本文選題：單邊聚焦 + 多通道　； 參考：《中國海洋大學(xué)》2015年博士論文

【摘要】：介質(zhì)成像是海洋聲學(xué)和地震勘探領(lǐng)域中重要的研究方向,提取介質(zhì)中聲波／地震波的格林函數(shù)對(duì)介質(zhì)成像具有重要價(jià)值。目前海洋聲學(xué)和地震學(xué)領(lǐng)域存在兩種重構(gòu)格林函數(shù)的方法：互相關(guān)格林函數(shù)重構(gòu)(地震學(xué)稱為地震干涉)和單邊聚焦格林函數(shù)重構(gòu)�；ハ嚓P(guān)格林函數(shù)重構(gòu)需要將接收器布設(shè)在介質(zhì)內(nèi)部虛擬源位置,相比之下,單邊聚焦格林函數(shù)重構(gòu)只需在介質(zhì)一側(cè)表面布設(shè)接收器并測(cè)量介質(zhì)的反射響應(yīng),因此更經(jīng)濟(jì)可行。然而,單邊聚焦格林函數(shù)重構(gòu)的核心問題——波動(dòng)方程的單邊聚焦,尚存幾個(gè)問題亟待解決：(1)一維單邊聚焦在介質(zhì)內(nèi)部的物理過程尚不清楚：(2)數(shù)學(xué)嚴(yán)格的一維單邊聚焦理論建立在完備性公式和Marchenko方程框架下,然而這種理論框架卻沒有推廣到高維。本文在Goupillaud分層介質(zhì)模型中研究一維聲場(chǎng)單邊聚焦,該模型中的聲場(chǎng)可以在傳播時(shí)間圖中直觀顯示。本文直觀地揭示出一維離散聲場(chǎng)單邊聚焦在介質(zhì)內(nèi)部抵消非聚焦位置散射聲場(chǎng)的物理過程；基于上述物理圖像,本文提出一種遞推實(shí)現(xiàn)一維離散聲場(chǎng)單邊聚焦的方法,這種遞推方法本質(zhì)是遞推求解離散Marchenko方程。本文還研究將完備性公式和Marchenko方程框架下的單邊聚焦理論推廣到一維多通道薛定諤方程(即量子波導(dǎo))。為了避免復(fù)雜繁瑣的數(shù)學(xué)分析,本文討論門限能量和束縛態(tài)不存在的情形。本文提出一種一維多通道自動(dòng)單邊聚焦方法,用于構(gòu)造多通道單邊聚焦所需的入射波形,并通過數(shù)值仿真驗(yàn)證這種方法的有效性；本文從格林公式角度證明多通道薛定諤方程的完備性公式,并將多通道完備性公式物理解釋為量子波導(dǎo)的單邊聚焦。
[Abstract]:Dielectric imaging is an important research direction in the field of ocean acoustics and seismic exploration. The Green function of acoustic / seismic waves in the extraction medium is of great value to media imaging. There are two methods of reconstruction of Green's functions in the field of ocean acoustics and Seismology: the reconstruction of the number of Green functions (seismology called seismic interference) and single side The reconfiguration of focusing Green function. The reconstruction of the interrelated Green function needs to set the receiver in the virtual source position in the medium. In contrast, the single side focusing Green function reconfiguration only needs to set the receiver on the surface of the medium and measure the reflection response of the medium, so it is more economical. However, the core problem of the reconstruction of the single side focusing Green function The single side focusing of the wave equation remains to be solved urgently: (1) the physical process of one dimensional single side focusing in the medium is not clear: (2) the rigorous one-dimensional unilateral focusing theory is based on the completeness formula and the Marchenko equation framework. However, this theoretical framework is not popularized to the high dimension. This paper is in the Goupillaud point. In the layer medium model, the single side focus of one dimensional sound field is studied. The sound field in the model can be displayed intuitively in the propagation time graph. This paper directly reveals the physical process of the one dimensional discrete sound field single side focusing in the medium to counteract the unfocused scattering sound field. Based on the above physical image image, this paper presents a recursive realization of one dimensional dispersion. The method of single side focusing of the sound field is essentially a recursive solution to the dissociative scattered Marchenko equation. This paper also extends the completeness formula and the single edge focusing theory under the framework of Marchenko equation to the one-dimensional multi-channel Schrodinger equation (i.e. quantum waveguide). In order to avoid complicated and complicated mathematical analysis, the threshold energy and beam are discussed. In this paper, a one-dimensional multi channel automatic single side focusing method is proposed, which is used to construct the incident waveforms required for multi channel single side focusing. The validity of the method is verified by numerical simulation. The completeness formula of the multi-channel Schrodinger equation is proved from the Green formula and the multichannel completeness formula is given in this paper. Physics is interpreted as a single side focusing of a quantum waveguide.
【學(xué)位授予單位】：中國海洋大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類號(hào)】：P733.2;P631.46

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