Scattering in the Presence of Fold Caustics
Scattering in the Presence of Fold Caustics
复制标题
存在折叠焦散时的散射
DOI：
--
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发表时间：
2000
影响因子：
1.9
通讯作者：
C. Nolan
中科院分区：
文献类型：
--
作者：
C. Nolan
我们考虑声学的线性化散射算子，它将地球表面声速的奇点映射到地球表面测量的压力的奇点。声信号源集中在表面上的一个点上。将伴随散射算符应用于测量的压强是定位声速奇点的标准技术。得到的图像相当于将${\cal F}^**\cal F}$应用于声速奇点。如果不发生焦散，则${\cal F}^*{\cal F}$是一种伪微分运算符，这意味着当应用声速奇点时，它不会移动，并且可以获得可靠的图像。然而，如果存在焦散，则不能很好地理解${\cal F}^*{\cal F}$。我们的主要结果是，对于简单的折叠焦散(最常见的一种)，它是一种奇异的傅立叶积分算子，这意味着一些声速奇点将被传播。
We consider the linearized scattering operator ${\cal F}$ of acoustics which maps singularities in the sound speed in the subsurface of the earth to singularities in the measured pressure at the earth's surface. The source of the acoustic signal is concentrated at a point on the surface. Application ofthe adjoint scattering operator ${\cal F}^*$ to the measured pressure is a standard technique of locating sound speed singularities. The resulting image is equivalent to application of ${\cal F}^*{\cal F}$ to the sound speed singularities. Provided caustics do not occur, ${\cal F}^*{\cal F}$ is a pseudodifferential operator, meaning sound speed singularities do not move when it is applied and one obtains a reliable image. However, if caustics are present, ${\cal F}^*{\cal F}$ is not well understood. Our main result is that for the case of a simple fold caustic (the most common kind), ${\cal F}^*{\cal F}$ is a singular Fourier integral operator, meaning that some sound speed singularities will be propagated t...