Direct time-domain soil profile reconstruction for one-dimensional semi-infinite domains

We discuss the inverse medium problem associated with the reconstruction of the heterogeneous material profile of a semi-infinite (layered) soil medium, directly in the time domain, based on the complete waveform response of the medium to interrogating waves. To tackle the inversion process, we use a partial-differential-equation-constrained optimization approach, supplemented with a time-dependent regularization scheme. We introduce an absorbing boundary to truncate the semi-infinite extent of the physical domain, and propose two schemes to refine the reconstructed profiles: the first is based on iteratively re-positioning the truncation boundary until convergence, and the second is based on optimizing the observation period, so as to exclude records with information beyond the truncation boundary. We present numerical results that attest to the efficacy of the proposed schemes in reconstructing sharp profiles of semi-infinite soil domains using both noise-free and noisy data, while in the presence of absorbing boundaries.     

Semi-analytical evaluation of integral forms associated with Lamb's problem

The present work gives solutions of integrals resulting from Lamb's problem solution by an accurate and efficient approximation procedure. The formulation of the solutions requires the study of Green's function of Lamb problem solution. Unfortunately, this problem is associated to great mathematical difficulties and needs the evaluation of some complex integrals. We handled these integrals by an appropriate strategy based on decoupling their effects mathematically and solved by using the least squares method. The present solutions can be applied to study the dynamical interaction between soil and structures, to be used to determine the transient wave fields caused by a seismic source, and also to assess numerical computations with a different numerical methods program.     

地球弓激波及其与行星际激波相互作用

给定地球轨道附近的行星际条件和地球弓激波的几何位形,本文分析向阳侧弓激波强度参数沿激波阵面的分布,以及行星际激波与弓激波的相互作用.对于弓激波阵面相对日地连线轴对称的情形,得到如下结论：（1）弓激波强度参数分布相对由行星际磁场和日地连线构成的基准面对称,各激波强度参数的最大值出现在基准面上.磁压比在垂直激波线一侧较大,而气压比在平行激波点一侧较大,导致总压比相对日地连线大致呈轴对称分布.（2）随着行星际磁场与日地连线夹角的增大,弓激波强度参数的最大值有所减小,且位置朝远离日下点方向偏移;但气压比和总压比的分布基本上不受影响.（3）行星际激波透过弓激波之后,切向磁场比更接近于1,但总磁场跳变幅度增大.（4）透过弓激波之后,行星际准垂直激波的总磁场比更接近于1,准平行激波的总磁场比则反之.     

The spheroidal fixed–free two-boundary-value problem for geoid determination (the spheroidal Bruns' transform)

The target of the spheroidal Gauss–Listing geoid determination is presented as a solution of the spheroidal fixed–free two-boundary value problem based on a spheroidal Bruns' transformation (“spheroidal Bruns' formula”). The nonlinear spheroidal Bruns' transform (nonlinear spheroidal Bruns' formula), the spheroidal fixed part and the spheroidal free part of the two-boundary value problem are derived. Four different spheroidal gravity models are treated, in particular to determine whether they pass the test to fit to the postulate of a level ellipsoidal gravity field, namely of Somigliana–Pizzetti type. Received: 4 May 1999 / Accepted: 21 May 1999     

GPS对地震预报的推进和问题研究

以丽江Ms7.0地震和昆仑山Ms8.1级地震为例,论证了GPS在地震预报中的作用,以及面临的和亟待解决的问题:如分析研究落后于观测、怎样克服自身的局限性与其它手段结合互补、连续GPS台网密度太稀疏等。     

Identifying groundwater pumping source information using simulated annealing

This study develops an approach referred to as SA‐MF using simulated annealing (SA) and a three‐dimensional groundwater flow model (MODFLOW‐2000) to determine the pumping source information, namely the pumping source location, the pumping rate and the pumping period. Eight scenarios, each with various cases for aquifers with homogeneous or heterogeneous conductivities, are used to test the applicability and accuracy of SA‐MF in determining the pumping source information. The results show that at least five measured heads should be used to analyse the pumping source identification problem and at least three observation wells are required to effectively determine the pumping source information. The SA‐MF gives good estimated results in both synthetic and real problems even if the measured heads contain measurement errors. Copyright © 2008 John Wiley & Sons, Ltd.     

Variational coupling of Plinian column models and data: Application to El Chichón volcano

Many efforts have been done in the modelling of Plinian columns. However, until now, the inverse problem of the reconstruction of a Plinian event from observed data has been only roughly tackled. This paper discusses the efficient variational data assimilation (VDA) that manages the optimization iterate sequence by means of gradient computations. Theoretical developments of VDA are presented for both the Woods equations and a generic system allowing for the modelling of the Navier–Stokes equations. Two- and three-dimensional unsteady Plinian models being based on the latters, VDA could be clearly performed on their differentiable subset of equations.     

一维溶质运移源(汇)项系数反演的迭代正则化算法

对于多孔介质中发生物理化学反应的溶质运移现象,可以用带有非线性源（汇）项作用的一维对流弥散-反应扩散方程来描述,但方程中反映溶质吸附/解吸附能力的源(汇)项系数往往是未知的. 本文讨论了基于出流端浓度观测数据的源项系数反演问题. 根据Tikhonov正则化和矩阵的奇异值分解系统,建立了一种离散的迭代正则化算法,给出了算法实现步骤.数值模拟结果表明该算法不仅精度高,而且对于数据的随机扰动具有稳定性.最后应用建立的算法反演计算了一个具体的土柱试验源项系数,数值结果也表明文中所构造算法的有效性.     

无压渗流问题分析的多节点有限元方法

采用基于平均值插值的多节点有限元方法分析有自由面渗流问题。在自由面附近采用多节点单元逼近自由面,利用平均值插值建立多节点单元的形函数,在远离自由面的区域采用四边形/三角形单元剖分。给定一个初始自由面位置,通过对渗流控制方程的多节点有限元求解,根据自由面上节点水头值判断自由面节点的调整方向和大小,最终迭代求出自由面的位置。土坝渗流问题的数值分析表明了所提方法的有效性和足够的计算精度。