本文選題：三維均質(zhì)沉積盆地　切入點(diǎn)：三維層狀沉積盆地　出處：《天津城建大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：多次震害表明:不同場(chǎng)地條件下震害差異顯著,而沉積盆地作為一種典型復(fù)雜場(chǎng)地,對(duì)地震波具有顯著的放大作用。本文針對(duì)三維均質(zhì)沉積盆地和三維層狀沉積盆地對(duì)彈性波散射問題,采用離散單元少、精度高、自動(dòng)滿足無限遠(yuǎn)處邊界條件的間接邊界元方法(IBEM)進(jìn)行了求解,并通過精度驗(yàn)證,驗(yàn)證了該方法的精度。但是,由于IBEM在求解虛擬荷載密度時(shí),所形成的大矩陣為非對(duì)稱稠密矩陣,故求解所需計(jì)算量和存儲(chǔ)量巨大,無法有效計(jì)算大規(guī)模高頻實(shí)際問題。為了提高計(jì)算速度,減少計(jì)算內(nèi)存,本文引入了子結(jié)構(gòu)并行算法,該算法在一定程度上提高了計(jì)算速度,減少了計(jì)算內(nèi)存。但是采用該算法在計(jì)算大規(guī)模高頻實(shí)際問題時(shí),存儲(chǔ)量仍然十分巨大,無法應(yīng)用于大規(guī)模高頻實(shí)際問題。所以本文引入了被譽(yù)為二十世紀(jì)十大算法之一的快速多極算法(FMM),FMM算法通過樹結(jié)構(gòu),可將源點(diǎn)對(duì)場(chǎng)點(diǎn)的作用分類計(jì)算,然后迭代求解得到虛擬波源密度,而不需要求出和存儲(chǔ)大矩陣,該方法極大的降低了求解問題所需的計(jì)算量和存儲(chǔ)量,使該問題得到了妥善解決。目前,國內(nèi)大多數(shù)學(xué)者對(duì)于沉積盆地彈性波散射問題的研究還局限于理論分析階段,對(duì)于實(shí)際場(chǎng)地的分析較少,而在國外,許多學(xué)者已經(jīng)將研究成果應(yīng)用于實(shí)際場(chǎng)地中去,從而為實(shí)際工程建設(shè)、地震區(qū)劃提供理論依據(jù),因此,本文將快速多極間接邊界元方法(FM-IBEM)應(yīng)用于某三維復(fù)雜形狀均質(zhì)沉積盆地在SV波作用下的地震響應(yīng)求解和三維非水平層狀沉積盆地在P、SV波作用下的寬頻帶求解,得到了沉積盆地地表地震響應(yīng)的若干規(guī)律,同時(shí)檢驗(yàn)了本方法對(duì)各類復(fù)雜場(chǎng)地的適用性,計(jì)算結(jié)果也可為其他數(shù)值方法提供參考對(duì)照。研究結(jié)果表明:FM-IBEM作為一種新的高效算法和實(shí)用程序,適合于沉積盆地對(duì)彈性波散射問題的求解,可以極大地提高計(jì)算效率,有利于進(jìn)一步將該算法應(yīng)用于大規(guī)模高頻實(shí)際問題的求解中去,從而為復(fù)雜場(chǎng)地條件下地震區(qū)劃、城市地震危險(xiǎn)性評(píng)估、城市規(guī)劃及重大工程抗震設(shè)防提供重要理論依據(jù)和有力參考。
[Abstract]:The results of multiple earthquakes show that there are significant differences in earthquake damage under different site conditions, and sedimentary basin is a typical complex site. In this paper, the scattering of elastic waves by three-dimensional homogeneous sedimentary basins and three-dimensional stratified sedimentary basins is studied. The discrete elements are few and the accuracy is high. The indirect boundary element method (IBEM), which automatically satisfies the infinite boundary conditions, is solved, and the accuracy of the method is verified by accuracy verification. However, because IBEM is solving the virtual load density, The large matrix formed is asymmetric dense matrix, so the computation and storage required to solve the problem is too large to effectively calculate the large scale high-frequency practical problem. In order to improve the computing speed and reduce the computational memory, a substructure parallel algorithm is introduced. To a certain extent, the algorithm improves the computing speed and reduces the computational memory. However, when the algorithm is used to calculate large scale high-frequency practical problems, the storage capacity is still very large. This paper introduces a fast multipole algorithm known as one of the ten algorithms in the 20th century. By tree structure, we can classify and calculate the action of source point to field point. Then the virtual wave source density is obtained by iterative method without the need to calculate and store large matrices. This method greatly reduces the computational and storage requirements for solving the problem, and makes the problem well solved. The study of elastic wave scattering in sedimentary basins is still limited to the theoretical analysis stage, and the analysis of practical sites is less. In foreign countries, many scholars have applied the research results to the actual sites. So as to provide theoretical basis for practical engineering construction and seismic zoning, therefore, In this paper, the fast multipole indirect boundary element method (FM-IBEMEM) is applied to solve the seismic response of a three-dimensional homogeneous sedimentary basin with complex shape under SV waves and the broadband solution of 3-D non-horizontal stratified sedimentary basin under the action of PS-SV wave. Some laws of seismic response on the surface of sedimentary basins are obtained, and the applicability of this method to various complex sites is also tested. The results also provide a reference for other numerical methods. The results show that as a new and efficient algorithm and practical program, the solution to elastic wave scattering problem in sedimentary basins can greatly improve the computational efficiency. It is helpful to further apply this algorithm to the solution of large scale high-frequency practical problems, so that it can be used for seismic regionalization and urban seismic risk assessment under complex site conditions. Urban planning and seismic fortification of major projects provide important theoretical basis and powerful reference.
【學(xué)位授予單位】：天津城建大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：P315

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