MARS:A TUTORIAL     

SONJASEKULIC  BRUCER.KOWALSKI 《地理学报(英文版)》1992,(4)

This tutorial paper presents a simplified view of one of the more recently published multivariatecalibration methods particularly suited to dealing with non-linear data sets.The method is referred toas MARS and stands for multivariate adaptive regression splines.Simple examples are provided toexplain the workings of the method.  相似文献   

Groebner-basis solution of the three-dimensional resection problem (P4P)     

J. L. Awange  E. W. Grafarend 《Journal of Geodesy》2003,77(5-6):327-337

The three-dimensional (3-D) resection problem is usually solved by first obtaining the distances connecting the unknown point P{X,Y,Z} to the known points P_i{X_i,Y_i,Z_i}i=1,2,3 through the solution of the three nonlinear Grunert equations and then using the obtained distances to determine the position {X,Y,Z} and the 3-D orientation parameters {,, }. Starting from the work of the German J. A. Grunert (1841), the Grunert equations have been solved in several substitutional steps and the desire as evidenced by several publications has been to reduce these number of steps. Similarly, the 3-D ranging step for position determination which follows the distance determination step involves the solution of three nonlinear ranging (`Bogenschnitt') equations solved in several substitution steps. It is illustrated how the algebraic technique of Groebner basis solves explicitly the nonlinear Grunert distance equations and the nonlinear 3-D ranging (`Bogenschnitt') equations in a single step once the equations have been converted into algebraic (polynomial) form. In particular, the algebraic tool of the Groebner basis provides symbolic solutions to the problem of 3-D resection. The various forward and backward substitution steps inherent in the classical closed-form solutions of the problem are avoided. Similar to the Gauss elimination technique in linear systems of equations, the Groebner basis eliminates several variables in a multivariate system of nonlinear equations in such a manner that the end product normally consists of a univariate polynomial whose roots can be determined by existing programs e.g. by using the roots command in Matlab.Acknowledgments.The first author wishes to acknowledge the support of JSPS (Japan Society of Promotion of Science) for the financial support that enabled the completion of the write-up of the paper at Kyoto University, Japan. The author is further grateful for the warm welcome and the good working atmosphere provided by his hosts Professors S. Takemoto and Y. Fukuda of the Department of Geophysics, Graduate School of Science, Kyoto University, Japan.  相似文献   

Selection of ground motion time series and limits on scaling   总被引：4，自引：0，他引：4  

Jennie Watson-Lamprey  Norman Abrahamson 《Soil Dynamics and Earthquake Engineering》2006,26(5):477-482

A procedure to select time series for use in non-linear analyses that are intended to result in an average response of the non-linear system is proposed that is not based simply on magnitude, distance, and spectral shape. A simple model of a yielding system is used as a proxy for the non-linear behavior of a more complicated yielding system. As an example, Newmark displacements are used as a proxy for more complex slope-stability models. The candidate scaled time series are evaluated to find those that yield a response of the simple non-linear system that is near the expected response for the design event. Those scaled time series with responses near the expected value are selected as the optimum time series for defining average response even if the scale factors are larger than commonly accepted (e.g. scale factors >factor of 2).  相似文献   

An Aggregate Constraint Method for Inequality-constrained Least Squares Problems   总被引：3，自引：0，他引：3  

Junhuan Peng  Hongping Zhang  Suli Shong  Chunxi Guo 《Journal of Geodesy》2006,79(12):705-713

The inequality-constrained least squares (ICLS) problem can be solved by the simplex algorithm of quadratic programming. The ICLS problem may also be reformulated as a Bayesian problem and solved by using the Bayesian principle. This paper proposes using the aggregate constraint method of non-linear programming to solve the ICLS problem by converting many inequality constraints into one equality constraint, which is a basic augmented Lagrangean algorithm for deriving the solution to equality-constrained non-linear programming problems. Since the new approach finds the active constraints, we can derive the approximate algorithm-dependent statistical properties of the solution. As a result, some conclusions about the superiority of the estimator can be approximately made. Two simulated examples are given to show how to compute the approximate statistical properties and to show that the reasonable inequality constraints can improve the results of geodetic network with an ill-conditioned normal matrix.  相似文献   

Ground water contaminant transport by nondivergence-free, unsteady and nonstationary velocity fields     

Hakan Sirin   《Journal of Hydrology》2006,330(3-4):564-572

Pore flow velocity is assumed to be a nondivergence-free, unsteady, and nonstationary random function of space and time for ground water contaminant transport in a heterogeneous medium. The laboratory-scale stochastic contaminant transport equation is up scaled to field scale by taking the ensemble average of the equation by using the cumulant expansion method. A new velocity correction, which is a function of mean pore flow velocity divergence, is obtained due to strict second order cumulant expansion (without omitting any term after the expansion). The field scale transport equations under the divergence-free pore flow velocity field assumption are also derived by simplifying the nondivergence-free field scale equation. The significance of the new velocity correction term is investigated on a two dimensional transport problem driven by a density dependent flow.  相似文献   

一种新的地球物理反演方法——模拟原子跃迁反演法   总被引：12，自引：5，他引：12       下载免费PDF全文

师学明  王家映  易远元  苑新喜  王晓明  张云姝 《地球物理学报》2007,50(1):305-312

详细研究了一般地球物理反问题的迭代优化求解过程与物理学中原子跃迁过程的对应关系，建立了反演问题中模型空间、初始模型、局部极值模型、最优化模型等与原子的态空间、定态、激发态、基态等的对应关系. 在此基础上，模拟了物理学中原子从激发态向基态跃迁的物理过程，建立了一种与原子跃迁过程相对应的非线性随机跃迁数学模型和模型解跃迁搜索准则，导出了适用于一般地球物理资料的模拟原子跃迁的非线性反演算法. 用理论测试函数对这种新的反演方法进行了数值试验，结果表明该方法具有解不依赖于初始模型、收敛速度快等优点.  相似文献   

地震波的场方程矩阵和能量的正定二次型及其意义   总被引：2，自引：0，他引：2       下载免费PDF全文

牛滨华  孙晟  孙春岩  黄新武  李佳 《地球物理学进展》2007,22(2):353-358

场方程是能够表述半空间地震波场的整体特征.波动方程、速度方程和能量方程.通过分析可知每个场方程都具有各自的“场方程矩阵”.能量方程能够对所有场方程矩阵进行综合和贯通，给出了能量方程以“弹性矩阵”为核心的普适性表达形式.最后，运用矩阵的正定二次型理论阐述了“能量矩阵与弹性矩阵”之间一致的对称性和正定性.能量矩阵蕴含的动态力的平衡关系、速度的时间_空间分布和能量的传播及变化的物理意义，能够从能量矩阵的正定二次型特性表述出来.本文研究分析问题的方法完全适用于复杂介质模型，相关的认识和结论可以拓展到均匀黏弹性各向同性介质、均匀弹性各向异性介质、均匀黏弹性各向异性介质以及比奥饱和流体介质.  相似文献   

三角形网格下求解二维浅水方程的和谐Godunov格式   总被引：13，自引：3，他引：13       下载免费PDF全文

潘存鸿 《水科学进展》2007,18(2):204-209

为保证计算格式的和谐性,通过特殊的底坡源项处理技术,在三角形网格上建立了求解二维浅水流动方程的具有空间二阶精度的Godunov格式。应用准确Riemann解求解法向数值通量,用改正的干底Riemann解处理动边界问题。经典型算例和钱塘江河口涌潮计算验证,表明模型健全,分辨率高,具有较大的推广应用价值。  相似文献   

起伏地表条件下地震波场数值模拟有限积分变换有限差分方法     

李健  孙建国 《吉林大学学报(地球科学版)》2007,(Z1)

针对起伏地表条件下的地震波数值模拟问题,提出将起伏的地表映射到一个规则的长方形网格坐标系中,并在此基础上推导出变换域中的波动方程。根据导出来的波动方程应用有限余弦变换有限差分方法进行地震波场的数值模拟,以解决起伏地表条件下的数值模拟。  相似文献   

The solution of the Korn–Lichtenstein equations of conformal mapping: the direct generation of ellipsoidal Gauß–Krüger conformal coordinates or the Transverse Mercator Projection     

E. W. Grafarend  R. Syffus 《Journal of Geodesy》1998,72(5):282-293

The differential equations which generate a general conformal mapping of a two-dimensional Riemann manifold found by Korn and Lichtenstein are reviewed. The Korn–Lichtenstein equations subject to the integrability conditions of type vectorial Laplace–Beltrami equations are solved for the geometry of an ellipsoid of revolution (International Reference Ellipsoid), specifically in the function space of bivariate polynomials in terms of surface normal ellipsoidal longitude and ellipsoidal latitude. The related coefficient constraints are collected in two corollaries. We present the constraints to the general solution of the Korn–Lichtenstein equations which directly generates Gau?–Krüger conformal coordinates as well as the Universal Transverse Mercator Projection (UTM) avoiding any intermediate isometric coordinate representation. Namely, the equidistant mapping of a meridian of reference generates the constraints in question. Finally, the detailed computation of the solution is given in terms of bivariate polynomials up to degree five with coefficients listed in closed form. Received: 3 June 1997 / Accepted: 17 November 1997  相似文献