本文選題：大地電磁 + 頻率自適應(yīng)矢量有限元法��； 參考：《吉林大學(xué)》2017年碩士論文

【摘要】：大地電磁測(cè)深法(MT)是一種頻率域電磁勘探方法,它以天然交變電磁波為場(chǎng)源對(duì)地下介質(zhì)進(jìn)行研究;由于不需要人工源,因此其具有野外工作簡(jiǎn)單、成本低、受野外地質(zhì)條件約束較小等特點(diǎn)。此外,這種方法還有不會(huì)被高阻臨層屏蔽和對(duì)低阻體響應(yīng)敏感等優(yōu)點(diǎn),使其在區(qū)域性地質(zhì)調(diào)查、礦產(chǎn)普查、深部地質(zhì)構(gòu)造研究等領(lǐng)域得到廣泛的應(yīng)用。進(jìn)行大地電磁正演數(shù)值模擬,能讓我們對(duì)各種不同電性結(jié)構(gòu)所產(chǎn)生電磁場(chǎng)的規(guī)律有更深刻的認(rèn)識(shí)。本文應(yīng)用頻率自適應(yīng)矢量有限元法實(shí)現(xiàn)了大地電磁三維正演數(shù)值模擬并使用擬線性積分方程法進(jìn)行了特定模型電場(chǎng)值的快速計(jì)算。首先,本文從MAXWELL方程組出發(fā),根據(jù)三維大地電磁所滿足的邊值條件,利用Galerkin法推導(dǎo)了與三維大地電磁邊值問(wèn)題等價(jià)的變分方程。然后采用正六面體單元對(duì)計(jì)算區(qū)域進(jìn)行剖分,并使用矢量插值基函數(shù)進(jìn)行單元分析。最后把各個(gè)單元相加,形成巨大而稀疏的系數(shù)矩陣;進(jìn)而將矩陣儲(chǔ)存并求解。接著,我們發(fā)現(xiàn)當(dāng)對(duì)計(jì)算區(qū)域網(wǎng)格進(jìn)行正六面體剖分時(shí),在電性劇烈變化的區(qū)域,有可能因?yàn)榫W(wǎng)格剖分的不夠細(xì)致,從而導(dǎo)致六面體單元中的場(chǎng)值無(wú)法通過(guò)其十二條矢量邊的插值函數(shù)準(zhǔn)確表達(dá),造成誤差。另外,由于大地電磁場(chǎng)的邊界條件在無(wú)窮遠(yuǎn)處才能得到滿足;所以不恰當(dāng)?shù)木W(wǎng)格剖分策略可能造成數(shù)值模擬計(jì)算結(jié)果誤差過(guò)大。進(jìn)而,本文又研究了不同頻率下誤差產(chǎn)生的原因及規(guī)律。根據(jù)上述的誤差分析,本文提出了基于正六面體單元矢量有限元法網(wǎng)格劃分的基本原則,并據(jù)此原則對(duì)正演過(guò)程進(jìn)行改良,提出了頻率自適應(yīng)的想法,隨著頻率的變化不斷調(diào)整剖分網(wǎng)格的方式;在保證計(jì)算精度的情況下大幅提升了計(jì)算速度。最后,對(duì)一系列地質(zhì)模型進(jìn)行了正演模擬和分析,以及通過(guò)利用格林函數(shù)的空間對(duì)稱性和互換定理,壓縮了格林系數(shù)的計(jì)算量,加快系數(shù)矩陣的生成速度,實(shí)現(xiàn)快速擬線性近似方法,并使用擬線性積分方程法進(jìn)行了特定模型電場(chǎng)值的快速計(jì)算;并提出了一些不足以及對(duì)日后工作的建議。
[Abstract]:The magnetotelluric sounding method (MTM) is a frequency-domain electromagnetic exploration method, which uses natural alternating electromagnetic waves as a field source to study underground media. It is limited by field geological conditions and so on. In addition, this method has the advantages of not being shielded by high resistivity impending layer and being sensitive to the response of low resistivity bodies, which makes it widely used in regional geological survey, mineral survey, deep geological structure research and other fields. The numerical simulation of magnetotelluric forward modeling can give us a better understanding of the law of electromagnetic field generated by various electrical structures. In this paper, the frequency adaptive vector finite element method is used to realize the 3-D forward numerical simulation of magnetotelluric and the fast calculation of the electric field value of the specific model is carried out by using the quasilinear integral equation method. Firstly, based on the MAXWELL equations and the boundary conditions satisfied by 3D magnetotelluric, the variational equations equivalent to 3D magnetotelluric boundary value problems are derived by using Galerkin method. Then the normal hexahedron element is used to divide the calculation area and the vector interpolation basis function is used to analyze the element. Finally, the various elements are added together to form a large and sparse coefficient matrix, and then the matrix is stored and solved. Then, we find that when the computing area mesh is divided into hexahedron, it is possible that the grid is not detailed enough in the area where the electrical property changes dramatically. As a result, the field value in hexahedron element can not be accurately expressed by the interpolation function of its twelve vector edges, resulting in errors. In addition, the boundary conditions of the magnetotelluric field can only be satisfied at infinity, so the improper mesh generation strategy may cause the error of the numerical simulation results to be too large. Furthermore, the causes and rules of errors at different frequencies are studied. Based on the above error analysis, this paper puts forward the basic principle of mesh generation based on the vector finite element method of hexahedron element, and improves the forward modeling process according to the principle, and puts forward the idea of frequency adaptation. With the change of frequency, the method of mesh division is adjusted continuously, and the calculation speed is greatly improved under the condition of ensuring the accuracy of calculation. Finally, the forward modeling and analysis of a series of geological models are carried out, and by using the spatial symmetry of Green's function and the exchange theorem, the calculation of Green's coefficient is compressed, and the generation speed of coefficient matrix is accelerated. The fast quasilinear approximate method is realized, and the fast calculation of electric field value of a specific model is carried out by using the quasilinear integral equation method, and some shortcomings and suggestions for future work are put forward.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：P631.325

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