Passive & ambient-noise acquisition

Cross-correlating the traces recorded at two stations from ambient noise, ocean microseisms, urban traffic, wind, distant earthquakes, recovers the Green’s function between the two stations. No active source is required. Mathematically:

after integrating over many uncorrelated noise events surrounding the pair. The coherent arrivals at τ = ± d/v emerge from incoherent noise as integration time grows.

SNR scales as √t

Incoherent noise adds in energy linearly with time; coherent arrivals add in amplitude linearly. The SNR of the recovered Green’s function therefore grows as √t. Doubling the integration time gives −3 dB of improvement. Typical requirements: hours for short offsets (≤ 500 m), days for 1 km pairs, months for 10 km+ offsets.

Source-distribution bias

A fully omnidirectional source distribution around the pair recovers both causal (τ > 0) and acausal (τ < 0) lobes of the Green’s function. One-sided sources (e.g., coastal microseisms dominating from one compass direction) give only one lobe. The widget’s source-distribution slider makes this visible.

Application domains

Volcano monitoring (Mount St Helens, Merapi, Etna), arrival-time shifts of ≥1 ms signal magma movement before eruptions. Urban DAS on telecom fibre, traffic-generated noise produces usable Green’s functions for shallow imaging in cities. USArray passive tomography, a decade of continental-scale Green’s functions from year-long continuous records. CTBT nuclear-test verification, teleseismic noise cross-correlation detects clandestine underground explosions too small to trigger classical event-based monitoring.

References

• Aki, K., Richards, P. G. (2002). Quantitative Seismology (2nd ed.). University Science Books.
• Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge University Press.
• Yilmaz, Ö. (2001). Seismic Data Analysis: Processing, Inversion, and Interpretation of Seismic Data (2 vols.). SEG Investigations in Geophysics 10.