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地震干涉法或噪声相关法提供了走时层析成像的被动方法。然而尚不清楚的是所恢复的格林函数的振幅用于估计衰减结构是否可靠。最近建立的组合方程被认为是空间自相关(spatial autocorrelation,SPAC)法向衰减性介质的扩展,并已用于根据所恢复格林函数的振幅估计衰减结构。然而,该组合方程尚未通过进行数值和分析研究的明确检验证实。在本研究中,我首先对非均匀衰减性介质证实空间自相关法与地震干涉法之间的关系,然后借助该关系建立支持该组合方程的理论。该组合方程在假设(1)衰减弱和(2)台站间隔大于所考虑波长的情况下对均匀衰减性介质的推导证明是有效的。根据所得结果,应用地震干涉法估计衰减结构应在衰减弱的相对均匀地区进行。应用于非均匀地区的衰减层析成像仍需要在理论上研究。
Earthquake interferometry or noise correlation provides a passive approach to traveltime tomography. However, it is not clear that the amplitude of the recovered Green’s function is used to estimate the reliability of the attenuation structure. The recently established combination equation is considered as an extension of the normal decaying medium for spatial autocorrelation (SPAC) and has been used to estimate the attenuation structure based on the amplitude of the recovered Green’s function. However, the combined equation has not been confirmed by explicit tests of numerical and analytical studies. In this study, I first demonstrated the relationship between the spatial autocorrelation method and the seismic interferometry for a non-uniform decaying medium, and then used this relationship to establish a theory that supports this combined equation. This combination of equations proves to be effective on the assumption that (1) attenuation is weak and (2) station separation is greater than the considered wavelength. According to the results obtained, seismic attenuation method should be used to estimate the attenuation structure in a relatively uniform region with weak attenuation. Atomic attenuation tomography applied to non-uniform regions still needs to be studied theoretically.