{ "id": "eprp8qg4zb", "slug": "ambient-noise-tomography", "title": "Ambient noise tomography", "updated": "2026-10-25", "topic_path": [ { "id": "physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical" }, { "id": "physical.earth", "label": "Earth sciences", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.earth" }, { "id": "physical.earth.planet", "label": "Earth systems and geophysics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.earth.planet" }, { "id": "physical.earth.planet.seismic-tomography", "label": "Seismic tomography", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.earth.planet.seismic-tomography" } ], "geo": [ { "id": "geo.nongeo.t2001.physical.earth", "label": "Non-geographic · 2001 to 2020: Earth sciences", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.physical.earth", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t2001", "label": "Non-geographic · 2001 to 2020", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001" }, { "id": "geo.nongeo.t2001.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.physical" }, { "id": "geo.nongeo.t2001.physical.earth", "label": "Earth sciences", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.physical.earth" } ] } ], "excerpt": "Ambient noise tomography is a seismic imaging technique that cross-correlates continuous background noise recorded at station pairs to build 3D shear-wave velocity models of the crust.", "snippet": "Ambient noise tomography is a seismic imaging technique that cross-correlates continuous background noise recorded at station pairs to build 3D shear-wave velocity models of the crust.", "node": "physical.earth.planet.seismic-tomography", "markdown": "# Ambient noise tomography\n\nAmbient noise tomography (ANT) cross-correlates continuous ambient seismic noise recorded at pairs of stations to recover empirical Green's functions (A system's characteristic response to a point impulse) and invert surface-wave dispersion for shear-wave velocity models of the subsurface. It requires no earthquakes or active sources, so images can be built anywhere a seismic array operates, from urban basins to ocean floors.\n\n| Key fact | Detail |\n|---|---|\n| Primary output | Rayleigh- and Love-wave dispersion maps inverted into 3D shear-wave velocity (Vs) models of the crust and uppermost mantle [1](http://phys-geophys.colorado.edu/pubs/2011/ritzwoller%20comptes%20rendus%202011.pdf) |\n| Typical periods | About 8–40 s in continental studies; down to ~6 s from noise, below what earthquake tomography reaches; above 100 s at global scale [2](http://jspc-www.colorado.edu/pubs/2007/jgr_na_vers6.pdf) • [1](http://phys-geophys.colorado.edu/pubs/2011/ritzwoller%20comptes%20rendus%202011.pdf) |\n| Data needed | More than six months is generally recommended for stable extraction [3](https://www.science.org/doi/10.1126/science.1108339) • [4](https://link.springer.com/article/10.1007/s12303-025-00005-8) |\n| Resolution | Better than 100 km across much of the US at 8–40 s; eikonal tomography resolves roughly one station spacing (~70 km); dense arrays reach ~2/3 wavelength laterally [2](http://jspc-www.colorado.edu/pubs/2007/jgr_na_vers6.pdf) • [5](http://ciei.colorado.edu/ambient_noise/pubs/lin_eikonal_09.pdf) • [6](https://www.frontiersin.org/journals/earth-science/articles/10.3389/feart.2025.1660737/full) |\n| Spacing rule | Dispersion is measured only up to a period (s) equal to interstation distance (km) divided by 12; a 40 s measurement needs ~500 km spacing [7](https://academic.oup.com/gji/article-pdf/169/3/1239/6082124/169-3-1239.pdf) |\n| Main failure mode | Non-uniform, seasonal noise sources bias traveltimes and velocities; corrections and careful processing are required [8](http://en.dzkx.org/article/doi/10.6038/cjg2025S0673) • [9](https://academic.oup.com/gji/article/171/1/223/601710) |\n| Cost position | A cost-effective alternative to earthquake-based and active-source surveys; ~100 nodal instruments for 6 weeks can image the top 5 km [10](https://www.earthdoc.org/content/papers/10.3997/2214-4609.2024101124) |\n\n## How it works\n\nThe theoretical basis is that, for a sufficiently diffuse or equipartitioned wavefield, the cross-correlation computed between a pair of receivers is proportional to a symmetrized Green function between those receivers, and depending on the formulation to its time derivative, rather than simply to the Green function waveform itself.[3](https://www.science.org/doi/10.1126/science.1108339) In a diffuse field, contributions from sources on a ring around the stations add constructively only at the interstation propagation time, producing causal and anticausal peaks; the amplitude asymmetry between the two sides of the correlation reflects the asymmetry of the source distribution around the pair.[11](https://www.kweemstra.com/publications/articles/Boschi_and_Weemstra_RofG_15.pdf) The connection to the fluctuation-dissipation theorem formalizes why the correlation of a diffuse field recovers the deterministic response.[12](https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2004GL019491)\n\nIn practice the noise field is never perfectly diffuse. Under conditions of sufficiently long stacking time and a uniform distribution of noise sources, the time cross-correlation between stations approximates the Green function.[13](https://www.sciencedirect.com/science/article/abs/pii/S0926985125001387) The illumination is dominated by surface waves of period roughly 5–30 s generated by ocean–solid Earth coupling, which is why most ANT images the crust and lithosphere; low-frequency noise below 1 Hz comes from ocean–shelf and coastline interactions, deep ocean currents, and atmospheric changes, while noise above 1 Hz carries diurnal and weekly patterns tied to human activity.[11](https://www.kweemstra.com/publications/articles/Boschi_and_Weemstra_RofG_15.pdf) • [13](https://www.sciencedirect.com/science/article/abs/pii/S0926985125001387)\n\n## How it is done\n\nThe standard processing workflow divides into four phases: single-station data preparation, cross-correlation and temporal stacking, dispersion-curve measurement by frequency-time analysis (FTAN), and quality control with error analysis.[7](https://academic.oup.com/gji/article-pdf/169/3/1239/6082124/169-3-1239.pdf)\n\n1. **Single-station preparation.** Time-domain normalization (one-bit normalization or running absolute mean weights) down-weights energetic transient signals such as earthquakes; spectral whitening reduces narrowband spectral dominance such as persistent microseism peaks, broadening the bandwidth of the recovered [Green's function](https://www.edgepedia.org/greens-function), though neither operation alone corrects azimuthal source imbalance.[7](https://academic.oup.com/gji/article-pdf/169/3/1239/6082124/169-3-1239.pdf)\n2. **Cross-correlation and stacking.** Correlations are computed for all \\( n \\cdot (n-1)/2 \\) station pairs, typically daily in the frequency domain, then stacked into longer series. Signal to trailing noise grows approximately as the square root of the time-series length.[7](https://academic.oup.com/gji/article-pdf/169/3/1239/6082124/169-3-1239.pdf)\n3. **Dispersion measurement.** FTAN applies a sequence of Gaussian filters at discrete periods and measures group arrival times on the filtered envelopes; phase speeds are measured in the time domain (far-field, valid beyond roughly two wavelengths) or with the frequency-domain method of Aki and Ekström, which involves no far-field approximation and is preferable for closely spaced stations.[2](http://jspc-www.colorado.edu/pubs/2007/jgr_na_vers6.pdf) • [14](http://ciei.colorado.edu/pubs/2019/Ritzwoller_from_book_SeismicAmbientNoise_2019.pdf) • [15](https://www.kweemstra.com/publications/articles/Boschi_et_al_GJI_13.pdf)\n4. **Quality control and inversion.** The principal quality metric is stability, the robustness of the measurement to perturbations in the conditions under which it is obtained; a common rule retains measurements with SNR > 15 and imposes a minimum three-wavelength interstation distance.[7](https://academic.oup.com/gji/article-pdf/169/3/1239/6082124/169-3-1239.pdf) • [2](http://jspc-www.colorado.edu/pubs/2007/jgr_na_vers6.pdf) Dispersion maps are then inverted, often station by station for 1D Vs models that are interpolated to 3D.[4](https://link.springer.com/article/10.1007/s12303-025-00005-8)\n\n## Origin\n\nThe method was reported independently for [Southern California](https://www.edgepedia.org/southern-california) by two groups in 2005: one cross-correlated one month of noise at 62 [USArray](https://www.edgepedia.org/usarray) stations [3](https://www.science.org/doi/10.1126/science.1108339), and another used 148 broadband stations, taking the time-derivative of the noise cross-correlation function as the Green's function estimate and amplitude clipping instead of one-bit normalization.[16](https://noiselab.ucsd.edu/papers/Sabra05tomo.pdf)\n\n## Variants\n\n**Continental-scale tomography.** A continental US application used nearly two years of noise from about 200 stations across the US, southern Canada, and northern Mexico, producing Rayleigh-wave maps for 8–70 s and Love-wave maps for 8–25 s with resolution better than 100 km across much of the country.[2](http://jspc-www.colorado.edu/pubs/2007/jgr_na_vers6.pdf) Eikonal tomography applies the eikonal equation (equation describing wave traveltime surfaces in high-frequency limit) to phase traveltime surfaces measured across dense arrays such as USArray; each station acts as an effective source, the gradient of the traveltime surface gives local phase speed and direction, resolution approximates the station spacing (~70 km in the western US), and azimuthal anisotropy is measured directly without assuming a functional form.[5](http://ciei.colorado.edu/ambient_noise/pubs/lin_eikonal_09.pdf) Applied to more than 1000 USArray stations, it yielded isotropic and azimuthally anisotropic 3D Vs models of the crust and uppermost mantle of the central and western US.[1](http://phys-geophys.colorado.edu/pubs/2011/ritzwoller%20comptes%20rendus%202011.pdf)\n\n**Dense-array and Bayesian methods.** Iterative matched filtering isolates coherent wavefronts across dense large-N arrays without the diffusive-noise assumptions of standard ANT, preserves amplitude information, and exploits strongly directional sources.[17](https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020JB019363) Multimode double-beamforming determines local phase velocities across dense linear arrays and jointly inverts fundamental- and higher-mode Rayleigh waves with [Bayesian inversion](https://www.edgepedia.org/bayesian-inversion).[18](https://par.nsf.gov/biblio/10616768-multimode-ambient-noise-double-beamforming-tomography-dense-linear-array-revealing-accretionary-wedge-architecture-across-central-taiwan) Transdimensional Bayesian inversion with adaptive Voronoi parameterization and reversible-jump MCMC quantifies uncertainty in fully 3D models.[6](https://www.frontiersin.org/journals/earth-science/articles/10.3389/feart.2025.1660737/full) Full-waveform ambient noise inversion bypasses Green's function retrieval entirely by directly modeling interstation correlations for arbitrary noise sources.[19](https://ethz.ch/content/dam/ethz/special-interest/erdw/geophysics/computational-seismology-dam/documents/Papers/Fichtner_GJI_2020.pdf)\n\n**Beyond surface waves.** Body waves and overtones have been extracted from noise, including imaging of [Earth's mantle](https://www.edgepedia.org/earths-mantle) discontinuities from ambient noise.[1](http://phys-geophys.colorado.edu/pubs/2011/ritzwoller%20comptes%20rendus%202011.pdf) • [20](http://en.dzkx.org/article/doi/10.6038/pg2022FF0241)\n\n## Applications\n\nThe earliest California maps showed low-speed anomalies corresponding to the main sedimentary basins and high-speed anomalies corresponding to the igneous cores of the major mountain ranges.[3](https://www.science.org/doi/10.1126/science.1108339) Dense urban arrays have resolved 3D shallow crustal structure, for example in [Long Beach, California](https://www.edgepedia.org/long-beach-california) [20](http://en.dzkx.org/article/doi/10.6038/pg2022FF0241), and in the Santa Clara Valley, where five months of data resolved two concealed basins with basement depths of about 2.5–3 km and small basins of roughly 25–100 km².[4](https://link.springer.com/article/10.1007/s12303-025-00005-8) In exploration, an array of about 100 nodal instruments operated for 6 weeks in the Vienna Basin imaged shear-wave velocity of the top 5 km for geothermal exploration.[10](https://www.earthdoc.org/content/papers/10.3997/2214-4609.2024101124) A dense linear array in central Taiwan produced a 2D shear-velocity model of the upper crust to about 10 km depth across an accretionary wedge.[18](https://par.nsf.gov/biblio/10616768-multimode-ambient-noise-double-beamforming-tomography-dense-linear-array-revealing-accretionary-wedge-architecture-across-central-taiwan) On the ocean floor, tilt noise from seafloor currents and compliance noise from ocean gravity waves degrade long-period correlations, but both can be reduced by predicting their effect on the vertical component from horizontal components and a co-located pressure gauge.[7](https://academic.oup.com/gji/article-pdf/169/3/1239/6082124/169-3-1239.pdf) • [14](http://ciei.colorado.edu/pubs/2019/Ritzwoller_from_book_SeismicAmbientNoise_2019.pdf)\n\n## Limitations and alternatives\n\n**Uneven noise sources.** The uniform-source assumption overlooks spatial heterogeneity and temporal variation of real noise fields; 2D simulations show that source heterogeneity causes travel-time discrepancies and waveform distortions, producing biased velocity imaging and inaccurate velocity-change monitoring.[8](http://en.dzkx.org/article/doi/10.6038/cjg2025S0673) Seasonal relocation of noise sources causes traveltime fluctuations of up to 0.5 s with a nearly 1-year period in the 10–20 s band, so accuracy cannot be achieved from only one month of stacking.[9](https://academic.oup.com/gji/article/171/1/223/601710) Comparing the causal and anticausal parts of correlations helps separate medium changes from clock drift and source-location effects.[9](https://academic.oup.com/gji/article/171/1/223/601710)\n\n**Processing bias.** Processing choices matter: in a 47-geophone nodal array at Lost Hills, unphysical processing components introduced traveltime biases averaging about 2.9% of total traveltimes.[19](https://ethz.ch/content/dam/ethz/special-interest/erdw/geophysics/computational-seismology-dam/documents/Papers/Fichtner_GJI_2020.pdf)\n\n**Spacing and period limits.** The distance/12 rule caps the usable period for a given station spacing, and the far-field approximation for time-domain measurements is valid beyond roughly two wavelengths.[7](https://academic.oup.com/gji/article-pdf/169/3/1239/6082124/169-3-1239.pdf) • [14](http://ciei.colorado.edu/pubs/2019/Ritzwoller_from_book_SeismicAmbientNoise_2019.pdf) Finite-frequency effects can be ignored below 40–50 s period, but above 50 s a Laplacian (Helmholtz) correction must be introduced.[1](http://phys-geophys.colorado.edu/pubs/2011/ritzwoller%20comptes%20rendus%202011.pdf)\n\n**Compared with alternatives.** Relative to earthquake-based surface-wave tomography, ANT reaches shorter periods (down to ~6 s), needs no seismicity, and offers good repeatability and long observation time.[2](http://jspc-www.colorado.edu/pubs/2007/jgr_na_vers6.pdf) • [20](http://en.dzkx.org/article/doi/10.6038/pg2022FF0241) Economical nodal seismometers and ultra-dense observation systems are extending scalable deployments.[13](https://www.sciencedirect.com/science/article/abs/pii/S0926985125001387)\n\n## References\n\n1. [Ambient noise tomography with a large seismic array (Ritzwoller et al., 2011, Comptes Rendus Geoscience)](http://phys-geophys.colorado.edu/pubs/2011/ritzwoller%20comptes%20rendus%202011.pdf)\n2. [Broad-band ambient noise surface wave tomography across the United States (Bensen et al., 2008, JGR)](http://jspc-www.colorado.edu/pubs/2007/jgr_na_vers6.pdf)\n3. [High-Resolution Surface-Wave Tomography from Ambient Seismic Noise (Shapiro et al., 2005, Science)](https://www.science.org/doi/10.1126/science.1108339)\n4. [Imaging the 3D basin structure of the Santa Clara Valley by ambient noise tomography (Geosciences Journal, 2025)](https://link.springer.com/article/10.1007/s12303-025-00005-8)\n5. [Eikonal tomography: surface wave tomography by phase front tracking across a regional broad-band seismic array (Lin, Ritzwoller, Snieder, 2009, GJI)](http://ciei.colorado.edu/ambient_noise/pubs/lin_eikonal_09.pdf)\n6. [Uncertainty-quantified 3D ambient noise tomography using transdimensional Monte Carlo inversion (Frontiers in Earth Science, 2025)](https://www.frontiersin.org/journals/earth-science/articles/10.3389/feart.2025.1660737/full)\n7. [Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements (Bensen et al., 2007, GJI)](https://academic.oup.com/gji/article-pdf/169/3/1239/6082124/169-3-1239.pdf)\n8. [Influence of non-uniform noise source distribution on ambient noise imaging: Insights from 2D numerical simulations (2025)](http://en.dzkx.org/article/doi/10.6038/cjg2025S0673)\n9. [Traveltime measurements from noise correlation: stability and detection of instrumental time-shifts (Stehly et al., 2007, GJI)](https://academic.oup.com/gji/article/171/1/223/601710)\n10. [Seismic Ambient Noise Tomography for Geothermal Exploration: the Eastern Vienna Array (EAGE 2024)](https://www.earthdoc.org/content/papers/10.3997/2214-4609.2024101124)\n11. [Stationary-phase integrals in the cross correlation of ambient noise (Boschi & Weemstra, 2015, Reviews of Geophysics)](https://www.kweemstra.com/publications/articles/Boschi_and_Weemstra_RofG_15.pdf)\n12. [Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise (Shapiro & Campillo, 2004, GRL)](https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2004GL019491)\n13. [A comprehensive overview of seismic ambient noise method: Maturity or stagnation? (2025 review)](https://www.sciencedirect.com/science/article/abs/pii/S0926985125001387)\n14. [Overview of pre- and post-processing of ambient-noise correlations (Ritzwoller & Feng, 2019 book chapter)](http://ciei.colorado.edu/pubs/2019/Ritzwoller_from_book_SeismicAmbientNoise_2019.pdf)\n15. [On measuring surface wave phase velocity from station–station cross-correlation of ambient signal (Boschi et al., 2013, GJI)](https://www.kweemstra.com/publications/articles/Boschi_et_al_GJI_13.pdf)\n16. [Surface wave tomography from microseisms in Southern California (Sabra et al., 2005, GRL)](https://noiselab.ucsd.edu/papers/Sabra05tomo.pdf)\n17. [Eikonal Tomography Using Coherent Surface Waves Extracted From Ambient Noise by Iterative Matched Filtering, Application to the Large-N Maupasacq Array (JGR 2020)](https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020JB019363)\n18. [Multimode ambient noise double-beamforming tomography with a dense linear array: revealing accretionary wedge architecture across Central Taiwan (GJI, 2024)](https://par.nsf.gov/biblio/10616768-multimode-ambient-noise-double-beamforming-tomography-dense-linear-array-revealing-accretionary-wedge-architecture-across-central-taiwan)\n19. [Optimal processing for seismic noise correlations (Fichtner et al., 2020, GJI)](https://ethz.ch/content/dam/ethz/special-interest/erdw/geophysics/computational-seismology-dam/documents/Papers/Fichtner_GJI_2020.pdf)\n20. [Research progress and prospect of seismic ambient noise tomography (2022 review)](http://en.dzkx.org/article/doi/10.6038/pg2022FF0241)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Earth sciences › Earth systems and geophysics › Seismic tomography*\n\n*Initially written Sep 29, 2026 · Edited: Oct 15, 2026; Oct 25, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [], "url": "https://www.edgepedia.org/ambient-noise-tomography", "markdown_url": "https://www.edgepedia.org/ambient-noise-tomography.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Ambient noise tomography\", Edgepedia (EdgeChat), https://www.edgepedia.org/ambient-noise-tomography. Edgepedia Community License 1.0.", "credit_md": "\"[Ambient noise tomography](https://www.edgepedia.org/ambient-noise-tomography)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/ambient-noise-tomography](https://www.edgepedia.org/ambient-noise-tomography). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Ambient noise tomography\", Edgepedia (EdgeChat), https://www.edgepedia.org/ambient-noise-tomography. Edgepedia Community License 1.0.", "speakable": "Ambient noise tomography is a seismic imaging technique that cross-correlates continuous background noise recorded at station pairs to build 3D shear-wave velocity models of the crust." }