用球面调和函数拟合地震波Q值空间分布收敛性的研究

本文从球面调和多项式的数学理论方面研究了用球函数拟合地慢地震波Q 值空间分布方法的收敛性的问题。运用一种逼近的球面多项式的误差公式,证明用球谐函数拟合地幔地震波Q 值空间分布的方法是收敛性的;也提出从地震P 波的振幅A 和周期T 拟合、反演地幔范围P 波品质因数空间分布的误差Qer 与P 波(A、T)的观测数目N 的增加,Qer 的减少来予以验证。     

A fast direct solution method for nonlinear equations in an analytic element model

The analytic element method, like the boundary integral equation method, gives rise to a system of equations with a fully populated coefficient matrix. For simple problems, these systems of equations are linear, and a direct solution method, such as Gauss elimination, offers the most efficient solution strategy. However, more realistic models of regional ground water flow involve nonlinear equations, particularly when including surface water and ground water interactions. The problem may still be solved by use of Gauss elimination, but it requires an iterative procedure with a reconstruction and decomposition of the coefficient matrix at every iteration step. The nonlinearities manifest themselves as changes in individual matrix coefficients and the elimination (or reintroduction) of several equations between one iteration and the other. The repeated matrix reconstruction and decomposition is computationally intense and may be avoided by use of the Sherman-Morrison formula, which can be used to modify the original solution in accordance with (small) changes in the coefficient matrix. The computational efficiency of the Sherman-Morrison formula decreases with increasing numbers of equations to be modified. In view of this, the Sherman-Morrison formula is only used to remove equations from the original set of equations, while treating all other nonlinearities by use of an iterative refinement procedure.     

A whole-space transform formula of cylindrical wave functions for scattering problems

The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf’s addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf’s addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.     

Seismic displacement demand prediction in non-linear domain: Optimization of the N2 method

In Europe, computation of displacement demand for seismic assessment of existing buildings is essentially based on a simplified formulation of the N2 method as prescribed by Eurocode 8(EC8). However, a lack of accuracy of the N2 method in certain conditions has been pointed out by several studies. This paper addresses the assessment of effectiveness of the N2 method in seismic displacement demand determination in non-linear domain. The objective of this work is to investigate the accuracy of the N2 method through comparison with displacement demands computed using non-linear timehistory analysis(NLTHA). Results show that the original N2 method may lead to overestimation or underestimation of displacement demand predictions. This may affect results of mechanical model-based assessment of seismic vulnerability at an urban scale. Hence, the second part of this paper addresses an improvement of the N2 method formula by empirical evaluation of NLTHA results based on EC8 ground-classes. This task is formulated as a mathematical programming problem in which coefficients are obtained by minimizing the overall discrepancy between NLTHA and modified formula results. Various settings of the mathematical programming problem have been solved using a global optimization metaheuristic. An extensive comparison between the original N2 method formulation and optimized formulae highlights benefits of the strategy.     

APPROXIMATE SOLUTION USING A PERTURBATION METHOD FOR DETENTION POND DESIGN

1 INTRODUCTION Mountains higher than 100m occupy 63% of the land area in Taiwan. Serious flood disasters and muddy flows usually occur in the rainy season. To reduce the disasters from hillslope development, the government published the Norm of Soil and Water Conservation Treatment (NSWCT) in 1994. One of the most important treatments is that detention ponds and grit chambers are essential facilities for reducing increased peak flow disasters and sediment yield. 309 volumes on soil…     

地方震尾波震级的初步研究

地方震尾波由地壳横向不均匀性而产生的反向散射波组成。从这一观点出发,根据尾波随掠过时间的衰减特性,结合地震矩对数和地方震里克特地震级的线性关系,导出利用任一掠过时间的震尾来计算的尾波震级Mc公式。它的简化形式可以和持续时间震级的表达式近似一致。尾波震级可作为持续时间震级的一种广义形式,它是直接从震源地震矩导出的震级标度,从而为解释持续时间震级物理基础提供了可能的途径。应用于丹江地震台的资料,得到丹江口及邻区的尾波品质因子和介质函数以及地震矩对数和震级的期望关系,同时得到实用于该台的持续时间震级和简化尾波震级公式。     

Two-dimensionality on spherical earth — A problem in gravity reductions

Summary A mass distribution which remains constant perpendicular to a diameter, within the walls of a vertical cylinder, is defined as a bounded two-dimensional mass distribution. Assumption of such a distribution may be more realistic than the assumption of an unbounded two-dimensional distribution in many situations. The gravity effect of such a distribution is comparable with the effect calculated by conventional three-dimensional methods of reduction. The effect of sphericity of the earth may be allowed as an additional correction. For the calculation of the gravitational effect of this distribution, a formula for the attraction of a cylindrical strip, at a point on the axis, is derived. The effect is compared with that of a two-dimensional distribution. To calculate the effect of sphericity, a formula for the attraction of a spherical cap is derived and this attraction is compared with that of a flat disc. The proposed distribution and the correction for sphericity are particularly applicable in marine gravity reductions.     

射线法在粘-弹性介質中的推广

一、引言在完全弹性介貭中,弹性波的传播問題已經研究得比較深入,尤其用射綫法来解决波的传播強度問題,有了一套完善的方法。实际上,大地岩层近于粘-弹性介貭,地震波在传播过程中要受到內摩擦的作用,振幅随距离逐漸衰減。衰減規律,現在均根据經驗公式来确定。在理論上,虽然可以通过解波动方程的方法解决这問题,但所得結果,即使极簡单的問題也是十分复杂的。在完全弹性介貭中,也存在同样的情形,但如应用射线法,則变得較为方便。     

对利用跨断层基线和水准测量资料推算断层活动参数公式的改进

分析了利用两条跨断层基线和水准测量资料推算断层三维活动参数传统公式存在的问题,指出传统的计算公式实际是一个要求两侧点位处于同一水平面时的近似公式。本文对这一公式重新进行了严格的数学推导,得到了适用于一般情况的改进后的计算公式,并以实际算例指出传统公式对计算结果可能造成的误差量级。     

地震面波产生的地震动转动分量研究

本文利用弹性波动理论对地面转动分量，即瑞利（Rayleigh)波和乐夫（Love)波产生的转动分量进行了研究，给出了相应的计算公式和计算方法，特别注意到面波的散射效应对转动分量的影响，并将这一特性引入到转动分量的求取中，使问题的解决更切合于实际，最后选取实际地震记录，利用得到的公式计算出地震面波产生的转动分量。     

沉积盆地中地震波速度与地层年代的关系

地层年代确定是地质学研究领域的重要课题,地质类定年方法具有各种不利因素.本文选择地球物理方法确定地层年代,以中国大陆沉积盆地为研究区,通过对盆地中实测速度、深度和年代三者间关系的深入研究,应用统计、拟合和扫描的方法,建立了中国大陆沉积盆地中速度、深度和年代之间的定量关系,此关系式为测定年代提供了一种新的方法.利用此关系式计算了沉积盆地基底的年代范围,并与同位素实测的年龄作了比较,表明该方法可以粗略确定稳定基底年代.计算基底年龄和实测数据之间存在误差,其原因主要是本文把中国大陆沉积盆地看作一个构造单元所致.     

有限长圆柱体磁异常场全空间正演方法

在经典位场理论中,许多简单形体位场异常难以通过积分得到全空间的解析式.圆柱体是一类很重要的理论模型体,常用于模拟圆柱状地质体或非地质体(如管线),但目前还不能用解析公式正演有限长圆柱体在三维空间里的磁异常,而多是采用近似简化为有限长磁偶极子或线模型代替.对于有限长圆柱体,特别是半径相对于上顶埋深较大时,这种近似的误差不可忽略.本文利用共轭复数变量替换法,推导出有限长圆柱体在全空间的引力位一阶、二阶导数,利用Poisson关系得到磁异常正演公式,进而利用有限长圆柱体磁异常正演公式求解管状体的磁异常,得到不同磁化方向、不同大小的管线产生的磁场的特征,并将其推广到截面为椭圆的情况.最后通过模拟计算定量给出了将圆柱体近似为线模型的条件.     

平面不规则结构的实用多维反应谱计算方法

因地震动输入方向对平面不规则结构响应的影响显著,所以本文对该类的实用多维反应谱计算方法进行了研究。首先,基于多维加速度功率谱矩阵的研究成果,引入激励输入角度和相应参数,推导了能合理考虑激励输入方向的加速度功率谱和基于平稳随机振动求解响应的计算公式。然后再引入位移谱,利用其能合理考虑激励非平稳性的特点,提出了水平双向的实用反应谱法计算公式。最后,以平面为L形的空间钢结构为例,对不同输入角度时的节点位移公式计算值与多条地震波的时程响应值进行了比较,证明该计算方法是合理的,可供结构抗震设计与分析作参考。     

地震信号瞬时频率的估算

本文比较了四类计算瞬时频率的方法.基于相位差分的方法对噪声敏感;基于零交叉点的方法是针对周期信号提出的,对非周期信号效果不理想,通过插值改善估算结果;基于FIR微分器的方法有三种,基于两点的FIR方法与标准公式较为接近,但会引入半个采样间隔的时移;基于三点的FIR方法可以消除时移,但计算结果会出现负频尖峰;Claerbout方法不仅会引入半个采样间隔的时移,而且估算的频率值可能超过Nyqusit频率.本文在Claerbout公式的基础上导出了一种估算瞬时频率的公式,该公式消除了时移,且负频尖峰也得到抑制;基于时频表示一阶矩的方法的计算结果较为平滑,同时具有一定的抗噪能力.最后用本文导出的公式和时频表示一阶矩两种方法计算了南海东北部一条地震剖面的瞬时频率,并将其结果与Seismic Unix中相关函数的计算结果做了比较,表明本文导出公式的计算结果较为理想.     

近震震级测定方法研究

本文根据北京电信传输地震台网在1978-1984年期间的395次地震[1.0ML6.2;10△600km]资料,讨论了近震震级 ML 的量规函数、台基校正、仪器分量校正和震源区校正等,并着重研究了信号持续时间震级 MD 的不同测定方法和误差.结果表明,如果采用本文中所述的方法,不需添加任何校正值,只用少数几个台甚至仅用一个台的资料就可逼近无偏震级.必须指出,持续时间震级 MD 在震级大于4.8时可产生震级饱和现象,对此,用另一条具有较大斜率的方程拟合便可得到满意的结果.      

基于方位各向异性弹性阻抗的裂缝岩石物理参数反演方法研究

裂缝储层岩石物理参数的准确获得对地下裂缝预测具有重要意义,而叠前地震反演是获得裂缝岩石物理参数的有效手段.本文从裂缝岩石物理等效模型的构建出发,从测井数据上估测了裂缝岩石物理参数,通过推导含裂缝岩石物理参数的方位各向异性弹性阻抗公式,探讨了基于方位各向异性弹性阻抗的裂缝岩石物理参数地震反演方法.实际工区地震数据应用表明,基于方位各向异性弹性阻抗的裂缝岩石物理参数反演方法合理、可靠,可以降低裂缝岩石物理参数估测的不确定性,为地下裂缝预测提供有力的依据.     

Estimates of heat and pyroclast discharge by volcanic eruptions based upon the eruption cloud and steady plume observations

Fumarolic steam plumes and eruption clouds rise like convetive turbulent columns into the atmosphere. Formulae are presented here for estimating the heat power of plumes, the production rate of juvenile pyroclasts ejected during eruptions and the heat output of fumaroles. Their accuracy is tested using the well-studied examples of eruptions of Kamchatkan volcanoes.The Briggs (1969) formula may be used in observing the ascending part of a plume in crosswinds. The best results have been obtained using the CONCAWE formula which permits estimation of the heat power in crosswinds based on the axis height of a horizontal part of a maintained plume. Three connected equations have been suggested for a stable atmosphere and calm weather conditions. The first one, which is applicable for heights ranging from 100 m to 1 km, is the formula proposed by Morton et al. (1956). This equation changes for higher layers of the troposphere (1–10 km) and stratosphere (10–55 km).A classification scale was constructed allowing us to compare volcanic eruptions and fumarolic activity in terms of the intensity of their plumes.The described method is useful for volcano surveillance; it helps in the study of the energetics and mechanics of volcanic and magmatic processes.     

基于改进Parker-Oldenburg界面反演方法计算青海省居里面深度

居里面深度的起伏可以大致反映地壳深部温度场的分布特征,从而间接指示干热岩的赋存情况,因此研究居里面的起伏特征十分重要.本文针对经典的Parker-Oldenburg界面反演方法存在的计算不稳定、结果精度低的问题,通过公式推导,将界面反演公式与向下延拓公式进行类比,利用稳定的波数域正则-积分迭代下延法对经典的Parker...     

Evaluation of the fourth-order tesseroid formula and new combination approach to precisely determine gravitational potential

Calculating topographic gravitational potential (GP) is a time-consuming process in terms of efficiency. Prism, mass-point, mass-line, and tesseroid formulas are generally used to calculate the topographic GP effect. In this study, we reformulate the higher-order formula of the tesseroid by Taylor series expansion and then evaluate the fourth-order formula by numerical tests. Different simulation computations show that the fourth-order formula is reliable. Using the conventional approach in numerical calculations, the approximation errors in the areas of the north and south poles are extremely large. Thus, in this study we propose an approach combining the precise numerical formula and tesseroid formulas, which can satisfactorily solve the calculation problem when the computation point is located in the polar areas or areas very near the surface. Furthermore, we suggest a “best matching choice” of new combination approach to calculate the GP precisely by conducting various experiments. Given the computation point at different positions, we may use different strategies. In the low latitude, we use a precise numerical formula, the fourth-order tesseroid formula, the second-order tesseroid formula, and the zero-order formula, in the 1° range (from the computation point), 1° to 15° range, 15° to 40° range, and the range outside 40°, respectively. The accuracy can reach 2 × 10^?5 m² s^?2. For the high latitude, we use the precise numerical formula, fourth-order tesseroid, second-order tesseroid, and zero-order tesseroid formulas in the ranges of 0° to 1°, 1° to 10°, 10° to 30°, and the zones outside 30°, respectively. However, if an accuracy level of 2 × 10^?5 m² s^?2 is required, the zero-order tesseroid formulas should not be used and the second-order tesseroid formula should be used in the region outside 15° for the low latitude and in the region outside 10° for the high latitude.     

A method for predicting co-seismic displacements of slopes for landslide hazard zonation

Landslide hazard zonation based on co-seismic slope displacements has been applied in many regions. As there are a large number of slopes to be analyzed and it is impossible to obtain actual acceleration time histories for each of these slopes, the co-seismic displacements are often estimated by some simple empirical formulas, which are derived through regression analysis based on a certain set of acceleration time histories and can only be validly applied to regions similar to where the time history data were recorded. In this paper, treating the ground motion as a random process, a formula for calculating the expected value of Newmark displacement with the acceleration amplitude spectrum as input is derived. Since the formula is theoretically equivalent to the double integration procedure in a rigorous Newmark analysis, which has also been verified by careful comparisons of the calculated results, it can be applied for different regions. By combining the formula with ground motion simulations, a new method for estimating co-seismic slope displacements is proposed. The application of the method in the seriously struck area by Wenchuan earthquake shows that it is an effective tool for predicting co-seismic slope displacements as the predicted landslide distribution by using its estimated results agrees reasonably with the actual observations.