A second-order dynamic subgrid-scale stress model

A second-order dynamic model based on the general relation between the subgrid-scale stress and the velocity gradient tensors was proposed. A priori test of the second-order model was made using moderate resolution direct numerical simulation date at high Reynolds number ( Taylor microscale Reynolds number R-lambda = 102 similar to 216) for homogeneous, isotropic forced flow, decaying flow, and homogeneous rotating flow. Numerical testing shows that the second-order dynamic model significantly improves the correlation coefficient when compared to the first-order dynamic models.

High order asymptotic field for plane stress crack problem

This paper presents an exact analysis for high order asymptotic field of the plane stress crack problem. It has been shown that the second order asymptotic field is not an independent eigen field and should be matched with the elastic strain term of the first order asymptotic field. The second order stress field ahead of the crack tip is quite small compared with the first order stress field. The stress field ahead of crack tip is characterized by the HRR field. Hence the J integral can be used as a criterion for crack initiation.

Static equilibrium of horizontal ring prominence

In 1980 the Beijing Observatory had successively observed sevesal rare completely closed ring prominences whose ring plane was approximately parallel to the solar surface with a characteristic life about 1—2 days. In this paper we discuss the static equilibrium of this kind of horizontal ring plasma under the simultaneous actions of magnetic force, gravity and pressure gradients. Assuming ring plasma with axisymmetry and rectangular plasma cross-section and adopting closed magnetic field boundary condition from the basic equations we obtain the exact zero order general solutions for magnetic field (force-free field) and density (pressure). We further obtain an eigen-solution for the zero order magnetic field and density as well as the first order magnetic field, thus giving a kind of the possible distribution of magnetic field and density for the horizontal closed ring prominence. The closed magnetic structure of ring prominence as presented in this paper, has no link with the force lines of the outside corona magnetic field. This is helpful to explain the great temperature difference between prominenee and corona.

Displacive To Order-Disorder Two-Step Phase Transition Model For Para-Ferroelectric Transition

Two-step phase transition model, displacive to order-disorder, is proposed. The driving forces for these two transitions are fundamentally different. The displacive phase transition is one type of the structural phase transitions. We clearly define the structural phase transition as the symmetry broking of the unit cell and the electric dipole starts to form in the unit cell. Then the dipole-dipole interaction takes place as soon as the dipoles in unit cells are formed. We believe that the dipole-dipole interaction may cause an order-disorder phase transition following the displacive phase transition. Both structural and order-disorder phase transition can be first-order or second-order or in between. We found that the structural transition temperatures can be lower or equal or higher than the order-disorder transition temperature. The para-ferroelectric phase transition is the combination of the displacive and order-disorder phase transitions. It generates a variety of transition configurations along with confusions. In this paper, we discuss all these configurations using our displacive to order-disorder two-step phase transition model and clarified all the confusions.

Highly sensitive wave-front sensor with a non-zero-order phase plate

We propose a novel highly sensitive wave front detection method for a quick check of a flat wave front by taking advantage of a non-zero-order pi phase plate that yields a non-zero-order diffraction pattern. When a light beam with a flat wave front illuminates a phase plate, the zero-order intensity is zero. When there is a slight distortion of the wave front, the zero-order intensity increases. The ratio of first-order intensity to that of zero-order intensity is used as the criterion with which to judge whether the wave front under test is flat, eliminating the influence of background light. Experimental results demonstrate that this method is efficient, robust, and cost-effective and should be highly interesting for a quick check of a flat wave front of a large-aperture laser beam and adaptive optical systems. (c) 2005 Optical Society of America.

Optical generaton of millimeter-wave pulses using a fiber Bragg grating in a fiber-optics system

A scheme is proposed to transform an optical pulse into a millimeter-wave frequency modulation pulse by using a weak fiber Bragg grating (FBG) in a fiber-optics system. The Fourier transformation method is used to obtain the required spectrum response function of the FBG for the Gaussian pulse, soliton pulse, and Lorenz shape pulse. On the condition of the first-order Born approximation of the weak fiber grating, the relation of the refractive index distribution and the spectrum response function of the FBG satisfies the Fourier transformation, and the corresponding refractive index distribution forms are obtained for single-frequency modulation and linear-frequency modulation millimeter-wave pulse generation. The performances of the designed fiber gratings are also studied by a numerical simulation method for a supershort pulse transmission. (c) 2007 Optical Society of America.

Modelling and simulation of the second-order Doppler error of a laser dual-frequency interferometer

Only the first- order Doppler frequency shift is considered in current laser dual- frequency interferometers; however; the second- order Doppler frequency shift should be considered when the measurement corner cube ( MCC) moves at high velocity or variable velocity because it can cause considerable error. The influence of the second- order Doppler frequency shift on interferometer error is studied in this paper, and a model of the second- order Doppler error is put forward. Moreover, the model has been simulated with both high velocity and variable velocity motion. The simulated results show that the second- order Doppler error is proportional to the velocity of the MCC when it moves with uniform motion and the measured displacement is certain. When the MCC moves with variable motion, the second- order Doppler error concerns not only velocity but also acceleration. When muzzle velocity is zero the second- order Doppler error caused by an acceleration of 0.6g can be up to 2.5 nm in 0.4 s, which is not negligible in nanometric measurement. Moreover, when the muzzle velocity is nonzero, the accelerated motion may result in a greater error and decelerated motion may result in a smaller error.

亚硝化—厌氧氨氧化处理猪场废水研究

猪场废水COD浓度高、氨氮浓度高、悬浮物浓度高，已成为农村面源污染的主要来源，并严重威胁到农村饮用水安全。猪场废水氨氮浓度高、处理难度大，如何采用经济高效的方法，去除氨氮使其达到排放标准，一直是猪场废水处理中面临的重要难题。 厌氧氨氧化是近年受到国内外水处理研究者广泛关注的新型生物脱氮技术，具有不需要外加有机碳源、节省供氧量、降低能耗等优点。虽然国内外研究者对厌氧氨氧化过程的脱氮机理、厌氧氨氧化菌的生理生化特性等进行了多方面的研究，但已有的报道大多以模拟废水为研究对象，以猪场废水为研究对象的报道，在国内外文献中极少有报导。 本论文以猪场废水为主要研究对象，考察了猪场废水的亚硝化过程、厌氧氨氧化的启动过程，并对亚硝化和厌氧氨氧化联合用于猪场废水脱氮进行了探索。 1．论文首先研究了猪场废水的亚硝化过程，考察了废水水质和主要运行条件对亚硝化过程的影响。实验表明：（1）亚硝化阶段反应时间为8到10h时，出水中氨氮和亚硝酸盐浓度比可达到1：1～1：1.23，满足厌氧氨氧化反应对二者比例的要求；达到前述要求时，氨氮去除率达到58.3～65.6 %，亚硝化率在整个过程均保持在97 %以上，COD去除率在59.2～68.6 %；（2）曝气量（溶解氧）对亚硝化过程影响显著，随着曝气量增大，达到厌氧氨氧化要求的氨氮与亚硝酸盐氮浓度比例所需水力停留时间τ越短，pH出现明显下降的时间越短；（3）τ对应的pH在7.8～8.1之间，无需进行pH调节即可满足厌氧氨氧化反应对pH的要求；（4）氨氮和COD降解过程遵循一级反应动力学，氨氮和COD降解的速率常数分别为0.0656～0.0724 1/h和0.0491～0.0664 1/h。 2．在进行亚硝化过程研究的同时，以模拟废水为试验对象，进行厌氧氨氧化启动研究。以反硝化污泥和养殖厂储水池厌氧底泥的混合污泥作为接种污泥，历时大约100天，培育出具有厌氧氨氧化活性的污泥，氨氮和亚硝酸盐氮最高进水浓度分别为223.8 mg/L和171.4 mg/L，去除率最高分别达48%和41.5%，此时二者消耗比例为1.33：1。 3．在猪场废水的亚硝化研究完成和厌氧氨氧化过程初步启动成功后，在模拟废水中逐步加入猪场废水的亚硝化处理出水，逐步实现亚硝化和厌氧氨氧化的组合。亚硝化出水添加到厌氧反应器后，厌氧氨氧化反应仍可继续进行，且去除效率逐步提高。研究发现添加的亚硝化出水中携带的亚硝化细菌在厌氧氨氧化菌膜外层生长并累积，增加了厌氧氨氧化反应基质的传质阻力，妨碍了厌氧氨氧化效率的提高。 4．亚硝化－厌氧氨氧化实际工程应用探索中，生物接触氧化池可在有效去除废水中的有机物的同时实现亚硝化，出水中氨氮和亚硝酸盐比例平均为1.10，可满足后续厌氧氨氧化的要求；在适宜的进水浓度和温度下，ABR池出现了厌氧氨氧化启动的迹象；研究同时发现，水质的波动和气温的变化是工程中影响厌氧氨氧化菌活性的重要因素。 论文的主要创新点在于：（1）以猪场废水为研究对象，以实现厌氧氨氧化为目标，对亚硝化过程进行了比较详细的考察，获得了亚硝化出水满足厌氧氨氧化要求的工艺条件，通过对其COD和氨氮降解过程的考察，得出亚硝化阶段COD降解和氨氮去除的动力学模型；（2）对亚硝化－厌氧氨氧化处理猪场废水进行了探索，确立了影响其污染物去除率稳定的重要因素。 论文的上述研究成果，为厌氧氨氧化技术的实用性研究提供理论依据。 Piggery wastewater, which is characterized by high concentration of COD、ammonium and suspend substance, has become a most important source of non-point source pollution and also severely threats drinking water security in rural area. How to discharge piggery wastewater with the ammonium concentration meeting standard by economical and effective method? This is the most urgent problem in piggery wastewater treatment. As a new biological nitrogen removal technology, Anammox process has been paid more and more attention by researchers all over the world. Anammox has advantages of no need of organic carbon addition, low oxygen consumption and energy consumption. Plenty of investigations have been carried out to the mechanism, physiological and biochemical characteristic of bacteria about Anammox. Most of researches focused on synthetic wastewater, there is rare report about its application in piggery wastewater. In this paper，experimental studies were performed to investigate Sharon process in treatment of piggery wastewater，the start up process of Annammox using synthetic wastewater were studied, the feasibility of applying Sharon-Anammox process in the nitrogen removal of piggery wastewater was evaluated. 1. Sharon process of piggery wastewater was firstly investigated to analyze the effects of water quality and main running parameters, which meet the NH4+-N to NO2--N ratio requirement of successive Anammox. Results showed: (1)During Sharon Process，after 8～10 hours’ reaction the NH4+-N to NO2--N ratio in effluent reached 1:1.0～1:1.23, when the removal percentage of NH4+-N was 58.3～65.6 %, a semi-nitration rate of above 97 % was achieved during the process; meanwhile 59.2～68.6 % of the COD was also removed. (2)The aeration rate（oxygen） had obvious effect on the hydraulic retention time(τ) which met the NH4+-N to NO2--N ratio requirement of Anammox. As aeration rate increased, the hydraulic retention time(τ) was shortened. (3) The pH corresponding to τ was between 7.8 and 8.1, thus it needed no artificial adjustment. (4) The reduction of ammonia and COD followed the first-order reaction kinetics. The velocity constants of ammonia and COD were 0.0656～0.0724 1/h and 0.0491～0.0664 1/h, respectively. 2. The startup of Anammox process using the artificial wastewater was performed simultaneously with Sharon. The aim was to investigate the running parameters of Anammox and make foundation for the combination stage. By using the mixture of denitrifying sludge and anaerobic sludge in tank of the breeding factory, sludge of Anammox activity was cultivated in UASB after 100 days. The removal percentage of NH4+-N and NO2-N were up to 48% and 41.5%, respectively, when the NH4+-N and NO2-N influent concentration were 223.8 mg/L and 171.4 mg/L, respectively, the NH4+-N and NO2-N removal rate was 1.33:1. 3. After investigation of Sharon and startup of Anammox, effluent of Sharon process was added into the synthetic wastewater to combine Sharon and Anammox step by step. It took some time after the addition of Sharon effluent that Anammox reaction continued and the removal rate kept increasing. It indicated that nitrifying bacteria were carried by the Sharon effluent cumulated in the outer layer of Anammox. This enhanced transfer resistance of Anammox reaction and the increasing removal rate was restrained. 4. In the bio-contact oxidation pond of practical project, Sharon process were carried out successfully and organic compounds were removed effectively. An average NO2-N/ NH4+-N rate of 1:1.0 was achieved in the effluent, which met the requirement of successive Anammox. Under condition of suitable influent concentration and temperature, there was evidence that Anammox could start up in ABR. The variety of wastewater and temperature had great affects on Anammox activity in practical engineering. Innovation of this paper: (1) The Sharon process for treating piggery wastewater was discussed in details. Technological parameters that met requirement of Anammox were obtained. The dynamic models of COD and ammonium removal in the process were educed. (2) Sharon-Ananmmox for treatment of piggery wastewater was investigated, and the primary influencing factors was studied. This paper could be a theoretical consult for research of Anammox utility.

功能菌剂的混合发酵研究

随着化工行业的发展，大量有毒有害难降解有机物随工业废水的排放进入环境，这些物质能够在环境中长期存在、积累和扩散，通过食物链对动植物的生存及人类的健康造成不良影响。本文以苯酚、对氯硝基苯、氯苯和十六烷为模拟污染物，以前期研制的功能菌剂为对象，经过紫外线线诱变筛选出优于出发菌株的功能菌，对诱变后功能菌的理化性能进行了研究，对菌种进行了鉴定，在此基础上，就其相互之间的微生态关系进行研究，为混合发酵提供理论基础，并就其最佳发酵条件及发酵参数进行了研究，最后对发酵产品的性能进行了检测。目前，国内外有关功能菌剂的研究还存在多方面的不足，主要包括：①由于多菌种混合发酵过程较为复杂，各菌之间存在复杂的相互作用，影响因素较多，关于菌种之间的相互关系研究得很少，环境功能菌剂的发酵方法大多采用单独发酵后混合的方式。单独发酵对原材料、设备和能源的利用率较低，对于多菌种制剂发酵，在设备、能源和原材料的方面造成的浪费更大，将会大幅增加菌剂的生产成本，影响多菌种功能菌剂的发展；②功能菌剂生产过程的质量控制方面研究得较少；③功能菌剂产品的稳定性、抗冲击性能研究得较少，对环境微生物制剂的研究主要集中在菌种选育和培养条件优化方面。 通过本论文研究，得到以下主要结论。 （1）在紫外线诱变处理中，用紫外线对发生一定程度退化的出发菌株进行诱变处理后，六株具有高效降解性能的菌株被筛选出来，诱变筛选出的菌株形态和ERIC-PCR指纹图谱与出发菌株相比发生了明显改变；而且诱变后的菌株对目标难降解底物的降解能力均得到改善，其中，FPN、FCB、F14、FEm对目标底物的降解率提高了20%以上；诱变后菌株经过7次连续传代接种后，对目标难降解底物的降解率无显著变化，具有一定的遗传稳定性。并对诱变后的功能菌进行了初步的鉴定，这6株菌都分别是芽孢杆菌。 （2）对诱变后的功能菌相互之间的微生态关系进行了研究，通过抑菌实验、生长量以及基质消耗量的比较，确定它们之间的生长关系是无害共栖关系，可以进行混合发酵。 （3）对该功能菌剂进行发酵培养条件研究，结果表明发酵培养基的最佳成分（g/L）：葡萄糖 31.0g/L、玉米粉10.0g/L、磷酸氢二钾1.0g/L、硫酸铵1.1g/L、硫酸镁0.55g/L。通过研究不同的培养条件对菌体生长和降解性能的影响，确定了最佳培养条件：培养基初始pH7.5；最适温度32℃；培养基装液量125mL（250 mL三角瓶），以及培养时间对降解性能的影响，培养20 h的产物对降解最为有利。通过研究添加不同目标污染物对菌体生长和降解性能的影响，确定了添加目标污染物的最佳量以及最佳时间：苯酚投加量：1.125 g/L，对氯硝基苯投加量：0.1 g/L；最佳投加时间为发酵培养开始后4 h。 （4）以摇瓶分批发酵最优条件为基础，对FPN、F10、FCB、FNa、F14 和 FEm进行了摇瓶分批发酵试验。以摇瓶分批发酵试验数据为依据，对功能菌剂分批发酵动力学进行了研究，建立了菌体生长和基质消耗的动力学模型，拟合模型能较好的反映功能菌剂分批发酵过程。 （5）功能菌剂和活性污泥协同作用，可以提高系统的生物降解能力，功能菌剂投加量为2%，新鲜活性污泥3500 mg/L，降解24 h条件下，功能菌剂和活性污泥的协同作用对COD的去除率和对照组相比，最多的提高了36.8%。功能菌剂和活性污泥协同作用以及活性污泥的单独作用，其生物降解过程均符合一级反应动力学过程，功能菌剂和活性污泥协同作用的生物降解动力学方程为：，相关系数97%。采用SBR运行方式，引入功能菌剂的SBR系统明显能够改善和提高生物降解的效率。与仅有活性污泥的系统相比，系统对COD的平均去除率可以提高27.1%，同时，系统的耐负荷冲击以及耐毒害冲击的性能比仅有活性污泥的SBR系统强，特别是负荷冲击对引入功能菌剂的SBR系统影响很小。仅有活性污泥的SBR系统经过负荷冲击和毒害冲击之后，不能恢复到冲击之前的水平，而且系统有效作用时间的周期比引入功能菌剂的SBR系统相比大大缩短，而引入功能菌剂的SBR系统处理效果较为稳定，恢复能力很强。 Along with the development of industries, many recalcitrant organic chemicals have been discharged into natural environments together with wastewaters and can exist in waters, soil and sediments for a long time without degradation. These haz-ardous substances, their byporducts and metabolizabilities can be highly toxic, mu-tagenic and carcinogenic, thereby threatening animals, plants and human health through food chain. Consequently the removal of these compounds is of significant interest in the area of wastewater treatment. In this dissertation, the phenol, hydro-quinone, chlorobenzene and hexadecane treated as the model pollutants, the func-tional microorganism agent was used as the starting strains, they treated with ultra-violet light, and then the mutant strains with high degradation ability were screened out and identified primarily, the relationship between these stains were studied, the medium composition and fermentation conditions were optimized, the degradation ability of the fermented production was tested. The literature survey indicates that the study of the microorganism agent is far from complete and more information is re-quired on following problems. 1, Because of the complexity of relationship in mixed fermentation and the complicated factors, the study is hardly to process.2, There is a lack of information on the quality control of the producing process .3, And there is a lack of information on the stability about the microorganism agent. In this dissertation, the main results of the present study could be summarized as follows: (1)The degenerate starting strains were treated with the ultraviolet light, and six mutant strains with high biodegradation ability were screened out by using the me-dium with selective pressure of model pollutants. The mutant strains had great changes in colonialmorphology and ERIC-PCR fingerprinting. And the mutant strains got obvious advantages over the starting strains in degradation ability and over 20% improvement of removal rates was achieved for FPN、FCB、F14 and FEm. The de-gradation ability of the mutant strains was stable after seven generations. After that, the mutant strains were primarily identified as bacillus respectively. (2) The relationship between these mutant strains was studied. By the compari-son of antibiosis effect, biomass and consumption of substrate, the relationships were neutralism and they could be mixed fermented. (3) The optimized cultivation conditions were as follows: glucose 31.0 g/L, corn power 10 g/L, K2HPO4 1.0 g/L, (NH4)2SO4 1.1 g/L, MgSO4 0.55 g/L, initial pH7.5, temperature 32℃, working volume 125 mL/250 mL, and cultivation time 20h (con-sidering the time effect on degradation ability), adding pollutants phenol (1.125 g/L) and hydroquinone (0.1 g/L) into the broth at 4 h after cultivation. (4) Based on the above optimum condition, the batch fermentation was per-formed with strains FPN, F10, FCB, FNa, F14 and FEm in shake flask. The batch fermentation kinetics was studied based on the experimental data. Two kinetic models were constructed which could reflect the regularity of growth and substrate consump-tion in the process of batch fermentation. (5) The co-operation of functional microorganism agent and activated sludge could raise biodegradation of system by adding some microorganism agent and 3500 mg/L fresh activated sludge. Bioaugumentation by the addition of high effective deg-radation culture enhanced the treatment effect of SBR system and the COD removal rate was increased by 20%-36.8%. Its biodegradation matched first-order dynamical reaction equation, and the reaction equation was ln0.2327.391ct=−+. The micro-organism agent had the effect of optimization to activated sludge micro-ecosystem. The SBR system adding 2% microorganism agent, the average COD removal rate of that was increased by 27.1% and stronger anti-shock ability to load and toxicant were achieved (compared with SBR system just adding activated sludge). Especially the load-shock has barely effect to the SBR system adding microorganism agent. After the load and toxicant shock, the SBR system just adding activated sludge couldn’t come back to original level and the activated sludge micro-ecosystem was frustrated. The applying of microorganism agent increased biological activity and system’s re-sistance ability to load shock and toxicant shock.

Chemisorption and reaction characteristics of methyl radicals on Cu(110)

Methyl radicals are generated by pyrolysis of azomethane, and the condition for achieving neat adsorption on Cu(110) is described for studying their chemisorption and reaction characteristics. The radical-surface system is examined by X-ray photoemission spectroscopy, ultraviolet photoemission spectroscopy, temperature-programmed desorption, low-energy electron diffraction (LEED), and high-resolution electron energy loss spectroscopy under ultrahigh vacuum conditions. It is observed that a small fraction of impinging CH3 radicals decompose into methylene possibly on surface defect sites. This type of CH2 radical has no apparent effect on CH3(ads) surface chemistry initiated by dehydrogenation to form active CH2(ads) followed by chain reactions to yield high-mass alkyl products. All thermal desorption products, such as H-2, CH4, C2H4, C2H6, and C3H6, are detected with a single desorption peak near 475 K. The product yields increase with surface coverage until saturation corresponding to 0.50 monolayer of CH3(ads). The mass distribution is, however, invariant with initial CH3(ads) coverage, and all desorbed species exhibit first-order reaction kinetics. LEED measurement reveals a c(2 x 2) adsorbate structure independent of the amount of gaseous exposure. This strongly suggests that the radicals aggregate into close-packed two-dimensional islands at any exposure. The islanding behavior can be correlated with the reaction kinetics and is deemed to be essential for the chain propagation reactions. Some relevant aspects of the CH3/Cu(111) system are also presented. The new results are compared with those of prior studies employing methyl halides as radical sources. Major differences are found in the product distribution and desorption kinetics, and these are attributed to the influence of surface halogen atoms present in those earlier investigations.

Second-order Stokes solutions for internal waves in three-layer density-stratified fluid

In this paper, internal waves in three-layer stratified fluid are investigated by using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. As expected, the first-order solutions are consistent with ordinary linear theoretical results, and the second-order solutions describe the second-order modification on the linear theory and the interactions between the two interfacial waves. Both the first-order and second-order solutions derived depend on the depths and densities of the three-layer fluid. It is also noted that the solutions obtained from the present work include the theoretical results derived by Umeyama as special cases.

Representation of microscale ocean wavenumber spectrum correct to the second order

In this paper, the analytical representations of four wave source functions in high-frequency spectrum range are given on the basis of ocean wave theory and dimensional analysis, and the perturbation method is used to solve the governing equations of ocean wave high-frequency spectrum on the basis of the temporally stationary and locally homogeneous scale relations of microscale wave. The microscale ocean wavenumber spectrum correct to the second order has an explicit structure, its first order part represents the equilibrium between different source functions, and its second order part represents the contribution of microscale wave propagation.

Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current

In this paper, interfacial waves in three-layer stratified fluid with background current are investigated using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory, and the Kelvin-Helmholtz instability of interfacial waves is studied. As expected, for three-layer stratified fluid with background current, the first-order asymptotic solutions (linear wave solutions), dispersion relation and the second-order asymptotic solutions derived depend on not only the depths and densities of the three-layer fluid but also the background current of the fluids, and the second-order Stokes wave solutions of the associated elevations of the interfacial waves describe not only the second-order nonlinear wave-wave interactions between the interfacial waves but also the second-order nonlinear interactions between the interfacial waves and currents. It is also noted that the solutions obtained from the present work include the theoretical results derived by Chen et al (2005) as a special case. It also shows that with the given wave number k (real number) the interfacial waves may show Kelvin-Helmholtz instability.

地震波模拟：非规则网格离散的数值解法、吸收边界及其实际应用

This dissertation presents a series of irregular-grid based numerical technique for modeling seismic wave propagation in heterogeneous media. The study involves the generation of the irregular numerical mesh corresponding to the irregular grid scheme, the discretized version of motion equations under the unstructured mesh, and irregular-grid absorbing boundary conditions. The resulting numerical technique has been used in generating the synthetic data sets on the realistic complex geologic models that can examine the migration schemes. The motion equation discretization and modeling are based on Grid Method. The key idea is to use the integral equilibrium principle to replace the operator at each grid in Finite Difference scheme and variational formulation in Finite Element Method. The irregular grids of complex geologic model is generated by the Paving Method, which allow varying grid spacing according to meshing constraints. The grids have great quality at domain boundaries and contain equal quantities of nodes at interfaces, which avoids the interpolation of parameters and variables. The irregular grid absorbing boundary conditions is developed by extending the Perfectly Matched Layer method to the rotated local coordinates. The splitted PML equations of the first-order system is derived by using integral equilibrium principle. The proposed scheme can build PML boundary of arbitrary geometry in the computational domain, avoiding the special treatment at corners in a standard PML method and saving considerable memory and computation cost. The numerical implementation demonstrates the desired qualities of irregular grid based modeling technique. In particular, (1) smaller memory requirements and computational time are needed by changing the grid spacing according to local velocity; (2) Arbitrary surfaces and interface topographies are described accurately, thus removing the artificial reflection resulting from the stair approximation of the curved or dipping interfaces; (3) computational domain is significantly reduced by flexibly building the curved artificial boundaries using the irregular-grid absorbing boundary conditions. The proposed irregular grid approach is apply to reverse time migration as the extrapolation algorithm. It can discretize the smoothed velocity model by irregular grid of variable scale, which contributes to reduce the computation cost. The topography. It can also handle data set of arbitrary topography and no field correction is needed.

复杂介质中地震波场数值模拟研究——基于广义正交多项式迭积微分算子法

In this paper, we propose a new numerical modeling method – Convolutional Forsyte Polynomial Differentiator (CFPD), aimed at simulating seismic wave propagation in complex media with high efficiency and accuracy individually owned by short-scheme finite differentiator and general convolutional polynomial method. By adjusting the operator length and optimizing the operator coefficient, both global and local informations can be easily incorporated into the wavefield which is important to invert the undersurface geological structure. The key issue in this paper is to introduce the convolutional differentiator based on Forsyte generalized orthogonal polynomial in mathematics into the spatial differentiation of the first velocity-stress equation. To match the high accuracy of the spatial differentiator, this method in the time coordinate adopts staggered grid finite difference instead of conventional finite difference to model seismic wave propagation in heterogeneous media. To attenuate the reflection artifacts caused by artificial boundary, Perfectly Matched Layer (PML) absorbing boundary is also being considered in the method to deal with boundary problem due to its advantage of automatically handling large-angle emission. The PML formula for acoustic equation and first-order velocity-stress equation are also derived in this paper. There is little difference to implement the PML boundary condition in all kind of wave equations, but in Biot media, special attenuation factors should be taken. Numerical results demonstrate that the PML boundary condition is better than Cerjan absorbing boundary condition which makes it more suitable to hand the artificial boundary reflection. Based on the theories of anisotropy, Biot two-phase media and viscous-elasticity, this paper constructs the constitutive relationship for viscous-elastic and two-phase media, and further derives the first-order velocity-stress equation for 3D viscous-elastic and two-phase media. Numerical modeling using CFPD method is carried out in the above-mentioned media. The results modeled in the viscous-elastic media and the anisotropic pore elastic media can better explain wave phenomena of the true earth media, and can also prove that CFPD is a useful numerical tool to study the wave propagation in complex media.