本文選題：瞬變電磁 + 時(shí)域有限差分　； 參考：《長(zhǎng)安大學(xué)》2015年碩士論文

【摘要】：當(dāng)前,瞬變電磁不僅廣泛應(yīng)用在石油、金屬等礦產(chǎn)資源勘查領(lǐng)域,而且還廣泛應(yīng)用在探測(cè)采空區(qū)、探測(cè)基巖等工程領(lǐng)域。相比瞬變電磁實(shí)際應(yīng)用的發(fā)展速度,其處理解釋的技術(shù)卻相對(duì)落后,一方面是由于本身瞬變電磁的復(fù)雜性,另一方面是由于計(jì)算機(jī)硬件的落后所致。隨著計(jì)算硬件的快速發(fā)展,使較準(zhǔn)確地瞬變電磁場(chǎng)的正演模擬成為可能。而研究瞬變電磁正演模擬對(duì)瞬變電磁的資料處理及解釋來(lái)說(shuō)至關(guān)重要,正演模擬也是為進(jìn)一步研究瞬變電磁方法反演打下基礎(chǔ)。目前,瞬變電磁正演模擬的主要方法有:有限差分法,有限元法,積分方程法等。本文采用時(shí)域有限差分法,以二維情況下為例,本文介紹了Yee元胞模型[4],一步步推導(dǎo)出了顯式的和無(wú)條件穩(wěn)定的電磁場(chǎng)方程差分格式,討論近似加載源的方式,討論了地空邊界以及地下邊界的解決方案,給出比較合適的自適應(yīng)迭代步長(zhǎng)建議。在上述研究基礎(chǔ)上,使用C++完成了程序的編寫,圖形顯示主要采用python加matplotlib實(shí)現(xiàn)。主要的難點(diǎn)在于地空邊界條件的處理上。首先將非均勻網(wǎng)格剖分的地表場(chǎng)值用三次樣條插值插成成均勻網(wǎng)格,然后對(duì)其作傅里葉正變換,乘以延拓因子后做傅里葉逆變換。過(guò)程中所涉三次樣條插值及快速傅里葉變換分別采用的是開(kāi)源的GSL和FFTW3[32,33]。通過(guò)均勻半空間解析解與有限差分?jǐn)?shù)值解對(duì)比驗(yàn)證了算法的正確性,并完成了電性線源層狀介質(zhì)模型,直立和傾斜的低阻板狀體模型,雙直立低阻板狀體及低阻覆蓋層等模型的正演模擬。同時(shí),利用三維有限差分計(jì)算了多個(gè)模型,正演模擬的結(jié)算結(jié)果表明,時(shí)域有限差分法在TEM中的應(yīng)用是一種有效地正演方法。
[Abstract]:At present, transient electromagnetism is widely used not only in the exploration of petroleum, metal and other mineral resources, but also in the engineering fields of detecting goaf and bedrock. Compared with the development speed of the practical application of transient electromagnetic, the technology of processing explanation is relatively backward. On the one hand, it is due to the complexity of transient electromagnetism itself, on the other hand, it is caused by the backwardness of computer hardware. With the rapid development of computing hardware, it is possible to simulate the transient electromagnetic field accurately. The study of transient electromagnetic forward modeling is very important to the processing and interpretation of transient electromagnetic data, and the forward simulation is also a foundation for further research on transient electromagnetic method inversion. At present, the main methods of transient electromagnetic forward modeling are: finite difference method, finite element method, integral equation method and so on. In this paper, the finite difference time domain (FDTD) method is used to illustrate the Yee cell model [4]. The explicit and unconditionally stable difference scheme of electromagnetic field equations is derived step by step, and the approximate loading source is discussed. In this paper, the solutions of the ground and air boundary and the underground boundary are discussed, and a more suitable adaptive iterative step size proposal is given. On the basis of the above research, the program is written with C, and the graphic display is mainly realized by python and matplotlib. The main difficulty is to deal with the boundary conditions of the ground and air. The surface field values of non-uniform meshes are interpolated into uniform grids by cubic spline interpolation. Then Fourier positive transformation is performed on them and then Fourier inversion is performed after multiplying them with continuation factors. The cubic spline interpolation and fast Fourier transform are open source GSL and FFTW3 respectively. The correctness of the algorithm is verified by comparing the analytical solution of uniform half-space with the numerical solution of finite difference. The layered dielectric model of electrical line source and the low-resistance plate model of vertical and inclined are completed. Forward modeling of double vertical low resistance plate and low resistance overlay. At the same time, several models are calculated by using 3D finite-difference method. The results of forward simulation show that the finite-difference time-domain method is an effective forward modeling method in TEM.
【學(xué)位授予單位】：長(zhǎng)安大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：P631.325

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本文編號(hào)：1804018