Short note: Source geometry identification by simultaneous use of structural index and shape factor

A cross-plot of the shape factors and the structural indices, determined from gravity anomalies over various idealized sources, namely horizontal/vertical lines and vertical ribbons with various strike lengths and depth extents, forms a closed loop. Different segments of this loop, termed the source geometry identification loop (SGIL), correspond to different source geometries. Combined use of the structural index and the shape factor determined from an isolated gravity anomaly reduces the ambiguity in characterizing the source geometry. A simulated example and three field examples, namely a Cuban chromite anomaly, an Indian example over manganese ore and a sulphide ore from Quebec, have been analysed by the proposed method in order to identify their respective source geometries.     

Analysis of magnetic anomalies due to some two-dimensional bodies using the Mellin transform

An interpretation technique using the Mellin transform is suggested for the analysis of magnetic anomalies due to some two-dimensional structures namely (i) a vertical sheet of both finite and infinite depth extent, (ii) a thick dyke and (iii) a horizontal circular cylinder. The Mellin transformed magnetic anomalies resemble gamma functions which are amenable to an easy interpretation. This procedure is illustrated with a small number of synthetic examples in each case. The practicality of the method is exemplified with the well-known vertical magnetic anomalies of Kursk (USSR) in the case of an infinite sheet model and Karimnagar magnetic anomaly (India) in the case of a horizontal circular cylinder. The results are compared with the techniques already available and found to be reliable.     

Use of the Hilbert transform to interpret self-potential anomalies due to two-dimensional inclined sheets

Self-potential anomalies due to two-dimensional inclined sheet of finite depth extent are analysed from their horizontal and vertical derivatives via the Hilbert transform. The depths to the top and bottom of the sheet and the inclination are obtained by means of simple mathematical expressions. The method is applied to a theoretical example and to a field S.P. anomaly over a sulphide deposit in the Kalava fault zone of Cuddapah basin, India. The presence of random noise is analysed for various levels and its effect is discussed. This interpretation process can be automated for all practical purposes by simple programming.     

CORRECTIONS FOR CONDUCTIVITY ESTIMATES IN INDUCTION PROSPECTING OF SULPHIDE DYKES IN A LAYERED ENVIRONMENT*

In a weathered environment estimates of depth and conductance of metallic sulphide dykes from conventional anomaly index diagrams for a vertical half-plane in air have to be corrected, besides the usual corrections, for: 1. moderate conductivity of the host rocks, and 2. finiteness of strike length S and depth extent D. Model experiments have been carried out to evaluate the response variation of a vertical planar conductor with varying depth extent and strike length for both insulating and conductive surroundings. The results indicate: 1. A conductor with finite depth extent (D/L < 2.5) or strike length (S/L < 5.0) in an insulating medium yields a lower estimate of conductance (mineralization) and a greater depth. 2. A moderately-conductive host rock enhances the anomaly and rotates the phase so that the conductor appears to be more resistive (less mineralized) and shallower. The results have practical significance since in weathered surroundings a highly-mineralized body of finite size could be missed, or misjudged, because of low estimates of conductivity and depth.     

唐山地震震源应力场的数值模拟研究-三维有限单元法在计算震源应力场中的应用

震源机制结果与极震区地裂缝的力学性质,都说明唐山地震是以右旋剪切走向滑动为主且兼倾向滑动的主震型大地震。这说明唐山地震是在水平力和垂直力同时作用下产生的。本文利用三维有限单元法,采用弹性模式对唐山地震震源应力场进行了数值计算,並考虑了体力与表面力两种受力情况。表面力又分为水平作用应力与垂直作用应力,水平作用应力随深度变化,且最大水平压应力等于同一深度上静水压力的3倍,而最小水平压应力等于同一深度上静水压力。最大水平压应力取北85°东,即与唐山地震震源机制解的最大主压应力轴基本上是一致的。垂直力取其静水压力的1.5倍所得结果与地震实际发生的过程比较一致,所以,唐山地震很可能是在水平力与垂直力同时作用下产生的。     

The evaluation ofHeuman's Lambda function and its application to calculate the gravitational effect of a right circular cylinder

Summary A computational scheme has been derived to generateHeuman's Lambda function. This has been applied to compute the gravitational attraction of a right vertical circular cylinder. Test computations show that the error introduced by assuming a semifinite cylinder in place of a finite one of depth 30 times its radius is 1.77%.     

Seismic response of multi-layered basins with velocity gradients upon incidence of plane shear waves

A boundary integral scheme based on boundary-integral discrete-wave-number approach has been developed to compute the seismic response of two-dimensional irregular-shaped basins with horizontal soil layers. Each layer exhibits a linear gradient of shear wave velocity with depth. The approach combines the boundary-integral representation of the seismic wave field outside the basin with plane wave representation of the seismic wave field inside the basin. The propagation throughout the layers is performed by matrix propagators in which the effect of the vertical variation of the velocity is incorporated by using confluent hyper-geometric functions of the Whittaker type. Our method is tested against otherwell-accepted solutions for the case of a circular basin with excellent agreement. Test of the ground response for a semi-circular basin with radius a shows that stable solutions are obtained if the chosen model parameters satisfy following conditions: (1) the distance from the sources to the interface is greater than 0·1a; (2) the distance between the sources is smaller than a quarter of the incident wavelength; and (3) the discrete wave-number step is smaller than 2π/4a. The computation of ground response of basins with a sharp interface and several horizontal deposits leads to the following main results: (1) the amplification of a basin with velocity gradients is larger than that of a basin with homogeneous layers; (2) the frequencies of the second- and third-order harmonics for a basin with velocity gradients are lower than those of a basin with homogeneous layers; and (3) the response amplitude of the basin with velocity gradients attenuates more slowly in time domain than when layers are homogeneous. Since these results have been obtained for realistic values of basin geometrical and mechanical consideration, they should find some interest in earthquake engineering or seismic microzonation studies. © 1998 John Wiley & Sons, Ltd.     

Gravity and magnetic field characteristics and hydrocarbon prospects of the Tobago Basin

The Tobago Basin, which is located offshore northern Venezuela with a southern margin close to Trinidad and Tobago, has an area of approximately 59,600 km². The Tobago Basin has relatively favourable hydrocarbon prospects, and to date, exploration work has mainly concentrated on small areas of the southwestern portion of the basin. To conduct a comprehensive study of the structural framework of the basin and the characteristics of the basement in order to identify prospective zones for hydrocarbon exploration, shipborne‐measured and satellite‐measured gravity data, shipborne‐measured magnetic data, and aeromagnetic survey data were analysed. A regularisation filtering method was used to separate and obtain regional and residual gravity and magnetic anomalies. Directional gradients of gravity and magnetic anomalies and the total horizontal gradient and vertical second derivative of gravity anomalies were employed to extract information about fault structures. Regression analysis methods were used to determine the basement depth. The geological significance of the gravity and magnetic fields was examined, the structural framework of the basin was assessed, the basement depth was estimated, and favourable hydrocarbon exploration prospects within the basin were identified. The results show that the Tobago Basin contains complex structures consisting mainly of two groups of faults trending in northeasterly and northwesterly directions and that the major northeasterly trending faults control the main structural configuration and depositional system within the basin. The basement of the Tobago Basin has deep rises and falls. It can be divided into the following four secondary tectonic units: the western sub‐basin, the central uplift area, the southern sub‐basin, and the northeastern sub‐basin. The central uplift area and northeastern sub‐basin are most likely to have developed hydrocarbon accumulations and should be targeted for further exploration.     

Fast local wavenumber (FLW) method for the inversion of magnetic source parameters

The current local wavenumber methods for the interpretation of magnetic anomalies compute the locations of geological bodies by solving complex matrices. Presently, such methods require to know the structural index, which is a parameter that represents the source type. The structural index is hard to know in real data; consequently, the precision of current methods is low. We present the fast local wavenumber (FLW) method, and define the squared sum of the horizontal and vertical local wavenumbers as the cumulative local wavenumber. The FLW method is the linear combination of the umulative local wavenumberand other wavenumbers, and is used to compute the locations and structural index of the source without a priori information and matrix solution. We apply the FLW method to synthetic magnetic anomalies, and the results suggest that the FLW method is insensitive to background and oblique magnetization. Next, we apply the FLW method to real magnetic data to obtain the location and structural index of the source.     

Direct current electric potential computation in an inhomogeneous and arbitrarily anisotropic layered earthl

We consider the calculation of the electrical field quantities, electric potential and the vertical component of the total volume density of electric current, in a horizontally layered, piecewise homogeneous and arbitrarily anisotropic earth due to a system of direct current point sources. By applying Fourier transformation with respect to the horizontal space coordinates to the static field equations, the field quantities are obtained as the solutions of the system of transform-domain differential equations in the vertical (depth) coordinates. A recurrence scheme has been given to compute the tranform-domain field quantities at any depth. The corresponding space-domain quantities are then obtained by inverse Fast Fourier Transformation (FFT). A complete computer program has been developed for computing the electric potentials at any depth of the layered earth, which is composed of an arbitrary number of anisotropic layers with arbitrary conductivity tensors. By considering the point sources at different depths from the surface, equipotential contours on the surface of arbitrarily anisotropic layered earth models are given.     

Numerical and experimental models on the formation mechanism of collapse basins during the Green Tuff orogenesis of Japan

The geological model about volcanism of the Green Tuff geosyncline deduced from the field observations consists of the following processes:

1. Dome-shaped uplift with a mean diameter of 30 km.
2. Collapse of the central part of the domes forming basins with a mean diameter of 10 km.
3. Volcanic activity inside the collapse basins. It is considered that these consecutive processes resulted from the magmatic uplift from a deep part of the crust.

In finite element analyses performed as plane strain problems, earth's crust is assumed to be an elasto-plastic homogeneous layer and to undergo sinusoidal vertical displacement at the base of the layer due to an ascending magma reservoir. These analyses reveal that the diameter of the dome is proportional to the depth of the magma reservoir rather than to its size. The magma reservoir is estimated at 12 ～ 24 km in depth. Scale model experiments using powdered material were performed in order to reproduce a collapse basin. These three-dimensional models are reduced to a scale of 1:200,000 th of the natural size. The results of experiments show that radial and concentric cracks are produced on top of the dome and a central part encircled by concentric cracks collapses to form a basin. The boundary of the collapsed portion forms a steep cliff with a height of about 2 mm. This is equivalent to 400 m in natural size and is nearly similar to field observations.     

Walsh spectra of gravity anomalies over some simple sources

Walsh transform of gravity anomalies over a point mass, a horizontal and a vertical line mass have been computed to obtain a cyclic shift invariant differential energy density (DED) function. Quantitative relations between DED spectral characteristics with depth to centroid/top of the source have been established. The effects of profile length, sampling interval, random noise and zero padding have been investigated. Applicability of the proposed method has been evaluated through two field examples.     

Effect of coastal boundary resolution and mixing upon internal wave generation and propagation in coastal regions

A non-linear two-dimensional vertically stratified cross-sectional model of a constant depth basin without rotation is used to investigate the influence of vertical and horizontal diffusion upon the wind-driven circulation in the basin and the associated temperature field. The influence of horizontal grid resolution, in particular the application of an irregular grid with high resolution in the coastal boundary layer is examined. The calculations show that the initial response to a wind impulse is downwelling at the downwind end of the basin with upwelling and convective mixing at the opposite end. Results from a two-layer analytical model show that the initial response is the excitation of an infinite number of internal seiche modes in order to represent the initial response which is confined to a narrow near coastal region. As time progresses, at the downwind end of the basin a density front propagates away from the boundary, with the intensity of its horizontal gradient and associated vertical velocity determined by both horizontal and vertical viscosity values. Calculations demonstrate the importance of high horizontal grid resolution in resolving this density gradient together with an accurate density advection scheme. The application of an irregular grid in the horizontal with high grid resolution in the nearshore region enables the initial response to be accurately reproduced although physically unrealistic short waves appear as the frontal region propagates onto the coarser grid. Parameterization of horizontal viscosity using a Smagorinsky-type formulation acts as a selective grid size-dependent filter, and removes the short-wave problem although enhanced smoothing can occur if the scaling coefficient in the formulation is too large. Calculations clearly show the advantages of using an irregular grid but also the importance of using a grid size-dependent filter to avoid numerical problems.     

地震波传播的三维伪谱和高阶有限差分混合方法并行模拟

基于交错网格伪谱法和高阶精度有限差分方法,发展了模拟非均匀介质地震波传播的三维伪谱和有限差分混合算法.该方法在两个水平方向利用交错网格伪谱算子计算空间微分,保留了该方法高效、高精度的优势,在垂直方向采用交错网格高阶精度有限差分算子实现空间微分计算．利用有限差分方法的局部性特征,将三维计算区域在垂直方向上划分为一系列子区域,并分配给不同的处理器,实现了在并行计算机集群上的三维并行计算．通过模拟算例,与离散波数法比较,检验了该算法的精度．为了检验该方法的实用性,在64个处理器上,对三维沉积盆地模型进行了67108864个网格点的并行计算,模拟的波场主频率为1.25Hz,讨论了沉积盆地深度对三维沉积盆地地面运动的影响．      

A new formulation for a code-based vertical design spectrum

Consideration of vertical seismic design loads is important for long-span structural systems, short-period structures, and for some nonstructural components in the buildings. To this end, seismic design codes utilize alternative approaches to define vertical design spectrum at different levels of complexity: either as a fraction of horizontal design spectrum or using a separate functional form having features different than the horizontal spectrum. In all cases, a consistency between the horizontal and vertical design spectral ordinates is sought. In this paper, we consider a set of modern seismic design codes, horizontal and vertical ground-motion datasets, as well as ground-motion predictive models (GMPMs) to assess the accuracy of code-based vertical design spectrum expressions. We compute horizontal and vertical spectra for different earthquake scenarios (magnitude-distance-soil condition combinations) from the selected horizontal and vertical GMPMs for comparisons with their code-based (idealized) counterparts. Besides that, we study the vertical spectrum behavior from observed ground-motion data. Our observations suggest that the vertical design spectrum formulations by current codes do not fully explain the actual vertical spectral acceleration trends. We discuss the possible reasons behind the misrepresentation of vertical spectrum by the current code approach and introduce our own expressions to compute horizontal spectrum consistent vertical design spectrum from a comprehensive simulated dataset of correlated vertical and horizontal spectral ordinates.     

Improved Local Wavenumber Methods in the Interpretation of Potential Field Data

We present two new potential-inversion methods for estimating the depth and the nature (structural index) of the source, which use various combinations of different forms of local wavenumbers and the information about the horizontal location to estimate individually the depth and the nature of a magnetic source. The improved local wavenumber methods only use the horizontal offset and vertical offset of local wavenumbers to estimate the depth and the structural index of the source, so they yield more stable results compared with the results obtained by current methods that require the derivatives of local wavenumbers. Tests conducted with synthetic noise-free and noise-corrupted magnetic data show that the proposed methods can successfully estimate the depth and the nature of the geologic body. However, our methods are sensitive to high-wavenumber noise present in the data, and we reduced the noise effect by upward continuing the noise-corrupted magnetic data. The practical application of the new methods is tested on a real magnetic anomaly over a dike whose source parameters are known and the inversion results are consistent with the true values.     

基于电阻率敏感性函数的随钻电磁波测井探测特性研究

为研究地层电性变化时不同区域对电磁波测井响应的贡献分布,从响应信号对地层参数求偏导的角度,给出一种新的电阻率敏感性函数定义,引入模式匹配法对纵向成层、径向非均匀介质敏感性分布进行快速模拟;通过对敏感性函数纵、横向积分给出了单发双收线圈系纵、横向探测范围,研究了井眼、频率、背景地层电阻率等对探测特性的影响.结果表明:敏感性函数能够定量表征响应对地层纵向与径向微观与宏观敏感性,幅度比与相位差敏感性分布形态类似,幅度比较广较深,而相位差分辨率高,敏感范围小;敏感性函数进行径向积分后可表征仪器的探测深度,与伪几何因子对比达到了同样的效果;背景地层电阻率在1~100Ωm变化时,工作频率2 MHz下幅度比探测深度约为0.6~2.3m,相位差为0.3~0.8m,幅度比50%纵向积分敏感性层厚约为0.3~1.6m,相位差约为0.2~0.6m;异常体与背景地层电阻率对比度在1~50变化时,引起的探测深度与敏感性层厚差异约为0.1~0.2m,远小于地层电阻率的影响.     

Quantitative interpretation of self potential anomalies of some specific geometric bodies

Summary Some direct and quantitative methods of SP anomalies caused by some specific geometric bodies have been developed in this paper. The models of current sources which have been considered are i) single pole, ii) a doublet, iii) a pair of single point poles separated by a horizontal distance, iv) single finite line pole, v) single infinite line pole and vi) two similar double infinite vertical line poles separated by a horizontal distance.     

利用黄土剖面的古土壤年龄研究毛毛山断裂的滑动速率

利用１４Ｃ、热释光（ＴＬ）样品年代及扩散方程计算结果，结合区域黄土剖面中古土壤年龄，对毛毛山地区晚第四纪各级地貌年龄进行了对比研究。根据毛毛山活动断裂水平位移和垂直位移分布明显的分组特征，求得毛毛山断裂带不同段落不同时段的平均滑动速率。大约自中更新世晚期以来，毛毛山断裂走滑段的平均水平滑动速率为２．３～３．９ｍｍ／ａ，垂直滑动速率为０．０７～０．１９ｍｍ／ａ；天祝盆地倾滑段垂直滑动速率为０．１１～０．８６ｍｍ／ａ。沿断裂带滑动速率具明显的非均匀性特点，表现为自东向西水平位移具累积滑动亏损特征，垂直位移则具补偿性     

Hydraulics of a partially penetrating well with skin zone in a confined aquifer

A steady/quasi-steady model is developed for predicting flow into a partially penetrating well with skin zone in a confined aquifer overlying an impervious layer. The model takes into account flow through the bottom of the wellbore, finite skin thickness and finite horizontal and vertical extent of the aquifer. Moreover, the solution can be easily extended to include the mixed-type boundary condition at the well face, where a Dirichlet in the form of a specified hydraulic head and a Neumann in the form of zero flux coexist at the same time at different portions of the well face. The validity of the proposed solution is tested by comparing a few results obtained from the developed model with corresponding results obtained by analytical and numerical means. The study shows that, among other factors remaining constant, both the horizontal and vertical extent of an artesian aquifer, thickness of the skin zone, bottom flow and conductivity contrast of the skin and formation zones, play an important part in deciding flow to a well dug in the aquifer, and hence these factors must be considered while analyzing the problem. The model proposed here can be used to estimate skin thickness as well as hydraulic conductivities of the skin and formation zones of a well with skin zone in an artesian aquifer underlain by an impervious layer by utilizing pumping test data falling in the steady or quasi-steady state of a typical pumping test. As the proposed solution is of a general nature in the sense that it can handle, apart from partial penetration and bottom flow, the finite size skin zone and finite horizontal and vertical extent of an artesian aquifer together with the mixed-type boundary condition at the well face, it is hoped that the predictions coming out of the model will be more realistic than those obtained using solutions developed with more stringent assumptions.