A wave-equation-based Kirchhoff operator
A wave-equation-based Kirchhoff operator
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DOI：
10.1088/0266-5611/28/11/115013
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发表时间：
2012-11
期刊：
影响因子：
2.1
通讯作者：
F. Kroode
中科院分区：
文献类型：
--
作者：
F. Kroode
在本文中，我将研究一个基尔霍夫型积分，它可以被看作是一个线性算子映射的角度方位角相关的反射系数沿着反射到反射数据的声波方程。我将表明，一个小的适应建设的角度，方位角相关的图像所提出的Sava和Fomel导致左逆这个运营商，它的主要反射数据映射到角度，方位角相关的反射系数。新的结构自然会导致基尔霍夫算子的重新表述，作用于空间位移扩展图像，这可以完全实现的波动方程的基本解。我将研究这个新的波动方程为基础的基尔霍夫算子的组成与运营商形成空间移位扩展图像的数据。我将表明，这些运营商是部分逆的对方，他们的组成是伪微分算子，重建适当的微观局部版本的主要反射数据和扩展图像集中在空间移位为零。
In this paper, I will study a Kirchhoff-type integral, which can be seen as a linear operator mapping angle–azimuth-dependent reflection coefficients along a reflector into reflection data for the acoustic wave equation. I will show that a minor adaptation of a construction of angle–azimuth-dependent images as proposed by Sava and Fomel leads to a left inverse of this operator, which maps primary reflection data to angle–azimuth-dependent reflection coefficients. The new construction naturally leads to a reformulation of the Kirchhoff operator, acting on space-shift-extended images, which can be implemented completely in terms of the fundamental solutions of the wave equation. I will study the composition of this new wave-equation-based Kirchhoff operator with an operator forming space-shift-extended images from data. I will show that these operators are partial inverses of each other, with their compositions being pseudo-differential operators that reconstruct suitably microlocalized versions of primary reflection data and extended images focused at space-shift zero.