论文标题
分析瑞利系统在半空间中的泄漏模式或波数共振
Analysis of leaky modes or wavenumber resonances for the Rayleigh system in a half space
论文作者
论文摘要
我们对与雷利操作员相关的波数共振或漏水模式进行了全面分析，该模式在一个半空间中包含一个异质板的半空间，这是由地震学的动机。为此，我们在适当的Riemann表面，边界矩阵和反射矩阵上引入了JOST溶液，类似于与Schrödingeroberator相关的散射共振的研究。我们分析了它们的分析特性，并表征了这些波数共振的分布。此外，我们表明共振是分辨出对上述黎曼表面的非物理表与非物理板的阴极延续的极。
We present a comprehensive analysis of wavenumber resonances or leaky modes associated with the Rayleigh operator in a half space containing a heterogeneous slab, being motivated by seismology. To this end, we introduce Jost solutions on an appropriate Riemann surface, a boundary matrix and a reflection matrix in analogy to the studies of scattering resonances associated with the Schrödinger operator. We analyze their analytic properties and characterize the distribution of these wavenumber resonances. Furthermore, we show that the resonances appear as poles of the meromorphic continuation of the resolvent to the nonphysical sheets of the mentioned Riemann surface as expected.
