基于稀疏约束的自适应正则化迭代重建算法

本文针对ASD-POCS算法中约束项权重对不同应用的多变性引起的算法鲁棒性差等问题,提出了一种基于稀疏约束的自适应正则化迭代重建算法,该算法采用一种Lagendijk型的正则化策略构造最优化问题,分别采用局部方差、图像能量估计自适应地求取加权对角矩阵和全局正则化参数。最优化问题的求解过程中,采用SART算法和共轭梯度法求解保真项和约束项最优化问题。实验结果表明,AR-SART-CG算法能更好地权衡恢复图像边缘和平滑噪声的关系,更好地调节保真项和约束项的权重,得到更高质量的重建图像。     

地震层析成像反演中3种广义解的误差分析与评价

在地震波速度和地震波　值层析成像中,对于非线性反演问题解的可靠性研究非常重要．为了讨论ＡＲＴ（ＡｌｇｅｂｒａｉｃＲｅｃｏｎｓｔｒｕｃｔｉｏｎ　Ｔｅｃｈｎｉｑｕｅ）、ＳＶＤ（Ｓｉｎｇｕｌａｒ　ＶａｌｕｅＤｅｃｏｍｐｏｓｉｔｉｏｎ）、ＬＳＱＷ（ＬｅａｓｔＳｕａｒｅ）３种方法的算法稳定性以及反演效果,本研究将这３种算法用于求解非常病态问题和一般稳定问题,根据数值计算结果,分别给出了在非常病态问题和一般稳定问题中３种算法的相对误差及其算法稳定性评价．进而针对３种算法在同一地质模型上的速度成像结果进行了比较,为地震层析成像反演效果分析提供了定量参数．     

地震层析成像反演中3种广义解的误差分析与评价

在地震波速度和地震波　值层析成像中,对于非线性反演问题解的可靠性研究非常重要．为了讨论ＡＲＴ（ＡｌｇｅｂｒａｉｃＲｅｃｏｎｓｔｒｕｃｔｉｏｎ　Ｔｅｃｈｎｉｑｕｅ）、ＳＶＤ（Ｓｉｎｇｕｌａｒ　ＶａｌｕｅＤｅｃｏｍｐｏｓｉｔｉｏｎ）、ＬＳＱＷ（ＬｅａｓｔＳｕａｒｅ）３种方法的算法稳定性以及反演效果,本研究将这３种算法用于求解非常病态问题和一般稳定问题,根据数值计算结果,分别给出了在非常病态问题和一般稳定问题中３种算法的相对误差及其算法稳定性评价．进而针对３种算法在同一地质模型上的速度成像结果进行了比较,为地震层析成像反演效果分析提供了定量参数．     

二维波动方程参数反演的微分进化算法

利用微分进化算法进行二维波动方程参数反演的研究.微分进化算法属于全局最优化算法,具有鲁棒性强、收敛速度快、计算精度高的优点.把参数反演问题转化为非线性优化问题,通过保持在解空间不同区域中各个点的搜索,以最大的概率找到问题的全局最优解.同时还进行了数值模拟,结果令人满意.     

高阶方程偏移的分裂算法

对于用高阶偏微分方程进行地震偏移,本文提出一种分裂算法。有限差分法目前只能解波动方程的二阶和三阶的近似方程的偏移问题,更高阶的近似方程还没有一种有效的解法。利用高阶方程进行偏移会提高偏移的精度和效果。本文就是为了解决这个问题所进行的探索。 本文阐述了分裂算法的原理,并给出了应用该算法解决偏移问题的实例。     

基于混合差分进化算法的地球物理线性反演

地球物理反问题线性化处理之后, 各种反演算法归结为对病态线性方程组的求解. 为了快速准确地计算出地球物理参数, 本文提出了一种全新的基于LSQR算法的混合差分进化算法(Hybrid Differential Evolution Algorithm, HDE). 该算法利用LSQR算法给出DE算法的初始种群, 提高DE算法的计算速度和稳定性. 在不同噪声水平下, 对四种正则化方法Tikhonov、TSVD、LSQR和HDE的反演结果进行详细比较. 理论模型和实际数据反演的结果都表明: 改进的HDE算法应用于地球物理反问题的求解是成功的: 反演结果与原设定模型具有较高的相关性, 在稳定性和准确性上较常规的反演算法都具有一定的优势; 而且不需要给定正则化参数, 具有更强的实用性.     

基于Tikhonov正则化的双频电磁波电导率成像反演

本文将Tikhonov正则化方法与active-set算法相结合,利用双频电磁波电导率成像原理,求解其反演成像方程.不仅对现有算法进行了改进,也促进了算法的实际应用.本文研究了在双频电磁波电导率成像方程建立后,如何根据其严重病态性质,选择合适的算法求解矩阵成像方程.针对电导率非负的特性,引入正则化参数,将问题转化为一个非负最小二乘问题,并用active-set算法求解.采用改进后的迭代算法对理论模型进行了数值模拟计算,验证了该方法的有效性.应用到实际电导率成像反演,与常规的LSQR、SP-LSQR、Tikhonov正则化等算法进行比较,取得了满意的结果.     

关于不充分投影数据下的二维扇形束CT重建(英文)

在医学和其他的很多CT应用中,一个重要问题是如何从不充分的投影数据中重建出断层图像。近年来由于新兴的压缩传感理论,Total Variation最小化方法在求解这一问题中重新获得了重视。本文将该方法推广成一类更一般的不充分投影CT重建算法。这一类重建算法同样基于压缩传感理论,但是更加灵活,能适用于不同的应用背景。针对该类算法中的一个特例进行的理论分析和算法仿真展现了该算法的应用潜力。     

数字合成X射线体层成像的小波-伽辽金重建算法

数字合成X射线体层成像技术的重建问题是在有限投影数据条件下的病态重建问题。本文通过分析数字合成X射线体层成像技术的系统模型,获得重建问题的系统方程。在对系统方程进行正则化改造的基础上,提出了一种新的重建算法——自适应小波-伽辽金重建算法。该算法融合了伽辽金方法的计算简洁和小波内在的多尺度特性,更好地适应了待重建图像的求解。仿真实验结果表明,与ART重建算法相比,自适应小波-伽辽金重建算法在保证重建质量前提下能加快收敛,从而大大地节省了计算时间。     

基于支持向量机的信号自动检测算法

STA/LTA算法是信号自动检测中的经典算法. 这种算法中检测阈值的分布范围在0~infin;之间， 合适的检测阈值不但要根据实验反复调试， 而且要在误检率和漏检率之间取得平衡. 针对这一问题， 从模式识别的角度出发， 给出了一种基于支持向量机的信号检测算法. 讨论了该算法中数据预处理和模式特征提取的方法， 以及支持向量机中核函数的选择问题. 利用实际地震数据， 分析了这种算法的检测性能. 结果表明, 这种算法简化了检测阈值的选择. 在准确检测信号的同时，其误检率相对于STA/LTA算法可以降低约85％， 并且具有较强的抗噪性能.      

带阻尼的一维地震反射波成像

本文是文献［８］的继续，文中提出了地震勘探的带阻尼波动方程反演的新方法，应用此反演算法可以通过微机识别地层的波阻抗，这里把地层分成１００层，地震数据含有１０％的误差，且反演计算时间仅仅是正演计算时间的三倍．文献［１］－［４］的计算方法是基于波动方程的混合问题，而文献［８］所提出的反演算法是基于波动方程的哥西问题，许多例子充分说明后者更有效．     

Some geophysical constraints on the chemical composition of the earth's lower mantle

The physical properties(?, K, K′) of the adiabatically decompressed lower mantle are interpreted in terms of an (Mg,Fe)SiO₃ perovskite + magnesiowüstite mineralogy. The approach employed in this paper involves the removal of the relatively better characterised magnesiowüstite component from the two-phase mixture in order to highlight the physical properties required of the perovskite phase for consistency between the seismological data and any proposed compositional model. It is concluded that a wide tradeoff (emphasized by Davies [1]) between composition, temperature and the physical properties (especially thermal expansion) of the perovskite phase accommodates most recently proposed compositional models including Ringwood's [2] pyrolite and the more silicic models of Burdick and Anderson [3], Anderson [4], Sawamoto [5], Butler and Anderson [6], Liu [7,8] and Watt and Ahrens [9].     

On a method of computing the gravitational fields of inhomogeneous bodies

Summary A solution of the direct gravity problem for a finite body with variable density is given. The method is based on Green's formula and is applicable when a particular solution of Poisson's equation is known. The attraction due to the body is expressed by integrals over its surface The exact solution of the direct gravity problem, as known from the theory of two-dimensional fields [1–3], is closely connected with the problem of the analytic continuation of the exterior field of the attracting mass system into its interior. In the first place, this is a problem of determining the singularities of the exterior field, their distribution within the system and their nature. This approach to the solution of the direct problem is also meaningful from the point of view of determining the characteristics of the attracting system and, therefore, also of solving the inverse problem. In the case of two-dimensional fields the methods of analytical continuation were widely developed in a series of well-known papers by V. N. Strakhov, and they are mainly based on the methods of the theory of the functions of the complex variable. These methods were also successfully applied by Tsirulskii and Golizdra [1, 2] in treating the homogeneous and inhomogeneous, two-dimensional direct problem by means of Cauchy's integrals. However, as regards three-dimensional fields a number of fundamental problems has not been solved in this respect.Dedicated to 90th Birthday of Professor Frantiek Fiala     

电阻率测井响应的积分方程解法

从电流守恒条件出发,得到了两个积分方程.其中第一个和在1964年提出的相同,它的未知函数是边界面上的隐电流源分布密度;第二个积分方程的未知函数则是电位函数本身. 在的文章以及本文作者的另一篇文章中,供电电极和测量电极都被当成点电极处理.用这种方法来处理电位电极系和梯度电极系已不够准确,用来处理三侧向或双侧向等具有大电极的电极系则完全无能为力. 测井中所用的电极系是包着金属外皮的绝缘心棒,金属外皮就是电极.本文提出了处理这种电极系的方法.结果表明,第二个积分方程在处理这种电极系时有明显优点.     

High-pressure phases of CaCO3: Crystal structure prediction and experiment

Post-aragonite phase of CaCO₃, experimentally known to be stable above 40 GPa [S. Ono, T. Kikegawa, Y. Ohishi, J. Tsuchiya, Post-aragonite phase transformation in CaCO₃ at 40 GPa, Am. Mineral. 90 (2005) 667–671], is believed to be a major carbon-containing mineral in the Earth's mantle. Crystal structure of this mineral phase could not be solved using experimental data or traditional theoretical simulation methods and remained a controversial issue. Using a combination of advanced ab initio simulation techniques and high-pressure experiment, we have been able to determine the crystal structure of CaCO₃ post-aragonite. Here, we performed simulations with the USPEX code [C.W. Glass, A.R. Oganov, and N. Hansen, (in preparation). USPEX: a universal structure prediction program], which is based on an evolutionary algorithm using ab initio free energy as the fitness function. This novel methodology for crystal structure prediction, which uses only the chemical composition as input, is described in detail. For CaCO₃, we identify a number of energetically competitive structures, the most stable of which closely matches the experimental powder diffraction pattern and, in agreement with experiment, becomes more stable than aragonite above 42 GPa. This structure belongs to a new structure type, which is also adopted by the high-pressure post-aragonite phases of SrCO₃ and BaCO₃. It has 2 formula units in the orthorhombic unit cell (space group Pmmn) and contains triangular CO₃²⁻ ions and Ca²⁺ ions in the 12-fold coordination. Above 137 GPa, a pyroxene-type structure (space group C222₁) with chains of CO₄⁴⁻ tetrahedra becomes more stable than post-aragonite. For MgCO₃, this structure becomes more stable than magnesite above 106 GPa and is a good candidate structure for MgCO₃ post-magnesite.     

A methodology for the evaluation of long-term volcanic risk from pyroclastic flows in Campi Flegrei (Italy)

The volcanological history of Campi Flegrei suggests that the most frequent eruptions are characterized by the emplacement of pyroclastic flow and surge deposits erupted from different vents scattered over a 150-km² caldera. The evaluation of volcanic risk in volcanic fields is complex because of the lack of a central vent. To approach this problem, we subdivided the entire area of Campi Flegrei into a regular grid and evaluated the relative spatial probability of opening of vents based on geological, geophysical and geochemical data. We evaluated the volcanic risk caused by pyroclastic flows based on the formula proposed by UNESCO (1972), R=H×V×Va, where H is the hazard, V is the vulnerability and Va is the value of the elements at risk. The product H×V was obtained by performing simulations of type eruptions centered in each cell of the grid. The simulation is based on the energy cone scheme proposed by Sheridan and Malin [J. Volcanol. Geotherm. Res. 17 (1983) 187–202], hypothesizing a column collapse height of 100 m for eruptions of VEI=3 and 300 m for eruptions of VEI=4 with a slope angle of 6°. Each simulation has been given the relative probability value associated with the corresponding cell. We made use of the GIS software ArcView 3.2 to evaluate the intersection between the energy cone and the topography. The superposition of the areas invaded by pyroclastic flows (124 simulations for VEI=3 and 37 for VEI=4) was used to obtain the relative hazard map of the area. The relative volcanic risk map is obtained by superimposing the urbanization maps.     

Upscaling of Forchheimer flows

In this work we propose upscaling method for nonlinear Forchheimer flow in heterogeneous porous media. The generalized Forchheimer law is considered for incompressible and slightly-compressible single-phase flows. We use recently developed analytical results (Aulisa et al., 2009) [1] and formulate the resulting system in terms of a degenerate nonlinear flow equation for the pressure with the nonlinearity depending on the pressure gradient. The coarse scale parameters for the steady state problem are determined so that the volumetric average of velocity of the flow in the domain on fine scale and on coarse scale are close. A flow-based coarsening approach is used, where the equivalent permeability tensor is first evaluated following streamline methods for linear cases, and modified in order to take into account the nonlinear effects. Compared to previous works (Garibotti and Peszynska, 2009) [2], (Durlofsky and Karimi-Fard) [3], this approach can be combined with rigorous mathematical upscaling theory for monotone operators, (Efendiev et al., 2004) [4], using our recent theoretical results (Aulisa et al., 2009) [1]. The developed upscaling algorithm for nonlinear steady state problems is effectively used for variety of heterogeneities in the domain of computation. Direct numerical computations for average velocity and productivity index justify the usage of the coarse scale parameters obtained for the special steady state case in the fully transient problem. For nonlinear case analytical upscaling formulas in stratified domain are obtained. Numerical results were compared to these analytical formulas and proved to be highly accurate.     

The diurnalK 1 tide in the world ocean — A numerical investigation

Summary Based on a special numerical method (HN method) hydrodynamical processes in the sea were studied with an aim at their prediction. Within this framework, constantly checking the reliability of the numerical models, tides and wind driven motions have been investigated in estuaries, in marginal and adjacent seas, and in the oceans (seeH. Friedrich [1], W. Hansen [2–4], H. P. Schmitz [5]). Encouraged by the promising results, these numerical investigations have been extended by the author to the world ocean, initially to the semi-diurnalM ₂ tide ([8]) and now to theK ₁ tide. Results of computations carried out for theK ₁ tide are given in this paper.     

Linear vertical vibrations of suspension bridges: A review of continuum models and some new results

The classical continuum model for the linear vertical vibrations of a suspension bridge (Bleich et al., 1950 [1]) is re-examined. The primary objective of the study is to extend the definitive analytical and numerical results of Irvine and Caughey (1974) [2], Irvine and Griffin (1976) [3] and Irvine (1980, 1981) [4], [5] for the natural frequencies, mode shapes, and modal participation factors for an extensible suspension cable, which depend on one dimensionless parameter related to the elasticity of the cable, to the case of a stiffened suspension bridge in which the response depends also on a second dimensionless parameter related to the stiffness of the girder. The continuum suspension bridge model is also used to understand the pattern of variation of mode shapes as a function of cable elasticity and girder stiffness, which has been shown by West et al. (1984) [6] to be considerably more complex than that for a suspension cable. Finally, the threshold amplitudes of free vibrations that would result in the incipient slackening of the hangers are determined.     

Lead-strontium isotopic variations along the East Pacific Rise and the Mid-Atlantic Ridge: a comparative study

We have determined the Pb and Sr isotopic compositions in a number of fresh young oceanic basalts from the East Pacific Rise (between 20°N and 21°S latitudes), and from the Mid-Atlantic Ridge (between 65°N and 10°N).The results confirm the PbSr isotopic correlation for mid-ocean ridges basalts obtained by Allègre et al. [1], Cohen et al. [2], Dupréand Allègre [3], and the correlation between isotopic variation and the compatible trace elements ratios variation [1].A comparison between the Atlantic and Pacific results reveals that there is a wider range of values for the Atlantic than for the Pacific. After filtering the short wavelengths, a good correlation is obtained between long-wavelength bathymetric and isotopic variations for the Atlantic.The preferred model proposed to explain these differences involves the constant presence of hot spots under ridges. On slow-spreading ridges like the Atlantic, the hot spots signature is clearly visible in both bathymetry and isotopic ratios. On fast-spreading centers, the hot spot signature in both the bathymetry and isotopic signature may be diluted by the rapid supply of material coming from the asthenosphere.However, an alternative explanation for which no hot spot influence is found on the East Pacific Rise cannot be definitely ruled out.In two occurrences, south of the Hayes fracture zone (Atlantic), large isotopic heterogeneities are observed within a single dredge. This does not contradict the concept of regional isotopic regularities, but suggests that blob injection and source mixing may be observed at very different scales under the ridges.