EM AND IP RESPONSE OF A STEEL WELL CASING FOR A FOUR-ELECTRODE SURFACE ARRAY. PART I: THEORY*

The basic formulation for the mutual coupling between grounded circuits in the presence of a vertical conductor is used to examine the full electromagnetic and induced polarization response for a homogeneous half-space model. Both interfacial polarization at the steel/electrolyte boundary and induced eddy currents in the casing are accounted for in the analysis. It is shown that for mild steel casings the eddy currents, hitherto neglected, play an important role because of their strong frequency dependence. Calculated curves of the appar- ent complex resistivity as a function of frequency show that the overall response can be influenced by the state of corrosion at the surface of the casing.     

COMPATIBILITY OF EM AND IP SURVEYS *

Methods and typical case histories of EM and IP surveys are compared in order to check their compatibility for the investigation of large areas for base metal sulphides. It is demonstrated that the fast, low cost EM may miss sulphide concentrations which cause no reduction of apparent resistivity, or which act like horizontal slabs, where EM anomalies occur marginally. In such cases only IP can recognize the whole extent of the mineralization. The misleading role of graphite exists for both methods. The conclusion is that EM remains the only economical method to survey whole ore districts, but that the shortcomings should always be taken into account in the interpretation. They can be overcome by employing geological, geochemical or other geophysical indicators in selecting promising targets for follow-up IP. Even if less than 20% of the area is covered by the expensive IP, there is a fair chance that all sulphide bearing rocks will be found. Therefore, the question is not whether to apply EM or IP methods, but how to combine them best.     

三维导电导磁体电磁响应的数值解

本文提出一种关于自由空间三维导电导磁体在谐变磁偶极场中电磁响应的数值计算方法。从麦克斯韦方程组导出以体内涡流密度和磁化强度为未知函数的一个联立微分积分方程组。采用迭代方法计算涡流和极化磁矩之间的相互作用,使联立的微分积分方程转化为两个独立的积分方程,再用积分方程法和有限差分法来求解。这种混合方法的优点在于它的计算速度较快。     

三维导电导磁体电磁响应的数值解

本文提出一种关于自由空间三维导电导磁体在谐变磁偶极场中电磁响应的数值计算方法。从麦克斯韦方程组导出以体内涡流密度和磁化强度为未知函数的一个联立微分积分方程组。采用迭代方法计算涡流和极化磁矩之间的相互作用,使联立的微分积分方程转化为两个独立的积分方程,再用积分方程法和有限差分法来求解。这种混合方法的优点在于它的计算速度较快。     

TEST RESULTS OF A NEW TYPE OF EFFICIENT SMALL AIRGUN ARRAY*

Recently the author developed and demonstrated (Safar 1980) an efficient method for operating the airgun. The method involves the generation of a short seismic pulse from the pressure bubble pulses radiated by an airgun when fired several times at the same optimum depth but with different chamber pressures. The purpose of this paper is to present and discuss the test results obtained when implementing the same method using a two-dimensional airgun array. The array consists of seven 0.65 liter airguns fired simultaneously at the same depth but with different chamber pressures. It is shown that the far-field pressure pulse radiated by the seven 0.65 liter airgun array is similar to that radiated by the Flexichoc seismic source. It is concluded that the proposed airgun array can be used as a subarray to form an extremely powerful super-long array suitable for deep seismic exploration. The author would like to thank the Chairman and Board of Directors of the British Petroleum Co. Ltd for permission to publish this paper. Thanks are also due to Mike Symes and Lovell Cox for carrying out the field tests and Seismograph Service (England) Ltd for providing the airguns.     

IN-LOOP PULSE EM RESPONSE OF A STRATIFIED EARTH*

The in-loop pulse electromagnetic response of a stratified earth has been expressed in terms of an apparent resistivity- time plot using the PEM response over a homogeneous half-space which is typically unipolar with monotonic decay. This half-space response characteristic provides a unique relationship between Crone PEM channel amplitude and the apparent half-space resistivity. The possibility to resolve a thin intermediate conductive and resistive layer with the in-loop PEM system has been investigated. The system is well in shallow geoelectric mapping.     

A METHOD FOR CALCULATING IP ANOMALIES FOR MODELS WITH SURFACE POLARIZATION*

A numerical method is given for calculating resistivity and induced polarization anomalies produced by a surface polarization model. Surface polarization is generated when a purely electronic conductor is located in an electrolyte environment. The system that develops on the boundary between the conductor and the electrolyte is described macroscopically by a net surface charge distribution and an electric double layer. An integral equation is derived for the potential by assuming that the electronic conductor forms an equipotential system and that the polarization impedance across the boundary is linear. The integral equation is solved by means of the method of subsections. As an application some numerical modeling results are presented. The surface impedance values used in calculations are based on laboratory measurements that are briefly described. Implications of the results for scale modeling are discussed.     

EM COUPLING IN MULTIFREQUENCY IP AND A GENERALIZATION OF THE COLE-COLE IMPEDANCE MODEL*

The Cole-Cole relaxation model has been found to provide good fits to multifrequency IP data and is derivable mathematically from a reasonable, albeit greatly simplified, physical model of conduction in porous rocks. However, the Cole-Cole model is used to represent the mutual impedance due to inductive or electromagnetic coupling on an empirical basis: this use has not been similarly justified by derivation from any simple physical representation of, say, a half-space, layered or uniform. A uniform conductive half-space can be represented as a simple subsurface loop with particular resistive and inductive properties. Based upon this, a mathematical expression for the mutual impedance between the two pairs of electrodes of a dipole-dipole array is derived and designated “model I”. It is seen that a degenerate case of model I is the Cole-Cole model with frequency exponent c= 1. Model I is thus more general than the Cole-Cole expression and must provide at least as good a fit to a set of field data. Provision for variation of c from unity could be made in model I equally well as for the Cole-Cole model although, at present, this would be a purely empirical alteration. Model I contains four parameters, one of which is, in effect, the resistivity of the half-space. Therefore only three parameters are involved in the model I expressions for normalized amplitude and for phase of the EM-coupling mutual impedance. Model I is compared with previously published “standard” values for two different dipole separations. Under particular constraints, model I is shown to provide better fits than the Cole-Cole model (with c= 1) over particular frequency ranges, specifically at very low frequencies and at moderately high frequencies where the model I phase curve follows the standard phase curve across the axis to positive values (negative coupling).     

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.     

计算井水位对固体潮和气压滞后响应的新方法

提出了一种计算井水位对固体潮和气压滞后响应的新方法.利用杜得森潮汐展开和泰勒级数展开,导出了计算井水位固体潮系数和气压系数以及滞后时间公式,并给出了考虑滞后影响的井水位固体潮和气压改正公式.利用该法处理了鲁03井水位和气压观测资料,求出该井水位固体潮系数为1.8mm/10~_(-3),水位对固体潮响应的滞后时间为1.53小时,气压系数为6.4mm/hPa,滞后时间为1.5小时。与以前的一般回归分析方法相比,改正后的水位中误差明显减小,改正效果较好。     

THE USE OF TWO-ELECTRODE AND SCHLUMBERGER FILTERS FOR COMPUTING RESISTIVITY AND EM SOUNDING CURVES*

Different sets of filter coefficients for the linear filter technique for the computations of resistivity and EM sounding curves are evaluated for several electrode and coil configurations. Instead of this procedure, the two-electrode filter can be used for computations of Wenner, Schlumberger, and dipole—dipole apparent resistivity model curves by defining convolutional expressions which contain the new input functions in terms of the resistivity transform function. Similarly, the Schlumberger filter performs the computations of dipole—dipole apparent resistivity model curves. The Wenner, Schlumberger, and dipole—dipole filter functions are defined in terms of the two-electrode filter using the new convolutional expressions. A relationship between the Schlumberger and dipole—dipole filter functions is given. The above arguments are adopted for the computations of EM sounding curves. It is shown that the EM filter for the horizontal coplanar loop system (which is identical to the two-electrode filter) performs the computations of the mutual coupling ratios for perpendicular, vertical coplanar, and vertical coaxial loop systems. In the same way, the Schlumberger filter can be used to compute vertical coaxial sounding curves. The corresponding input functions are defined in terms of the EM kernel for all convolutional expressions presented. After these considerations, integral expressions of the mutual coupling ratios involving zero-order Bessel function are derived. The mutual coupling ratio for the vertical coaxial loop system is given in the same form as the mutual coupling ratio for the vertical coplanar loop system.     

THE AMPLITUDE AND PHASE RESPONSE OF A SEISMIC VIBRATOR*

The amplitude and phase response of a simple model is compared with the performance of a real vibrator working in the field. The field results show a characteristic phase response which confirms that the real drive force applied to the baseplate and its load impedance is faithfully represented by the acceleration of the reaction mass. It follows that all the parameters necessary to calculate the load impedance and the true power dissipated in the earth can be measured at the output of the vibrator. It also follows that the current method of baseplate phase compensation should be reconsidered.     

RESISTIVITY SOUNDING ON A MULTI-LAYERED EARTH WITH TRANSITIONAL LAYERS. PART II: THEORETICAL AND FIELD EXAMPLES *

This final part of our study of the resistivity sounding method in the presence of transitional layers deals with the direct application of the theoretical developments, previously reported, to both theoretical and field examples. The former are used to explain in more detail all steps of the direct procedure of interpreting resistivity measurements, when transitional layers with different dispositions are present in the assumed earth section. An alternate sequence of uniform and transitional layers is at first considered, then the case of a random sequence of these layers, and finally a sequence of only transitional layers. Then we give some logical considerations about the best fields of application of the new interpretation theory, with particular reference to hydrogeological, geological- structural, and mining exploration problems. Representative field examples are finally presented and discussed in detail for each of the exploration fields above listed. The comparison of the geophysical models obtained with the old interpretative scheme and the new system shows the greater resolving power of the new theory, provided that preliminary geological considerations, and where existing–borehole evidence justify the use of the new approach.     

中国东部六省的 Lg 震级(上)--测定方法和结果

本文系统地分析了根据 Lg 波埃里相和非埃里相衰减系数确定单台和台网震级公式、震级标准差以及台站校正值的方法.根据中国东部苏、鲁、豫、皖、冀、浙六省地区约1秒 Lg 波衰减系数的测定结果,导出六省地区的 Lg 震级公式:mLg(z,h)=lgdLg(z,h)+5/6lg+0.0019+2.09 mmx(z,h)=lgdmx(x,h)+lg+0.0013+1.27 计算了该区域内19个地震的各震级值,以及80个台站的台校值.单台震级标准差为0.15-016震级单位,台网震级标准差为0.03-0.04震级单位.此外,还测定了111个地震的 mmxz和 mmxh值,验证或补充了19个地震得出的某些关系和结果.     

LOW-PASS FILTERING OF NOISY FIELD SCHLUMBERGER SOUNDING CURVES PART II: APPLICATION*

The basic principles of the application of the linear system theory for smoothing noise-degraded d.c. geoelectrical sounding curves were recently established by Patella. A field Schlumberger sounding is presented to demonstrate first their application and validity. To achieve this purpose, firstly it is pointed out that the required smoothing or low-pass filtering can be considered as an intrinsic property of the transformation of original Schlumberger sounding curves into pole-pole (two-electrode) curves. Then we sketch a numerical algorithm to perform the transformation, opportunely modified from a known procedure for transforming dipole diagrams into Schlumberger ones. Finally we show a field example with the double aim of demonstrating (i) the high quality of the low-pass filtering, and (ii) the reliability of the transformed pole-pole curve as far as quantitative interpretation is concerned.     

THE EXACT SEISMIC RESPONSE OF AN OCEAN AND A N-LAYER CONFIGURATION*

The space-time acoustic wave motion generated by an impulsive monopole source is calculated with the aid of the Cagniard-de Hoop technique. Two configurations with plane interfaces are discussed: an air/fluid/solid configuration with the source and the receiver located in the fluid layer; and a stack of n fluid layers between two acoustic half-spaces where the source and the receiver are located in the upper half-space. Synthetic seismograms are generated for the pressure of the reflected wavefield, using the source signature of an airgun.     

在地震与爆炸以及冲击载荷作用下分层弹性地基场地土的竖向动力反应分析

对场地上按分层弹性地基土建立了合理的力学模型，通过动力分析，给出了分层弹性地基场地土竖向自振特性及在竖向地震与爆炸以及冲击载荷作用下强迫反应的解析解，文中的解析公式为分层弹性地基场地土的竖向动力反应分析提供了一种新的解析方法．