Deconvolution with wavelets and vaguelettes

The use of wavelets for the solution of convolution equations is studied as a possible alternative to the well-established Fast Fourier Transform (FFT) technique. Two possible solution strategies are investigated: (1) The use of wavelets for the representation of both the given data and the unknown solution. This leads to an algorithm with good de-noising and data-compression properties. In terms of computational efficiency this algorithm is inferior to FFT. (2) The use of wavelets for the representation of the unknown solution and of so-called vaguelettes for the representations of the given data. This leads to an algorithm which is even faster than FFT. Received: 14 October 1998 / Accepted: 30 November 1999     

平面Radon变换的反演公式

本文借助球面平均法和Ｈｉｌｂｅｒｔ空间算子理论,给出了平面上Ｒａｄｏｎ变换的反演公式,此公式是具体的、构造性的,便于数值计算,或者进一步探讨重建图象的性质。     

Pounding force assessment in performance‐based design of bridges

Bridges with deck supported on either sliding or elastomeric bearings are very common in mid‐seismicity regions. Their main seismic vulnerabilities are related to the pounding of the deck against abutments or between the different deck elements. A simplified model of the longitudinal behavior of those bridges will allow to characterize the reaction forces developed during pounding using the Pacific Earthquake Engineering Research Center framework formula. In order to ensure the general applicability of the results obtained, a large number of system parameter combinations will be considered. The heart of the formula is the identification of suitable intermediate variables. First, the pseudo acceleration spectral value for the fundamental period of the system (Sa(T_s)) will be used as an intensity measure (IM). This IM will result in a very large non‐explained variability of the engineering demand parameter. A portion of this variability will be proved to be related to the relative content of high‐frequency energy in the input motion. Two vector‐valued IMs including a second parameter taking this energy content into account will then be considered. For both of them, a suitable form for the conditional intensity dependence of the response will be obtained. The question of which one to choose will also be analyzed. Finally, additional issues related to the IM will be studied: its applicability to pulse‐type records, the validity of scaling records and the sufficiency of the IM. Copyright © 2009 John Wiley & Sons, Ltd.     

轻质土密度、强度与材料组成的关系研究

论述了轻质土试样的制备方法,对轻质土密度、无侧限抗压强度与材料组成之间的关系进行的研究表明：密度主要受到EPS颗粒添加量的影响;无侧限抗压强度主要受到水泥添加量、EPS颗粒添加量的影响。在此基础上给出了适合于工程应用的轻质土的配方公式。     

Analytical theories of satellite motion constructed with a new package of formula manipulation and compared with numerical integration

Specialized to the Lie series based perturbation method of Kirchgraber and Stiefel (1978) a new computer algebra package called ANALYTOS has been developed for constructing analytical orbital theories either in noncanonical or canonical form. We present results on the (extended) Main Problem of orbital theory of artificial earth satellites and related issues. The order of the solutions achieved is generally one order higher than those known from literature. Moreover, the analytical orbits have been checked succesfully against precise numerical ephemerides. This revised version was published online in July 2006 with corrections to the Cover Date.     

沙丘地植物固沙灌溉单元及其计算公式

确定轮灌区面积是沙丘地灌溉设计中最重要的问题。在塔克拉玛干沙漠腹地,通过计算沙丘地入渗率、测定入渗过程与深层损失率以及进行不同流量、不同灌溉面积的反复试验,提出了灌溉单元的定义及计算公式。灌溉单元是一定地区、一定土壤或母质、一定灌溉方式条件下,某一水流量的最大合理灌溉面积。它是确定轮灌区面积的基本单位。对于沟畦灌而言,灌溉单元是指单沟或单畦的最大合理灌溉面积;对于滴灌而言,灌溉单元是指单个支管所能控制的最大合理灌溉面积。     

柴达木盆地东部石炭系地震层速度求取方法的研究

在柴达木盆地东部石炭系地震勘探过程中,地震层速度是一个重要的参数。层速度不仅仅可以应用于时深转换,还可以应用于反映地层岩性、构造和地层压力等方面的信息,地震剖面与地震速度也密切相关。柴达木盆地东部石炭系由于资料所限,速度问题一直未能很好地解决,时深转换过程中速度误差较大。因此,为了解决研究过程中速度误差较严重的问题,文章在前人工作基础上,探索性地提出了一种新的层速度求取方法,以提高柴达木盆地东部石炭系地震勘探过程中层速度的精度,从而更好的认识本区的构造和地质特征。通过对单井速度分析和二维地震叠加速度多次拾取,保证了速度谱拾取的精度,然后将地震叠加速度换算成均方根速度,进而利用基于单井速度趋势模型约束Dix反演层速度技术将均方根速度转换成层速度,拟合出全区的平均速度场。同时在拟合后,以井上测井速度为控制点,对平均速度进行了合理校正,从而建立比较合理的研究区层速度模型。利用新建立的层速度模型,对原来的构造重新进行时深转换,取得了较好的效果。新的改进Dix公式层速度求取方法求取的速度模型与前人成果相比较,利用了单井速度约束Dix公式进行速度反演,因而比前人成果更精确,更符合单井速度趋势,因而更符合地质认识规律。     

Ellipsoidal corrections to order e 2 of geopotential coefficients and Stokes’ formula

Assuming that the gravity anomaly and disturbing potential are given on a reference ellipsoid, the result of Sjöberg (1988, Bull Geod 62:93–101) is applied to derive the potential coefficients on the bounding sphere of the ellipsoid to order e ² (i.e. the square of the eccentricity of the ellipsoid). By adding the potential coefficients and continuing the potential downward to the reference ellipsoid, the spherical Stokes formula and its ellipsoidal correction are obtained. The correction is presented in terms of an integral over the unit sphere with the spherical approximation of geoidal height as the argument and only three well-known kernel functions, namely those of Stokes, Vening-Meinesz and the inverse Stokes, lending the correction to practical computations. Finally, the ellipsoidal correction is presented also in terms of spherical harmonic functions. The frequently applied and sometimes questioned approximation of the constant m, a convenient abbreviation in normal gravity field representations, by e ²/2, as introduced by Moritz, is also discussed. It is concluded that this approximation does not significantly affect the ellipsoidal corrections to potential coefficients and Stokes formula. However, whether this standard approach to correct the gravity anomaly agrees with the pure ellipsoidal solution to Stokes formula is still an open question.     

A computational scheme to model the geoid by the modified Stokes formula without gravity reductions

In a modern application of Stokes formula for geoid determination, regional terrestrial gravity is combined with long-wavelength gravity information supplied by an Earth gravity model. Usually, several corrections must be added to gravity to be consistent with Stokes formula. In contrast, here all such corrections are applied directly to the approximate geoid height determined from the surface gravity anomalies. In this way, a more efficient workload is obtained. As an example, in applications of the direct and first and second indirect topographic effects significant long-wavelength contributions must be considered, all of which are time consuming to compute. By adding all three effects to produce a combined geoid effect, these long-wavelength features largely cancel. The computational scheme, including two least squares modifications of Stokes formula, is outlined, and the specific advantages of this technique, compared to traditional gravity reduction prior to Stokes integration, are summarised in the conclusions and final remarks. AcknowledgementsThis paper was written whilst the author was a visiting scientist at Curtin University of Technology, Perth, Australia. The hospitality and fruitful discussions with Professor W. Featherstone and his colleagues are gratefully acknowledged.     

The analytical continuation bias in geoid determination using potential coefficients and terrestrial gravity data

One important application of an Earth Gravity Model (EGM) is to determine the geoid. Since an EGM is represented by an external-type series of spherical harmonics, a biased geoid model is obtained when the EGM is applied inside the masses in continental regions. In order to convert the downward-continued height anomaly to the corresponding geoid undulation, a correction has to be applied for the analytical continuation bias of the geoid height. This technique is here called the geoid bias method. A correction for the geoid bias can also be utilised when an EGM is combined with terrestrial gravity data, using the combined approach to topographic corrections. The geoid bias can be computed either by a strict integral formula, or by means of one or more terms in a binomial expansion. The accuracy of the lowest binomial terms is studied numerically. It is concluded that the first term (of power H²) can be used with high accuracy up to degree 360 everywhere on Earth. If very high mountains are disregarded, then the use of the H² term can be extended up to maximum degrees as high as 1800. It is also shown that the geoid bias method is practically equal to the technique applied by Rapp, which utilises the quasigeoid-to-geoid separation. Another objective is to carefully consider how the combined approach to topographic corrections should be interpreted. This includes investigations of how the above-mentioned H² term should be computed, as well as how it can be improved by a correction for the residual geoid bias. It is concluded that the computation of the combined topographic effect is efficient in the case that the residual geoid bias can be neglected, since the computation of the latter is very time consuming. It is nevertheless important to be able to compute the residual bias for individual stations. For reasonable maximum degrees, this can be used to check the quality of the H² approximation in different situations.Acknowledgement The author would like to thank Prof. L.E. Sjöberg for several ideas and for reading two draft versions of the paper. His support and constructive remarks have improved its quality considerably. The valuable suggestions from three unknown reviewers are also appreciated.