Interpretation of Spatial AutoCorrelation Method Based on the Theory of Seismic Interferometry

Abstract eng:
In this paper, first we show the theoretical cross-check of SPatial AutoCorrelation method (SPAC) and Seismic Interferometry: the retrieval of the elastodynamic Green’s function. Their mutual consistency is almost complete. The only discrepancy is found on the average of the complex coherence function over azimuth in wave field dependent on azimuth. It is guessed in discussion that the discrepancy is owed by the way of representing wave field in the back ground theory of Seismic Interferometry that can produce only wave field moderately dependent on azimuth, and that the mentioned consequences of Seismic Interferometry also can make sense only in wave field moderately dependent on azimuth. Then, we show the result of the numerical experiments using the simulated microtremor records for given horizontally layered structures in order to confirm the formulas foreseen by the Seismic Interferometry to calculate the phase velocity in case of mixture of the fundamental and the first higher modes of Rayleigh waves, in that the eigen functions of both modes play the role of combining the their effects. The result clearly showed that these formulas can reproduce well the dispersion curves obtained by the conventional way of analysis by SPAC and Centerless Circular Array Method and therefore supports the way to estimate quantitatively the effect of the first higher mode on the dispersion curve.

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