Vertical propagation of low-frequency waves in finely layered media
Vertical propagation of low-frequency waves in finely layered media
复制标题
低频波在细层介质中的垂直传播
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
B. Arntsen
中科院分区：
文献类型：
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作者：
A. Stovas;B. Arntsen
精细层状沉积物中的多次散射对于解释地层数据、将测井数据与地震数据匹配以及地震建模是重要的。在地震应用中，有两种方法被用来处理这个问题：O 'Doherty-Anstey近似和Backus平均。O 'Doherty Anstey近似描述了地层过滤效应，而Backus平均定义了层堆叠的有效介质的弹性特性。了解层状介质何时可以被认为是有效介质是非常重要的。在本文中，我们只研究垂直传播。因此，不考虑各向异性效应。利用矩阵传播算子法，我们推导出水平层叠加的透射和反射响应方程。从传输响应，我们计算的相速度和比较的零频率限制与巴科斯平均的有效介质速度。我们还研究了从时间平均介质到有效介质的过渡如何取决于对比度;即，反射系数系列的强度。通过数值算例，我们证明了在有效介质低频极限和时均介质高频极限之间存在一个过渡区，该过渡区的宽度取决于反射系数级数的强度。
Multiple scattering in finely layered sediments is important for interpreting stratigraphic data, matching well-log data with seismic data, and seismic modeling. Two methods have been used to treat this problem in seismic applications: the O’Doherty-Anstey approximation and Backus averaging. The O’Doherty-Anstey approximation describes the stratigraphic-filtering effects, while Backus averaging defines the elastic properties for an effective medium from the stack of the layers. It is very important to know when the layered medium can be considered as an effective medium. In this paper, we only investigate vertical propagation. Therefore, no anisotropy effect is taken into consideration. Using the matrix-propagator method, we derive equations for transmission and reflection responses from the stack of horizontal layers. From the transmission response, we compute the phase velocity and compare the zero-frequency limit with the effective-medium velocity from Backus averaging. We also investigate how the transition from timeaverage medium to effective medium depends on contrast; i.e., strength of the reflection-coefficient series. Using numerical examples, we show that a transition zone exists between the effective medium low-frequency limit and the time-average medium high-frequency limit, and that the width of this zone depends on the strength of the reflectioncoefficient series.