Dynamic faulting under rate-dependent friction

We discuss the effects of rate-dependent friction on the propagation of seismic rupture on active faults. Several physicists using Burridge and Knopoff's box and spring model of faulting have proposed that fault complexity may arise from the spontaneous development of a self-similar stress distribution on the fault plane. If this model proves to be correct, it has important consequences for the origin of the complexity of seismic sources. In order to test these ideas on a more realistic earthquake model, we developed a new boundary integral equation method for studying rupture propagation along an antiplane fault in the presence of nonlinear rate-dependent friction. We study rupture dynamics of models with single and twin asperities. In our models, asperities are places on the fault with a higher value of prestress. Othewise all fault parameters are homogeneous. We show that for models with such asperities, a slip velocity weakening friction leads to the propagation of supersonic healing phases and to the spontaneous arrest of fracture if the prestress outside the asperities is low enough. For models with asperities, we can also observe narrow slip velocity pulses, qualitatively similar to the so-called Heaton pulses observed in some earthquake accelerograms. We also observe a complex distribution of stress after the rupture that depends on details of the initial distribution of asperities and on the details of the friction law.     

无结构网格上二维浅水流动的数值模拟

提出在无结构网格上建立有限体积高性能格式族的统一框架,通过引入跨单元界面法向数值通量的逆风分解,将一维Osher、TVD两种通量分裂格式自然地推广至二维浅水方程组。给出了各种情况下浅水方程组有限体积法边界处理的计算公式。最后,利用该格式对穹包溢流、陆地动边界和河口潮流三个问题进行计算。结果表明,这类守恒格式具有高精度、无振荡性以及处理复杂流态过渡、自动捕俘间断和模拟陆地动边界的功能。     

IMPLICIT NONLINEAR NORMAL MODE INITIALIZATION:A MULTIGRID APPROACH

The implicit nonlinear normal mode initialization (INMI) is applied to a tropical limited area shallow water modelin spherical coordinates.The boundary condition for the INMI scheme is based on the boundary formulation of themodel.The INMI scheme is found to be very efficient in suppressing spurious gravity wave oscillation and providing awell balanced initial data set for the model.The INMI scheme involves solving a number of elliptic type equations withvarying complexity.and hence an efficient numerical technique is required for solving such equations.In order to makeINMI computationally more attractive,we are employing the multigrid method for solving all the elliptic type equationsin the INMI scheme.The numerical procedures for the development of such multigrid solvers are briefly described.     

The SOMS model and its application to Lake Neuchâtel

A three-dimensional numerical circulation model (SOMS) based on primitive equations is described. The algorithm, by which Coriolis and vertical diffusion terms are treated implicitly while mass is still conserved exactly (algebraically), is discussed in detail. The model is applied to Lake Neuchâtel (Switzerland), to determine the general circulation under influence of the most prevailing wind.     

Development of the instantaneous unit hydrograph using stochastic differential equations

Recognizing that simple watershed conceptual models such as the Nash cascade ofn equal linear reservoirs continue to be reasonable means to approximate the Instantaneous Unit Hydrograph (IUH), it is natural to accept that random errors generated by climatological variability of data used in fitting an imprecise conceptual model will produce an IUH which is random itself. It is desirable to define the random properties of the IUH in a watershed in order to have a more realistic hydrologic application of this important function. Since in this case the IUH results from a series of differential equations where one or more of the uncertain parameters is treated in stochastic terms, then the statistical properties of the IUH are best described by the solution of the corresponding Stochastic Differential Equations (SDE's). This article attempts to present a methodology to derive the IUH in a small watershed by combining a classical conceptual model with the theory of SDE's. The procedure is illustrated with the application to the Middle Thames River, Ontario, Canada, and the model is verified by the comparison of the simulated statistical measures of the IUH with the corresponding observed ones with good agreement.     

Conditioning of coefficient matrices of Ordinary Kriging

The solution of a set of linear equations is central to Ordinary Kriging. Computers are commonly applied because of the amount of data and work involved. There has, until recently, been little attention devoted toward the conditioning of kriging matrices. This article considers implications of conditioning upon numerical stability, instead of on robustness which has been the main focus of past work. The effect of properties of the stationary covariance matrix on the conditioning of the kriging matrix is discussed. The relationship between the covariance and autocorrelation functions allows some conclusions about the conditioning of covariance matrices, based on past work in deconvolution. The conditioning of some coefficient matrices of stationary kriging, defined in terms of either the semivariogram or the covariance, is examined.     

二维全球气候模式的发展——由对流层向平流层的扩展

采用Arakawa的σ-p混合坐标，将李维亮等人发展的一个二维全球原始方程模式由对流层扩展到平流层中层(10 hPa)。垂直分层采用等lnp方案。发展后的模式不仅在计算上具有很好的稳定性，而且能较好地模拟平均温度场、平均纬向风场和平均经向风场及其季节性变化。同时，在模式对流层之上加上平流层后改善了对流层上层环流的模拟。     

有限元素法全倾角波动方程偏移

本文试图从两个方面提高波动方程偏移的效果:1.使用全方向波动方程进行偏移,使之适用于任意倾角界面的反射;2.使用有限元素法提高微分方程数值解法的精度。     

A review on stochastic differential equations for applications in hydrology

Fundamentals of the theory of stochastic calculus and stochastic differential equations (SDE's) which are finding increasing application in water resources engineering are reviewed. The basics of probability theory, mean square calculus and the Wiener, white Gaussian and compound Poisson processes are given in preparation for a discussion of the general Itô SDE with drift, diffusion and jump discontinuity terms driven by Gaussian white noise and compound Poissionian impulses. Also discussed are stochastic integration and the derivation of moment equations via the Itô differential rule. The lierature of SDE's is reviewed with an emphasis on the more accessible sources.     

利用二维DLT及光束法平差进行数字摄像机标定

利用共线方程和二维DLT之间的对应关系导出了由二维DLT的8个参数表达的主纵线方程式，讨论了主点初值和求解方法，给出了单张像片摄像机参数分解不惟一性及临界序列的证明，详细推导了利用二维DLT参数分解摄像机外方位元素初值的实用算法，论述了利用光束法平差进行摄像机标定的数学模型，实际图像数据实验取得了很好的结果，验证了本文所提出的摄像机标定算法的可行性。