Waves in space-dependent and time-dependent materials: A systematic comparison

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS
Kees Wapenaar , Johannes Aichele , Dirk-Jan van Manen
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引用次数: 0

Abstract

Waves in space-dependent and in time-dependent materials obey similar wave equations, with interchanged time- and space-coordinates. However, since the causality conditions are the same in both types of material (i.e., without interchangement of time- and space-coordinates), the solutions are dissimilar.

We present a systematic treatment of wave propagation and scattering in 1D space-dependent and in 1D time-dependent materials. After formulating unified equations, we discuss Green’s functions and simple wave field representations for both types of material. Next we discuss propagation invariants, i.e., quantities that are independent of the space coordinate in a space-dependent material (such as the net power-flux density) or of the time coordinate in a time-dependent material (such as the net field-momentum density). A discussion of general reciprocity theorems leads to the well-known source-receiver reciprocity relation for the Green’s function of a space-dependent material and a new source-receiver reciprocity relation for the Green’s function of a time-dependent material. A discussion of general wave field representations leads to the well-known expression for Green’s function retrieval from the correlation of passive measurements in a space-dependent material and a new expression for Green’s function retrieval in a time-dependent material.

After an introduction of a matrix–vector wave equation, we discuss propagator matrices for both types of material. Since the initial condition for a propagator matrix in a time-dependent material follows from the boundary condition for a propagator matrix in a space-dependent material by interchanging the time- and space-coordinates, the propagator matrices for both types of material are interrelated in the same way. This also applies to representations and reciprocity theorems involving propagator matrices, and to Marchenko-type focusing functions.

与空间有关和与时间有关的材料中的波:系统比较
与空间有关的材料中的波和与时间有关的材料中的波都服从类似的波方程,但时间坐标和空间坐标互换。然而,由于两类材料的因果关系条件相同(即不交换时间坐标和空间坐标),因此解法也不尽相同。我们对一维空间依赖材料和一维时间依赖材料中的波传播和散射进行了系统处理。在提出统一方程后,我们讨论了两类材料的格林函数和简单波场表示法。接下来我们讨论传播不变量,即与空间相关材料中的空间坐标(如净功率流密度)或时间相关材料中的时间坐标(如净场动量密度)无关的量。通过对一般互易定理的讨论,可以得出与空间有关的材料的格林函数的众所周知的源-受体互易关系,以及与时间有关的材料的格林函数的新的源-受体互易关系。通过对一般波场表示法的讨论,我们得出了从空间相关材料的被动测量相关性中检索格林函数的著名表达式,以及时间相关材料中检索格林函数的新表达式。在介绍了矩阵矢量波方程之后,我们讨论了这两类材料的传播矩阵。由于时间相关材料中传播矩阵的初始条件与空间相关材料中传播矩阵的边界条件是通过交换时间坐标和空间坐标来实现的,因此这两类材料的传播矩阵以相同的方式相互关联。这也适用于涉及传播矩阵的表示和互易定理,以及马琴科型聚焦函数。
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来源期刊
Wave Motion
Wave Motion 物理-力学
CiteScore
4.10
自引率
8.30%
发文量
118
审稿时长
3 months
期刊介绍: Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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