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.