Surface motion of a layered medium having an irregular interface due to incident plane SH waves
Surface motion of a layered medium having an irregular interface due to incident plane SH waves
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DOI：
10.1029/jb075i005p00933
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发表时间：
1970-02
影响因子：
--
通讯作者：
K. Aki;K. Larner
中科院分区：
文献类型：
--
作者：
K. Aki;K. Larner
提出了一种计算具有不规则界面的层状半空间介质中平面波从下方入射时弹性波场的实用方法。这种方法可以用来研究M不连续面的界面形状，例如，利用观测到的远震体波引起的频谱幅度和相位延迟异常。该方法也可用于不同截面软弱浅层地震运动的工程地震学研究。散射场被描述为平面波的叠加，在界面上应用连续性条件得到谱系数中的耦合积分方程组。当界面形状为周期时，方程在波数域内满足，并对方程进行傅立叶变换和截断。使用复频率的频率平滑减少了与周期性界面形状相关的横向干扰，并允许将计算结果与有限带宽观测获得的结果进行比较。对每个计算解的界面应力和位移中的残差进行分析，提供了误差估计。对于界面不规则性的幅度与最短波长具有可比性的问题，相对均方根残差一般小于5%，往往小于1%。将该方法应用于几种“软盆地”、“凹陷M面”和“阶梯M面”模型，并与平层理论和射线理论的结果进行了比较。除了平面层理论中常见的垂直干涉效应外，我们还观察到横向干涉以及射线几何对表面运动的影响。
A practical method is devised to calculate the elastic wave field in a layer-over-half-space medium with an irregular interface, when plane waves are incident from below. This method may be used for studying the interface shape of the M discontinuity, for example, using the observed spectral amplitude and phase-delay anomalies due to teleseismic body waves. The method is also useful for the engineering-seismological study of earthquake motions of soft superficial layers of various cross sections. The scattered field is described as a superposition of plane waves, and application of the continuity conditions at the interface yields coupled integral equations in the spectral coefficients. The equations are satisfied in the wave-number domain when the interface shape is made periodic and the equations are Fourier transformed and truncated. Frequency smoothing by using complex frequencies reduces lateral interferences associated with the periodic interface shape and permits comparison of computed results with those obtained from finite bandwidth observations. Analyses of the residuals in the interface stress and displacement, performed for each computed solution, provided estimates of the errors. The relative root-mean-square residual errors were generally less than 5% and often less than 1% for problems in which the amplitude of the interface irregularity and the shortest wavelength were comparable. The method is applied to several models of ‘soft basins’ ‘dented M discontinuity’ and ‘stepped M discontinuity’ The results are compared with those derived from the flat-layer theory and from the ray theory. In addition to vertical interference effects familiar in the flat-layer theory, we observe the effects of lateral interference as well as those of ray geometry on the motion at the surface.