1-D and 2-D spatial frequency analysis of self-potential field anomalies,produced by a polarized sphere

This paper gives analytical expressions for the 1-D and 2-D frequency spectra of the self-potential field produced by a polarized sphere. In 1-D, the amplitude spectrum of the potential field leads to a criterion for determination of the depthh to the centre of the sphere. The polarization angle of the buried sphere can be calculated from the maximum point of the amplitude spectrum of the electric field. In 2-D, the depth to the centre of the polarized sphere can be calculated if the polarization is vertical.     

Effects of transverse electric anisotropy on self-potential anomalies

In the present paper is studied the influence of transverse ground anisotropy on the formation of self-potential (SP) anomalies produced by polarized bodies. It is concluded that SP anomalies produced by vertical dipoles of infinite length are displaced in the opposite direction of the dip angle of anisotropy. The equipotential lines are generally ellipses. SP anomalies produced by a vertical dipole of finite length are also displaced, have a negative and a positive centre and present the characteristics of an SP field produced by an inclined dipole in a homogeneous and isotropic ground. In both models, significant errors in the quantitative interpretation of SP anomalies may result from not taking ground anisotropy into account.     

INTERPRETATION OF TRANSIENT EM COMMON-LOOP ANOMALIES BY RESPONSE CHARACTERISTICS*

Theoretically exact type curves for a semi-infinite thin conductor are presented for various dip, angles, depth of burial and conductance. The study shows that the common-loop response shape is sensitive to small changes in conductor dip, but is affected more subtly by comparable strike variations. For large sheet conductors a decrease in the strike angle results in a broadening but unlike that for a finite plate there is no reduction in peak amplitude. For dipping conductors, response asymmetry and the direction and magnitude of peak amplitude displacement can be used to assess the disposition and quality of the conductor. A generalized interpretation scheme is proposed, based on dimensionless response characteristics and normalized decay curves, to facilitate the rapid in-field determination of conductor dip, conductance and depth of burial, for any time regime.     

A Fourier transform method for the interpretation of self-potential anomalies due to two-dimensional inclined sheets of finite depth extent

The self-potential anomaly due to a two-dimensional inclined sheets of finite depth extent has been analysed in the frequency domain using the Fourier transform. Expression for the Fourier amplitude and phase spectra are derived. The Fourier amplitude and phase spectra are analysed so as to evaluate the parameters of the sheet. Application of this method on two anomalies (synthetic and field data) has given good results.     

The performance of inclined secant micro-pile walls as active vibration barriers

The isolation of vibrations from the surroundings is one of the important problems in the design of machine foundations. The use of open trenches, infilled trenches, single and multiple pile rows have been widely studied. In this paper, the vibration screening efficiency of an inclined secant micro-pile wall positioned as an active vibration barrier is investigated. The study is performed using three-dimensional time domain finite element analyses. Various parameters such as barrier depth, inclination, barrier distance and load excitation frequency were studied. The results show that inclined secant micro-pile walls are a viable vibration isolation option for a multitude of vibration problems. It is shown that varying barrier inclination angle from 90° to 120° improved vibration isolation performance as high as 44% relative to the vertical barrier for the active isolation case. The effectiveness of the barrier increases as its depth increases and also as the excitation frequency increases. The orientation of the inclined barrier towards or against vibration source is shown to be a fundamental design consideration.     

A NOTE ON THE USE OF A NOMOGRAM FOR SELF-POTENTIAL ANOMALIES*

A nomogram has been devised for situations, in which the source of a self-potential anomaly can be approximated by an obliquely polarized sphere or horizontal cylinder embedded in a homogeneous half space. The nomogram can be used for rapid determination of three parameters of the target: (1) depth to the centre, (2) angle between the axis of polarization and the horizontal, (3) shift of the point vertically above the centre of the body from zero potential value. The nomogram has been tested and the parameters determined for SP results obtained over ore bodies Weiss and Süleymanköy in the Ergani Copper district, Turkey. The curves computed for the estimated parameters match the field curves well.     

Direct interpretation of self-potential anomalies produced by a vertical dipole

In the present paper a new method is proposed for the quantitative interpretation of self-potential anomalies which are produced by a vertical dipole. First the mathematical expression of the wavenumber spectrum of the self-potential anomaly is deduced. It is pointed out that at relatively high wavenumbers the behavior of the amplitude spectrum is controlled by the closer to the surface pole at depth h. On the other hand, the “width” of the amplitude spectrum depends on the depth h and the dipole length L.Making a proper mathematical transformation of the amplitude spectrum, and applying the least squares method, it is possible to calculate the depth to the upper pole. The dipole length may then be calculated, by solving numerically a characteristic algebraic equation, as long as the “width” of the amplitude spectrum has been previously defined.The proposed method is applied on a well known self-potential profile from Greece. The calculated parameters of the polarized body are in good agreement with real data. Experimentation with synthetic models in which random noise was introduced, showed that this method gives reliable results if the noise amplitude is not more than 20% of the signal amplitude. It is clearly more efficient than the methods which are based on the model of the point pole or the dipole with a small length. It can also give good results if the horizontal extensions of the polarized body are not more than a few tenths of the depth of the upper pole. If the polarized body is tilted, the depth of the upper pole can be calculated with satisfactory accuracy.The direct interpretation method which is proposed in the present paper, may be useful in mineral exploration, and particularly if the target of interest is the detection of massive sulfide mineralization.     

HEAD WAVES IN TWO-DIMENSIONAL SEISMIC MODELS*

Studies made on head waves in a large number of two-dimensional horizontal and inclined layer seismic models are described. The assumption that the amplitude of head wave decreases exponentially with distance is found to be valid in horizontal layers. For the correct estimation of the head wave decay coefficient, the decrease of amplitude due to the divergence of wave energy should always be considered. The variations of head wave amplitude at large distances from the source appear to follow the theory of Heelan (1953). It is, however, concluded that the theory can only be verified from the measurements in models which have large velocity contrast and thick layer at the top. A prominent interference phenomenon between the direct and head wave has been observed near the critical distance. This is more marked for up-dip profile in the case of inclined layer models. The rate of head wave amplitude decrease with distance beyond the zone of interference is found to depend on dip angle, direction of the dip, and velocity contrast.     

河北南部及邻近地区中小地震震源机制特征分析

利用P波初动和振幅相结合的广义极性振幅技术法(GPAT),反演2007-2016年河北南部及邻近地区发生的368个ML≥2.0中小地震震源机制解,利用统计方法和系统聚类方法,分析震源机制解参数特征。结果表明,河北南部及邻区中小地震以走滑地震为主;正断层和逆断层相对较少,断层面以倾斜或直立为主,断层运动表现为左旋走滑和右旋走滑,应力作用以水平和近水平推扭方式为主。     

远震体波有限破裂过程反演敏感性测试及其在汶川地震上的应用

本文利用远震P和SH波反演得到2008年5月12日汶川大地震(M_W=7.9)的一系列有限破裂模型。使用一种基于小波变换的模拟退火非线性反演方法, 我们将主断层划分成若干个子断层, 在反演时同时确定每个子断层上的滑移量、 滑动角、 上升时间(rise time)以及平均破裂速度。我们首先根据一个假定的破裂模型生成理论地震图, 将该理论地震数据作为输入进行反演, 对该有限破裂反演方法进行了一系列测试, 以验证反演对断层倾角、 平均破裂速度、 最大破裂深度等参数的敏感性。然后我们采用4个不同倾角的断层面来对汶川地震远震体波记录进行反演。结果表明, 若对只在一个断层面上模拟该地震, 30°倾角是个较为合适的值。反演的结果还表明, 此次地震有两个主要的能量释放区域, 并且主断层面存在倾角变化的可能性。在将来的研究中, 可以结合GPS, InSAR测地学以及强震等数据, 来对强震的破裂过程做更细致的研究。     

A Least-squares Approach to Depth Determination from Numerical Horizontal Self-potential Gradients

We have developed a least-squares minimization approach to depth determination of a buried ore deposit from numerical horizontal gradients obtained from self-potential (SP) data using filters of successive window lengths (graticule spacings). The problem of depth determination from SP gradients has been transformed into the problem of finding a solution to a nonlinear equation of the form f(z)=0. Formulas have been derived for vertical and horizontal cylinders and spheres. Procedures are also formulated to estimate the electrical dipole moment and the polarization angle. The method is applied to synthetic data with and without random noise. Finally, the validity of the method is tested on two field examples. In both cases, the depth obtained is found to be in a very good agreement with that obtained from drilling information.     

Least-squares Minimization Approaches to Interpret Total Magnetic Anomalies Due to Spheres

We have developed three different least-squares approaches to determine successively: the depth, magnetic angle, and amplitude coefficient of a buried sphere from a total magnetic anomaly. By defining the anomaly value at the origin and the nearest zero-anomaly distance from the origin on the profile, the problem of depth determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(z)=0. Knowing the depth and applying the least-squares method, the magnetic angle and amplitude coefficient are determined using two simple linear equations. In this way, the depth, magnetic angle, and amplitude coefficient are determined individually from all observed total magnetic data. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal, West Africa. In all cases, the depth solutions are in good agreement with the actual ones.     

日本海及中国东北地震的深度分布及其应力状态

本文分析了日本海及中国东北的地震深度分布。证实了日本本州北部至中国东北的贝尼奥夫带(Benioff)基本是连续的,该带的倾向约为北85°西,倾角约为29°,深度在150公里以下贝尼奥夫带厚度约为20公里。研究了日本本州北部至中国东北的震级M_b≥5.0地震的震源机制解,发现中国东北地壳应力场与日本海地壳的应力场方向一致,来源于太平洋板块的挤压。在俯冲带上,深度在100公里到200公里之间的情况较为复杂,大多数地震显示的主压应力方向与贝尼奥夫带的倾向、倾角一致,有的T轴取向与贝尼奥夫带的倾向、倾角一致,有的特征方向与贝尼奥夫带倾向、倾角均不一致。深度在200公里至500公里之间,主压应力方向近于水平,并与贝尼奥夫带走向垂直,张应力轴相对集中。深度大于500公里时,主压应力方向与贝尼奥夫带的倾向、倾角一致,张应力轴相对集中     

NOMOGRAMS TO INTERPRET CRONE PEM DATA USING A DIPPING SHEET MODEL*

The response of a rectangular plate to the Crone PEM system has been investigated for different values of depth, dip and conductance parameters. The conductance aperture diagram is presented to estimate the conductance and depth to the top of a vertical sheet. Information regarding dip and depth may be obtained using the appropriate nomogram.     

倾斜界面和各向异性对谐波分解方法的影响研究

利用接收函数谐波分解方法可以提取地壳下方的不均匀信息,但当多种不均匀性同时存在时,该方法反演结果的准确性目前尚不十分清楚。基于5组20个理论模型,研究了倾斜界面和各向异性对谐波分解方法的影响。结果表明,对于只存在倾斜界面的情况,利用谐波分解方法可以很好地得到模型参数。在各向异性和倾斜界面同时存在的情况下,各向异性的存在会影响谐波分解得到的倾斜界面振幅信息,而且这种影响还和倾斜界面的走向有关。倾斜轴各向异性谐波分解得到的各向异性强度与倾斜轴倾角大小有关,与快轴方向关系不大。使用谐波分解方法对江西九江台进行分析,结果表明,台站下方倾斜和各向异性共存,快轴方向约为86°,时间延迟约为0.46 s。     

A New Best-Estimate Methodology for Determining Magnetic Parameters Related to Field Anomalies Produced by Buried Thin Dikes and Horizontal Cylinder-like Structures

A new best estimate methodology is proposed and oriented towards the determination of parameters related to a magnetic field anomaly produced by a simple geometric-shaped model or body such as a thin dike and horizontal cylinder. This approach is mainly based on solving a system of algebraic linear equations for estimating the three model parameters, e.g., the depth to the top (center) of the body (z), the index parameter or the effective magnetization angle (θ) and the amplitude coefficient or the effective magnetization intensity (k). The utility and validity of this method is demonstrated by analyzing two synthetic magnetic anomalies, using simulated data generated from a known model with different random errors components and a known statistical distribution. This approach was also examined and applied to two real field magnetic anomalies from the United States and Brazil. The agreement between the results obtained by the proposed method and those obtained by other interpretation methods is good and comparable. Moreover, the depth obtained by such an approach is found to be in high accordance with that obtained from drilling information. The advantages of such a proposed method over other existing interpretative techniques are clarified, where it can be generalized to be automatically applicable for interpreting other geological structures described by mathematical formulations.     

二维激电中梯数据磁类比拟合反演研究

本文通过柯尔-柯尔模型研究地下不同几何参数的极化椭球体在地表的中梯双频激电响应,从而了解不同产状极化体产生极化率的特征,便于后期交互建模。由理论推导可知,任何具有激发极化特征的地质体在地表产生的激电异常都可近似为一个地下电偶极子的三维空间积分,这个积分形式与磁场正演计算公式一致,这意味着我们可以用解释磁法异常的方法解释激电异常,即磁类比法。只要根据先验信息实时改变模型,使激电正演得到的曲线与实测激电曲线逼近,当拟合差小于均方误差时,我们将最后一次模型近似看作是真实模型,由此获得地下极化体的顶埋深、倾角和几何大小等空间参数。实测数据测试表明,这种磁类比人机交互方法加入矿体的一些已知信息后,其拟合反演结果比自动反演更具合理性。      

A Nonlinear Programming Technique for the Interpretation of Self-potential Anomalies

v--vUsing Frank and Wolfe's algorithm, a new interesting nonlinear programming technique has been developed in an attempt to estimate the geometric shape factor of a buried polarized body from a residual self-potential anomaly. Furthermore, the depth, the polarization angle and the electrical dipole moment have also been derived. This algorithm is noted to be robust and its application to SP data converges rapidly towards the optimal solution. The developed technique is tested through studying synthetic data with and without random noise. As a result, the near agreement between the model geometric shape factor and the evaluated one is well recognized. The validity of this proposed technique is tested on a field example from the Ergani Copper district, Turkey. The superiority of the nonlinear programming technique over other recently published methods is shown.     

基于地震活动性资料估计海原断裂倾角

本文以海原断裂带区域活动构造为基础,将海原断裂划分为西、中、东3段.基于1999年12月26日至2010年7月26日间的精定位小震目录,估计了海原断裂带各段的倾角.考虑海原断裂沿走向可能存在南倾与北倾两种情况,将倾角的范围设置为.首先运用网格搜索法确定了平面断层模型,其次以特征深度节点为基础数据运用多项式构建了曲面断层模型.结果表明：当进行平面拟合时,海原断裂西段与中段、东段的倾向不同,西段为南倾,其倾角值为71°,而中段、东段为北倾,其倾角值分别为72°、65°,各段的倾角值均由地表以下8 km地震资料确定.当进行曲面拟合时,在8 km深度以内海原断裂西段、中段、东段的倾角均处于80°左右,即接近陡立.西段的倾角在深度为9 km处出现转换,之后倾角接近陡立;中段的倾角在深度为16 km处出现转换,之后倾角逐渐减小,当深度为18 km时倾角为30°;东段的倾角在深度为11 km处出现转换,倾角为42°,在深度为16 km处出现第二次转换,倾角为55°,之后倾角逐渐减小.结合震源机制解和大地测量观测资料反演拟合的合理性,验证了本文所估计倾角的可靠性.     

Quantitative Interpretation of Self-Potential Anomalies of Some Simple Geometric Bodies

We have developed a new numerical method to determine the shape (shape factor), depth, polarization angle, and electric dipole moment of a buried structure from residual self-potential (SP) anomalies. The method is based on defining the anomaly value at the origin and four characteristic points and their corresponding distances on the anomaly profile. The problem of shape determination from residual SP anomaly has been transformed into the problem of finding a solution to a nonlinear equation of the form q = f (q). Knowing the shape, the depth, polarization angle and the electric dipole moment are determined individually using three linear equations. Formulas have been derived for spheres and cylinders. By using all possible combinations of the four characteristic points and their corresponding distances, a procedure is developed for automated determination of the best-fit-model parameters of the buried structure from SP anomalies. The method was applied to synthetic data with 5% random errors and tested on a field example from Colorado. In both cases, the model parameters obtained by the present method, particularly the shape and depth of the buried structures are found in good agreement with the actual ones. The present method has the capability of avoiding highly noisy data points and enforcing the incorporation of points of the least random errors to enhance the interpretation results.