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.     

A New Algorithm for Depth Determination from Total Magnetic Anomalies due to Spheres

We have developed an automatic method to determine the depth of a buried sphere from numerical second horizontal derivative anomalies obtained from total field magnetic data. The method is based on using a relationship between the depth and a combination of observations at symmetric points with respect to the coordinate of the projection of the center of the source in the plane of the measurement points with a free parameter (graticule spacing). The problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of f(z) = 0. Procedures are also formulated to determine the magnetic moment and the effective angle of magnetization. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal. In all cases, the depth solutions are in good agreement with the actual ones.     

A new least-squares minimization approach to depth and shape determination from magnetic data

We have developed a least‐squares minimization approach to depth determination using numerical second horizontal derivative anomalies obtained from magnetic data with filters of successive window lengths (graticule spacings). The problem of depth determination from second‐derivative magnetic anomalies has been transformed into finding a solution to a non‐linear equation of the form, f(z) = 0. Formulae have been derived for a sphere, a horizontal cylinder, a dike and a geological contact. Procedures are also formulated to estimate the magnetic angle and the amplitude coefficient. We have also developed a simple method to define simultaneously the shape (shape factor) and the depth of a buried structure from magnetic data. The method is based on computing the variance of depths determined from all second‐derivative anomaly profiles using the above method. The variance is considered a criterion for determining the correct shape and depth of the buried structure. When the correct shape factor is used, the variance of depths is less than the variances computed using incorrect shape factors. The method is applied to synthetic data with and without random errors, complicated regionals, and interference from neighbouring magnetic rocks. Finally, the method is tested on a field example from India. In all the cases examined, the depth and the shape parameters are found to be in good agreement with the actual parameters.     

A Least-squares Minimization Approach to Depth Determination from Magnetic Data

—We have developed a least-squares minimization approach to depth determination from magnetic data. By defining the anomaly value T(0) at the origin and the anomaly value T(N) at any other distance (N) on the profile, the problem of depth determination from magnetic data has been transformed into finding a solution to a nonlinear equation of the form f(z)=0. Formulas have been derived for a sphere, horizontal cylinder, dike, and for a geologic contact. Procedures are also formulated to estimate the effective magnetization intensity and the effective magnetization inclination. A scheme for analyzing the magnetic data has been formulated for determining the model parameters of the causative sources. The method is applied to synthetic data with and without random errors. Finally, the method is applied to two field examples from Canada and Arizona. In all cases examined, the estimated depths are found to be in goodagreement with actual values.     

A Numerical Approach to Depth Determination from Residual Gravity Anomaly Due to Two Structures

—The residual anomaly expression due to two simple geologic structures can be represented by the sum of fields produced by two known source bodies whose depths are to be determined. For a few fixed characteristic points and distances along the residual anomaly profile, the depth to the upper structure is determined iteratively using a simple formula for each depth of the lower structure. The computed depths to the lower structure are plotted against the depths to the upper structure representing a depth curve. The solution for the depths to both structures is read at the common intersection of the depth curves. Procedures are also formulated to estimate the radii of the two buried structures. The method is a powerful technique for separating the composite residual anomaly into two residual components due to two structures. The method is applied to theoretical data with and without random errors and tested on a field example from U.S.A.     

Spatial correlation for horizontal and vertical components of acceleration from northern Iran seismic events

The evaluation of seismic risk of spatially distributed systems requires the spatial correlation model for ground motion intensity measures. This study investigates the spatial correlation of four earthquakes recorded in northern Iran. The intra-event spatial correlation for both horizontal and vertical components of spectral acceleration at eight periods in the range of 0.0–3.0 s is estimated using geostatistical tools. An exponential form is chosen to fit experimental semivariograms, and the correlation ranges of spectral accelerations as a function of period are derived. The results show similar trend of correlation ranges for both components. It should be mentioned that the ranges for the vertical component, in general, are higher than those observed for the horizontal one. For both components, the correlation ranges as a function of period are divided into three segments. The first and the third one are increasing while the second one is decreasing with increasing period.     

A Least-squares Approach to Shape Determination from Residual Self-potential Anomalies

—We have developed a least-squares minimization approach to determine the shape (shape-factor) of a buried polarized body from a residual self-potential anomaly profile. By defining the zero anomaly distance and the anomaly value at the origin on the profile, the problem of the shape-factor determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(q) = 0. Procedures are also formulated to estimate the depth of polarization angle, and the electric dipole moment. The method is applied to synthetic data with and without random noise. The obtained shape-factor agrees very well with the model shape-factor when using synthetic data. After adding ± 2 percent random error in the synthetic data, the shape factor obtained is within ± 4 percent. Finally the validity of the method is tested on a field example from the Ergani copper district, Turkey.     

Estimation of anisotropic hydraulic conductivity using geophysical data in a coastal aquifer of Karnataka,India

Estimation of hydraulic parameters is essential to understand the interaction between groundwater flow and seawater intrusion. Though several studies have addressed hydraulic parameter estimation, based on pumping tests as well as geophysical methods, not many studies have addressed the problem with clayey formations being present. In this study, a methodology is proposed to estimate anisotropic hydraulic conductivity and porosity values for the coastal aquifer with unconsolidated formations. For this purpose, the one-dimensional resistivity of the aquifer and the groundwater conductivity data are used to estimate porosity at discrete points. The hydraulic conductivity values are estimated by its mutual dependence with porosity and petrophysical parameters. From these estimated values, the bilinear relationship between hydraulic conductivity and aquifer resistivity is established based on the clay content of the sampled formation. The methodology is applied on a coastal aquifer along with the coastal Karnataka, India, which has significant clayey formations embedded in unconsolidated rock. The estimation of hydraulic conductivity values from the established correlations has a correlation coefficient of 0.83 with pumping test data, indicating good reliability of the methodology. The established correlations also enable the estimation of horizontal hydraulic conductivity on two-dimensional resistivity sections, which was not addressed by earlier studies. The inventive approach of using the established bilinear correlations at one-dimensional to two-dimensional resistivity sections is verified by the comparison method. The horizontal hydraulic conductivity agrees with previous findings from inverse modelling. Additionally, this study provides critical insights into the estimation of vertical hydraulic conductivity and an equation is formulated which relates vertical hydraulic conductivity with horizontal. Based on the approach presented, the anisotropic hydraulic conductivity of any type aquifer with embedded clayey formations can be estimated. The anisotropic hydraulic conductivity has the potential to be used as an important input to the groundwater models.     

Hysteretic behavior and strength capacity of shallowly embedded steel column bases with SFRCC slab

A series of shallowly embedded steel column bases consisting of an exposed column base and a floor slab is tested under horizontal cyclic loading to very large deformation. The effects of floor slabs on strength and ductility are examined using concrete and Steel fiber‐reinforced cementitous composites (SFRCC) for the floor slab. The elastic stiffness, maximum strength, and dissipated energy of the column bases when they include SFRCC increase by 40, 70, and 70% over those of corresponding column bases with concrete floor slab. Better bonding behavior is notable for SFRCC, and the maximum strength and dissipated energy further increase by 15–30% and 70–90%, respectively, owing to the careful arrangement of reinforcing bars. Numerical models are developed to enhance the understanding the behavior of shallowly embedded column bases. Procedures for estimating the elastic stiffness and maximum strength of shallowly embedded column bases with conventional concrete are calibrated for their applicability to those with SFRCC slab. Copyright © 2011 John Wiley & Sons, Ltd.     

A Least-squares Window Curves Method for Interpretation of Magnetic Anomalies Caused by Dipping Dikes

We have developed a least-squares method to determine simultaneously the depth and the width of a buried thick dipping dike from residualized magnetic data using filters of successive window lengths. The method involves using a relationship between the depth and the half-width of the source and a combination of windowed observations. The relationship represents a family of curves (window curves). For a fixed window length, the depth is determined for each half-width value by solving one nonlinear equation of the form f (z) = 0 using the least-squares method. The computed depths are plotted against the width values representing a continuous curve. The solution for the depth and the width of the buried dike is read at the common intersection of the window curves. The method involves using a dike model convolved with the same moving average filter as applied to the observed data. As a result, this method can be applied to residuals as well as to measured magnetic data. Procedures are also formulated to estimate the amplitude coefficient and the index parameter. The method is applied to theoretical data with and without random errors. The validity of the method is tested on airborne magnetic data from Canada and on a vertical component magnetic anomaly from Turkey. In all cases examined, the model parameters obtained are in good agreement with the actual ones and with those given in the published literature.     

Deterministic sliding block methods for estimating seismic displacements of earth structures

A review and quantitative comparison of existing deterministic sliding block methods for predicting permanent displacements of earth structures subjected to seismic loading is presented. The reviewed sliding block methods are divided into two main groups based on the characteristic earthquake parameters referenced in each method. One group uses the maximum horizontal ground acceleration and velocity, and the other uses the maximum horizontal ground acceleration and the predominant period of the acceleration spectrum. Displacement functions published by previous authors are reformulated to give common non-dimensionalized displacement functions of the critical acceleration ratio which are then used to compare the different methods for the estimate of permanent seismic displacement of soil structures. The results show that despite the fact that the different methods were formulated using a wide range of earthquake records and different characteristic seismic parameters, permanent displacement values predicted using these methods fall within a reasonably narrow band. Selected acceleration data from three recent earthquakes that occurred in California are used to evaluate and compare the accuracy of the reviewed displacement methods for practical applications.     

虚分量感应电磁法的一个变种

利用直流电法测量大地电导率,不仅其装备笨重给野外工作带来许多麻烦,而且测量信号中包含激发极化信号,测量数据不很准确。 目前采用的许多电磁感应法由于其异常值与电导率σ之间的函数关系很复杂,不能直观地看出其间的关系。所以,仅以异常值或相对异常值来表示不均匀体的响应,无疑是这类方法的一个缺点,不可能用地电断面的属性--电导率直接表示出异常值。     

朝阳台VP型宽频带倾斜仪与SQ70石英水平摆倾斜仪数据对比分析

运用频谱分析、互相关分析及观测精度等方法,对朝阳地震台石英水平摆倾斜仪与VP宽频带倾斜仪2014年1月至8月的数据进行分析。通过分析得出,VP记录的频率成份较石英水平摆多且复杂,其记录的信息要多于后者,VP垂直摆观测精度总体上优于模拟观测,可以替代石英水平摆。     

Radar determination of the spatial structure of hydraulic conductivity

Spatial variability of hydraulic conductivity exerts a predominant control on the flow of fluid through porous media. Heterogeneities influence advective pathways, hydrodynamic dispersion, and density-dependent dispersion; they are, therefore, a key concern for studies of ground water resource development, contaminant transport, and reservoir engineering. Ground-penetrating radar contributes to the remote, geophysical characterization of the macroscale variability of natural porous media. On a controlled excavation of a glacial-fluvial sand and gravel deposit in the Fanshawe Delta area (Ontario, Canada), the hydraulic conductivity field of a 45 x 3 m vertical exposure was characterized using constant-head permeameter measurements performed on undisturbed horizontal sediment cores. Ground-penetrating radar data were collected along the excavation face in the form of both reflection and common midpoint surveys. Comparison of geostatistical analyses of the permeameter measurements and the radar data suggests thatthe horizontal correlation structure of radar stack velocity can be used to directly infer the horizontal correlation structure of hydraulic conductivity. The averaging nature of the common midpoint survey is manifest in the vertical correlation structure of stack velocity, making it less useful. Radar reflection data do not exhibit a spatial structure similar to that of hydraulic conductivity possibly because reflections are a result of material property contrasts rather than the material properties themselves.     

Nonhydrostatic Atmospheric Normal Modes on Beta-Planes

--To facilitate the understanding of nonhydrostatic effect in global and regional nonhydrostatic models, the normal modes of a nonhydrostatic, stratified, and compressible atmosphere are studied using Cartesian coordinates on midlatitude and equatorial #-planes. The dynamical equations without forcing and dissipation are linearized around the basic state at rest, and solved by using the method of separation of variables. An eigenvalue-eigenfunction problem is formulated, consisting of the horizontal and vertical structure equations with suitable boundary conditions. The wave frequency and the separation parameter, referred to as "equivalent height," appear in both the horizontal and vertical characteristic equations as a coupled problem, unlike the hydrostatic case. Therefore, the nonhydrostatic equivalent height depends not only on the vertical modal scale, as in the hydrostatic case, but also on the zonal and meridional modal scales. Numerical resu lts on the dispersion relations are presented for an isothermal atmosphere. Three kinds of normal modes, namely acoustic, gravity, and Rossby modes, are solved and compared with the corresponding global solutions. Nonhydrostatic effects are studied in terms of normal modes in a wide range of wavelengths from small to planetary scales. It is demonstrated that Rossby modes are hardly affected by nonhydrostatic effects regardless of wavelengths. However, nonhydrostatic effects on gravity modes become significant for smaller horizontal and deeper vertical scales of motion. The equivalent height plays a particularly important role in evaluating nonhydrostatic effects of normal modes on the equatorial #-plane, because the equivalent height appears in the scaling of meridional distance variable of the eigenfunctions. The implementation of nonhydrostatic normal mode analysis on high-resolution numerical modeling is also discussed.     

Generalization of the Rayleigh-Tikhonov stationary geothermal problem for a horizontal layer

The Rayleigh-Tikhonov generalized stationary geothermal problem is formulated and solved exactly for a set of homogeneous horizontal infinite plane-parallel layers located in a lower half-space. The known solutions follow as particular cases of the solutions found. The results obtained in this work are usable for 1-D approximations of many important problems of geophysics, tectonophysics, and geology.     

Determination of the excess density in a horizontal layered model

The inversion gravity problem formulated as follows is solved. The excess density in each layer of a fixed horizontal stratified model is a function of horizontal coordinates (σ(ξ, η)) approximated by a specially constructed function. The problem is to reconstruct the function σ = σ(ξ, η) from the external gravity field. If the geological model includes more than one layer, the problem is solved with the use of a set of reference points at which the sought function is given. Variations in a gravity anomaly with respect to the field at a fixed point are used in solving this problem.     

新疆温泉水平摆年变影响因素分析

以温泉水平摆观测数据及温泉气象资料为研究对象,利用相关、回归分析,讨论温泉水平摆两分向年变的影响因素,研究结果表明:①气温、水位是影响温泉水平摆NS向年变主要因素,它们之间具有准线性关系,NS向相位滞后气温约51天、滞后水位约17天;②气温是影响温泉水平摆EW向年变的主要因素,它们之间具有准线性关系,EW向滞后气温27天,但是水位与温泉水平摆EW向年变基本无关;③气压与温泉水平摆两分向年变基本无关。     

Modal analysis of a DAM–Foundation system based on an FE–BE method in the time domain

A modal analysis procedure based on an FE–BE method in the time domain is first formulated and then applied to a dam–foundation system. In the application, horizontal and vertical impulsive responses are calculated for the system having six different impedance ratios. Modal characteristics such as natural frequencies, damping ratios and mode shapes are evaluated from the Fourier spectra of the responses. The proposed procedure allows analysis of not only the underdamped but also the overdamped modes. According to the analysis, the radiation damping pertinent to the vertical vibration is half of that pertinent to the horizontal vibration and the interaction effect on the modes is not negligibly small when the impedance ratio exceeds 0·3.