Impact of difference accuracy on computational properties of vertical grids for a nonhydrostatic model

Starting from nonhydrostatic Boussinesq approximation equations, a general method is introduced to deduce the dispersion relationships. A comparative investigation is performed on inertia-gravity wave with horizontal lengths of 100, 10 and 1 km. These are examined using the second-order central difference scheme and the fourth-order compact difference scheme on vertical grids that are currently available from the perspectives of frequency, horizontal and vertical component of group velocity. These findings are compared to analytical solutions. The obtained results suggest that whether for the second-order central difference scheme or for the fourth-order compact difference scheme, Charny-Phillips and Lorenz ( L) grids are suitable for studying waves at the above-mentioned horizontal scales; the Lorenz time-staggered and Charny-Phillips time staggered (CPTS) grids are applicable only to the horizontal scales of less than 10 km, and N grid ( unstaggered grid) is unsuitable for simulating waves at any horizontal scale. Furthermore, by using fourth-order compact difference scheme with higher difference precision, the errors of frequency and group velocity in horizontal and vertical directions produced on all vertical grids in describing the waves with horizontal lengths of 1, 10 and 100 km cannot inevitably be decreased. So in developing a numerical model, the higher-order finite difference scheme, like fourth-order compact difference scheme, should be avoided as much as possible, typically on L and CPTS grids, since it will not only take many efforts to design program but also make the calculated group velocity in horizontal and vertical directions even worse in accuracy.

三种海水经济鱼类早期发育生物学的研究

海水经济鱼类的养殖在我国已经形成第四次海水养殖浪潮，经济效益显著，有力地推动了我国海水养殖的产业结构调整和可持续发展。然而在海水养殖发展过程中也存在着诸多问题，尤其是早期发育阶段的高死亡率，严重制约了我国海水养殖产业的稳定和健康发展。 海水鱼类养殖的关键为高质量，高存活率苗种的生产和培育，由于鱼类种类繁多，生物多样性丰富，对应实际的繁育技术，尤其是新品种的开发，必须要做出相应的调整。这就要求我们必须对每一种鱼类早期发育有所了解，并将形态和组织上的数据用于指导生产。 本文通过显微观察和组织学研究，主要描述和研究了我国北方三种重要的海水经济鱼类(条斑星鲽、杂交鲆、条石鲷)的早期发育生物学，并结合实际生产进一步阐明关键期的产生原因，机理以及采用相应的对策。具体结果如下： 1.条斑星鲽：作为冷温性鲆鲽鱼类，条斑星鲽早期发育过程的特征主要有： ① 条斑星鲽受精卵无油球，卵子呈半浮性；不同步卵裂现象提前，发生在第三次卵裂；卵裂期裂球大小差异大。孵化过程较长，在水温8 ± 0.3℃，盐度33的条件下，经9 d孵化。条斑星鲽胚胎发育的不同时期对温度的敏感性不同，其中原肠期对温度比较敏感。 ②在8-10℃，盐度33的条件下，8-9 dph开口摄食。且开口时，其吻前端出现有一点状黑褐色素，构成了条斑星鲽仔鱼“开口期”的重要标志。卵黄囊于消失。在后期仔鱼末期，背鳍和臀鳍上形成特有的黑褐色条斑带。 ③杯状细胞首先出现在咽腔后部和食道前段，胃腺和幽门盲囊出现于29 dph，变态期始于30dph。在条斑星鲽早期发育过程中，观察到其直肠粘膜层细胞质出现大量嗜伊红颗粒，为仔鱼肠道上皮吸收的蛋白质。 ④首先淋巴化的免疫器官是头肾，然后是胸腺和脾脏，这与大部分硬骨鱼类不同。条斑星鲽除头肾和脾脏外，胸腺实质也形成MMCs。其中以脾脏形成MMCs最为丰富，形态多样。 2. 杂交鲆：为同属的牙鲆和夏鲆间的远缘杂交种，其发育过程的特点为： ① 在温度为15.4～16.0℃，杂交鲆胚胎从受精到孵化所需的时间为76 h左右，胚孔关闭前期，胚胎先出现视囊及克氏囊，而后形成体节。孵出前胚体在卵膜内环绕不到1周。 ② 孵化后消失。杂交鲆群体变态间隔长(34-60 dph)，且变态高峰期出现的冠状幼鳍不明显(与母本牙鲆相比)，数量为7-8根。 ③组织学观察发现，其消化系统中胃腺出现较晚，且胃腺发育过程缓慢(与母本牙鲆相比)。甲状腺滤泡增生不明显，颜色较浅，数量较少。杂交鲆在早期发育过程中，并没有出现鳔原基。 3. 条石鲷作为岩礁性的暖水性鱼类，早期发育过程也较为特殊，包括外形以及内部的器官结构。主要特点有： ① 受精卵：受精卵卵黄上具有龟裂结构，为鱼卵的分类特征之一。 ② 初孵仔鱼：初孵仔鱼背鳍膜上的黑色素，从体背面向背鳍膜边缘移动，到3dph仔鱼基本消失，此为本种仔鱼发育所特有的特点。 ③ 后期仔鱼和稚鱼：肠道肌肉层加厚明显，仔稚鱼胃肠排空率急剧上升，死亡率增加，通过改善常规的投饵方式部分解决了这个死亡高峰的问题。在幼鱼初期，牙齿融合为骨喙，为石鲷科鱼类的特征。 ④胸腺上皮分泌细胞：类似的现象同样在虹鳟鱼中发现，但是虹鳟鱼胸腺上皮分泌细胞不如条石鲷的丰富，同样也不如条石鲷的排列整齐，而是零星分布在胸腺上皮与咽腔接触的表面。除了正常的造血器官—脾脏和头肾外，肝脏、胰腺和鳔等多种组织等也出现MMCs，此现象在硬骨鱼类不多见，一般发生在软骨鱼类。

Holosticha hamulata n. sp and Holosticha heterofoissneri Hu and Song, 2001, two urostylid ciliates (Protozoa, Ciliophora) from intertidal sediments of the Yellow Sea

Two marine urostylid ciliates, Holosticha hamulata n. sp. and Holosticha heterofoissneri Hu and Song, 2001, were investigated using live observation and protargol impregnation. Both species were isolated from Korean intertidal sediments of the Yellow Sea. Holosticha hamulata measures about 150 x 25 pro in vivo, and is characterized by a tripartite body shape with a narrow head, an inflated trunk, and a tail that distally projects ventrally forming a hook-like structure. It is the characteristic body shape that distinguishes H. hamulata distinctly from congeners. Holosticha hamulata differs from H. heterofoissneri, possibly the nearest relative, also by the location of the contractile vacuole (ahead of mid-body versus near posterior body third) and the configuration of the macronucleus (on average, 33 scattered nodules assuming a Y-shape versus 17 nodules that may form a U shape). The average number of the macronuclear nodules is a pronounced feature showing great consistency in populations of each species. However, their arrangement is variable in H. heterofoissneri where the nodules are basically scattered or connected by fine fibers forming an elongate U-shape. The location of the contractile vacuole as a taxonomic feature is discussed and a dichotomous key to the species of Holosticha sensu stricto is provided.

Morphology and infraciliature of three species of Metaurostylopsis (Ciliophora, Stichotrichia): M. songi n. sp., M. salina n. sp., and M. marina (Kahl 1932) from sediments, saline ponds, and coastal waters.

Two new urostylid ciliates, Metaurostylopsis songi n. sp. and Metaurostylopsis salina n. sp. and Metaurostylopsis marina (Kahl 1932) are investigated using live observation and protargol impregnation. These species were isolated in Korea from intertidal sediments, saline ponds, and coastal waters. Metaurostylopsis songi is in vivo about 120 pm x 25 mu m, has a slenderly ellipsoidal body, colorless cortical granules in rows on ventral and dorsal body sides, about 54 macronuclear nodules, 28-47 adoral membranelles, five frontal, two or three frontoterminal and six or seven transverse cirri, and 9-12 midventral cirral pairs followed posteriorly by 1-3 single cirri. In vivo M. salina is about 60 pin x 25 mu m, has a pyriform body, colorless cortical granules irregularly arranged, about 45 macronuclear nodules, 18-23 adoral membranelles, three frontal, three to five frontoterminal and two to five transverse cirri, and four or five midventral cirral pairs followed posteriorly by five to seven single cirri. Both species have three marginal cirral rows on each body side and 3 long dorsal kineties. The Korean specimens of M. marina match the Chinese population in all main features. Metaurostylopsis songi differs from M. marina by the more slender body, the number of frontal cirri (invariably five vs. four), and the arrangement of cortical granules (in rows on dorsal and ventral cortex vs. only along dorsal kinetics and anterior body margin). Metaurostylopsis salina differs from its congeners by the distinctly smaller size, the pyriform body shape, the scattered cortical granules (vs. in rows), and number of frontal cirri. It differs from M. marina also by the number of midventral cirral pairs (four or five vs. seven to 11).

Laurencia nanhaiense sp nov., a new species of the genus Laurencia(Rhodomelaceae, Rhodophyta) from China

Laurencia nanhaiense sp. nov. (Rhodomelaceae, Rhodophyta) is described from Hainan and Guangdong Provinces, China. The new species clearly displays one of the defining features of the genus, viz. four periaxial cells per vegetative axial segment. It differs from other closely related species in having a combination of features such as terete axes from a basal system composed of a primary, discoid holdfast and a secondary attachment to give rise to many short rhizoids, branching oppositely and alternately, irregularly tristichous or subverticillately polystichous, having more curve branches with very sparse, adventitious ultimate branchlets, non-projecting superficial cortical cells at the apices of ultimate branchlets, presence of longitudinally oriented secondary pit-connections between contiguous superficial cortical cells, absence of lenticular thickenings in the walls of medullary cells, parallel arrangement of tetrasporangia along the axis of stichidia, and presence of intercellular spaces between medullary cells.

A new spirofilid ciliate from the yellow sea: Metastrongylidium distichum n gen, n sp (ciliophora, stichotrichia)

The morphology and infraciliature of a new ciliate, Metastrongylidium distichum, isolated from the Yellow Sea, are investigated using live observation and protargol impregnation. Metastrongylidium distichum is about 170 x 40 pm in vivo, clavate to elongate ellipsoidal with bluntly pointed posterior end, and has two macronuclear nodules, six distinctly large buccal and frontal cirri, three dorsal kineties and two each of spiralled ventral and marginal cirral rows. These features indicate a generic allocation in Strongylidium Sterki, 1878. However, the new ciliate has a distinct feature not recognizable in Strongylidiurn, viz., the presence of (three or four) transverse cirri. Thus, we propose a new genus Metastrongylidium for the new species, M distichum nov. gen., n. sp. Metastrongylidium belongs to the family Spirofilidae, where it differs from Mucotrichidium by the lack of postperistomial cirrus and the different frontal and ventral cirral pattern. Metastrongylidium distichum is easily distinguishable from the seemingly similar species Strongylidium californicum Kahl, 1932 by the macronuclear pattern (invariably 2 vs. many nodules). It highly resembles the poorly known species S. contortum (Gelei 1954) Borror, 1972 in the body outline and nuclear pattern, differing in the biotope, the posterior cirral pattern, and the arrangement of right marginal row.

Molecular phylogeny and biogeography of the Qinghai-Tibet Plateau endemic Nannoglottis (Asteraceae)

All taxa endemic to the Qinghai-Tibet Plateau are hypothesized to have originated in situ or from immediately adjacent areas because of the relatively recent formation of the plateau since the Pliocene, followed by the large-scaled biota extinction and recession caused by the Quaternary ice sheet. However, identification of specific progenitors remains difficult for some endemics, especially some endemic genera. Nannoglottis, with about eight species endemic to this region, is one such genus. Past taxonomic treatments have suggested its relationships with four different tribes of Asteraceae. We intend to identify the closest relatives of Nannoglottis by evaluating the level of monophyly, tribal delimitation, and systematic position of the genus by using molecular data from ndhF gene, trnL-F, and ITS region sequences. We find that all sampled species of Nannoglottis are a well-defined monophyly. This supports all recent taxonomic treatments of Nannoglottis, in which all sampled species were placed in one broadly re-circumscribed genus. Nannoglottis is most closely related to the Astereae, but stands as an isolated genus as the first diverging lineage of the tribe, without close relatives. A tentative relationship was suggested for Nannoglottis and the next lineage of the tribe was based on the ITS topology, the "basal group," which consists of seven genera from the Southern Hemisphere. Such a relationship is supported by some commonly shared plesiomorphic morphological characters. Despite the very early divergence of Nannoglottis in the Astereae, the tribe must be regarded to have its origin in Southern Hemisphere rather than in Asia, because based on all morphological, molecular, biogeographical, and fossil data, the Asteraceae and its major lineages (tribes) are supposed to have originated in the former area. Long-distance dispersal using Southeast Asia as a steppingstone from Southern Hemisphere to the Qinghai-Tibet Plateau is the most likely explanation for this unusual biogeographic link of Nannoglottis. The 23-32-million-year divergence time between Nannoglottis and the other Astereae estimated by DNA sequences predated the formation of the plateau. This estimation is further favored by the fossil record of the Asteraceae and the possible time of origin of the Astereae. Nannoglottis seems to have reached the Qinghai-Tibet area in the Oligocene-Eocene and then re-diversified with the uplift of the plateau. The molecular infragenetic phylogeny of the genus identifies two distinct clades, which reject the earlier infrageneric classification based on the arrangement of the involucral bracts and the length of the ligules, but agree well with the habits and ecological preferences of its current species. The "alpine shrub" vs. "coniferous forest" divergence within Nannoglottis was estimated at about 3.4 million years ago when the plateau began its first large-scale uplifting and the coniferous vegetation began to appear. Most of the current species at the "coniferous forest" clade of the genus are estimated to have originated from 1.02 to 1.94 million years ago, when the second and third uprisings of the plateau occurred, the climate oscillated and the habitats were strongly changed. The assumed evolution, speciation diversity, and radiation of Nannoglottis based on molecular phylogeny and divergence times agree well with the known geological and paleobotanical histories of the Qinghai-Tibet Plateau. (C) 2002 Elsevier Science (USA). All rights reserved.

水下滑翔机器人运动分析与载体设计

水下滑翔机器人是一种新型水下机器人,具有噪声低、航行距离远、续航时间长、成本低等特点。分析了水下滑翔机器人的驱动机理和运动实现,给出了水下滑翔机器人典型运动的仿真结果,并以正在设计的一水下滑翔机试验样机为研究对象,描述了样机的整体结构布局,详细研究了浮力调节机构、俯仰调节机构和横滚调节机构的实现方法,并就样机中各执行机构的设计实现进行了论述。

基于广义正交多项式迭积微分算子的地震波场数值模拟研究

Seismic Numerical Modeling is one of bases of the Exploratory Seismology and Academic Seismology, also is a research field in great demand. Essence of seismic numerical modeling is to assume that structure and parameters of the underground media model are known, simulate the wave-field and calculate the numerical seismic record that should be observed. Seismic numerical modeling is not only a means to know the seismic wave-field in complex inhomogeneous media, but also a test to the application effect by all kinds of methods. There are many seismic numerical modeling methods, each method has its own merits and drawbacks. During the forward modeling, the computation precision and the efficiency are two pivotal questions to evaluate the validity and superiority of the method. The target of my dissertation is to find a new method to possibly improve the computation precision and efficiency, and apply the new forward method to modeling the wave-field in the complex inhomogeneous media. Convolutional Forsyte polynomial differentiator (CFPD) approach developed in this dissertation is robust and efficient, it shares some of the advantages of the high precision of generalized orthogonal polynomial and the high speed of the short operator finite-difference. By adjusting the operator length and optimizing the operator coefficient, the method can involve whole and local information of the wave-field. One of main tasks of the dissertation is to develop a creative, generalized and high precision method. The author introduce convolutional Forsyte polynomial differentiator to calculate the spatial derivative of seismic wave equation, and apply the time staggered grid finite-difference which can better meet the high precision of the convolutional differentiator to substitute the conventional finite-difference to calculate the time derivative of seismic wave equation, then creating a new forward method to modeling the wave-field in complex inhomogeneous media. Comparing with Fourier pseudo-spectral method, Chebyshev pseudo-spectral method, staggered- grid finite difference method and finite element method, convolutional Forsyte polynomial differentiator (CFPD) method has many advantages: 1. Comparing with Fourier pseudo-spectral method. Fourier pseudo-spectral method (FPS) is a local operator, its results have Gibbs effects when the media parameters change, then arose great errors. Therefore, Fourier pseudo-spectral method can not deal with special complex and random heterogeneous media. But convolutional Forsyte polynomial differentiator method can cover global and local information. So for complex inhomogeneous media, CFPD is more efficient. 2. Comparing with staggered-grid high-order finite-difference method, CFPD takes less dots than FD at single wave length, and the number does not increase with the widening of the studying area. 3. Comparing with Chebyshev pseudo-spectral method (CPS). The calculation region of Chebyshev pseudo-spectral method is fixed in , under the condition of unchangeable precision, the augmentation of calculation is unacceptable. Thus Chebyshev pseudo-spectral method is inapplicable to large area. CFPD method is more applicable to large area. 4. Comparing with finite element method (FE), CFPD can use lager grids. The other task of this dissertation is to study 2.5 dimension (2.5D) seismic wave-field. The author reviews the development and present situation of 2.5D problem, expatiates the essentiality of studying the 2.5D problem, apply CFPD method to simulate the seismic wave-field in 2.5D inhomogeneous media. The results indicate that 2.5D numerical modeling is efficient to simulate one of the sections of 3D media, 2.5D calculation is much less time-consuming than 3D calculation, and the wave dispersion of 2.5D modeling is obviously less than that of 3D modeling. Question on applying time staggered-grid convolutional differentiator based on CFPD to modeling 2.5D complex inhomogeneous media was not studied by any geophysicists before, it is a fire-new creation absolutely. The theory and practices prove that the new method can efficiently model the seismic wave-field in complex media. Proposing and developing this new method can provide more choices to study the seismic wave-field modeling, seismic wave migration, seismic inversion, and seismic wave imaging.

波动方程模拟与偏移的实用化方法研究

Along with the widespread and in-depth applications in petroleum prospecting and development, the seismic modeling and migration technologies are proposed with a higher requirement by oil industrial, and the related practical demand is getting more and more urgent. Based on theories of modeling and migration methods for wave equation, both related with velocity model, I thoroughly research and develop some methods for the goal of highly effective and practical in this dissertation. In the first part, this dissertation probes into the layout designing by wave equations modeling, focusing on the target-oriented layout designing method guided by wave equation modeling in complicated structure areas. It is implemented by using the fourth order staggered grid finite difference (FD) method in velocity-stress 2D acoustic wave equations plus perfectly matched layer (PML) absorbing boundary condition. To design target-oriented layout: (a) match the synthetic record on the surface with events of subsurface structures by analyzing the snapshots of theoretical model; (b) determine the shot-gather distance by tracking the events of target areas and measuring the receiving range when it reaches the surface; (c) restrict the range of valid shot-gather distance by drawing seismic windows in single shot records; (d) choose the best trace distance by comparing the resolution of prospecting targets from the simulated records with different trace distance. Eventually, we obtained the observation system parameters, which achieve the design requirements. In the second part, this dissertation presents the practical method to improve the 3D Fourier Finite Difference (FFD) migration, and carefully analyzes all the factors which influence 3D FFD migration’s efficiency. In which, one of the most important parameters of migration is the extrapolating step. This dissertation presents an efficient 3D FFD migration algorithm, which use FFD propagator to extrapolate wavefields over big layers, and use Born-Kirchhoff interpolator to image wavefields over small layers between the big ones. Finally, I show the effectiveness of this hybrid migration method by comparing migration results from 3D SEG/EAGE model with different methods.

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.

离散裂缝诱导各向异性粘弹性地震波模拟与特征分析

The real media always attenuate and distort seismic waves as they propagate in the earth. This behavior can be modeled with a viscoelastic and anisotropic wave equation. The real media can be described as fractured media. In this thesis, we present a high-order staggered grid finite-difference scheme for 2-D viscoelastic wave propagation in a medium containing a large number of small finite length fractures. We use the effective medium approach to compute the anisotropic parameters in each grid cell. By comparing our synthetic seismogram by staggered-grid finite-difference with that by complex-ray parameter ray tracing method, we conclude that the high-order staggered-grid finite-difference technique can effectively used to simulate seismic propagation in viscoelastic-anisotropic media. Synthetic seismograms demonstrate that strong attenuation and significant frequency dispersion due to viscosity are important factors of reducing amplitude and delaying arrival time varying with incidence angle or offset. On the other hand, the amount of scattered energy not only provides an indicator of orientation of fracture sets, but can also provide information about the fracture spacing. Analysis of synthetic seismograms from dry- and fluid-filled fractures indicates that dry-filled fractures show more significant scattering on seismic wavefields than fluid-filled ones, and offset-variations in P-wave amplitude are observable. We also analyze seismic response of an anticlinal trap model that includes a gas-filled fractured reservoir with high attenuation, which attenuates and distorts the so-called bright spot.

石油二次运移机理物理模拟研究

Oil and gas migration is very important for theoretical hydrocarbon geology study and exploration practice, but related research is weak. Physical simulation is a main method to study oil migration. Systematic experiments were done to quantitatively describe the migration patterns, path characters and oil saturation by adjusting the possible dynamic factors respectively. The following conclusions were drawn. 1. Darcy velocity and pore throat diameter were calculated according to seepage cross-sectional area and glass beads arrangement. With such normalized Darcy velocity and pore throat diameter, the date from one and two dimensional experiments can be reasonably drawn in two phase diagrams. It is found that the migration pattern can be identified using only one dimensionless number L which is defined as the ration of capillary number and Bond number. 2. Oil saturated in the pores between glass beads was used as calibration and oil saturation in the path was measured by magnetic resonance imaging. The results show that oil saturation in the center of migration path can reach 100%, is higher than oil saturation in the edge of migration path. 3. Percolation backbone during secondary oil migration was identified experimentally using Hele-Shaw cell. The backbone formed mainly because of the spatial variation of the cluster conductivity caused by oil saturation heterogeneity, main resistant force change, and path shrinkage and snap-off. Percolation backbone improves hydrocarbon migration efficiency and is a favorable factor for reservoir forming. 4. In the three dimensional filling models, the thickness of the secondary migration path is mall. It is only 2.5cm even for the piston pattern. Inclination of the model is the main influencing factor of the secondary path width.

粘弹性介质中的地震波传播与波形反演研究

The real earth is far away from an ideal elastic ball. The movement of structures or fluid and scattering of thin-layer would inevitably affect seismic wave propagation, which is demonstrated mainly as energy nongeometrical attenuation. Today, most of theoretical researches and applications take the assumption that all media studied are fully elastic. Ignoring the viscoelastic property would, in some circumstances, lead to amplitude and phase distortion, which will indirectly affect extraction of traveltime and waveform we use in imaging and inversion. In order to investigate the response of seismic wave propagation and improve the imaging and inversion quality in complex media, we need not only consider into attenuation of the real media but also implement it by means of efficient numerical methods and imaging techniques. As for numerical modeling, most widely used methods, such as finite difference, finite element and pseudospectral algorithms, have difficulty in dealing with problem of simultaneously improving accuracy and efficiency in computation. To partially overcome this difficulty, this paper devises a matrix differentiator method and an optimal convolutional differentiator method based on staggered-grid Fourier pseudospectral differentiation, and a staggered-grid optimal Shannon singular kernel convolutional differentiator by function distribution theory, which then are used to study seismic wave propagation in viscoelastic media. Results through comparisons and accuracy analysis demonstrate that optimal convolutional differentiator methods can solve well the incompatibility between accuracy and efficiency, and are almost twice more accurate than the same-length finite difference. They can efficiently reduce dispersion and provide high-precision waveform data. On the basis of frequency-domain wavefield modeling, we discuss how to directly solve linear equations and point out that when compared to the time-domain methods, frequency-domain methods would be more convenient to handle the multi-source problem and be much easier to incorporate medium attenuation. We also prove the equivalence of the time- and frequency-domain methods by using numerical tests when assumptions with non-relaxation modulus and quality factor are made, and analyze the reason that causes waveform difference. In frequency-domain waveform inversion, experiments have been conducted with transmission, crosshole and reflection data. By using the relation between media scales and characteristic frequencies, we analyze the capacity of the frequency-domain sequential inversion method in anti-noising and dealing with non-uniqueness of nonlinear optimization. In crosshole experiments, we find the main sources of inversion error and figure out how incorrect quality factor would affect inverted results. When dealing with surface reflection data, several frequencies have been chosen with optimal frequency selection strategy, with which we use to carry out sequential and simultaneous inversions to verify how important low frequency data are to the inverted results and the functionality of simultaneous inversion in anti-noising. Finally, I come with some conclusions about the whole work I have done in this dissertation and discuss detailly the existing and would-be problems in it. I also point out the possible directions and theories we should go and deepen, which, to some extent, would provide a helpful reference to researchers who are interested in seismic wave propagation and imaging in complex media.

均质弹性条件下多洞平面问题解析算法及其应用研究

The scholars in the world have been trying to find an effective analytic algorithm of multiple hole problems usually meet in engineering designs. Though some studies on circular or elliptic holes had been achieved under specific conditions, no efforts were made to any multiple hole problems that is most significant for engineering designs. The author has made further studies on any multiple hole problems, using complex variable function method and Schwarz alternating method. After solving a series of technological difficulties, the author obtains an effective analytic algorithm, and acquires stress field and displacement field with high accuracy, which can be conducted for arbitrary many iterations according to practical accuracy requirements. In addition, th solution of stress and displacement fields, even for multiple holes of complex shapes and smaller distances. Further, the author made preliminary studies on viscoelastic displacement solution for any double holes. In terms of the obtained displacement solution of any multiple holes, this paper studies displacement back-analysis for the excavations of two tunnels, and find that the back-analysis method is accurate. Additionally, the author presents the mathematical prove of inversion uniqueness for ground stresses, elastic modulus and Poisson ratio. The author believes that the accurate analytic algorithm provided in this paper will presents an effective way to stress and displacement analysis for any multiple hole problems, optimal arrangement of multiple holes, hole shape optimization of multiple holes, etc..