![]() ![]() 2000 Weaver and Lobkis 2006 Sánchez-Sesma et al. In strictly theoretical terms, a perfect diffuse system is defined under the theorem of the modal energy equipartitioning (e.g., Hodgson 1996 Hennino et al. Another prerequisite is the availability of a diffusive seismic noise. The first precondition for the successful implementation of this method is that noise sources are uncorrelated such that the cross-correlations of signals coming from simultaneously acting sources located in different places (the “cross-terms”) nullify each other reciprocally (e.g., Snieder 2004 Weemstra et al. 2019 and references therein), provided that certain conditions are fulfilled. In brief, theoretical studies have shown that the ensemble-averaging of cross-correlations of random seismic noises records over available time windows is a straightforward way to retrieve the Empirical Green’s functions (EGFs) between a pair of stations (for a comprehensive review, see Wapenaar et al. Since the beginning of the current century, a new field of research called seismic interferometry has provided an overarching theoretical framework to translate this visionary ambition into a concrete reality. Historically speaking, seismologists have long dreamed of turning ambient seismic noise into useful signals. In this paper, by simulating the records of a benchmark earthquake M N 5.2 with the help of empirical Green’s functions (EGF) obtained after the Ahar-Varzeghan Earthquake Doublet (M N 6.4 and M N 6.3), it is shown that the amplitude-unbiased phase cross-correlation is a relatively efficient approach in the face of the issues concerning long-standing cluster events. Therefore, the only solution left in such a situation is to use stronger non-linear time-dependent weights (e.g., square of the running average or one-bit normalization), which may cause Green’s function amplitude information to be lost. ![]() With regard to the suppression of these cluster earthquakes, commonly used solutions for dealing with monochromatic microseismic cluster events (e.g., implementing a band-reject filter around a comparatively narrow frequency band or whitening the amplitude spectra before calculating the cross-spectrum between two signals) may not have the necessary efficiency since earthquake clusters are generally a collection of events with different magnitudes, each having its own frequency and energy contents. However, small earthquakes can also have a disturbing effect on the accuracy of interpretations if they are persistently clustered right next to the perpendicular bisector of the line joining station pairs or in close proximity to one of the stations. To address the problems that arise from spatially scattered and temporally transient enormous earthquakes, preference is usually given to the use of time-dependent weights. Although research on seismic interferometry is now entering a phase of maturity, earthquakes are still the most troublesome issues that plague the process in real applications. ![]()
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