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

Abstract

Exact normal-mode solutions for the seismic noise-correlation method are derived by assuming that excitation sources of seismic noise are distributed over the globe uniformly. While a previous derivation by Snieder was for propagating waves, using the stationary-phase approach, our results show that the method could work for normal modes. Comparison of the formula for the cross-correlated seismogram (correlogram) against the Green's function shows differences in four aspects: (1) the correlogram is proportional to the number of sources (density of sources), (2) depends on excitation-source spectra, (3) shows a larger weight on high-frequency band (inversely proportional to the square of modal mass) and (4) has time dependence which requires one extra integration over time. Waveform modelling of the correlograms seems difficult in practice, particularly because of the lack of information on the excitation sources, often the temporarily changing ocean waves. On the other hand, phase and group velocity measurements should be possible as long as the correlograms contain good surface wave signals. © 2008 The Authors Journal compilation © 2008 RAS.