AN ITERATIVE METHOD FOR THE SOLUTION OF ANON-LINEAR INVERSE PROBLEM IN MAGNETIC INTERPRETATION*

A method is presented for determining the lower surface of a two-dimensional body producing a magnetic anomaly when its upper surface and the intensity of magnetization are given. The magnetization vector is assumed to lie along a specified direction but the sense of magnetization may be different in different vertical sections of the body and may be regarded as unknown. The method is illustrated using the computed anomalies of some theoretical models.     

A TIME-DOMAIN APPROACH TO THE NORMAL-INCIDENCE INVERSE PROBLEM*

This tutorial paper presents a time-domain derivation of the Normal equations which are associated with the normal-incidence inverse problem. Connections are made between our time-domain derivation and the more familiar z-transform transfer function derivation.     

A SOLUTION OF THE DIPPING INTERFACE PROBLEM USING THE SQUARE ARRAY RESISTIVITY TECHNIQUE*

Apparent resistivity measurements with the square array technique in the vicinity of a dipping interface have the advantage over collinear array methods that they are less dependent on orientation of the array. In order to exploit this, existing potential solutions for the dipping interface problem have been adapted for the computation of apparent resistivities over such a feature using a square array. Comprehensive interpretation techniques covering this problem are given and the limitations imposed by residual array orientation effects are discussed.     

环域大地逆边值问题解的诠释

在用环域大地边值理论求解大地水准面的基础上对环域大地逆边值问题的解式作进一步研究.结果表明:①在线性化模式下,环域大地逆边值问题的解与确定大地水准面的传统的移去-恢复法解具有一致性;②在采用移去-恢复法时应注意,尽管移去过程中需调整地球质量,但不能调整参考正常重力场值;③若边界观测采用重力异常值,在采用移去-恢复法时应注意不能恢复移去物质对大地水准面的一阶项影响;④移去-恢复法的向下归算是环域大地逆边值问题解中的调和延拓的线性近似.本文既是对利用环域大地边值理论求解大地水准面的有效性的重要论证,也是对传统的确定大地水准面的移去-恢复法的数学证明.     

一维地震预报评分问题

本文对当前应用较多的各种基于22列联表的一维地震预报评分进行了较全面地评述,文中论及: 1.从统计相关性着眼,Wallen评分V=QS是最合理的预报评分. 2.顾氏评分S、许氏评分R及O评分Q虽便于使用,但各有不足. 3.由V可引入一系列评分,S与Q的调和均值、Hedike评分SH皆在此系列中.定理5-3列出了常见评分的顺序. 4.从重合程度着眼给出了评分W,并由之引出另一个标准化评分列————W系列(标准化后的有效指数h。在其中居于最严的位置).     

THEORETICAL APPROACH TO THE SOLUTION OF THE INFILTRATION PROBLEM

ABSTRACT

The one-dimensional transient downward entry of water in unsaturated soils is investigated theoretically. The mathematical equation describing the infiltration process is derived by combining Darcy's dynamic equation of motion with the continuity and thermodynamic state equations adjusted for the unsaturated flow conditions. The resulting equation together with the corresponding initial and boundary conditions constitues a mathematical initial boundary value problem requiring the solution of a nonlinear partial differential equation of the parabolic type. The volumetric water content is taken as the dependent variable and the time and the position along the vertical direction are taken as the independent variables. The governing equation is of such nature that a solution exists for t > 0 and is uniquely determined if two relationships are defined, together with the specified state of the system, at the initial time t = 0 and at the two boundaries. The two required relations are those of pressure versus permeability and pressure versus volumetric water content.

Since the partial differential equation has strong non-linear terms, a discrete solution is obtained by approximating the derivatives with finite-differences at discrete mesh points in the solution domain and integrated for the corresponding initial and boundary conditions. The use of an implicit difference scheme is employed in order to generate a system of simultaneous non-linear equations that has to be solved for each time increment. For n mesh points the two boundary conditions provide two equations and the repetition of the recurrence formula provides n—2 equations, the total being n equations for each time increment. The solution of the system is obtained by matrix inversion and particularly with a back-substitution technique. The FORTRAN statements used for obtaining the solution with an electronic digital computer (IBM 704) are presented together with the input data.

Analysis of the errors involved in the numerical solution is made and the stability and convergence of the solution of the approximate difference equation to that of the differential equation is investigated. The method applied is that of making a Fourier series expansion of a whole line of errors and then following the progress of the general term of the series expansion and also the behavior of each constituent harmonic. The errors (forming a continuous function of points in an abstract Banach space) are represented by vectors with the Fourier coefficients constituting a second Banach space. The amplification factor of the difference equation is shown to be always less than unity which guarantees the stability of the employed implicit recurrence scheme.

Experiments conducted on a vertical column packed uniformly with very fine sand, show a satisfactory agreement between the theoretically and experimentally obtained values. Many experimental results are shown in an attempt to explain the infiltration phenomenon with emphasis on the shape and movement of the wet front, and the effects of the degree of compaction, initial water content and deaired water on the infiltration rate.     

电极型电阻率测井反演算法研究

低频电极型测井仪的响应总是受井眼、围岩和侵入的影响,而传统的测井综合解释无法完全有效地校正这些影响．本文将收敛速度快而效果好的变形波恩迭代（DBIM）方法用于处理轴对称二维非均匀介质分布的电导率反演问题．在每次迭代过程中采用了快速的半解析的模式匹配的正演方法,半解析地表达出反演中所需计算的格林函数的偏导数;并在此基础上半解析地求出了反演的非线性积分方程中的积分运算,大大提高了反演速度和精度．     

时间域内有限地震断层的反演问题

为了解决有限地震断层破裂过程研究中的正演和反演问题,本文提出：（1）用广义反射、透射系数矩阵和广义射线理论计算上地幔及远场范围体波理论地震图的混合方法．同时采用格林函数的一种新的组合方式,可节约1／3计算机内存．（2）采用基于模拟退火的热浴算法进行全局搜索反演,不仅提高了在计算过程中新模型被接收的可能性,而且使得在时间域内目标函数的计算速度提高了近二个数量级．对1994年台湾海峡地震震源破裂过程的研究结果表明,这次地震的破裂过程相对比较简单．在前4．0s内地震断层的破裂相当剧烈,错动距离的平均值随着破裂时间增加而迅速减少．开始时破裂速度较高,前4．0s的平均值为3．1km／s,之后逐渐降至2．2km／s．错动方向随破裂的变化不大．     

时间域内有限地震断层的反演问题

为了解决有限地震断层破裂过程研究中的正演和反演问题，本文提出：（1）用广义反射、透射系数矩阵和广义射线理论计算上地幔及远场范围体波理论地震图的混合方法．同时采用格林函数的一种新的组合方式，可节约1／3计算机内存．（2）采用基于模拟退火的热浴算法进行全局搜索反演，不仅提高了在计算过程中新模型被接收的可能性，而且使得在时间域内目标函数的计算速度提高了近二个数量级．对1994年台湾海峡地震震源破裂过程的研究结果表明，这次地震的破裂过程相对比较简单．在前4．0s内地震断层的破裂相当剧烈，错动距离的平均值随着破裂时间增加而迅速减少．开始时破裂速度较高，前4．0s的平均值为3．1km／s，之后逐渐降至2．2km／s．错动方向随破裂的变化不大．     

电极型电阻率测井反演算法研究

低频电极型测井仪的响应总是受井眼、围岩和侵入的影响，而传统的测井综合解释无法完全有效地校正这些影响．本文将收敛速度快而效果好的变形波恩迭代（DBIM）方法用于处理轴对称二维非均匀介质分布的电导率反演问题．在每次迭代过程中采用了快速的半解析的模式匹配的正演方法，半解析地表达出反演中所需计算的格林函数的偏导数；并在此基础上半解析地求出了反演的非线性积分方程中的积分运算，大大提高了反演速度和精度．     

CHEBYSHEV EXPANSIONS FOR THE SOLUTION OF THE FORWARD GRAVITY PROBLEM1

Chebyshev expansions are used to solve the 3D forward gravity problem. Since the matrix factorization method is used to solve the coefficient equation system and the fast Fourier transform (FFT) technique is used to compute the forward and backward Chebyshev expansions, this method is very fast. Multipole expansions are used to calculate approximate boundary conditions (BCs) for realistic problems. When the length of any source-body dimension is less than 70% of the minimum dimension of the computational domain, the relative error caused by the approximate BCs is about 1%. A cell-average discretization method is suggested. The accuracy obtained by the cell-average discretization is much better than that obtained by the traditional point-injection discretization. The Chebyshev expansion technique was applied to four density models including a complex geological structure consisting of two normally faulted layers. Models which were finely sampled had a maximum relative error of about 1%.     

振动反问题在工程中的应用

利用振动反问题理论，结合现场无损检测技术，通过工程结构动态参数测试，给出工程结构强度评定方法。解决工程施工质量鉴定，设计强度满足程度和建筑结构故障诊断等问题。     

ON THE APPLICATION OF INVERSE THEORY TO GRAVITY INTERPRETATION*

Numerical investigations have been carried out on suitable interpretation schemes for gravity, based upon Backus-Gilbert inverse theory. A two-dimensional linear model consisting of horizontal prisms (grid shape) has been adopted for interpretation of gravity profiles. An inversion technique, which uses a linear approach suitable for rapid computation, and studies with synthetic bodies have led to improvements in the method, mainly by applying weighting factors, which improve the solution in the final stages of computational work. Gravity data from the well-known Cyprus island positive anomaly were inverted to demonstrate the feasibility of the method.     

ON TIMING THE VSP FIRST ARRIVAL*

The advent of signal energy on a VSP or check-shot trace may be defined as the first break. An accurate pick of this first break would be possible in the absence of noise. However, real data traces are inevitably corrupted by noise and this leads to difficulty in identifying a break because the signal-to-noise ratio is low in its neighbourhood. Under such conditions, an obvious alternative is to pick “troughs” where the local signal-to-noise ratio is likely to be much higher. Although trough picking is an effective way to minimize the noise problem, it is sensitive to signal properties (such as absorption and multiple reflections) which have no effect upon the accuracy of break picks. Thus, trough picking is signal-sensitive and break picking is noise-sensitive. Clearly, an ideal first-arrival picking scheme would combine the noise-tolerant features of trough picking with the signal-tolerant features of break picking. This ideal may be approached by exploiting known properties of the VSP trace using conventional signal processing techniques. The result of such processing is to reduce the problem to that of picking a trough correctly centered about the true break time.     

QUASI-ANALYTIC CONVOLUTION SOLUTION OF THE ELECTROMAGNETIC FIELD*

The objective of this study is to generate the separation-distance-domain (r-domain) transformation of the theoretically calculated wave number domain (m-domain) electromagnetic induction field component B_z(m, ω) of a stratified medium and to search for interpretive information which has been absent in the previously achieved numerical solutions of the problem. The r-domain kernel R?(r, ω) function defining the induction field appears to adequately reflect the layering and electrical properties of the medium if it is expressed as a function of the frequency if the source-receiver separation r is small with respect to the thickness of the first layer. However, exact values of the conductivity cannot be distinguished from those of the neighboring values unless a resistive basement layer is present. This feature is the result of the truncation in series representation of the kernel function R?(m, ω). However, this truncation is regarded as significant in the case of a conductive first layer. In m-domain static-zone studies, a conductive first layer slightly influences its r-domain correspondent. Although the computational cost of obtaining the kernel B(r, ω) by evaluation of the convolution in a cylindrical coordinate system is high, this semi-analytic solution is still superior to those based on the asymptotic assumptions.     

变密度体重力勘探反演的多解性问题

本文利用经典位论中格林层的概念,证明了: 1.在一个物体内可以有多种密度分布,使其总质量为零,在物体外任一点的位为零; 2.当总质量不变时,在一个固定形状及体积的物体中,可以有多种密度分布,并且处处密度为正,使物体外任一点的位相同; 3.当总质量不变时,在不同形状及不同体积的物体内,可以有多种密度分布,并且处处密度为正,使物体外任一点的位相同。 由此得出结论:总质量不变,若物体的密度不均匀（而且处处为正）,根据重力异常作反演,不能唯一地求出物体的形状;当物体的形状已知时,也不能唯一地求出其密度分布。     

变密度体重力勘探反演的多解性问题

本文利用经典位论中格林层的概念,证明了: 1.在一个物体内可以有多种密度分布,使其总质量为零,在物体外任一点的位为零; 2.当总质量不变时,在一个固定形状及体积的物体中,可以有多种密度分布,并且处处密度为正,使物体外任一点的位相同; 3.当总质量不变时,在不同形状及不同体积的物体内,可以有多种密度分布,并且处处密度为正,使物体外任一点的位相同。 由此得出结论:总质量不变,若物体的密度不均匀（而且处处为正）,根据重力异常作反演,不能唯一地求出物体的形状;当物体的形状已知时,也不能唯一地求出其密度分布。     

APPLICATION OF THE GENERAL COMPLEX COMPLIANCE MODEL TO THE DIRECT-DETECTION PROBLEM*

A methodology is outlined for using general complex compliance functions—which contain the constant-Q case and any kind of fluid saturant as special cases—to determine the nature of that saturant from seismic reflections observed on seismic records. The important attribute of such a formulation based upon complex compliance functions is that the presence of any kind of saturant is indicated by the values of the parameters contained within the complex compliance function, the latter having the same mathematical form for all rocks under any conditions as long as it remains a crystalline solid.     

VERTICAL HETEROGENEITY AND MOVEOUT IN THE ONE-DIMENSIONAL MEDIUM*

Since the important contributions of Dürbaum and Dix, 30 years ago, velocity profile estimation procedures on horizontally layered and vertically heterogeneous media from seismic probing data have been based largely on hyperbolic moveout models and RMS and stacking velocity concepts. Re-examination of the fundamentals reveals that quantitative velocity heterogeneity and canonical valocity profiles have been implicit factors for moveout modelling and for profile inversion in the use of the Dix procedure. Heterogeneity h is the ratio (and v_RMS the geometric or harmonic mean) of the path-average and time-average velocities for a raypath or, in a more restricted sense, for the normal ray belonging to a velocity profile. The canonical profile for a given velocity profile or profile segment is a moveout-equivalent monotonically increasing ramp-like profile. The ramp or constant gradient in depth is the simplest velocity profile approximator which can explicitly accommodate velocity heterogeneity. A ramp model structure is detailed which facilitates moveout simulation and model parameter estimation, and the parametric effects are explored. The horizontal offset range is quantified for which this model can give good moveout approximations.     

磁各向异性条件下的磁法勘探正问题及其解法

本文利用磁化率张量k、导磁率张量μ和剩余磁化强度J_r的概念表征磁性体的各向异性,给出了磁法勘探正问题在磁各向异性条件下的数学提法,即总磁位U应由下列的偏微分方程和定解条件确定: 其中,A₁⁺是磁性体Q₁的边界面,S₁^-和S_大分别是无磁性空间Q₀的内外边界面,n为各区域封闭界面上一点的外法线向量,ρ_r是剩余磁荷密度,U₀是地磁场的磁位。 然后,又给出了应用有限元法解上述正问题的计算公式（二度）和实例。