卫星测高问题的球谐级数解法

研究了球界面下卫星测高问题的解法，利用有限逼近方法得到了下列结论：若陆地部分是球冠，则卫星测高问题的解可以转换成关于球谐级数位系统的线性方程组。同时证明了常用的Stokes问题、Dirichlet问题、Neumann问题可以看成卫星测高问题的特殊情况。     

车辆导航系统中定位数据处理和地图匹配技术

分析了GPS误差来源，并提出了相应的处理办法；融合电子地图中的道路数据和GPS所提供的定位数据的地图匹配算法，可以有效地提高车辆导航的定位精度。在分析各种地图匹配算法基础上，提出了一种实用的地图匹配方法，并且在实践中得到了验证。     

Construction of Green's function to the external Dirichlet boundary-value problem for the Laplace equation on an ellipsoid of revolution

Green's function to the external Dirichlet boundary-value problem for the Laplace equation with data distributed on an ellipsoid of revolution has been constructed in a closed form. The ellipsoidal Poisson kernel describing the effect of the ellipticity of the boundary on the solution of the investigated boundary-value problem has been expressed as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Poisson kernel at the singular point ψ = 0. We have shown that the degree of singularity of the ellipsoidal Poisson kernel in the vicinity of its singular point is of the same degree as that of the original spherical Poisson kernel. Received: 4 June 1996 / Accepted: 7 April 1997     

非均匀层结下的对称不稳定

研究了非均匀层结下的对称不稳定，给出了不稳定发生的判据，并将该微分方程的特征值问题化为一个实对称矩阵的特征值问题，还取不同的层结廓线进行了数值计算。     

P-SH conversions in a flat-layered medium with anisotropy of arbitrary orientation

P-SH conversion is commonly observed in teleseismic P waves, and is often attributed to dipping interfaces beneath the receiver. Our modelling suggests an alternative explanation in terms of flat-layered anisotropy. We use reflectivity techniques to compute three-component synthetic seismograms in a 1-D anisotropic layered medium. For each layer of the medium, we prescribe values of seismic velocities and hexagonally symmetric anisotropy about a common symmetry axis of arbitrary orientation. A compressional wave in an anisotropic velocity structure suffers conversion to both SV -and SH -polarized shear waves, unless the axis of symmetry is everywhere vertical or the wave travels parallel to all symmetry axes. The P-SV conversion forms the basis of the widely used 'receiver function' technique. The P-SH conversion occurs at interfaces where one or both layers are anisotropic. A tilted axis of symmetry and a dipping interface in isotropic media produce similar amplitudes of both direct ( P ) and converted ( Ps ) phases, leaving the backazimuth variation of the P-Ps delay as the main discriminant. Seismic anisotropy with a tilted symmetry axis leads to complex synthetic seismograms in velocity models composed of just a few flat homogeneous layers. It is possible therefore to model observations of P coda with prominent transverse components with relatively simple 1-D velocity structures. Successful retrieval of salient model characteristics appears possible using multiple realizations of a genetic-algorithm (GA) inversion of P coda from several backazimuths. Using GA inversion, we determine that six P coda recorded at station ARU in central Russia are consistent with models that possess strong (> 10 per cent) anisotropy in the top 5 km and between 30 and 43 km depth. The symmetry axes are tilted, and appear aligned with the seismic anisotropy orientation in the mantle under ARU suggested by SKS splitting.     

Time-domain electromagnetic migration in the solution of inverse problems

Time-domain electromagnetic (TDEM) migration is based on downward extrapolation of the observed field in reverse time. In fact, the migrated EM field is the solution of the boundary-value problem for the adjoint Maxwell's equations. The important question is how this imaging technique can be related to the solution of the geoelectrical inverse problem. In this paper we introduce a new formulation of the inverse problem, based on the minimization of the residual-field energy flow through the surface or profile of observations. We demonstrate that TDEM migration can be interpreted as the first step in the solution of this specially formulated TDEM inverse problem. However, in many practical situations this first step produces a very efficient approximation to the geoelectrical model, which makes electromagnetic migration so attractive for practical applications. We demonstrate the effectiveness of this approach in inverting synthetic and practical TDEM data.     

Comment on 'Estimation of resolution and covariance for large matrix inversions' by J. Zhang and G. A. McMechan

When inverting large matrices, iterative techniques are necessary because of their speed and low memory requirements, as opposed to singular value decomposition (SVD). Recently, there have been attempts to obtain information on the quality of the solutions calculated using conjugate gradient (CG) methods such as LSQR. The purpose of this note is to comment on the paper titled "Estimation of resolution and covariance for large matrix inversions' by Zhang & McMechan (1995), who extend Paige and Saunders' LSQR algorithm to obtain an orthonormal basis used to approximate resolution and covariance. We show that for larger problems, where the number of orthogonal vectors is several orders of magnitude smaller than the number of model parameters, the vectors obtained do not adequately span the range of the model space. We use a synthetic borehole experiment to illustrate the differences between the singular value spectrum obtained through the more complete method of SVD and the Ritz value spectrum that results from a simple extension of LSQR, We also present a trivial numerical example to illustrate the differences between Zhang & McMechan's approximate resolution matrix and the true resolution.