnetic induction in the San Juan Bay region of Vancouver Island

The response of the electric and magnetic field variations over the San Juan Bay region of Vancouver Island is studied using a scaled laboratory analogue model. The laboratory frequencies simulate periods of 10 and 100 s in the geophysical problem. The model results indicate that, for both E- and H-polarization of the source field, induced current in the ocean is deflected around Cape Flattery and channelled into the Juan de Fuca Strait. With increasing period, the proportion of current channelled into the Strait decreases sharply. Induced current in the strait is also funnelled into San Juan Bay, a finger-shaped bay ca. 4 km wide and 7.5 km long, for both polarizations of the source field. The effect of the Bay on the field response is confined to the local region, within approximately 6 km of the centre of the Bay. Good agreement between field station and analogue model H_z results was obtained for the San Juan Bay. The behaviour of the Parkinson arrow for these two stations is examined with the aid of the analogue model results.