A multi-moment finite volume formulation for shallow water equations on unstructured mesh

A novel and accurate finite volume method has been presented to solve the shallow water equations on unstructured grid in plane geometry. In addition to the volume integrated average (VIA moment) for each mesh cell, the point values (PV moment) defined on cell boundary are also treated as the model variables. The volume integrated average is updated via a finite volume formulation, and thus is numerically conserved, while the point value is computed by a point-wise Riemann solver. The cell-wise local interpolation reconstruction is built based on both the VIA and the PV moments, which results in a scheme of almost third order accuracy. Efforts have also been made to formulate the source term of the bottom topography in a way to balance the numerical flux function to satisfy the so-called C-property. The proposed numerical model is validated by numerical tests in comparison with other methods reported in the literature. (C) 2010 Elsevier Inc. All rights reserved.

Design of slow extraction system for therapy synchrotron

Based on the optimized design of the lattice for therapy synchrotron and considering the requirement of radiation therapy, the third order resonant extraction is adopted. Using the momentum-amplitude selection method, the extraction system is designed and optimized. An extraction efficiency of more than 97% and a momentum spread less than 0.11% are obtained.

Design of synchrotron for hadron therapy

According to the operation and development of radiation therapy in the world, in order to further promote the radiation therapy of tumour in China, a design of a special synchrotron with two super-periodicity for hadron therapy is presented, including lattice, injection system, RF acceleration and slow extraction of the third order resonance. The synchrotron accelerates the proton beam to 250MeV and the carbon beam to 4000MeV/u.

Preparation and nonlinear optical properties of ultrathin composite films containing both a polyoxometalate anion and a binuclear phthalocyanine

An ultrathin composite film containing both polyoxometalate anion [PMo12O40](3-) ( PMo12) and a planar binuclear phthalocyanine, bi-CoPc, has been prepared by the electrostatic layer-by-layer self-assembly method. UV-vis measurements revealed regular film growth with each four-layer {PMo12/bi-CoPc/PSS/PAH} adsorption. The lm structure was characterized by small-angle X-ray reflectivity measurements, X-ray photoelectron spectra, and AFM images. The nanothick film shows a third-order nonlinear optical response of chi((3)) = 4.21 x 10(-12) esu. Experimental investigations also indicate that the combination of polyoxometalate anions [PMo12O40](3-) with the phthalocyanine bi-CoPc in multilayer films can enhance the third-order NLO susceptibility and modify the third-order NLO absorption of bi-CoPc.

Studies on two coordination polymers [M(mu(4)-pz25dc)](n) (M = Cd or Zn, pz25dc=pyrazine-2,5-dicarboxylato) with three-dimensional pillared-layer three-nodal framework: Synthesis, structural characterization, strong optical non-linearities and optical limiting properties

Two isomorphous new candidates [M(mu(4)-pz25dc)](n) (M = Cd, 1; Zn, 2; pz25dc = pyrazine-2,5-dicarboxylato)for nonlinear optical (NLO) materials have been synthesized hydrothermally and characterized crystallographically as pillared-layer three-nodal frameworks with one four-connected metal nodes and two crystallographically different four-connected ligand nodes. Their optical non-linearities are measured by the Z-Scan technique with an 8 ns pulsed laser at 532 nm. These two coordination polymers both exhibit strong NLO absorptive abilities [alpha(2) = (63 +/- 6) x 10 (12) mW (1) 1, ( 46 +/- 6) x 10 (11) mW (1) 2] and effective self-focusing performance [n(2) = (67 +/- 5) x 10 (18) 1, (13 +/- 3) x 10 (18) m(2) W (1) 2] in 1.02 x 10 (4) 1 and 1.05 x 10 (4) mol dm (3) 2 DMF solution separately. The values of the limiting threshold are also measured from the optical limiting experimental data. The heavy atom effect plays important role in the enhancement of optical non-linearities and optical limiting properties. (C) 2009 Elsevier B. V. All rights reserved.

电视精密跟踪控制系统的设计和应用

本文介绍了一个用于实际的电视精密跟踪控制系统,该控制系统在外场跟踪飞行体时稳定可靠,跟踪精度为数角秒.文中论述了人参与的复合捕获控制系统,找到了该系统参数的设计准则,即在切换时要满足相对变化量Δ≤15%.其次,重点论述了三阶无静差电视精密跟踪控制系统的设计方法,即利用 Z 变换直接求解,使得系统满足最佳条件旬(?)_(max)/(?)K_i=0和(?)_(max)/(?)K_f~2>0,从而,使得该控制系统满足了高稳定度和高精度的技术指标,并在实际中获得了应用.

层析静校正技术研究和应用

Static correction is one of the indispensable steps in the conventional onshore seismic data processing, particularly in the western part of China; it is theoretically and practically significant to resolve the issue of static correction. Conventional refraction static correction is put forward under the assumption that layered medium is horizontal and evenly distributed. The complicated nature of the near surface from western part of China is far from the assumption. Therefore, the essential way to resolve the static correction problem from the complex area is to develop a new theory. In this paper, a high-precision non-linear first arrival tomography is applied to solve the problem, it moved beyond the conventional refraction algorithm based on the layered medium and can be used to modeling the complex near surface. Some of the new and creative work done is as follows: One. In the process of first arrival tomographic image modeling, a fast high-order step algorithm is used to calculate the travel time for first arrival and ray path and various factors concerning the fast step ray tracing algorithm is analyzed. Then the second-order and third-order differential format is applied to the step algorithm which greatly increased the calculation precision of the ray tracing and there is no constraint to the velocity distribution from the complex areas. This method has very strong adaptability and it can meet the needs of great velocity variation from the complicated areas. Based on the numerical calculation, a fast high-order step is a fast, non-conditional and stable high-precision tomographic modeling algorithm. Two, in the tomographic inversion, due to the uneven fold coverage and insufficient information, the inversion result is unstable and less reliable. In the paper, wavelet transform is applied to the tomographic inversion which has achieved a good result. Based on the result of the inversion from the real data, wavelet tomographic inversion has increased the reliability and stability of the inversion. Three. Apply the constrained high-precision wavelet tomographic image to the static correction processing from the complex area. During tomographic imaging, by using uphole survey, refraction shooting or other weathering layer method, weathering layer can be identified before the image. Because the group interval for the shot first arrival is relatively big, there is a lack of precision for the near surface inversion. In this paper, an inversion method of the layer constraint and well constraint is put forward, which can be used to compensate the shallow velocity of the inversion for the shot first arrival and increase the precision of the tomographic inversion. Key words: Tomography ，Fast marching method，Wavelet transform, Static corrections, First break

准噶尔盆地西北缘三叠系层序地层及有利勘探目标选择

Based on outcrop, borehole, seismic and regional geological data, the sequence stratigraphy, sedimentary facies of the Triassic in the western margin of the Zhugaer basin was studied, and favorable exploration target was forecasted. The major achievements include: (1) the Triassic in the western margin of the Zhugaer basin can be divided into 1 second-order sequence and 5 third-order sequences, which are, in ascending order, TSQ1, TSQ2, TSQ3, TSQ4, and TSQ5. TSQ1 is equivolent to Baikouquan formation, TSQ2 is equivolent to lower Kelamayi formation, TSQ3 is equivolent to upper Kelamai formation, TSQ4 is equivolent to lower and middle Baijiantan formation, and TSQ5 is equivolent to upper Baijiantan formation. Each sequence is divided into transgressive and regressive system tracts. Thus the sequence correlation framework is established. (2) The factors controlling development of sequences are analyzed, and it is believed that tectonic is the major controlling factor. Model of sequence development is summarized. (3)Through study on sedimentary facies, 6 types of facies are recognized: alluvial fan, fan delta, braided river, braided delta, delta and lake. Their microfacies are also recognized. In this study, it is proposed that the upper and lower Kelamayi formation（TSQ2、 TSQ3）is deposited by braided river instead of alluvial fan. This conclusion is of important theoretical and practical significance.(4) The sedimentary facies map of each sequence is compiled, and the sedimentary facies developed in each sequence is determined. In TSQ1, the sedimentary facies developed is alluvial fan and fan delta. In TSQ2, the sedimentary facies developed is mainly alluvial fan and fan delta in the north, and braided river and braided delta in the south. In TSQ3, the sedimentary facies developed is mainly braided river and braided delta. In TSQ4, the sedimentary facies developed is mainly braided delta in the north, and meandering delta in the south. In TSQ5, the sedimentary facies developed is mainly braided river and braided delta. (5) In the framework of sequence stratigrahpy, favorable areas for concealed traps are forecasted, and different types of traps are developed in different system tracts. (6) Favorable areas for future exploration are predicted.

砂砾岩油藏精细油藏描述–以准噶尔盆地西北缘八区下乌尔禾组油藏为例

Glutenite reservoir is one of the most important reservoir types in china. Because of its particularity of rock structure and pore structure, it is usually difficult in development, especially for its serious heterogeneity. On the basis of seismic, well logs, core data and production performance, the lower Wuerhe group can be divided into one second-order sequences, two third-order sequences and twenty two subsequences, corresponding to the five stages and twenty two minlayers. In addition, the fault systems are interpreted and the control action of fault systems to reservoir development is also described. The lower Wuerhe formation of 8th district belongs to fluvial-dominated fan delta sedimentation, according to the analysis of well logs, logging data and core data. It can be subdivided into two kinds of subfacies and nine kinds of microfacies. The fan delta plain subfacies mainly consist of braided channel, unconcentrated flow, mud flow and sieve deposit microfacies. The fan delta front subfacies include subaqueous distributary channel, subaqueous interdistributary channel, debris flow, subaqueous barrier and grain flow microfacies. Combined with the regional geological characteristics, the porosity model of lower Wuerhe formation is performed using core data. A permeability model based on the flow zone index is also formed according to the pore throat characteristics and flow property. Finally, the heterogeneity is analyzed. The result shows that the lower Wuerhe formation has a feature of middle-high heterogeneity, and it is controlled by material sources and sedimentary facies belt.

柴西南区下干柴沟组下段层序地层格架内沉积相展布及有利储集砂体分布研究

Lower member of the lower Ganchaigou Formation in the southwestern of Qaidam Basin is one of the main targeted exploration zones. With the advancement of exploration, the targets are gradually switching into the lithologic reservoirs and it is urgent to gain the more precise research results in distribution of sedimentary facies and sandstones. Guided by the theory of sequence stratigraphy and sedimentology as well as on the basis of many logging data, drillings, seismic data and chemical tests, the paper comprehensively analyzes the sedimentary facies and sandstones in the lower member of lower Ganchaigou Formation in the southern of Chaixi. According to the identification marks of the key interface in sequence stratigraphy, the key interfaces in lower member of lower Ganchaigou Formation in the southwestern of Qaidam Basin are identified as two third-order sequences SQ1、SQ2. By calibrating the synthetic seismogram, the seismic sequence, well drilling and logging sequences are united. Based on the works above, this paper chooses seven primary cross-sections and builds connecting-well stratigraphic correlation of seven main connecting-well sections. Ultimately, the high-resolution sequence stratigraphic frameworks in the lower member of the lower Ganchaigou Formation, which are uniform to logging and seismic data, are figured out. In terms of study on each sequence features, the main style of the base-level cycle overlay which forms the third-order sequence is confirmed. It contains asymmetric “becoming deep upward” style and symmetry style. Researching on the spreading characters of sequence stratigraphy indicates that SQ1 and SQ2 are rather thicker near northwest well Shashen 20 and Shaxin1 while they are quite thiner near Hongcan 1, Yuejin, Qie 4 and Dong8-Wu3, and the thickness of SQ1 is thicker than SQ2.Based on the deep analysis of the marks for depositional facies, it is proposed that the lake facies and braid river deltas facies mainly occurred in study areas. Besides, the sorts of sub-facies and micro-facies model are divided and described. Under the control of high-resolution sequence stratigraphic framework, three source directions from Arlarer Mountain、Qimantage Mountain and Dongchai Mountain are identified by using the features of heavy mineral assemblage and paleogeomorphy. In addition, regularities of distribution sedimentary facies in sequence stratigraphic framework are studied in accordance with research thinking of the "point" (single well) "line" (section) "face" (plane). In the stage of lower member in the lower Ganchaigou Formation in the southwestern of Qaidam Basin, it is at the early phrase of evolution of the lake basin with the gradual outspread and the rise of the lake level. Combined with physical analysis of reservoir sands formed in different sedimentary environment, the paper studies the style of favorable sandstone bodies that are underwater distributary channel of braided rive delta front, coarse sand in mouth bar and the sand body in sand flat of shore-shallow lacustrine facies. Finally, this article comprehensively analyzes the distribution relationship between sedimentary facies and favorable sandstone body and proposes the ideas that sequence SQ1 Yuejin area, well east 8-wu3 area, well qie4-qie1 area and well hongcan2 area are distributed areas of favorable sandstone.

东营凹陷下第三系岩性油气藏形成条件与预测

The Dongying depression, located in the northern part of the jiyang Sag in the Buohaiwan Basin, comprises one of the major oil-producing bases of the Shengli oil-field. The prediction and exploration of subtle or litho1ogical oil traps in the oil-field has become the major confronted target. This is also one of the frontier study areas in the highly-explored oil-bearing basins in East China and abroad. Based on the integrated analysis of the geological, seismic and logging data and the theories of sequence stratigraphy, tectono-stratigraphy and petroleum system, the paper has attempted to document the characteristics of the sequence stratigraphic and structural frameworks of the low Tertiary, the syndepositional faults and their control on deposition, and then to investigate the forming conditions and distribution of the tithological oil traps in the depression. The study has set up a set of analysis methods, which can be used to effectively analysis the sequence stratigraphy of inland basins and predict the distribution of sandstone reservoirs in the basins. The major achievements of the study are as follows: 1. The low Tertiary can be divided into 4 second-order sequences and 13 third-order sequences, and the systems tracts in the third-order sequences have been also identified based on the examination and correction of well logging data and seismic profiles. At the same time, the parasequences and their stacking pattern in the deltaic systems of the third member of the Shahejie Formation have been recognized in the key study area. It has been documented that the genetic relation of different order sequences to tectonic, climatic and sediment supply changes. The study suggested that the formation of the second-order sequences was related to multiple rifting, while the activity of the syndepositional faults controlled the stacking pattern of parasequences of the axial deltaic system in the depression. 2. A number of depositional facies have been recognized in the low Tertiary on the basis of seismic facies and well logging analysis. They include alluvial fan, fan delta or braided delta, axial delta, lowstand fan, lacustrine and gravity flow deposits. The lacustrine lowstand fan deposits are firstly recognized in the depression, and their facies architecture and distribution have been investigated. The study has shown that the lowstand fan deposits are the important sandstone reservoirs as lithological oil traps in the depression. 3. The mapping of depositional systems within sequences has revealed the time and special distrbution of depositional systems developed in the basin. It is pointed out that major elastic systems comprise the northern marginal depositional systems consisting of alluvial fan, fan delta and offshore lowstand fan deposits, the southern gentle slope elastic deposits composed of shallow lacustrine, braided delta and lowstand fan deposits and the axial deltaic systems including those from eastern and western ends of the depression. 4. The genetic relationship between the syndepositional faults and the distribution of sandstones has been studied in the paper, upper on the analysis of structural framework and syndepositional fault systems in the depression. The concept of structural slope-break has been firstly introduced into the study and the role of syndepositional faults controlling the development of sequence architecture and distribution of sandstones along the hinged and faulted margins have been widely investigated. It is suggested that structural styles of the structural slope-break controlled the distribution of lowstand fan deposits and formed a favorable zone for the formation of lithological or structure-lithological oil traps in the basin. 5. The paper has made a deep investigation into the forming condition and processes of the lithological traps in the depression, based the analysis of composition of reservoir, seal and resource rocks. It is pointed out that there were two major oil pool-forming periods, namely the end of the Dongying and Guangtao periods, and the later one is the most important. 6. The study has finally predicted a number of favorable targets for exploration of lithologieal traps in the depression. Most of them have been drilled and made great succeed with new discovered thousands tons of raw oil reserves.

断层封闭性及其与油气成藏的关系研究-以沾化凹陷孤岛地区为例

Godao area, located in the east of the Zhanhua depression of Jirang sag in Bohai Bay Basin, is the studying area in my dissertation. It is first time that fault sealing properties and the related relationship with the pool forming are studied in Gudao area. On the base of the analysis of the regional tectonics, the author has studied the tertiary structural evolution of the Gudao area and distinguished the fault's level and put forward the distinguishing principle. The geometrical feature, mechanical characters, developmental mechanism and history of the boundary faults in the tectonic unit of this area are all studied and emphasized especially. The buried history of oil-generating depression (that is Gudao depression) and the history of oil and gas migration simultaneously are discussed, the juxtaposition relationship between boundary fault evolutionary history and oil and gas migrated history are expatiated. To the geological condition of the Gudao area, three level faults sealing properties of this area were discussed in detail. Their characteristics of behavior and the intrinsic relationship between their sealing and oil and gas migrated reservoir are elucidated. The pool-forming models related to fault seal are exposed. The author has studied the lithologies of different order of faults, the relationship of occurrence assemblage analysis, normal stress of fault plane in different depth and shale smear factor faults. Then analysis their role in the various faults sealing and confirms fault sealing marks of three different orders faults and exposes the mechanism of fault sealing. Shale smear zone formed by first order fault in lasting activities is one different type of fault breccia and mainly controlled factor to its entrapment of petroleum. Effective sealing threshold value and fault displacement is ascertained. Mainly controlled factor of second fault sealing is bigger compressive stress loaded on fault plane. According to this, quantitatively evaluated index is given. Shale smear zone is necessary condition for second fault stress entrapment. The juxtaposed relationship between the different lithologies within third order faults is most important controlled factor for its sealing. Based on various order of fault sealing features and mechanism in Gudao area, the author proposed three orders of fault sealing models. Shale smear zone sealing model, normal stress sealing model and lithologies juxtaposed sealing model are suggested to first, second and third order fault respectively. The conclusion of this studying has not only the very important theoretical significance and practical value in Gudo area but also the very important guiding role for other areas of related aspects.

孤北洼陷沙三-沙四段隐蔽油藏形成机制及其预测

Based on the study of sequence stratigraphy, modern sedimentary, basin analysis, and petroleum system in Gubei depression, this paper builds high resolution sequence stratigraphic structure, sedimentary system, sandbody distribution, the effect of tectonic in sequence and sedimentary system evolution and model of tectonic-lithofacies. The pool formation mechanism of subtle trap is developed. There are some conclusions and views as follows. 1.With the synthetic sequence analysis of drilling, seismic, and well log, the highly resolution sequence structure is build in Gubei depression. They are divided two secondary sequences and seven three-order sequences in Shahejie formation. They are include 4 kinds of system traces and 7 kinds of sedimentary systems which are alluvial fan, under water fan, alluvial fan and fan-delta, fan-delta, lacustrine-fan, fluvial-delta-turbidite, lakeshore beach and bar, and deep lake system. Sandbody distribution is show base on third order sequence. 2.Based on a lot of experiment and well log, it is point out that there are many types of pore in reservoir with the styles of corrosion pore, weak cementing, matrix cementing, impure filling, and 7 kinds of diagenetic facies. These reservoirs are evaluated by lateral and profile characteristics of diagenetic facies and reservoir properties. 3.The effect of simultaneous faulting on sediment process is analyzed from abrupt slope, gentle slope, and hollow zone. The 4 kinds of tectonic lithofacies models are developed in several periods in Gubei depression; the regional distribution of subtle trap is predicted by hydro accumulation characteristics of different tectonic lithofacies. 4.There are 4 types of compacting process, which are normal compaction, abnormal high pressure, abnormal low pressure and complex abnormal pressure. The domain type is normal compaction that locates any area of depression, but normal high pressure is located only deep hollow zone (depth more than 3000m), abnormal low pressures are located gentle slope and faulted abrupt slope (depth between 1200~2500m). 5.Two types dynamic systems of pool formation (enclosed and partly enclosed system) are recognized. They are composed by which source rocks are from Es3 and Es4, cap rocks are deep lacustrine shale of Esl and Es3, and sandstone reservoirs are 7 kinds of sedimentary system in Es3 and Es4. According to theory of petroleum system, two petroleum systems are divided in Es3 and Es4 of Gubei depression, which are high or normal pressure self-source system and normal or low pressure external-source system. 6.There are 3 kinds of combination model of pool formation, the first is litholgical pool of inner depression (high or normal pressure self-source type), the second is fault block or fault nose pool in marginal of depression (normal type), the third is fault block-lithological pool of central low lifted block (high or normal pressure type). The lithological pool is located central of depression, other pool are located gentle or abrupt slope that are controlled by lithological, faulting, unconfirmed. 7.This paper raise a new technique and process of exploration subtle trap which include geological modeling, coring description and logging recognition, and well log constrained inversion. These are composed to method and theory of predicting subtle trap. Application these methods and techniques, 6 hydro objects are predicted in three zone of depression.

东营凹陷成藏组合体研究与勘探实践

With the development of petroleum exploration, subtle reservoir has become the main exploration object in Dongying Depression, which requires some new technologies and methods to further reveal the geological characteristics in step with the mature exploration stage. In this paper, on the references to the studies of petroleum system and multiple oil-gas accumulation belt with flexible maneuverability, and the application of systematic theory, the concept of reservoir assemblage is initially defined as "the association of active source rock(s) and hydrocarbon reservoir(s) that are genetically related, with the bridge of pathway system in an oil and gas bearing basin". Compared with the theories of petroleum system and multiple oil-gas accumulation belts, it emphasizes on the processes of petroleum migration and accumulation and the correlation among active source rock, trapped hydrocarbon and migration pathway, and has been confirmed to be more suitably applied to high maturely explored basin. In the first study of this paper, sequence stratigraphy and subtle analytical technology of source rock have been employed to find that two categories of source rock with their characteristic types of organic matter and substantial states occurred in Dongying Depression. The first category, consisting of the oil shales within the third-order sequences of lacustrine expanding system tracts in the upper interval of the fourth Member of Shahejie Formation and both in the middle and lower intervals of the third Member of Shahejie Formation, is featured with the highest abundance of total organic matter (TOC) and the strongest abilities of hydrocarbon generation and expulsion, which is classified into the standard of good hydrocarbon source rock. Exploration assessment confirmed that about 70-80% of hydrocarbon in Dongying Depression came from this set of source rock for which the low sedimentary rate and strong oxygen-free environment would play the key role during its generation. The second category, composed of organic matter of dark mudstone in high stand system tracts in the upper and middle intervals of the third Member of Shahejie Formation, has been characterized by low content of total organic matter which mostly dispersedly distributes, and formed in the pre-delta to delta front environments. In classification, it belongs to the ordinary standard of source rocks. In the second research part, through the studies of high frequency sequence stratigraphy, fault geometry and active history combining with geochemistry of fluid inclusion and nitrogen compound and simulation test of hydrocarbon migration and accumulation, the faults have been thought to be the principal conduits, and the sandy bodies and unconformities might played the complementary pathways for hydrocarbon migration and accumulation in Dongying Depression of the continental faulted basin. Therefore, the fault activities may mainly constrain on the development of hydrocarbon pathways in space and time. Even more, using homogenization temperatures of fluid inclusion in digenetic minerals, three critical moments for hydrocarbon accumulation have been determined as well in Dongying Depression, which happened during the late stage of Dongying Formation (Ed), the early stage of Guantao Formation (Nig) and the early stage of Minghuazhen Formation (Nim), respectively. Comparatively, the last stage is looked as the main forming-reservoir period, which has also been supported by the results of geochemical analysis and simulation experiments of hydrocarbon generation and expulsion. Clearly, the times of hydrocarbon migration and accumulation are consistent with those of the fault activities in Dongying Depression, which indicate that tectonic activities would control the forming-reservoir. A conceptual model of faulting-episodic expulsion coupled with episodic forming-reservoir has then been established in this study. In the third part of this paper, some focusing areas were selected for the fine descriptions of pathway distribution and forming-reservoir, which has given four types of reservoir assemblage in terms of the main pathway and its correlation with the reservoir and trap: (1) mainly consisted of sandy bodies; (2) mainly consisted of faults; (3) mainly consisted of unconformities; and (4) their complex with two or three types of pathways. This classified criteria has also been applied to access the risk of some prospected traps in Dongying Depression. Finally, through the application of reservoir assemblage integrated with pathway distribution to all the prospective targets in Dongying Depression, the new favorably hydrocarbon accumulated belts have been figured out, and more subtle reservoirs have also been found. For examples, during 2000 and 2002, in the mature exploration areas, such as Liangjialou and Shengtuo structural closures etc., newly proved reserves were 2274 * 104t, and forecasted oil reserves 5660-5860xl04t; and in the predicted favorable areas, newly additional controlled oil reserves was 3355xl04t. Besides those, many other favorable exploration areas need to be further appraised.

各向异性与非线性介质中弹性波场传播特征研究

The topic of this study is about the propagation features of elastic waves in the anisotropic and nonlinear media by numerical methods with high accuracy and stability. The main achievements of this paper are as followings: Firstly, basing on the third order elastic energy formula, principle of energy conservation and circumvolved matrix method, we firstly reported the equations of non-linear elastic waves with two dimensions and three components in VTI media. Secondly, several conclusions about some numerical methods have been obtained in this paper. Namely, the minimum suitable sample stepth in space is about 1/8-1/12 of the main wavelength in order to distinctly reduce the numerical dispersion resulted from the numerical mehtod, at the same time, the higher order conventional finite difference (CFD) schemes will give little contribution to avoid the numerical solutions error accumulating with time. To get the similar accuracy with the fourth order center finite difference method, the half truncation length of SFFT should be no less than 7. The FDFCT method can present with the numerical solutions without obvious dispersion when the paprameters of FCT is suitable (we think they should be in the scope from 0.0001 to 0.07). Fortunately, the NADM method not only can reported us with the higher order accuracy solutions (higher than that of the fourth order finite difference method and lower than that of the sixth order finite difference method), but also can distinctly reduce the numerical dispersion. Thirdly, basing on the numerial and theoretical analysis, we reported such nonlinear response accumulating with time as waveform aberration, harmonic generation and resonant peak shift shown by the propagation of one- and two-dimensional non-linear elasticwaves in this paper. And then, we drew the conclusion that these nonlinear responses are controlled by the product between nonlinear strength (SN) and the amplitude of the source. At last, the modified FDFCT numerical method presented by this paper is used to model the two-dimensional non-linear elastic waves propagating in VTI media. Subsequently, the wavelet analysis and polarization are adopted to investigate and understand the numerical results. And then, we found the following principles (attention: the nonlinear strength presented by this paper is weak, the thickness of the -nonlinear media is thin (200m), the initial energy of the source is weak and the anisotropy of the media is weak too): The non-linear response shown by the elastic waves in VTI media is anisotropic too; The instantaneous main frequency sections of seismic records resulted from the media with a non-linear layer have about 1/4 to 1/2 changes of the initial main frequency of source with that resulted from the media without non-linear layer; The responses shown by the elasic waves about the anisotropy and nonlinearity have obvious mutual reformation, namely, the non-linear response will be stronger in some directions because of the anisotropy and the anisotropic strength shown by the elastic waves will be stronger when the media is nonlinear.