IMPEDANCE OF A PLANE ELECTROMAGNETIC WAVE AT THE SURFACE OF A LAYERED CONDUCTING EARTH WITH DIPPING ANISOTROPY*

The problem of a plane wave incident on a non-isotropic dipping layer lying over an isotropic conducting substratum has been studied and some numerical results are presented to show the effects of

• 1) degree of anisotropy m,
• 2) conductivity contrast between the substratum to the upper layer b,
• 3) angle of inclination of the axis of anisotropy α,

on the variation of amplitude and phase difference of the wave impedance with the normalized skin-depth (d/δ₁).     

QUASI-STATIC ELECTROMAGNETIC FIELDS OF A HORIZONTAL ELECTRICAL DIPOLE ON THE SURFACE OF A POLARIZABLE HALF-SPACE *

The expressions for quasi-static electromagnetic fields of a horizontal electrical dipole placed on the surface of a polarizable half-space have been derived for low and high values of induced polarization parameter and presented along with numerical results. It has been observed that the polarity of the mutual impedance function is negative for low values and positive for high values of the induced polarization parameter in the entire time domain, whereas the induced voltage function is positive for low values of induced polarization parameter and becomes negative for high values. In the case of low values of induced polarization parameter the transient electromagnetic field in the beginning increases with time, later on it starts to decay with time. The present study shows that the decay rate of electromagnetic field is highly dependent upon the induced polarization parameter. In the light of the present study the conductivity of the polarizable medium may be determined more accurately.     

均匀大地上空的时间域电磁响应

为了脉冲式航空电磁法的应用,本文介绍了均匀大地上空的时间域电磁响应。用傅里叶变换由频率域公式导出了时间域的响应公式。然后以国产脉冲式航电系统的参数计算了二次场的水平分量和垂直分量。根据时间域的计算结果,本文给出了一些解释的图件,可以用来解决两个主要问题。其一是解释在不同飞行高度测得的时间域航空电磁法资料,从而提供大地电阻率;其二是如果给出了大地电阻率,则可计算时间域的航空电磁响应,因此可以校正由飞行高度改变引起的假异常。     

均匀大地上空的时间域电磁响应

为了脉冲式航空电磁法的应用,本文介绍了均匀大地上空的时间域电磁响应。用傅里叶变换由频率域公式导出了时间域的响应公式。然后以国产脉冲式航电系统的参数计算了二次场的水平分量和垂直分量。根据时间域的计算结果,本文给出了一些解释的图件,可以用来解决两个主要问题。其一是解释在不同飞行高度测得的时间域航空电磁法资料,从而提供大地电阻率;其二是如果给出了大地电阻率,则可计算时间域的航空电磁响应,因此可以校正由飞行高度改变引起的假异常。     

A FIELD OCCURRENCE OF SIGN REVERSALS WITH THE TRANSIENT ELECTROMAGNETIC METHOD*

Sign reversals have been observed with the one-loop version of the TEM method in an area near Cloncurry, Queensland. This is the only area in which such a response has been recorded in seven years of field surveys by the Australian Bureau of Mineral Resources. The geology of the area consists mainly of pyrrhotitic graphitic shale, which has resistivities as low as 0.1 Ωm and frequency effects up to 30%. The sign reversals could be due to magnetic phenomena, reflections from layers, or complex conductivity effects.     

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.     

复相位匹配方法及其在具有弯曲界面层状均匀结构问题中的应用（Ⅰ）——理论

本文提出了利用复射线束相位匹配原理合成地震图方法——复相位匹配方法。该方法系利用相位匹配原理把复数域中波传播方程的解和界面联系起来得到的,可解决具有任意形状、光滑曲面界面的层状均匀弹性空间波场计算问题,克服了广义射线法应用于这个问题所遇到的困难。     

复相位匹配方法及其在具有弯曲界面层状均匀结构问题中的应用（Ⅰ）——理论

本文提出了利用复射线束相位匹配原理合成地震图方法--复相位匹配方法。该方法系利用相位匹配原理把复数域中波传播方程的解和界面联系起来得到的,可解决具有任意形状、光滑曲面界面的层状均匀弹性空间波场计算问题,克服了广义射线法应用于这个问题所遇到的困难。     

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.     

A FIRST-ORDER CORRECTION TO THE THEORY FOR THE ELECTROMAGNETIC RESPONSE OF A THIN CONDUCTING SHEET1

The eddy currents induced in a thin conducting sheet by a sinusoidally varying primary magnetic field are investigated in the low-frequency limit when the depth of penetration of the primary field is much greater than the thickness of the sheet. A perturbation scheme in terms of the small parameter, δ, which is the ratio of the thickness of the sheet to the length scale of the primary field is initiated. The zero-order terms in δ give the familiar results that were first obtained by Maxwell. The first-order terms in δ depend on the tangential as well as the normal component of the primary field and give eddy-current distributions that vary quadratically across the sheet. The boundary conditions that determine the accompanying secondary magnetic field are derived. Detailed results are given when the primary field is that due to a dipole.     

TRANSIENT ELECTROMAGNETIC FIELD OF A POLARIZABLE HALF-SPACE DUE TO VARIOUS CURRENT PULSES *

In this paper, the expressions for the induced voltage function V(T) and mutual impedance function Z_m(T) have been derived for specific range of time T and specific values of induced polarization parameters a for ramp and saw-tooth type of current pulses. The computed results for various cases are also presented. The low values of induced polarization parameter a represent the medium possessing membrane polarization, whereas high values exhibit electrode polarization medium. The method has practical applicability and is best suited for the interpretation of transient electromagnetic fields over a polarizable half-space.     

A FIELD EXAMPLE OF THE USE OF ANISOTROPY PARAMETERS DERIVED FROM RESISTIVITY SOUNDINGS*

In areas where steep dips are encountered conventional practice in resistivity work has involved orienting arrays favourably in relation to the geological strike. In concealed conditions, however, the geological strike may not be known; moreover, strike may change with depth. Considerable advantage is to be gained, in such circumstances, by the use of crossed square arrays in that these yield orientationally insensitive resistivity measurements and also allow strike determinations and measurements of the effective vertical anisotropy. Two traverses of crossed square array observations are presented, together with one deeper sounding. The results show that, in favourable circumstances, reliable data on concealed strike directions can be obtained, and that the anisotropy findings greatly assist the subsequent interpretation. Model results pertinent to the field material are presented and discussed.     

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.     

ESTIMATION OF THE SIGNAL-TO-NOISE RATIO OF SEISMIC DATA WITH AN APPLICATION TO STACKING*

The amplitude of the signal and the energy of the noise on each of at least three traces can be estimated provided that the signal has the same form (but not necessarily the same amplitude) on these traces and that the noise on any trace is correlated with neither the signal nor the noise on any other trace. This estimation of signal amplitude and noise energy can be achieved by a rather simple algorithm. The accuracy of the estimate depends, of course, on the degree to which the assumption that signal and noise on the different traces are mutually uncorrelated is actually met. The accuracy tends to improve with increasing number of traces.     

COMPUTATION OF TYPE CURVES FOR ELECTROMAGNETIC DEPTH SOUNDING WITH A HORIZONTAL TRANSMITTING COIL BY MEANS OF A DIGITAL LINEAR FILTER*

The computation method described in this paper is based on the existence of a linear relationship between the mutual coupling ratio and the kernel function in the integral expression for it. Accordingly, the mutual coupling ratio can be determined by first computing sample values of the kernel function and then subjecting these to a digital linear filter. In the present paper the appropriate sampling distance is determined and the values of the digital filter coefficients are computed, both for electromagnetic sounding with horizontal coils and for electromagnetic sounding with perpendicular coils.     

ESTIMATION OF THE MINIMUM DENSITY CONTRAST OF A HOMOGENEOUS BODY AS AN AID TO THE INTERPRETATION OF GRAVITY ANOMALIES*

Goodacre A.K. 1980, Estimation of the Minimum Density Contrast of a Homogenous Body as an Aid to the Interpretation of Gravity Anomalies, Geophysical Prospecting 28, 408–414. The minimum density contrast value for which a homogeneous body will accurately reproduce an observed gravity low can often be used to determine whether the causative body is a low-density granite batholith or a sedimentary basin. If the minimum density contrast value is large, the anomaly source is probably a sedimentary basin; if it is small, the source may be either a sedimentary basin or a granite batholith. The minimum density contrast method is tested on the Cheshire Basin and the Weardale Granite.     

A NEW DERIVATION OF THE WAVEFRONT CURVATURE TRANSFORMATION AT AN INTERFACE BETWEEN TWO INHOMOGENEOUS MEDIA*

The principles for ray-tracing and wavefront curvature calculations in a three-dimensional medium are reviewed. A new derivation of the transformation of the wavefront curvature matrix at an interface between two inhomogeneous media is given. The derivation is based on a Taylor series expansion of the ray refraction equation at the interface between two inhomogeneous media, and only elementary geometric arguments are used. The wave-front curvature transformation at the interface is obtained by neglecting all terms in the direction of the surface normal. With proper definition of the variables, the derivation is also valid for a reflected wave-front. A simplified transformation rule is derived for a reflected wave of the same type as the incident wave.     

RESOLUTION OF RESPONSES DUE TO CONDUCTIVE OVERBURDEN AND ORE-BODY THROUGH TIME-DOMAIN ELECTROMAGNETIC MEASUREMENTS—A FIELD EXAMPLE*

A technique is suggested to separate the effect of conductive overburden from the recorded time-domain electromagnetic anomalies. Such a separation leads one to construct a relatively undistorted picture of the conductor underlying a conductive overburden. A parameter τ (with dimensions of time) is introduced to characterize various conductors. To illustrate the applicability of the technique, four ‘Input’ (Mark V) anomalies obtained over the Cuddapah District, A.P., India have been analyzed and different values of the time-parameter τ corresponding to the overburden and the mineralized zones are obtained.     

地表破裂型逆断层地表缩短量计算方法探讨——以汶川MS 8.0地震地表变形为例

合理估计逆断层地表破裂缩短量是全面认识同震地表变形参数的核心内容,目前还没有较成熟的方法。以汶川MS8.0地震地表破裂为例,尝试通过探槽开挖来研究逆断层水平缩短量的计算问题。在分析汶川地震同震变形的基础上,总结了3种陡坎的成因模式:断层断错地表型、挠曲型、断层与挠曲叠加型,并依据这些模型提出了一些水平缩短量的计算方法及其限制条件,以及如何理解逆断层地表破裂探槽开挖所揭示的信息。最后给出了汶川MS8.0地震白鹿中心学校和汉旺全新村两地点水平缩短量的求解过程及结论,计算得到白鹿中心学校探槽水平缩短量为(2.83±0.3)m,汉旺全新村探槽水平缩短量为(0.61±0.11)m     

APPLICATION OF A HILBERT TRANSFORM METHOD TO THE INTERPRETATION OF SURFACE-VEHICLE MAGNETIC DATA*

The development of an alkali vapour vehicle borne magnetometer providing very high resolution and a high sampling rate has called for reconsideration of interpretation procedures. With continuous profiling at ground level, the close proximity to near surface structures requires that the precise interpretation of geological boundaries be of paramount importance. Rapid digital recording also demands efficient data processing. Both these requirements can be met by the method described. Essentially the method reduces to a simple Hilbert transform of the magnetic profile. The calculation provides an extremely well defined position of the contact and accurate specification of the dip, strike, depth of overburden, and magnetic susceptibility parameters. Particular advantages are tolerance to high frequency noise, independence from a predetermined origin and baseline, and freedom from subjective judgements.