Formulation of the spatial autocorrelation (SPAC) method in dissipative media
Formulation of the spatial autocorrelation (SPAC) method in dissipative media
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DOI：
10.1111/j.1365-246x.2012.05591.x
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发表时间：
2012-09
影响因子：
2.8
通讯作者：
H. Nakahara
中科院分区：
文献类型：
--
作者：
H. Nakahara
空间自相关（SPAC）方法是基于广义波动方程或广义电报方程，在耗散介质中对一维、二维和三维（1-D、2-D和3-D）标量波场进行求解的方法。一个相当直接的推导是可能的，通过使用SPAC方法和地震干涉测量之间的密切数学关系，虽然模型设置应修改，包括衰减。对于三维情况，耗散介质中标量波场的归一化互谱与非耗散介质中标量波场的归一化互谱仅相差一个指数阻尼项。然而，1-D和2-D情况的表达式并不像3-D情况那样简单，这意味着归一化互谱中不仅幅度而且相位都被衰减修改。推导出的SPAC表达式被认为适用于相当均匀的衰减分布。对于衰减的估计，SPAC方法需要用于比传统SPAC方法更大的站间距。对二维情况下SPAC表达式的分析表明，Prieto等人（2009）的猜想并不严格，但对于小衰减近似是好的。该研究为从环境噪声分析中估计相速度和衰减提供了理论依据。
SUMMARY Spatial autocorrelation (SPAC) method is formulated in dissipative media for one-, two- and three-dimensional (1-D, 2-D and 3-D) scalar wavefields based on the generalized wave equation or the generalized telegraph equation. A rather straightforward derivation is possible by using a close mathematical relation between the SPAC method and seismic interferometry, though a model set-up should be modified by including attenuation. For 3-D cases, the normalized cross spectrum of a scalar wavefield in a dissipative medium is found to be different from that in a non-dissipative medium merely by an exponentially damping term. However, expressions for 1-D and 2-D cases are not as simple as 3-D cases meaning that not only amplitude but also phase in the normalized cross-spectrum are modified by attenuation. The SPAC expressions derived are considered to be applied to rather homogeneous distribution of attenuation. For the estimation of attenuation, the SPAC method needs to be used for larger station separations than the traditional SPAC method does. Analysis of the SPAC expressions for 2-D cases shows that the conjecture of Prieto et al. (2009) is not strict but approximately good for small attenuation. This study will provide a theoretical basis to estimate not only phase velocity but also attenuation from analysis of ambient noises.