基于显式分形插值的高保真地震数据重建方法研究

Based on the fractal theories, contractive mapping principles as well as the fixed point theory, by means of affine transform, this dissertation develops a novel Explicit Fractal Interpolation Function（EFIF）which can be used to reconstruct the seismic data with high fidelity and precision. Spatial trace interpolation is one of the important issues in seismic data processing. Under the ideal circumstances, seismic data should be sampled with a uniform spatial coverage. However, practical constraints such as the complex surface conditions indicate that the sampling density may be sparse or for other reasons some traces may be lost. The wide spacing between receivers can result in sparse sampling along traverse lines, thus result in a spatial aliasing of short-wavelength features. Hence, the method of interpolation is of very importance. It not only needs to make the amplitude information obvious but the phase information, especially that of the point that the phase changes acutely. Many people put forward several interpolation methods, yet this dissertation focuses attention on a special class of fractal interpolation function, referred to as explicit fractal interpolation function to improve the accuracy of the interpolation reconstruction and to make the local information obvious. The traditional fractal interpolation method mainly based on the randomly Fractional Brown Motion (FBM) model, furthermore, the vertical scaling factor which plays a critical role in the implementation of fractal interpolation is assigned the same value during the whole interpolating process, so it can not make the local information obvious. In addition, the maximal defect of the traditional fractal interpolation method is that it cannot obtain the function values on each interpolating nodes, thereby it cannot analyze the node error quantitatively and cannot evaluate the feasibility of this method. Detailed discussions about the applications of fractal interpolation in seismology have not been given by the pioneers, let alone the interpolating processing of the single trace seismogram. On the basis of the previous work and fractal theory this dissertation discusses the fractal interpolation thoroughly and the stability of this special kind of interpolating function is discussed, at the same time the explicit presentation of the vertical scaling factor which controls the precision of the interpolation has been proposed. This novel method develops the traditional fractal interpolation method and converts the fractal interpolation with random algorithms into the interpolation with determined algorithms. The data structure of binary tree method has been applied during the process of interpolation, and it avoids the process of iteration that is inevitable in traditional fractal interpolation and improves the computation efficiency. To illustrate the validity of the novel method, this dissertation develops several theoretical models and synthesizes the common shot gathers and seismograms and reconstructs the traces that were erased from the initial section using the explicit fractal interpolation method. In order to compare the differences between the theoretical traces that were erased in the initial section and the resulting traces after reconstruction on waveform and amplitudes quantitatively, each missing traces are reconstructed and the residuals are analyzed. The numerical experiments demonstrate that the novel fractal interpolation method is not only applicable to reconstruct the seismograms with small offset but to the seismograms with large offset. The seismograms reconstructed by explicit fractal interpolation method resemble the original ones well. The waveform of the missing traces could be estimated very well and also the amplitudes of the interpolated traces are a good approximation of the original ones. The high precision and computational efficiency of the explicit fractal interpolation make it a useful tool to reconstruct the seismic data; it can not only make the local information obvious but preserve the overall characteristics of the object investigated. To illustrate the influence of the explicit fractal interpolation method to the accuracy of the imaging of the structure in the earth’s interior, this dissertation applies the method mentioned above to the reverse-time migration. The imaging sections obtained by using the fractal interpolated reflected data resemble the original ones very well. The numerical experiments demonstrate that even with the sparse sampling we can still obtain the high accurate imaging of the earth’s interior’s structure by means of the explicit fractal interpolation method. So we can obtain the imaging results of the earth’s interior with fine quality by using relatively small number of seismic stations. With the fractal interpolation method we will improve the efficiency and the accuracy of the reverse-time migration under economic conditions. To verify the application effect to real data of the method presented in this paper, we tested the method by using the real data provided by the Broadband Seismic Array Laboratory, IGGCAS. The results demonstrate that the accuracy of explicit fractal interpolation is still very high even with the real data with large epicenter and large offset. The amplitudes and the phase of the reconstructed station data resemble the original ones that were erased in the initial section very well. Altogether, the novel fractal interpolation function provides a new and useful tool to reconstruct the seismic data with high precision and efficiency, and presents an alternative to image the deep structure of the earth accurately.

地震波散射非线性反演问题不动点理论及方法的研究

How to create a new method to solve the problem or reduce the influence of that the result of the seismic waves scattering nonlinear inversion is not uniqueness is a main purpose of this research work in the paper. On the background of research into the seismic inversion, new progress of the nonlinear inversion is introduced at the first chapter in this paper. Especially, the development, basic theories and assumptions on some major theories of seismic inversion are analyzed, discussed and summarized in mathematics and physics. Also, the problems faced by the mathematical basis of investigations of the seismic inversion are discussed, and inverse questions of strongly seismic scattering due to strong heterogeneous media in the Earth interior are analyzed and viewed. What the kernel of paper is that gathers all our attention making a new nonlinear inversion method of seismic scattering. The paper provides a theory and method of how to introduce the fixed-point theory into the nonlinear seismic scattering inversion and how to obtain the solution, and gives the actually method to create a serials of contractive mappings of velocity parameter's in the mapping space of wave. Therefore, the results testify the existence of fixed point of velocity parameter and give the method the find it. Further, the paper proves the conclusion that the value obtained by taking the fixed point of velocity parameter into wave equation is the fixed point of the wave of the contractive mapping. Thence, the fixed point is the global minima since the stabilities quality of the fixed point. Based on the new theory, in the chapter three, many inverse results are obtained in the numerical value test. By analysis the results one could find a basic facts that all the results, which are inversed by the different initial model, are tended to the true value in theoretical true model. In other words, the new method mostly eliminates the non-uniqueness that which is existed in seismic waves scattering nonlinear inversion in degree. But, since the test results are quite finite now, more test is need here to positive our theory. As a new theoretical method, it must be existed many weaken in it. The chapter four points out all the questions which is bother us. We hope more people to join us to solve the problem together.

Trace theory

The concept of traces has been introduced for describing non-sequential behaviour of concurrent systems via its sequential observations. Traces represent concurrent processes in the same way as strings represent sequential ones. The theory of traces can be used as a tool for reasoning about nets and it is hoped that applying this theory one can get a calculus of the concurrent processes anologous to that available for sequential systems. The following topics will be discussed: algebraic properties of traces, trace models of some concurrency phenomena, fixed-point calculus for finding the behaviour of nets, modularity, and some applications of the presented theory.

Experimental-study of free-surface oscillations of a liquid bridge by optical diagnostics

A non-contact optical method, consisting of a projecting grating technique for the relative measurement of a surface, and a technique of absolute measurement at a fixed point on the surface, are applied to measure the free surface vibration in a liquid bridge of half floating zone with small typical scale of a few of mm for emphasizing the thermocapillary effect in comparison with the effect of buoyancy. The radii variations in both longitudinal and azimuthal directions are obtained, and, then, the feature of surface wave could be analyzed in detail. The results show that there are values of principal oscillatory frequencies at different positions of free surface. The amplitudes of surface waves in longitudinal and azimuthal directions are several mum and several tenths of mum in order of magnitude. The phase of two-dimensional surface waves is different at different height for fixed cross section or at different azimuthal angle for fixed height. The wave features are discussed for the cases of typical parameter ranges.

The strange attractor of a kind of 2-dimensional map and dynamical properties on it

On the basis of previous works, the strange attractor in real physical systems is discussed. Louwerier attractor is used as an example to illustrate the geometric structure and dynamical properties of strange attractor. Then the strange attractor of a kind of two-dimensional map is analysed. Based on some conditions, it is proved that the closure of the unstable manifolds of hyberbolic fixed point of map is a strange attractor in real physical systems.

Distribution, stability, bifurcations and catastrophe of steady rotation of a symmetrical heavy gyroscope with viscous-liquid-filled cavity

The number, the angles of orientation and the stability in Rumyantsev Movchan's sense of oblique steady rotations of a symmetric heavy gyroscope with a cavity completely filled with a uniform viscous liquid, possessing a fixed point 0 on its symmetric axis. are given for various values of the parameters. By taking the square of the upright component of the angular momentum M2 as a control parameter, three types of bifurcation diagrams of the steady rotations, two types of jumps and two kinds of local catastrophes, one being the symmetric reduced cusp type and the other being of the symmetric reduced butterfly type, are obtained. By taking account of the M2-damping owing to the moment of unavoidable faint friction, two different modes for the gyroscope, initially in a stable quasi-steady upright rotation with a nutation angle theta(s) equal to zero, to topple over are found.

Self-formation of quasiperiodic void structure in CaF2 induced by femtosecond laser irradiation

We report the self-formation of quasiperiodic void structure with the length of several hundred micrometers inside the CaF2 crystal. The quasiperiodical voids along the propagation direction of the laser beam were formed spontaneously after the irradiation of a single femtosecond laser beam which was focused at a fixed point inside the crystal sample. The length of the void array varied with the focal depth beneath the sample surface. The possible mechanism of the self-formed void structure was discussed. (c) 2007 American Institute of Physics.

单束飞秒激光在氧化铝晶体中诱导自组装微米点阵

报道了单束飞秒激光在氧化铝晶体中诱导自组装微米点阵的有关研究进展。当单束飞秒激光被透镜聚焦到氧化铝晶体的内部某固定点， 微米点阵就在聚焦点的下方自动生成。我们发现能否产生自组装点阵和光束的聚焦点距离样品表面的深度有关。通过比较在氧化铝晶体和氟化钙晶体中能够产生点阵的深度，我们发现在氧化铝中较浅的位置即能诱导出点阵，而在氟化钙中则要求深度较深。具体的机理在文中进行了讨论。

Self-organized microvoid array perpendicular to the femtosecond laser beam in CaF2 crystals

Microvoid arrays were self-organized when femtosecond laser beam was tightly focused at a fixed point inside CaF2 crystal sample. Except void array grown below the focal point which had been reported before, we found another void array grown vertical to the laser propagation direction. This result has potential application in the fabrication of integrated micro-optic elements and photonic crystals. The possible mechanism of the phenomenon was proposed and verified experimentally.

The Category-Theoretic Solution of Recursive Domain Equations

Recursive specifications of domains plays a crucial role in denotational semantics as developed by Scott and Strachey and their followers. The purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place. The idea is to follow the well-known analogy between partial orders and categories, generalizing from least fixed-points of continuous functions over cpos to initial ones of continuous functors over $\omega $-categories. To apply these general ideas we introduce Wand's ${\bf O}$-categories where the morphism-sets have a partial order structure and which include almost all the categories occurring in semantics. The idea is to find solutions in a derived category of embeddings and we give order-theoretic conditions which are easy to verify and which imply the needed categorical ones. The main tool is a very general form of the limit-colimit coincidence remarked by Scott. In the concluding section we outline how compatibility considerations are to be included in the framework. A future paper will show how Scott's universal domain method can be included too.

谓词μ演算和模态图的语义一致性

模态图是谓词μ演算的一种有效的图形表示形式。证明了谓词μ演算和模态图的语义一致性，详细讨论了谓词μ演算公式、嵌套谓词等式系和模态图之间的关系，并给出了一种优化的从线性公式到嵌套谓词等式系的转换算法。

牦牛粪便对青藏高原东部高寒草甸土壤养分系统的影响

川西北高寒草甸位于青藏高原东部地区，是我国四大牧区之一，也是长江和黄河等江河源区的重要水源涵养功能区。近几十年来，大量牦牛粪便被牧民作为生物能源、肥料或者食用菌产业的原料而利用，为草原生态系统的养分平衡增加了生态风险。鉴于在青藏高原地区针对牦牛粪便的相关研究尚未见报道，本文从粪便和土壤养分相互变化趋势的角度出发，研究了粪便在夏秋两季的分解状况和粪便其下及其周围土壤的养分变化。通过此研究，将有助于了解牦牛粪便在自然状态下的分解速率以及粪便对土壤养分及土壤微生物生物量的影响，为粪便对草地土壤生态系统的贡献提供概念性认识，同时也为高寒草甸草地这种脆弱生态系统的可持续管理提供理论依据。 针对牦牛粪便自身养分释放及其对土壤在时间和空间尺度上的影响，本文通过模拟牛粪堆积，在不同时间和固定区域内对牛粪和土壤进行了夏秋两季的采样测定，分析了牛粪及土壤NO3--N、NH4+-N、速效K、无机P、有机C、全N 和全P 含量随时间的变化趋势。得到如下结果： 1. 在研究区域内，牛粪对草地生态系统具有较强的养分（N、P）贡献能力。据初步统计，其估值大致为氮素699~932 kg ha-1，P 素为110~147 kg ha-1。牛粪（湿重、干重）在夏秋季节的分解速率具有较大差异，夏季显著快于秋季。夏季牛粪湿重、干重在2 个月左右之后分别降为初期的14%和24%，而秋季同期分别降为35%和52%。牛粪养分（NO3--N、NH4+-N、速效K、无机P、有机C、全N 和全P）的分解速率在夏季也要显著快于秋季。秋季经过2 个月左右的分解之后，牛粪以上含量分别降至初始态的32%、60%、36%、64%、58%、63%和43%，远高于夏季的同期水平。 2. 在不同季节，牛粪周围的土壤养分（NO3--N、NH4+-N、速效K 和无机P）含量变化随时间改变呈现相同的趋势。但是，牛粪周围不同远近下土壤养分随时间的动态变化幅度略有不同。粪下土壤养分含量随时间变化波动较大，距粪便越远，随时间变化的变幅越为平缓。总体来说，在夏季由于粪便分解较快，对土壤养分的持续作用时间不及秋季，秋季粪便分解变慢，表现出养分的缓释特征。其次，牛粪对粪下土壤影响的持续时间也长于对周围土壤的作用时间。 3. 粪便对土壤养分（NO3--N、NH4+-N、速效K、无机P）影响的范围在不同季节具有差异。夏季要高于秋季，但对周围土壤养分影响的持续时间低于秋季。在夏季短期内，牛粪对土壤NO3--N 和速效K 含量的影响范围能够超过30cm，而对NH4+-N 和无机P 的影响范围则介于10cm 和30cm 之间。在2 个月左右之后，牛粪对周围土壤养分的影响能力基本消失。在秋季，牛粪对周围土壤养分影响范围难以达到30cm 处。粪便在夏季对其下土壤和周围土壤的有机C、全N 和全P 含量并无显著影响，但在秋季能显著增加其下土壤有机C、全N 和全P 含量。 4. 牛粪在秋季对土壤SMB-C、SMB-N 和SMB-P 含量的影响能够持续2 个月以上，由于秋冬季节牛粪分解缓慢，因此推断这种效应持续时间至少能够1 年左右。另一方面，牛粪在秋季对土壤SMB-C、SMB-N 和SMB-P 含量的影响范围主要集中在其下土壤，而周围的影响效应并不明显。 The grassland on the eastern fringe of Qinghai-Tibetan Plateau was one of the four greatest pasture zones in our country and the main water conservation function zones in the hesastream of Yangtse River and Huanghe river. Rencent years, lots of dung in this area was used as biological energy, fertilizer or material of fungoid growing, leading to high risk of nutrient banlance in grassland ecosystem. In view of the researches on the impact of yak dung in this area are relatively rare, the present study focused on the relationship of dung and soil nutrient transformation in sunmer and autumn, which could profoundly illuminate the mechanism of dung decomposition and the effect of dung on soil chemical properties and soil microbe biomass. The present study also contributed to a basic understand and provided scientific management in the high-frigid ecosystem. Decomposition of yak dung and its effect on soil chemical properties in eastern grassland of Qinghai-Tibetan Plateau were determined. The study simulated the real dung pats, took dung and soil samples at different time and fixed-point in summer and autumn. The samples were analysed for NO3--N, NH4+-N, available K, inorganic P, total organic C (TOC), total N (TN), total P (TP). It was concluded that: 1. In study area, the yak dung supplied to ecosystem substantial nutrient. It is estimated that the N contribution of dung was approximately 699~932 kg ha-1, P contribution was approximately 110~147 kg ha-1. The rate of yak decomposition was more rapid in summer than autumn, the wet and dry weight of yak decreased to 14% and 24% respectively after 2 months when dung excreted in summer, with 35% and 52% in autumn. The content of NO3--N、NH4+-N、available K、inorganic P、TOC、TN and TP in dung decomposed more rapid in summer too. After 2 months when dung excreted in autumn, the content of above nutrient decreased to 32%、60%、36%、64%、58%、63% and 43% respectively，which were significantly higher than summer. 2. The content of NO3--N、NH4+-N、available K and inorganic P in soil around dung had the same transformation trend in each season, whereas it was distinguishing at different gradient of distance from dung, the nutrient in soil below dung had the most significant change while the more far from dung, the less change in soil. It was concluded that the yak dung had prolong impacts on soil in autumn compared with summer, besides, it aslo showed that the yak dung had protract effect on soil below dung compared with soil around dung. 3. The yak dung had expansive impact on soil around dung in summer whereas had relatively short effect compared with autumn. In short-term at summer, there was a significant increase about the content of NO3--N and available K around 30cm radius from dung pat while the content of NH4+-N and inorganic P between 10cm to 30cm. After 2 months, the impact almost disappeared. In autumn, the effect was hard to reach 30cm. The yak dung had no significant effects on the content of TOC、TN and TP in soil below or around dung in summer whereas there was a obvious increase in soil below dung pat in autumn. 4. The duration of effect of yak dung on soil microbial biomass(SMB) C、N and P was at least 2 months, maybe even more than 1 year. On the other hand, the impact of dung on SMB-C、SMB-N and SMB-P mainly acted on soil below dung while no obious effect on soil around dung.

S／T曲线速度规划在定点DSP上的实现

本文将S／T曲线速度规划的思想引入全数字伺服驱动系统中,通过提高速度的平滑性,特别是高速启、制动状态,来提高伺服系统的整体控制性能。基于定点数字信号处理器DSP芯片对提出的算法进行了实现。由于定点运算的限制,算法在实现中需要进行特殊的处理,本文对此进行了研究,并提出了一种余码补偿方案。实验研究表明,使用本文提出的方法可以提高系统运行的平稳性和控制的精确度。

7000米载人潜水器推进器故障容错控制分配研究

介绍了7000米载人潜水器推进系统的组成和推进器布置,描述了潜水器控制分配问题,对推进器推力和期望控制量进行了归一化处理.根据载人潜水器的推进器布置,建立了系统的控制分配模型,设计了推进器故障容错处理策略,研究了基于推力最小二范数的载人潜水器控制分配求解方法.采用基于伪逆矩阵与定点分配的混合控制分配求解算法,在半物理仿真平台上实验验证了控制分配求解算法的正确性和有效性.

工业机器人的小脑模型控制

本文为动力学控制工业机器人提出了一种综合学习算法,这种学习算法可将以前所学的信息用于新的控制输入.这种控制方法不需要事先知道机器人动力学,它易于应用于特殊的控制问题或修改以适应实际系统中的变化,控制方法在时间上是有效的,且很适合于定点实现.学习控制算法的有效性通过4自由度的直接驱动机器人前两个关节在重复运动中的计算机仿真实验得到了验证.