Sensitivity equations for hyperbolic conservation law-based flow models

The present paper focuses on the governing equations for the sensitivity of the variables to the parameters in flow models that can be described by one-dimensional scalar, hyperbolic conservation laws. The sensitivity is shown to obey a hyperbolic, scalar conservation law. The sensitivity is a conserved scalar except in the case of discontinuous flow solutions, where an extra, point source term must be added to the equations in order to enforce conservation. The propagation speed of the sensitivity waves being identical to that of the conserved variable in the original conservation law, the system of conservation laws formed by the original hyperbolic equation and the equation satisfied by the sensitivity is linearly degenerate. A consequence on the solution of the Riemann problem is that rarefaction waves for the variable of the original equation result in vacuum regions for the sensitivity. The numerical solution of the hyperbolic conservation law for the sensitivity by finite volume methods requires the implementation of a specific shock detection procedure. A set of necessary conditions is defined for the discretisation of the source term in the sensitivity equation. An application to the one-dimensional kinematic wave equation shows that the proposed numerical technique allows analytical solutions to be reproduced correctly. The computational examples show that first-order numerical schemes do not yield satisfactory numerical solutions in the neighbourhood of moving shocks and that higher-order schemes, such as the MUSCL scheme, should be used for sharp transients.     

Coseismic deformation and slip distribution of the 1997 7.5 Manyi, Tibet, earthquake from InSAR measurements

We use interferometric synthetic aperture radar (InSAR) observations to investigate the coseismic deformation and slip distribution of the 1997 M_w7.5 Manyi earthquake, a left-lateral strike-slip earthquake occurred on the west portion of the Kunlun fault in the northern Tibet, China. The fault trace is constrained by the combination of interferometric coherence image and azimuth offset image. The total length of the identified fault is about 170 km. We estimate the source parameters using a seven-segment fault model in a homogeneous elastic half-space. We first use a uniform slip model to estimate the slip, width, dip and rake for each segment, resulting in a maximum slip of 5.5 m with a depth of 11 km on the fourth segment. The average dip of the uniform slip model is about 93° northward and the average rake is about −2°. We then use a distributed slip model to estimate the pure strike-slip and oblique slip distribution, respectively. In the distributed slip model, the fault plane is discretized into 225 patches, each of them 4 km × 4 km. We fix the optimal geometric parameters and solve for the slip distribution using a bounded variable least-squares (BVLS) method. We find a geodetic moment of 1.91 × 10²⁰ Nm (M_w7.5), of which almost 68% released in the uppermost 8 km and 82% in the uppermost 12 km. For all the models used in this study, the synthetic profiles along strike show asymmetric displacements on the opposite sides of the fault, which are in agreement with the observations. This suggests that a linear elastic model with variable and non-vertical dips is also reasonable for the mechanism of the Manyi earthquake.     

大地主题解算方法综述

大地主题解算是大地测量中的重要问题,由于椭球的复杂性,随之产生的解算方法也是多种多样。本文分析了大地主题解算的一般方法及其公式的适用范围,指出了它们的特点和不足,讨论了现今常用解算方法存在的问题和进一步的研究方向。     

Uniaxial Compression of Synthetic, Poorly Consolidated Granular Rock with a Bimodal Grain-size Distribution

Summary. We attempted to gain some insight into the mechanical properties of poorly consolidated granular rock by preparing and testing synthetic rock specimens in which different cement content and bimodal grain-size distributions were used. We mixed various proportions of fine and coarse sand, Portland cement, and water. The mixture was cast in a mold and left pressure-free during curing, thus ensuring that the final material was poorly consolidated. The specimens were tested in a uniaxial press. During these tests, the static Youngs modulus was measured by performing small stress excursions at discrete intervals along the stress-strain curve. We observed significant non-linear elasticity (i.e., Youngs modulus increased with stress) in all the specimens. As expected, the uniaxial compressive strength increased with increasing cement content. Furthermore, we observed a transition from grain-size sensitivity of strength at cement contents less than 20–30% to grain-size independence above this value. At high cement content, the measured values of Youngs modulus are relatively well explained by a model based on rigid inclusions embedded in a soft matrix. At low cement content, we suggest that modelling the individual cemented grain-to-grain contacts becomes necessary. But this could not be done here for lack of microstructural information.     

The GPS-gravimetry boundary value problem

Boundary value problem (BVP) plays a funda-mental role in physical geodesy that aims at determin-ing the earth’s shape and its external gravity field. TheMolodensky BVP and the Stokes BVP are typical inphysical geodesy, and the gravity anomaly is a kind ofbasic data. With the wide use of GPS, measurementaccuracy of the earth’s surface can reach one centime-ter, while that of the gravity measurement can reachμgals. Hence, it is necessary to establish a new kind ofBVP which can satisfy…     

Geometry of Poincaré's Variables and the Secular Planetary Problem

A method for the expansion of the perturbative Hamiltonian in the planetary problem is presented, which allows one to immediately detect the terms vanishing under the averaging process. The method bases itself on a geometrical analysis, through the groups SO(3) and SU(2), of the Poincaré canonical variables or of the similar Laplace variables. As an outcome, one obtains a MAPLE program, which calculates the first averaged terms of the perturbative Hamiltonian. This revised version was published online in July 2006 with corrections to the Cover Date.     

Symmetries, Reduction and Relative Equilibria for a Gyrostat in the Three-body Problem

The problem of three bodies when one of them is a gyrostat is considered. Using the symmetries of the system we carry out two reductions. Global considerations about the conditions for relative equilibria are made. Finally, we restrict to an approximated model of the dynamics and a complete study of the relative equilibria is made.     

基于双相介质理论的AVO属性交汇图识别天然气水合物

天然气水合物(gas hydrates)作为一种新的潜在能源 是目前世界范围内研究的热点和难点之一。目前 普遍认为拟海底反射(简称BSR)是天然气水合物存 在的重要标志之一,但有关水合物的识别仍有很 多问题需要解决。例如世界各地已发现水合物的 例证表明在没有BSR的情况下仍然存在水合物,在 没有BSR的情况下如何识别水合物仍是没有解决 的研究课题。本文以天然气水合物的识别为研究 目的,以AVO属性交汇图为研究手段,通过双相介 质正演理论模型研究了当地层含有天然气水合物 或游离气时的AVO属性特征,并与由双相介质的 交错网格有限差分法得到的合成地震记录所反演 得出的AVO交汇图进行了对比,得到高度一致的 对比结果,表明利用AVO属性交汇图是识别天然 气水合物和游离气并能估测其含量的有效技术。     

Generalized Problem of Two and Four Newtonian Centers

We consider integrable spherical analog of the Darboux potential, which appear in the problem (and its generalizations) of the planar motion of a particle in the field of two and four fixed Newtonian centers. The obtained results can be useful when constructing a theory of motion of satellites in the field of an oblate spheroid in constant curvature spaces.     

Symmetric and Asymmetric Librations in Planetary and Satellite Systems at the 2/1 Resonance

Families of asymmetric periodic orbits at the 2/1 resonance are computed for different mass ratios. The existence of the asymmetric families depends on the ratio of the planetary (or satellite) masses. As models we used the Io-Europa system of the satellites of Jupiter for the case m₁>m₂, the system HD82943 for the new masses, for the case m₁=m₂ and the same system HD82943 for the values of the masses m₁<m₂ given in previous work. In the case m₁≥ m₂ there is a family of asymmetric orbits that bifurcates from a family of symmetric periodic orbits, but there exist also an asymmetric family that is independent of the symmetric families. In the case m₁<m₂ all the asymmetric families are independent from the symmetric families. In many cases the asymmetry, as measured by and by the mean anomaly M of the outer planet when the inner planet is at perihelion, is very large. The stability of these asymmetric families has been studied and it is found that there exist large regions in phase space where we have stable asymmetric librations. It is also shown that the asymmetry is a stabilizing factor. A shift from asymmetry to symmetry, other elements being the same, may destabilize the system.