Quantifying the effects of non-diffuse noise on ballistic and coda wave
amplitude from variances of seismic noise interferometry in Southern
California
Abstract
We develop a new approach based on the variance of noise
cross-correlation to characterize the noise source and wave propagation
under the influence of a non-diffuse noise field. Based on the random
errors for the Fourier spectra of stacked noise cross-correlation (Liu
et al. 2016) and the assumption of diffuse field, we derive an
analytical expression for the variance of every time point in the
stacked cross-correlation and validate the theory using synthetic
diffuse noise data. The ambient seismic noise field in Southern
California is, however, not fully diffuse. The observed correlated
neighboring frequencies in the noise data – a definitive character of
the non-diffuse field (Liu & Ben-Zion 2016), map into the noise
cross-correlation, biasing its variances from theoretical predictions
under fully diffuse field assumption. For the secondary ocean
microseism, we find strong positive correlation between the correlated
neighboring frequencies and the deviations from diffuse field theory
predicted variances. The ballistic arrivals on average contain more
significant bias than the coda segments of the noise cross-correlation,
which agrees with previous time-lapse monitoring studies based on
ambient seismic noise. In addition, the station pairs having significant
bias between actual and diffuse field theory predicted variances are
aligned with the strongest source direction and exhibit significant
beamforming source fluctuation.