Improving C1 and C3 empirical Green’s functions from ambient seismic noise in NW Iran using RMS ratio stacking method

  • Mahsa SafarkhaniEmail author
  • Taghi Shirzad
Original Article


The retrieval of stable and reliable empirical Green’s functions using ambient seismic noise plays a major role when studying the Earth’s structure at various scales. High-resolution noise correlation functions are obtained in the NW of Iran by processing techniques including dividing the continuously recorded raw data into short (i.e., 10 min) overlapping (i.e., 80%) time windows. We compare four stacking methods (i.e., linear, RMS, RMS ratio, and Nth-root stacking methods) to study robust and stable inter-station empirical Green’s functions. Our results indicate that the new RMS ratio method of stacking would be the optimal method to stack coherent signals. In other words, this method tackles problems including low signal-to-noise ratio (hereafter SNR) value, distortion of wave shape, and phase instability/unstable polarity treatment. In addition to noise correlation functions, we propose another strategy for the computation of the empirical Green’s functions. In this technique, the cross-correlation of scattered coda waves of the calculated noise correlation functions is performed individually. In addition to coda window length, we also investigate another effective parameter, the geometry of various virtual stations to obtain reliable empirical Green’s functions from the scattered coda waves of correlation functions with high SNR. The error of the velocities of Rayleigh wave empirical Green’s functions is on the order of approximately 0.6%, when compared to ambient seismic noise and scattered coda waves for a period band range of 3–10 s.


Ambient seismic noise Cross-correlation RMS ratio stacking Scattered coda waves Virtual stations geometry Empirical Green’s functions 



The digital ambient seismic noise dataset has been collected by the Iranian Seismological Center (IrSC) at the University of Tehran/Iran (; not openly available to public; last accessed Feb. 2017). The earthquake waveform used in this study was obtained through the IrSC. All plots were also made using Generic Mapping Tools (GMT) version 4 (Wessel and Smith 1998;, last accessed May 2019). We would also like to thank the editor and four anonymous reviewers for their constructive comments and useful suggestions.

Funding information

This work was supported by the (FAPESP), Sao Paulo, Brazil (grant numbers 2016/20952-4).


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Institute of GeophysicsUniversity of TehranTehranIran
  2. 2.Institute of Astronomy, Geophysics and Atmospheric ScienceUniversity of Sao PauloSao PauloBrazil

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