波速线性变化介质中地震波传播特征

根据变速介质中地震波传播所满足的变系数波动方程,推导出波速线性变化介质中一维波动方程的解析解,讨论了波速不均匀性对地震波传播的影响：地震波振幅衰减大小与介质速度梯度有关;频率转折点两侧地震波传播性质;频率与地震波波速关系。     

关于动力Alfven波的色散与朗道阻尼

根据完全动力论理论,证明了可由简化漂移动力论方程求得动力Ａｌｆｖｅｎ波色散方程,即横向用磁流体力学方程,纵向用Ｖｌａｓｏｖ方程,在初级近似下由此推导出适合于日冕和太阳风的色散关系和Ｌａｎｄａｕ阻尼,得到在性质上与ＭＨＤ　Ａｌｆｖｅｎ波完全不同的动力Ａｌｆｖｅｎ波,太阳风中Ａｌｆｖｅｎ湍流很容易由动力Ａｌｆｖｅｎ波演化而来。提出由动力Ａｌｆｒｅｎ波构筑太阳风高速流模型将更符合观测结果。     

一维有耗散波动方程的奇性分析与小波

对系数有强奇性（间断）的波动方程,用通常的线性化简的方法时往往会将数值小但奇性强的项略去,导致结果严重失真。利用小波变换这一工具,可以在化简时保留奇性的主要部分,使所得的结果从奇性分析的观点看来更为精确。此方法曾被用来处理系数有间断的一维波动方程,得到了与精确解的奇性主部完全一致的解．在本文中,我们改进了用小波变换作奇性化简的方法,对系数有间断的一维有耗散波动方程求得了与精确解奇性主部完全一致的解。这说明利用小波分析作奇性化简的方法对高频近似及奇性分析问题是普遍适用的．     

Modelling of water table variation in response to time-varying recharge from multiple basins using the linearised Boussinesq equation

A mathematical model is presented to describe the variations of the water table in an unconfined aquifer due to time-varying recharge applied from four rectangular basins. The model is developed by solving the linearised Boussinesq equation using the extended finite Fourier cosine transform. The time-varying recharge rate is approximated by a number of piecewise linear elements of different lengths and slopes depending on the nature of the variation in recharge rate. Application of this model for the prediction of water table fluctuations and in the sensitivity analysis of various controlling parameters on the aquifer response is demonstrated in an example.     

Application of Numerical Models in Marine Pollution Research in China

Like many countries in the world, China is also facing serious problems of marine pollution in the coastal zone. The prevailing concern is eutrophication of the coastal water due to river inputs and, in some bays, also due to the over-expansion of aquaculture. As part of the marine pollution research activities in China, applications of mathematical models are also widely used, both to understand the present and to project the future. In this paper, selected Chinese works are reviewed, especially with respect to the effort in reducing the errors introduced in the numerical treatment of the water quality equation.     

GPS动态定位中机动随机模型分析

给出了载体状态方程的严密公式和常用近似公式,详细讨论了两者之间的区别。在高精度ＧＰＳ动态定位中的应用证明,常用近似公式对载体速度和加速度有显著的影响。     

Computation of solitary waves during propagation and runup on a slope

A numerical time-simulation algorithm for analysing highly nonlinear solitary waves interacting with plane gentle and steep slopes is described by employing a mixed Eulerian–Lagrangian method. The full nonlinear free surface conditions are considered here in a Lagrangian frame of reference without any analytical approximations, and thus the method is valid for very steep waves including overturning. It is found that the runup height is crucially dependent on the wave steepness and the slope of the plane. Pressures and forces exerted on impermeable walls of different inclinations (slopes) by progressive shallow water solitary waves are studied. Strong nonlinear features in the form of pronounced double peaks are visible in the time history of pressure and force signals with increasing heights of the oncoming solitary waves. The effect of nonlinearity is less pronounced as the inclination of the wall decreases with respect to the bottom surface.     

Multiscale Gravitational Field Recovery from GPS-Satellite-to-Satellite Tracking

The purpose of GPS-satellite-to-satellite tracking (GPS-SST) is to determine the gravitational potential at the earth's surface from measured ranges (geometrical distances) between a low-flying satellite and the high-flying satellites of the Global Positioning System (GPS). In this paper, GPS-satellite-to-satellite tracking is reformulated as the problem of determining the gravitational potential of the earth from given gradients at satellite altitude. The uniqueness and stability of the solution are investigated. The essential tool is to split the gradient field into a normal part (i.e. the first-order radial derivative) and a tangential part (i.e. the surface gradient). Uniqueness is proved for polar, circular orbits corresponding to both types of data (first radial derivative and/or surface gradient). In both cases gravity recovery based on satellite-to-satellite tracking turns out to be an exponentially ill-posed problem. Regularization in terms of spherical wavelets is proposed as an appropriate solution method, based on the knowledge of the singular system. Finally, the extension of this method is generalized to a nonspherical earth and a non-spherical orbital surface, based on combined terrestrial and satellite data.     

Vertical dynamic response of a disk on a saturated poroelastic half-space

This paper considers the vertical dynamic response of a disk on a saturated poroelastic half-space. Firstly the pressure-solid displacement form of the harmonic equations of motion for a poroelastic solid are developed from the form of the equations originally presented by Biot. These equations are solved by a new method. Then the mixed boundary value problem for the vertical harmonic vibration of a disk on a poroelastic half-space is studied. The two types of drainage conditions at the surface of the poroelastic half-space are considered: (a) the surface of the poroelastic half-space is assumed to be completely pervious both within and exterior to the plate; (b) The interface between the plate and the poroelastic half-space is assumed to be impervious and the exterior region is assumed to be pervious. By using the Hankel transform techniques, the paper develops the governing dual integral equations. These governing integral equations are further reduced to systems of standard Fredholm integral equations of the second kind by Abel transform.     

Preparation of volume table of SAL (Shorea robusta) - an approach using satellite data

Sal (Shorea robusta) is an important forest tree species in north and north-eastern India. Large-scale plantations of this species have been raised there under taungya and coppice system of management. The conventional volume table prepared for high sal forest is referred to infer the volume of production of this species. Earlier workers have used aerial remote sensing data to develop volume tables of this species. In the present study a volume table for sal is developed based on remotely sensed satellite data using a regression technique. A two-step method was developed to estimate mean tree volume from satellite data. In step 1, mean crown diameter — an intermediate variable - was estimated from satellite data. In step 2, the estimated mean crown diameter was used to estimate the mean tree volume. Addition of age of the crop as an independent variable improved the predictive ability of the regression equation.