Fluctuations in the cross-correlation for fields lacking full diffusivity: The statistics of spurious features

Area of Science:

• Geophysics
• Seismology
• Acoustics

Background:

• Ambient noise fields are not always diffuse, raising questions about noise cross-correlation convergence to Green's function.
• Theoretical estimates suggest convergence quality depends on integration time and bandwidth, but natural environments show discrepancies.

Purpose of the Study:

• To investigate why empirical seismic correlations deviate from theoretical predictions.
• To determine if spurious arrivals or insufficient integration time are the primary cause of these deviations.

Main Methods:

• Analyzed cross-correlations from a model with a finite density of point sources.
• Calculated the mean and variance of these cross-correlations.
• Conducted numerical simulations to support theoretical estimates.

Main Results:

• Empirical seismic correlations are affected by spurious arrivals from scatterers, not insufficient integration time.
• The variance of cross-correlations has support for all times, peaking at the main arrival.
• Signal-to-noise ratio scales with the square root of source density.

Conclusions:

• Spurious arrivals significantly impact the identification of cross-correlations with Green's function.
• These arrivals can affect amplitude estimates, hindering efforts to infer seismic attenuation.