ENHANCEMENT OF ELECTROMAGNETIC ANOMALIES BY A CONDUCTING OVERBURDEN II *

The influence of a partially conducting overburden/host rock on the electromagnetic response of a horizontal, tabular conducting ore body, investigated with the aid of quantitative scale model experiments, was discussed in an earlier paper (Gaur, Verma and Gupta 1971), which will be referred to as I. This paper presents the results of more comprehensive experiments subsequently carried out to study the combined effect of various geological parameters, namely: the dip and depth of burial of the ore body, its electrical conductivity and that of the zone surrounding it. These results obtained for four different transmitter-receiver configurations confirm the general enhancement of response in varying degrees, brought about by a conducting overburden. However, the transformation of the shapes of the anomaly profiles with increasing overburden conductivity is observed to depend on the dip of the ore body, being more drastic for gently dipping ones. Variations in the inphase and quadrature components as well as in the phase of the anomaly have been studied for varying depths of burial of the ore body and for a number of values of the solution conductivity. Anomaly index diagrams have been constructed with a view to predicting possible values of the geological parameters from a knowledge of the anomaly components. It is felt that the notable overburden effects are caused by a drastic redistribution and concentration of currents, mostly in a narrow loop at the top of the ore body, brought about by its galvanic contact with an extended medium of relatively poorer conductivity.     

TRANSIENT ELECTROMAGNETIC RESPONSE OF A CONDUCTING SPHERE EXCITED BY DIFFERENT TYPES OF INPUT PULSES*

A technique utilizing the convolution theorem is developed to obtain the time-domain electromagnetic response for a number of input pulses from the given step-function response. For illustration an idealized model of a homogeneously conducting non-permeable sphere placed in a uniform field is considered. The nature of the responses due to different types of pulses and their usefulness in estimating the constitution parameter of the sphere are discussed. To show the applicability of the suggested technique to generalized systems, calculations for a conducting permeable sphere are presented in the appendix.     

CONDUCTING SPHERE IN ELECTROMAGNETIC INPUT FIELD*

A frequency-domain analysis is outlined for a conducting sphere in a uniform Input field: inequispaced alternating half-sine wave pulses. The Barringer Input air-borne electromagnetic exploration system uses such source fields. Theoretical profiles of Hρ(t), the horizontal magnetic component over the sphere from different elevations and for various conductivity and geometrical factors are presented. Based on these results some useful features such as penetration and detectibility are discussed.     

导电率随时间变化的导电球的电磁响应问题

本文采用非齐次麦克斯韦方程组,给出了导电率随时间变化时均匀的和非均匀的导电球,在均匀的和非均匀的外激励场的作用下的电磁响应问题的解析解。并简单讨论了这类电磁响应问题在地球物理学中的可能应用。     

Quasi-stationary electromagnetic response of covered permeable conductors to some pulses of spatially uniform magnetic field

Summary The quasi-stationary electromagnetic response of permeable conductors surrounded by conducting halo and excited by a uniform magnetic field having a step function time dependence has been obtained theoretically for both spherical and cylindrical conductors. For the magnetic conductors the results give the long period limit of the response and define a critical time complementary to critical frequency (Ward [1]²)) which may be used to estimate the magnetic content. Further utilizing the principle of superposition the responses to ramp, half-sine, saw tooth and triangular pulse excitations are also given.National Geophysical Research Institute, Hyderabad-7, (A.P.), India. NGRI Contribution No. 72-363.     

The response of a horizontal conducting cylinder embedded in a uniform earth for uniform and line current sources

The response of a horizontal conducting cylinder embedded in a uniform conducting earth is studied using mathematical models of uniform and line current source excitation for the period range 10 to 10⁴ s. The line current source is located at heights ranging from 100–750 km above the surface of the earth. From the calculated results, it is shown that for periods greater than 10³ s the ratioE _x /H _y at the surface of the earth for localized fields, such as the auroral and equatorial electrojet normally situated at heights of about 100 km, is considerably different from that for a uniform source. The results presented also show that the magneto-telluric method of geophysical prospecting for ore bodies in regions of the electrojet may not be very practicable for periods exceeding 10³ s.     

SCALE MODEL ELECTROMAGNETIC RESPONSE TO INLINE AND BROADSIDE SYSTEMS AT SKEW TRAVERSES OF A DIPPING HALF PLANE EMBEDDED IN A CONDUCTING HOST ROCK*

Laboratory scale model experiments have been performed to obtain the electromagnetic response of a finitely conducting half plane embedded in resistive/conductive surrounding and excited by an oscillating magnetic dipole. Inphase and quadrature profiles are presented for two horizontal coplanar transmitter-receiver systems (inline and broadside) for normal and skew traverses and for different dips of the conductor. It is observed that the broadside system is more diagnostic in delineating the strike and dip of the conductor and is more sensitive to the conducting host rock. The broadside profile over a vertical or dipping half plane is characterized, when traversing perpendicular to strike, by two positive peaks flanking a zero response when the coils are over the top edge of the conductor. For skew traverses a negative peak replaces the zero response. An increasing asymmetry in the anomalies is caused by changing the dip of the conductor from the vertical in both the systems, but it is more pronounced for the broadside system. The quadrature response in the broadside system changes in a characteristic way when the target is surrounded by a conducting host rock. The comparative results of the two systems may, therefore, be useful in the induction prospecting for ore deposits approximated by a half plane, especially in delineating the strike, dip, and effect of conductive host rock.     

THE TRANSIENT ELECTROMAGNETIC RESPONSE OF A POLARIZABLE SPHERE IN A CONDUCTING HALF SPACE1

A polarizable sphere embedded in a conducting half-space can give rise to negative voltage transients in a coincident-loop time-domain electromagnetic system. Such transients have been observed in field situations. Our results are obtained from a model in which the contributions of the host rock, the currents in the sphere, and the interaction between the sphere and the host rock are separated and superposed. This model uses approximations to the integral equation solutions rather than finite-element or finite-difference approximations, and so allows very rapid computation. The theoretical demonstration suggests that interpretation of the negative voltage transients as a polarization response is valid, but more detailed interpretation of polarization properties may not be possible, because the superposition of the polarization response on the normal response depends strongly on the position of the target.     

TRANSIENT ELECTROMAGNETIC RESPONSE OF A SPHERE IN A LAYERED MEDIUM*

The Galerkin method of solving integral equations is well suited to the solution of the integral equations describing the transient response of a sphere embedded in a layered medium, which is excited by a large co-axial loop. The transient response is calculated by transforming the steady state solutions obtained in the frequency domain. The analysis shows that the scattering matrix is extremely diagonally dominant and the maximum number of modes required to obtain convergence does not rapidly increase with frequency. The number of modes required is about eight. This type of scattering matrix can be taken to be an expression of the principle of elementary superposition. This principle is reflected in the decay curves. These show that the early part of the decay curves asymptotically approach the decay curves to be expected for a layered structure without the sphere. The slope of the latter stages of the decay curve gives a decay constant that is the same as was obtained for spheres in free space excited by planar or dipolar sources. The point of departure in time of these curves from the layered ground curves is delayed either by placing the sphere at a greater depth or by placing a more conductive overburden above the sphere.     

THE INDUCTIVE RESPONSE OF A HORIZONTAL CONDUCTING CYLINDER BURIED IN A UNIFORM EARTH FOR A UNIFORM INDUCING FIELD*

The inductive response of a conducting horizontal cylinder embedded in a uniform earth is studied using numerical results obtained for an analytical solution for the problem of a conducting cylinder buried in a homogeneous earth for the case of a uniform inducing field. A check of the validity of the numerical results is made by a comparison with analogue model measurements for a number of cases. Numerical results for a range of cylinder radii (a = 1–10 km), depths of burial (d= 0–4 km), conductivity contrasts (σ₂= 10^?2-10 Sm^?1), and source frequencies (f= 10^?1-10^?4 Hz) of interest in the interpretation of magnetotelluric field measurements are presented. The results indicate that for a uniform inducing field the conductivity and depth of burial of a horizontal cylindrical inhomogeneity are best determined through a measurement of the amplitudes H_y, H_z and E_x and the phases φ_y and Ψ_x.     

MATHEMATICAL MODELS OF CONDUCTING ORE BODIES FOR DIRECT CURRENT ELECTRICAL PROSPECTING *

The authors generalize a method expounded in a previous paper (1971, Geoph. Prosp. 18, 786-799) to the case of a local conductivity σ(M) of the infinite medium satisfying the relation where the R_i's are the distances from the point M to n fixed points S_i (i= 1,. n), k is a positive real constant and C_i, C_ii are constants ensuring the condition α > O. The sub-surface conductivity distributions (half-spaces) complying with (1) provide a wide variety of conducting structures, which can fit quite successfully the rather complicated distributions of conductivity occurring in natural ore bodies. An exact algebraic calculation of the apparent resistivity for these grounds, valid for any dc electrical prospecting devices (Wenner, Schlumberger, dipole, etc.) leads to a set of simultaneous linear equations, with a matrix which is invariant with respect to the position of the quadrupole being used. This greatly simplifies the numerical computation. We also present some examples of cross sections for the real and apparent resistivity obtained by this method.     

TRANSIENT EM RESPONSE OF A LARGE LOOP ON A LAYERED GROUND *

The voltage induced in a horizontal loop on a layered ground has been calculated for the case where the loop is excited by a step current and measurements are made during the off-cycle. The expressions derived for a uniform ground show that for large time t the induced voltage E(t) is approximately given by E(t)?— (Ibαμ/20t) (σμ²/t)^3/2 where σ is the conductivity of the ground, μ the permeability, b the loop radius, and I the amplitude of the current step. For small times the corresponding result is E(t)?—Ibμ/2t. When the ground is composed of a number of layers a numerical procedure for calculating the induced voltage is described. The calculated responses of various multilayered structures show that at short times the induced voltage is asymptotic to that produced in the case of a uniform ground of conductivity equal to the top layer. Interference effects in the top layer can lead to anomalous decay curves which may result in the underestimation of the conductivity of a buried layer.     

Scattering ofP andS waves by a spherically symmetric inclusion

Scattering of an arbitrary elastic wave incident upon a spherically symmetric inclusion is considered and solutions are developed in terms of the spherical vector system of Petrashen, which produces results in terms of displacements rather than displacement potentials and in a form suitable for accurate numerical computations. Analytical expressions for canonical scattering coefficients are obtained for both the cases of incidentP waves and incidentS waves. Calculations of energy flux in the scattered waves lead to elastic optical theorems for bothP andS waves, which relate the scattering cross sections to the amplitude of the scattered fields in the forward direction. The properties of the solutions for a homogeneous elastic sphere, a sphere filled by fluid, and a spherical cavity are illustrated with scattering cross sections that demonstrate important differences between these types of obstacles. A general result is that the frequency dependence of the scattering is defined by the wavelength of the scattered wave rather than the wavelength of the incident wave. This is consistent with the finding that the intensity of thePS scattering is generally much stronger than theSP scattering. When averaged over all scattering angles, the mean intensity of thePS converted waves is2V _p ² /V _s ⁴ times the mean intensity of theSP converted waves, and this ratio is independent of frequency. The exact solutions reduce to simple and easily used expressions in the case of the low frequency (Rayleigh) approximation and the low contrast (Rayleigh-Born) approximation. The case of energy absorbing inclusions can also be obtained by assigning complex values to the elastic parameters, which leads to the result that an increase in attenuation within the inclusion causes an increased scattering cross section with a marked preference for scatteredS waves. The complete generality of the results is demonstrated by showing waves scattered by the earth's core in the time domain, an example of high-frequency scattering that reveals a very complex relationship between geometrical arrivals and diffracted waves.     

Strong Potential Magnetic Field Influence on Slightly Differentially Rotating Spherical Shell

An electrically conducting viscous fluid-filled spherical shell is permeated by an axisymmetric strong potential magnetic field with large Elssaser number ² 1. We describe analytically the steady flow driven by a slightly faster rotation of the conducting inner boundary of the shell. The main flow is controlled by Ekman-Hartmann boundary layers with a small thickness /, where ² is the Ekman number. Asymptotics based on small ^–1 1 reveal the nature of a free shear layer O((/)^1/2) and a super-rotation that allows a part of the fluid to rotate faster than the inner sphere. The free shear is following an imposed field line that is tangent to the inner or outer sphere. Meridional flux is concentrated in the shear and boundary layers. Fluid tends to rotate with the inner sphere and to expel azimuthal magnetic field from an -region restricted by the free shear in the spherical shell. For an imposed axial uniform magnetic field, this -region is outside the cylinder tangent to the inner sphere and rotates with the outer sphere. Weak differential rotation O(/) is inside the cylinder, while almost all difference in rotation rates between spheres is accommodated in the thin O((/)^1/2) free shear. For an imposed dipole magnet, the region has a shape of a lobe touching the outer equator. Inside a super-rotation exists; this is the common case for such when the source of the imposed field is inside.     

The zero-line method of interpreting total field magnetic anomalies of spherical ore-bodies

Summary A method called the zero-line method for interpreting the total field magnetic anomalies of spherical bodies is described. The contour of zero-anomaly is controlled by a linear equation of the typeAx ² +By ² +Cxy +Dx +Ey +F = 0, where the coefficientsA toF are related to the depth of the sphere and the parameters relating to its position and magnetisation. From the coordinates (x, y) of the various points lying on the zero-contour, five normal equations for the above equation are set and solved for the various coefficients. The various parameters relating to the position and magnetisation of the sphere are then determined from these coefficients. It is expected that similar methods can be developed for interpreting magnetic anomalies of other three dimensional bodies also.     

Analogue model measurements for a horizontal magnetic dipole embedded within a conducting medium

The validity of an analogue model method employing a horizontal magnetic dipole source situated within a conducting layer for the cases of a poorly conducting model earth and a highly conducting model ocean is studied by comparing model magnetic field measurements with theoretical calculations. The model is then used to study one example for each case; the response of a conducting cylinder simulating an ore body embedded in the earth, and the response of a conducting wedge simulating a shelving ocean.     

Bifurcations in Spherical MHD Models

A series of numerical studies on the behaviour of magnetic fields and motions in a spherical body of an electrically conducting incompressible fluid have been carried out. The magnetic field was assumed to be maintained by a given electromotive force inside the body and to continue as a potential field in outer space. In view of the motion an external forcing was taken into account, and boundary conditions were considered which correspond to a stress-free surface. The stability of several steady states has been studied as well as the evolutions starting from unstable states. In this paper a configuration with a poloidal magnetic field and a differential rotation, both symmetric about the same axis, is considered. This configuration is stable only for sufficiently small Hartmann numbers but evolves, if disturbed, in the case of larger Hartmann numbers toward a non-axisymmetric state. In this case the well-known symmetrization effect of differential rotation in magnetic fields is destroyed.     

THE EFFECT OF A SUPERPARAMAGNETIC LAYER ON THE TRANSIENT ELECTROMAGNETIC RESPONSE OF A GROUND*

A thin superparamagnetic layer on the earth's surface greatly affects the transient electromagnetic response of a conducting ground. The effect of the layer is most evident for singleloop transient electromagnetic data where transient voltages decay as 1/t. Even when a separate transmitter and receiver are used, the effect of the superparamagnetic layer is still pronounced. In this case the effect of the 1/t term in the equation is much less. More dominant now is a 1/t² term. The effect of the superparamagnetism can readily be seen in the analytical expressions for the apparent resistivities. If the presence of the superparamagnetic layer is not recognized, then the apparent resistivities decrease with time rather than approach the true value of the host rock.     

On dynamo action in the high-conductivity limit

Abstract

This paper builds on a speculation by Moffatt (1979) on an apparent conflict between two results of dynamo theory in the high conductivity limit. Firstly, the finding by Bondi and Gold (1950) on the boundedness of the magnetic dipole moment of a perfectly conducting fluid body is, for a sphere, extended to all magnetic multipole moments. Secondly, a refined version is considered of the simple spherical mean-field dynamo model proposed by Krause and Steenbeck (1967). Some constraints on the mean electromotive force near the boundary of the conducting body are taken into account, which have not been recognized up to now. In the framework of the second order correlation approximation it is shown that it is just these constraints that ensure the boundedness of the magnetic multipole moments in the high conductivity limit. Thus the apparent conflict is resolved. In this context another possible source of error in mean-field dynamo models is pointed out. The present theory also adds insight into dynamo process in cosmical objects, in a way that is briefly discussed.     

Body waveform inversion for the source process of the February 3, 1996 Lijiang, Yunnan earthquake

The source process of February 3, 1996 Lijiang earthquake in Yunnan was studied by body waveform inversion using teleseismic data from IRIS. Two normal double-couple subevents with different strikes were obtained. The difference of the onset time between these two subevents, which are 15 km apart in space, is 7 s. The total seismic moment is 3.81 × 10¹⁸ Nm (M _w=6.3). The total fault area S is about 720 km² from the aftershock data and the average dislocation is about ū=0.18 m. Considering both the result of inversion and tectonic environment around the source, the first rupture might result from the extension along the NNW directed Zhongdian-Yongsheng fault belt where an earthquake of M=6.4 occurred in 1966. Then, the second started along the NE directed the eastern foot of Snow Mountain fault where rupture seemed to be able to propagate more easily.