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Normal-mode solution for the seismic noise cross-correlation method

Toshiro Tanimoto

Published 2008, SCEC Contribution #1218

Exact normal-mode solutions for the seismic noise-correlation method are derived by assuming that excitation sources of seismic noise are distributed <br/>over the globe uniformly. While a previous derivation by Snieder was for propagating waves, using the stationary phase approach, <br/>our results show that the method could work for normal modes. <br/>Comparison of the formula for the correlation (correlogram) with the Green's function <br/>shows differences in four aspects: (1) the correlogram is <br/>proportional to the number of sources (density of sources), <br/>(2) depends on excitation-source spectra, <br/>(3) shows a larger weight on high-frequency band (inversely proportional to the square of modal mass), <br/>and (4) has time dependence which requires one extra integration over time. <br/>Waveform modelling of the correlograms seems difficult in practice, <br/>particularly because of <br/>the lack of information on the excitation sources, often the temporarily changing ocean <br/>waves. On the other hand, phase and group velocity measurements should be possible as long as <br/>the correlograms contain good surface-wave signals. <br/> <br/>

Tanimoto, T. (2008). Normal-mode solution for the seismic noise cross-correlation method. Geophysical Journal International, 175, 1169-1175. doi: 10.1111/j.1365-246X.2008.03959.x.