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.     

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.     

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.     

最小二乘傅立叶有限差分偏移

一般偏移算法是用反演算子通过解析方法求解.最小二乘偏移方法采用另一种思路,即采用数值方法,通过解一个线性离散反问题来索求解.这样我们试着寻找一个模型匹配地震数据并能表现出其某些特点来得到偏移图像.最小二乘法能减少偏移赝像,得到更精确的偏移效果.Kirchhoff算子在最小二乘偏移方法中应用较广,但需要较多的迭代次数,而且具有Kirchhoff偏移的缺点.本文把最小二乘方法运用到基于波长延拓的波动方程偏移方法中,为提高最小二乘偏移的效率,可采用效率较高的正传播算子和反传播算子.我们利用效率较高,能适应剧烈横向变速的傅立叶有限差分正传播和反传播算子来做叠后最小二乘偏移.数值实例表明,通过少数的共轭梯度法迭代,就能得到与真实模型差别很微小的偏移效果.对于傅式变换我们采用了数值软件FFTW,其变换速度比常规FFT算法一般要快六倍以上,进一步提高了效率.本文算法很容易在并行机上实现,这些特点在处理大型数据时大有裨益.     

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.     

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 Constrained Nonlinear Inversion Approach to Quantitative Interpretation of Self-potential Anomalies Caused by Cylinders,Spheres and Sheet-like Structures

An interpretative method based on a nonlinearly mathematical optimization concept has been developed in this paper, in order to interpret self-potential anomalies (SP) due to horizontal cylinder, vertical cylinder, sphere and sheet-like structures. This interpretative method comprises three main steps. The first step is to formulate mathematically a nonlinearly constrained minimization problem (NCMP) to describe the geophysical problem related to the studied structure. The second one is to suggest an interior penalty function in order to convert the nonlinearly constrained minimization problem (NCMP) into a nonlinearly unconstrained minimization one (NUMP). The third step is to solve the converted nonlinearly unconstrained minimization problem (NUMP) by the well-known Hooke and Jeeves direct search algorithm in order to estimate the geophysical parameters of the studied structure, i.e., depth, polarization angle, electric dipole moment (magnitude of polarization) and geometric shape factor. The Hooke and Jeeves direct search algorithm is purposely chosen for being robust and its application to SP data allows a rapid convergence towards the optimal estimate of parameters. This interpretative method was first tested on theoretical synthetic models with different random noise, where a very close agreement was obtained between assumed and evaluated parameters.The validity of the proposed interpretative method is also tested on practical field examples taken from Turkey, India and Germany, where available SP data existed and was previously analyzed by different interpretative methods. The agreement between the results obtained by the developed method and those obtained by other published methods is good.Acknowledgment Authors would like to thank Dr. I. Othman Director General of the Atomic Energy Commission of Syria for his interest and continuous encouragement to achieve this work. Special thanks to the reviewers for their constructive suggestions aimed at enhancing the quality of this paper.     

A Least-Squares Standard Deviation Method to Interpret Gravity Data due to Finite Vertical Cylinders and Sheets

We have developed a least-squares approach to determine simultaneously the depth to both the top and base of a buried finite vertical cylinder (vertical line element approximation) and a 2-D vertical thin sheet from moving average residual anomaly profiles obtained from gravity data using filters of successive window lengths. The method involves using a relationship between the depth to the top, and base of the source and a combination of windowed observations. The method is based on computing the standard deviation of the depths to the top, determined from all moving average residual anomalies for each value of the depth to the base. The standard deviation may generally be considered a criterion for determining the correct depth to the top and base of the buried structure. When the correct depth to the base value is used, the standard deviation of the depths to the top is less than the standard deviation using incorrect values of the depth to the base. This method can be applied to residuals as well as to the observed gravity data. The method is applied to synthetic examples with and without random errors and tested on two field examples from the USA and Canada.     

A Best-Estimate Approach for Determining Self-potential Parameters Related to Simple Geometric Shaped Structures

A new approach is proposed in order to interpret field self-potential (SP) anomalies related to simple geometric-shaped models such as sphere, horizontal cylinder, and vertical cylinder. This approach is mainly based on solving a set of algebraic linear equations, and directed towards the best estimate of the three model parameters, e.g., electric dipole moment, depth, and polarization angle. Its utility and validity are demonstrated through studying and analyzing synthetic self-potential anomalies obtained by using simulated data generated from a known model and a statistical distribution with different random errors components. Being theoretically tested and proven, this approach has been consequently applied on two real field self-potential anomalies taken from Colorado and Turkey. A comparable and acceptable agreement is obtained between the results derived by the new proposed method and those deduced by other interpretation methods. Moreover, the depth obtained by such an approach is found to be very close to that obtained by drilling information.     

Point Mass Method Applied to the Regional Gravimetric Determination of the Geoid

The determination of the local gravity field by means of the point mass inversion method can be performed as an alternative to conventional numerical methods, such as the least-squares collocation. Based on the first derivative of the inverse-distance Newtonian potential for the representation of the gravity anomaly data, it is possible to compute any wavelength component of the geoid in planar approximation with sufficient accuracy. In order to exemplify the theoretical concept, two applications are presented of the computation of two different wavelength components of the geoid, the long wavelength component in a local solution and the short wavelength component in a regional solution. The results are compared with corresponding least-squares collocation solutions, using a global geopotential model to remove and to restore the long wavelength component.     

可控震源非线性扫描地震响应的数值模拟

讨论了几种非线性扫描信号自相关函数的旁瓣特性.对可控震源非线性扫描的地震响应进行了数值模拟.当震源扫描持续时间是检波器接收时间的一半时,相关运算把反射扫描信号压缩成脉冲信号的效果是显著的.有限度地增加震源扫描持续时间以及与之相适应的接收时间可以使反射扫描信号得到进一步的压缩,但在固定扫描与接收时间的条件下,增加采样点个数对反射扫描信号的压缩并不起作用.采用具有低频相关子波特性的非线性扫描震源信号,将有利于相关噪声的消除.模拟结果还证实了二次扫描在某些特定条件下会出现鞍点效应这样一个事实.     

太湖水体的总磷分布及湖流对其影响的数值研究

用数值模拟的方法研究了太湖水体中ＴＰ分布特征及湖流对其影响,推导,建立了包括平流,水平扩散,沉降和底泥释放的浅水湖泊中污染物浓度分布计算的二维迎风有限元数值模式,并在给定若干点源条件下计算各种稳态流场下太湖水体中的ＴＰ分布。     

用正演数值计算方法开展双侧向测井对裂缝的响应研究

采用有限元分析软件ANSYS对裂缝的双侧向测井视电阻率与裂缝孔隙度、泥浆电阻率、裂缝倾角和基岩电阻率的关系进行了计算. 在大量正演数据的基础上得出双侧向测井响应反演公式和裂缝孔隙度计算公式,提出更为精细的裂缝倾角的弹性划分模型,用双侧向视电阻率值近似估算裂缝倾角的方法,提高了利用双侧向测井求裂缝产状与裂缝孔隙度（裂缝宽度）的精度.     

A Tikhonov regularization method to estimate Earth's oblateness variations from global GPS observations

Earth's oblateness is varying due to the redistribution of Earth's fluid mass and the interaction of various components in the Earth system. Nowadays, continuous Global Positioning System (GPS) observations can estimate Earth's oblateness (J₂) variations with the least squares method, but are subject to ill-conditioned equations with limited GPS observations and aliasing errors from truncated degrees. In this paper, a Tikhonov regularization method is used to estimate J₂ variations from global continuous GPS observations. Results show that the J₂ has been better estimated from GPS observations based on a Tikhonov regularization method than the usual least squares method when compared to SLR solutions. Furthermore, the amplitudes and phases of the annual and semi-annual J₂ variations are closer to the SLR results with truncated degrees from 2 to 5. Higher truncated degrees will degrade the J₂ estimate. Annual J₂ variations are best estimated from GPS observations with truncated degree 4 and semi-annual J₂ variations are best estimated with truncated degree 2.     

南极中山站至Dome A考察断面湍流参数特征近地层湍流参数特征

利用南极中山站至Dome A考察断面上3个自动气象站2005～2007年的观测资料和2008年夏季在中山站附近冰盖获取的湍流观测资料,应用空气动力学方法和涡动相关法计算分析了中山站至Dome A断面上近地层各种湍流参数(感热通量,潜热通量,湍流温度、湿度和速度尺度,地表粗糙度,大气稳定度及动量输送系数)的季节变化、日变...     

基于数值模拟和地震活动性统计的混合地震预测: 在中国地震科学实验场的应用

地震数值预测是近年来最为前沿的科学研究问题之一,但是大部分地震数值预测的探索都受困于数值模拟步长的问题.本文引入混合预测方法,探索了较短预测时长的地震数值预测方法,并在中国地震科学实验场区中进行应用.该混合预测方法主要建立在活动块体理论和构造力学分析的基础上,利用数值模拟推测未来长时间的应力变化量,并引入上一次7级地震之后数十年间,中等强度地震同震应力的影响,最后通过重分类和加权,在应力变化量上叠加年尺度小地震活动异常的统计,从而实现区域地震危险程度的混合评估.基于该方法,我们将地震数值预测的预测时间尺度缩短到年尺度,以年为单位滚动预测了中国地震科学实验场自2021—2030年或更长时间段内可能出现中强地震的区域.2022年芦山6.1级地震、2021年漾濞6.4级地震、2021年泸州6.0级地震和2022年泸定6.8级地震均发生在危险性较高的区域,而2022年马尔康6.0级地震则不在预测区域内.本文展示的混合预测尝试为地震数值预测研究提供了一个可供参考的例证,也为解决数值预测步长控制难的问题提供了一个可能的探索途径.

     

A hydrographic method to identify the groundwater net recharge,barometric effect and evapotranspiration from a complicated semidiurnal water table fluctuation

A hydrographic method was proposed to separate out the hourly scaled groundwater level changes caused by net recharge, barometric effects and evapotranspiration from a semidiurnal water table fluctuation. A characteristic midnight time, with a turning point of the barometric pressure change and high relative air humidity, which meant that neither the barometric effect nor groundwater evapotranspiration occurred, was proposed for determining the net recharge rate r_net. Then, the barometric efficiency f_bar was estimated using the other time period without evapotranspiration, and the evapotranspiration rate r_ETG was finally obtained using the remainder of the water level changes. A case example illustrated that estimation of f_bar using the proposed method was more accurate than that using the traditional error analysis method, which may result in a significant underestimation under the condition of the present water level changes. Additionally, the abnormal semidiurnal fluctuations, more specifically, two step-down fluctuations, which may be a common pattern when the groundwater level is controlled by net recharge, barometric effects and evapotranspiration, can be well understood using the three components separated out. The results also showed that nighttime groundwater evapotranspiration, accounting for an average of 23% of that during the daytime, cannot be ignored.