THE TRANSIENT ELECTROMAGNETIC RESPONSE OF A CONDUCTING SPHERE IN AN IMPERFECTLY CONDUCTING HALF-SPACE*

The presence of a conducting environment about a spherical ore body must be considered when calculating the transient electromagnetic response of the ore body due to a step current flowing in a large circular loop at the earth's surface. Failure to do this can easily lead to errors in excess of 10% in numerical calculations. Moreover, there is only a limited time interval in which the response of the spherical conductor is easily seen. In a poorly conducting ground the resonance response of the sphere is the first to be excited. Later, however, the non-resonance or wave-type response is excited. These waves destructively interfere and finally the response of the sphere decays with time as t^?7/2. For a range of times and depths the best loop for detecting the sphere has about the same radius as the sphere.     

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。     

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.     

On the time-domain electromagnetic response of a conductive permeable sphere

The time-domain EM response of a conducting sphere has been subject of past studies with a particular goal of understanding the response of steel unexploded ordnance items. A change in formulas and parameter definition between authors has created inconsistency between published results and analytic formulas. Correction of formulas is required for further studies based on the conducting permeable sphere.     

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.     

The electrostatic force between a charged conducting sphere and a charged dielectric sphere in an arbitrarily oriented external electric field

Summary The electrostatic force between a charged conducting sphere and a charged dielectric sphere in a uniform, arbitrarily oriented external electric field is obtained and presented in terms of force coefficients which depend only on the relative geometry of the two spheres and the dielectric constants of the dielectric sphere and the medium. When the dielectric constant of the dielectric sphere is allowed to approach infinity, the resulting computed force agrees with that ofDavis (1964) for two conducting spheres, and when the external field and the charge on the dielectric sphere are set to zero, the resulting force agrees with that ofHall andBeard (1975) for a charged conducting sphere near an uncharged dielectric sphere.     

TIME DOMAIN ELECTROMAGNETIC RESPONSE OF A SHIELDED CONDUCTOR*

Velekin and Bulgakov (1967) in an interesting model experiment while studying the transient electromagnetic response of a conductive sphere placed below a thin conductive sheet found that at the earlier stages of the transience, the composite system response corresponded to the response due to the overlying sheet alone and at the later stages, it corresponded to that of the sphere alone. To examine whether such a separation of responses due to individual components can be analytically studied and applied to other source configurations, we have analyzed an idealized model consisting of two spherical shells. We find that in corroboration with the above results, the general nature of the curve consists of two humps representing the responses dominated by the outer shell and the inner shell respectively. In addition, however, we find that the two humps gradually disappear to yield a smooth decay curve for increasing values of the ratio σd₁b/σ₂d₂a (where σ₁, σ₂ are the conductivities, d₁, d₂ are the thicknesses of the outer and inner shells respectively, and b and a are their respective distances from the centre) and the effect of inner shell on the composite system response is considerably reduced.     

ON THE ELECTROMAGNETIC RESPONSE OF CONDUCTORS IN THE INDUCTIVE METHOD OF PROSPECTING (MODEL STUDIES)*

In the inductive method of prospecting, information on conductivity and size of conducting ore-bodies located in non-conducting host rocks, can be conveniently obtained by studying amplitude-frequency relation or amplitude-phase relation of their response with the help of suitable Master-curves. Experiments carried out in the laboratory on the scale-model method show these Master-curves to be different depending on the type of primary excitation and the shape of conductor. Cases of sphere, plate and disc in uniform field, field of line source and dipole field have been studied with an Amplitude-Phase Meter specially constructed in the laboratory for this purpose.     

ON THE ELECTROMAGNETIC RESPONSE OF CONDUCTORS IN THE INDUCTIVE METHOD OF PROSPECTING (MODEL STUDIES)*

In the inductive method of prospecting, information on conductivity and size of conducting ore-bodies located in non-conducting host rocks, can be conveniently obtained by studying amplitude-frequency relation or amplitude-phase relation of their response with the help of suitable Master-curves. Experiments carried out in the laboratory on the scale-model method show these Master-curves to be different depending on the type of primary excitation and the shape of conductor. Cases of sphere, plate and disc in uniform field, field of line source and dipole field have been studied with an Amplitude-Phase Meter specially constructed in the laboratory for this purpose.     

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.     

近断层速度脉冲的地震动特性研究

在搜集了大量近断层具有速度脉冲的记录后,对有速度脉冲和无速度脉冲的记录的反应谱和特征周期进行了对比,将近断层记录的反应谱与我国规范标准反应谱进行了比较, 还将各次地震有速度脉冲记录的反应谱和特征周期与规范标准谱及规范给出的特征周期进行了比较. 通过比较可知,在长周期段（大约在1.5 s以后）,有速度脉冲记录的反应谱值要比无速度脉冲记录的反应谱值大;计算特征周期时,对于近断层记录,T1和T2有后延的趋势, 采用不固定频段的方法计算更加合理; 无论是相对我国规范的Ⅰ类还是Ⅱ类场地, 有速度脉冲记录的特征周期比规范中给出的值都要大,均在规范值的2倍以上.      

ANALYSIS AND IMPROVEMENT OF THE PRIMARY FIELD WAVEFORM OF THE GROUND TEM METHOD*

Many ground TEM systems use an on-off type of primary field waveform and measure the secondary field only in the transmitter off-time, so as to realize the pure secondary field measurement. The width of the trailing edge of the primary pulses and the duration of the transmitter on-time form a time-constant (T_c) window. Most effective excitation is achieved if the target conductor has a T_c falling into this window. To be able to measure in the transmitter on-time, two primary field waveforms are proposed. The first is a series of unipolar pulses with identical steep ramps at both leading and trailing edges. Measurements made in the on-time after the leading edges simply reduce the stacking time needed and power consumption by half. Also, long- T_c conductors are better excited. The second is a series of bipolar pulses with long ramps as the leading edges and short ramps as the trailing edges. This waveform presents two different T_c-windows at the same time and helps to improve the detection of long-T_c conductors in the presence of short- T_c ones.     

EFFICIENT DESIGN OF AIR-GUN ARRAYS*

A new technique is developed for shaping the pressure bubble pulse radiated by an array of air-guns. It involves the proper spacing of identical units. It is shown that considerable shortening of the pressure bubble pulse can be achieved provided there is sufficient mutual coupling between all the air-guns. The existing air-gun array technique for reducing the bubble pulse involves the redistribution of the energy of the bubble pulses which are produced by an array of variable sized air-guns such that no energy of the bubble pulses is radiated along the perpendicular to the array axis and only the sum of the initial pulses produced by the air-guns forming the array is radiated along that direction. However, the new air-guns array technique involves the damping of the bubble pulses which are produced by an array of identical air-guns by means of mutual interaction and the effective pressure pulse radiated by the array is given by the sum of the damped bubble pulses produced by the mutually coupled identical air-guns. Preliminary field trials gave results consistent with the theoretical predictions. A comparison between the waveforms of the pressure bubble pulses radiated by a single air-gun and by an array of four identical air-guns shows that, due to the presence of mutual coupling between the four air-guns, effective damping of the bubble pulse radiated by the array is about 50% greater than that of the bubble pulse radiated by the single air-gun.     

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.     

RESISTIVITY ANALYSIS FOR MODELS OF A SPHERE IN A HALF-SPACE WITH BURIED CURRENT SOURCES*

Boundary-value problems in steady-state current flow were solved numerically in bispherical coordinates for a sphere of arbitrary conductivity in a half-space. Solutions for the potential on the surface of the half-space were examined for the cases where both current sources were on the surface, one source on the surface and the second between the surface and the sphere, and one source on the surface and the other in the sphere. Results show a great similarity with the layered case when the buried electrode is placed between the surface and the conducting region. Such a buried electrode configuration makes it possible to obtain an accurate measurement of the depth to the conductor in both cases. A model with the current electrode placed in a conductive sphere is compared with a three-layered model with the source in a conductive intermediate layer, and results indicate that the lateral extent of a finite anomalous zone can be estimated using these limiting curves. The validity of these theoretical calculations for buried spheres was confirmed experimentally by tests conducted on an analog model.     

ESTIMATION OF THE PRIMARY SEISMIC PULSE *

A seismic trace after application of suitable amplitude recovery may be treated as a stationary time-series. Such a trace, or a portion of it, is modelled by the expression where j represents trace number on the record, t is time, α_j is a time delay, α (t) is the seismic wavelet, s(t) is the reflection impulse response of the ground and n_j is uncorrelated noise. With the common assumption that s(t) is white, random, and stationary, estimates of the energy spectrum (or auto-correlation function) of the pulse α(t) are obtained by statistical analysis of the multitrace record. The time-domain pulse itself is then reconstituted under the assumption of minimum-phase. Three techniques for obtaining the phase spectrum have been evaluated: (A) use of the Hilbert transform, (B) Use of the z-transform, (C) a fast method based on inverting the least-squares inverse of the wavelets, i.e. inverting the normal time-domain deconvolution operator. Problems associated with these three methods are most acute when the z-transform of α(t) has zeroes on or near the unit circle. Such zeroes result from oversampling or from highly resonant wavelets. The behaviour of the three methods when the energy spectra are perturbed by measurement errors is studied. It is concluded that method (A) is the best of the three. Examples of reconstituted pulses are given which illustrate the variability from trace-to-trace, from shot-to-shot, and from one shot-point medium to another. There is reasonable agreement between the minimum-phase pulses obtained by this statistical analysis of operational records and those estimated from measurements close to the source. However, this comparison incorporates a “fudge-factor” since an allowance for absorption has to be made in order to attenuate the high frequencies present in the pulse measured close to the shot.     

Pattern of induced currents in a conducting sphere in an oscillating uniform field and their contribution to the measured signal

Summary Expressions are obtained for the currents induced in a conducting sphere placed in an oscillating uniform field. The induced currents are plane circular loops around the axis of symmetry with respect to the external field. Current profiles are presented at three latitudinal planes inside the sphere for three parametric values of that are of importance in prospecting. Magnetic fields created by these currents loops at a point on the axis of the sphere are calculated. This study reveals some interesting results like the existence of zones contributing positively and negatively to the signal measured outside the sphere and behaviour of these zones with parameter.     

Some new results on spherical dynamos

Small-scale motions in the Earth's liquid core are likely to be highly anisotropic because of the effects of rotation. Guided by physical considerations, the “-effect” described by an anisotropic tensor _ik is formulated and the corresponding boundary value problem for a sphere is solved for a variety of boundary conditions. A converged solution has been obtained only in the case of the Fermi condition of an infinitely conducting exterior of the sphere. In a second part of the paper, some remarks are made on the hypothetical upper bound on magnetic field strengths in planetary cores originally proposed by Busse (1976).     

Near-fault acceleration pulses and non-acceleration pulses: Effects on the inelastic displacement ratio

Near-fault ground motions can impose particularly high seismic demands on the structures due to the pulses that are typically observed in the velocity time-histories. The velocity pulses can be further categorized into either a distinct acceleration pulse (acc-pulse) or a succession of high-frequency, one-sided acceleration spikes (non-acc-pulse). The different characteristics of velocity pulses imply different frequency content of the ground motions, potentially causing different seismic effects on the structures. This study aims to investigate the characteristics of the two types of velocity pulses and their impacts on the inelastic displacement ratio (C_R) of single-degree-of-freedom systems. First, a new method that enables an automated classification of velocity pulses is used to compile a ground motion dataset which consists of 74 acc-pulses and 45 non-acc-pulses. Several intensity measures characterizing different seismological features are then compared using the two groups of records. Finally, the influences of acc-pulses and non-acc-pulses on the C_R spectra are studied; the effects of pulse period and hysteretic behavior are also considered. Results indicate that the characteristics of the two types of velocity pulses differ significantly, resulting in clearly distinct C_R spectral properties between acc-pulses and non-acc-pulses. Interestingly, mixing acc-pulses and non-acc-pulses can lead to local “bumps” that were found in the C_R spectral shape by previous studies. The findings of this study highlight the importance of distinguishing velocity pulses of different types when selecting near-fault ground motions for assessing the nonlinear dynamic response of structures.