声场单边聚焦

发布时间：2018-05-25 06:03

本文选题：单边聚焦 + 多通道　；参考：《中国海洋大学》2015年博士论文

【摘要】：介质成像是海洋声学和地震勘探领域中重要的研究方向,提取介质中声波／地震波的格林函数对介质成像具有重要价值。目前海洋声学和地震学领域存在两种重构格林函数的方法：互相关格林函数重构(地震学称为地震干涉)和单边聚焦格林函数重构。互相关格林函数重构需要将接收器布设在介质内部虚拟源位置,相比之下,单边聚焦格林函数重构只需在介质一侧表面布设接收器并测量介质的反射响应,因此更经济可行。然而,单边聚焦格林函数重构的核心问题——波动方程的单边聚焦,尚存几个问题亟待解决：(1)一维单边聚焦在介质内部的物理过程尚不清楚：(2)数学严格的一维单边聚焦理论建立在完备性公式和Marchenko方程框架下,然而这种理论框架却没有推广到高维。本文在Goupillaud分层介质模型中研究一维声场单边聚焦,该模型中的声场可以在传播时间图中直观显示。本文直观地揭示出一维离散声场单边聚焦在介质内部抵消非聚焦位置散射声场的物理过程；基于上述物理图像,本文提出一种递推实现一维离散声场单边聚焦的方法,这种递推方法本质是递推求解离散Marchenko方程。本文还研究将完备性公式和Marchenko方程框架下的单边聚焦理论推广到一维多通道薛定谔方程(即量子波导)。为了避免复杂繁琐的数学分析,本文讨论门限能量和束缚态不存在的情形。本文提出一种一维多通道自动单边聚焦方法,用于构造多通道单边聚焦所需的入射波形,并通过数值仿真验证这种方法的有效性；本文从格林公式角度证明多通道薛定谔方程的完备性公式,并将多通道完备性公式物理解释为量子波导的单边聚焦。
[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.
【学位授予单位】：中国海洋大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：P733.2;P631.46

【相似文献】