Introduction
Seismic noise denotes the persistent ground vibrations recorded by seismometers that are generally generated at or near the Earth’s surface and are therefore strongly controlled by elastic surface-wave propagation. By convention the ambient field is partitioned by frequency: signals below about 1 Hz are usually labeled microseisms, while those above 1 Hz are called microtremors, reflecting distinct source processes and propagation behaviour across that threshold.
A wide variety of surface and near-surface processes produce seismic noise, including anthropogenic activities (e.g., traffic and industrial operations), atmospheric forcing such as wind and storms, fluvial dynamics in rivers, and ocean wave action at coasts. In applied contexts the persistent wavefield is often referred to as the ambient wavefield or ambient vibrations; however, the term “ambient vibrations” can ambiguously include airborne or structure-borne oscillations (through buildings or supports), so careful definition is required in any study.
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Although seismic noise is an unwanted contaminant for low-noise ground measurements—masking seismic signals of interest and complicating earthquake monitoring and research—it also interferes with sensitive technologies (for example, precision manufacturing, astronomical telescopes, gravitational-wave observatories, and crystal-growth facilities). Conversely, the same ambient field provides useful information: passive monitoring of low-strain, time-varying dynamic properties permits structural-health assessment of bridges, buildings, and dams without active sources.
Ambient seismic energy is likewise exploited to image the subsurface via seismic interferometry and ambient-noise correlation, which recover Green’s or transfer functions between stations from continuous recordings. Environmental applications include fluvial seismology, where river-generated seismic signals reveal flow dynamics and sediment transport and enable detection of temporal changes in surface processes. Finally, ambient measurements contribute to seismic microzonation and site-response studies by characterizing local amplification and improving urban and regional earthquake-engineering assessments.
Causes
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Seismic noise exhibits a clear frequency-dependent partitioning of sources. At periods longer than 1 s (frequencies below 1 Hz) natural processes dominate, with ocean waves being the primary contributor; in particular, a ubiquitous spectral peak between 0.1 and 0.3 Hz is attributed to the interaction of nearly equal-frequency water waves propagating in opposite directions, which generates coherent ground motion. Above 1 Hz the noise field is largely shaped by human activities—notably road traffic and industrial operations—although rivers, wind and other atmospheric phenomena can also supply substantial high-frequency energy. Anthropogenic signals can remain detectable even during otherwise quiet intervals (for example, stadium “footquakes” produced by synchronized stamping). Separately, a distinct non‑anthropogenic pulsed signal with a 26–28 s period (0.036–0.038 Hz) has been observed centered on the Bight of Bonny; this feature is interpreted as storm-wave energy reflected and focused by the African coastline and acting on shallow bathymetry, yielding a regionally concentrated low‑frequency signature. Overall, the seismic-noise spectrum therefore reflects different dominant generators by band, while coastal geometry and seafloor depth can locally focus and amplify low‑frequency signals.
Physical characteristics
Ambient seismic vibrations at the Earth’s surface typically exhibit ground-velocity amplitudes in the range of about 0.1–10 μm/s; global spectral models of high- and low-background noise quantify how this energy is distributed across frequency. Although continuous seismic records contain some body-wave energy (compressional P and shear S phases), most of the ambient signal is carried by surface waves—principally Love and Rayleigh modes—because near-surface sources preferentially excite energy that propagates along the exterior. Surface-wave propagation in ambient noise is dispersive: phase velocity depends on frequency, and in typical near-surface materials higher frequencies tend to travel more slowly than lower frequencies. This frequency dependence is captured by a dispersion curve (phase velocity or slowness plotted versus frequency), which summarizes how different spectral components sample the medium. Because short-period (high-frequency) surface waves are sensitive to shallow layers while long-period (low-frequency) waves sample greater depth, the form of the dispersion curve is directly controlled by the depth variation of shear-wave velocity (VS). Consequently, measured dispersion curves provide a non‑invasive observational constraint that can be inverted to estimate vertical VS profiles and thereby reveal subsurface seismic structure beneath recording sites.
History
Ambient seismic noise was initially overlooked because its amplitudes under ordinary conditions are exceedingly small and fell below the detection thresholds of late-19th-century instruments. Early progress came when Fusakichi Omori exploited structural amplification within buildings to record these weak ground motions; measurements of building vibrations allowed him to identify natural frequencies of structures and to track changes in those frequencies as damage accumulated, thereby linking continuous ambient excitation to structural response and deterioration.
Parallel advances in global seismology recognized a coherent band of long-period noise (roughly 30–5 s) whose spatial consistency and spectral shape pointed to an oceanic source. A rigorous theoretical explanation for how ocean processes generate this microseismic energy was provided by Longuet-Higgins in 1950, establishing the mechanism that connects wave–wave interactions at sea with observable seismic signals on land.
In the early 21st century, particularly from about 2005 onward, theoretical developments, methodological innovations, and the growing availability of extensive, high-quality seismic records spurred a renewed and rapid expansion of research and practical applications that harness ambient seismic noise—most notably through seismic interferometry and related techniques.
Ambient-vibration (seismic‑noise) measurement in civil engineering originated as an empirical tool for characterizing building dynamic behavior after the 1933 Long Beach earthquake: D. S. Carder’s 1935 campaign recorded ambient vibrations in more than 200 buildings and produced resonance‑frequency data later incorporated into design practice. Interest in ambient methods waned until the 1950s, when earthquake engineers (notably G. Housner, D. Hudson, K. Kanai and T. Tanaka) renewed research in California and Japan. During the mid‑20th century ambient techniques were largely displaced by forced‑vibration testing because controlled, larger input amplitudes simplified system identification and produced clearer modal estimates. M. Trifunac’s 1972 work demonstrated the methodological equivalence of ambient and forced approaches for dynamic characterization, but ambient methods did not regain wide use until the late 1990s. Their revival was driven by lower cost, operational convenience, and advances in sensors and computational processing that improved data quality and interpretation. Today ambient‑vibration testing is valued for low‑strain probing of structures; studies show that, for buildings not subject to severe damage, dynamic properties derived from ambient noise closely match those observed under strong shaking. The historical arc—empirical genesis (1935), mid‑century methodological competition, theoretical unification (1972), and a technological/operational revival in the late 1990s—has established ambient‑vibration methods as a cost‑effective means of estimating resonance frequencies and dynamic properties in seismic design and assessment, particularly in regions with strong seismic interest.
Scientific study and applications in geology and geophysics
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Ambient seismic noise methods developed from mid-20th-century array theory and late-20th-century instrumental advances into routine geophysical tools for site characterization and seismic-hazard assessment. Improvements in seismometer sensitivity and the deployment of seismic arrays—initially driven by requirements to detect and monitor nuclear tests—created the observational foundation that made noise-based approaches practicable.
Foundational theoretical work in the 1950s and 1960s introduced array-based procedures (notably spatial autocorrelation, frequency–wavenumber analysis, and correlation methods) for probing local subsurface structure. Early implementations were limited by the timing and synchronization accuracy of stations, so these concepts awaited later gains in instrumentation and processing. A single-station approach re-emerged in 1989 with the horizontal-to-vertical spectral ratio (H/V) technique, which interprets the ratio as indicative of a site’s resonance and, under the assumption that shear waves dominate ambient vibrations, as a proxy for the S‑wave transfer function between surface and bedrock.
Subsequent work in the late 1990s showed that array-derived noise processing could, in practice, recover shear-wave velocity (Vs) profiles and other subsurface parameters, enabling quantitative estimation of local site response. The European SESAME project (2004–2006) sought to codify measurement protocols and best practices, assess the limits of H/V and array methods, and establish standards for using ambient-noise data to evaluate local amplification of earthquake shaking. SESAME and related studies also emphasized methodological caution: the simplifying assumption that horizontal-to-vertical ratios directly represent S‑wave transfer functions is not universally valid and must be tested with complementary observations.
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Taken together, the historical development reflects a progression from theoretical array concepts to operational techniques: once measurement fidelity and analytical algorithms improved, ambient-noise approaches matured into validated means to estimate site resonance, S‑wave behaviour, and Vs structure—parameters central to local seismic-hazard analysis.
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Characterization of subsurface properties using ambient seismic noise relies on extracting complementary observables from the random seismic wavefield—power spectra, horizontal‑to‑vertical spectral ratios (HVSR), dispersion curves and autocorrelation/cross‑correlation functions—to constrain layering and shear‑velocity structure. Single‑station power spectral density (PSD) analysis of background microseisms and the Earth’s hum provides proxy information on ocean wave energy and its temporal variations; these PSD signals are particularly sensitive to near‑shore forcing and to seasonal changes in polar sea‑ice extent that modulate ocean wave attenuation.
The HVSR method identifies spectral peaks in ambient vibration recordings that often mark a site’s fundamental resonance frequency. Depending on the dominant noise composition, an HVSR peak may arise from Rayleigh‑wave ellipticity, the Airy phase of Love waves or SH resonances; in many common ground conditions these different origins coincide in frequency, so the HVSR peak reliably estimates the resonant frequency though it supplies only a single frequency constraint rather than a full velocity profile. For the simplest layer‑over‑bedrock model the fundamental frequency f0 is related to shear‑wave velocity Vs and layer thickness H by f0 = Vs/(4H), enabling depth mapping where Vs is known. Crucially, HVSR peak amplitude should not be interpreted as a quantitative measure of site amplification, since empirical studies show no robust correlation between peak height and true amplification level.
Spatially distributed sensor arrays and three‑component recordings markedly improve subsurface resolution. Arrays permit beamforming and spatial‑correlation techniques that separate incoming wavefields and recover dispersion, while merging results from arrays of different apertures allows imaging across scales from near‑surface layers to greater depths. Vertical‑component data are dominated by Rayleigh waves and are often straightforward to interpret in terms of ellipticity; incorporating transverse and radial components brings Love‑wave information and thus stronger constraints on layered shear properties and lateral or azimuthal anisotropy.
Correlation‑based approaches, including seismic interferometry and ambient‑noise cross‑correlation, extract Green’s functions from continuous noise records and have been widely adopted to retrieve impulse responses and dispersion information at scales from engineered near‑surface investigations to continental studies. Common processing tools used to isolate dispersion and wavefield characteristics include FK and HRFK beamforming, the SPAC (spatial autocorrelation) method, ambient‑noise correlation/interferometry and refraction microtremor (ReMi); each technique emphasizes different aspects of the wavefield and, when combined, yields more robust velocity models than any single method alone.
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Characterization of the vibration properties of civil engineering structures
Ambient environmental and operational excitations continuously induce measurable dynamic responses in civil infrastructure (bridges, buildings, dams). Operational Modal Analysis (OMA, or output‑only modal analysis) comprises the analytical framework used to infer modal frequencies, damping and mode shapes from these responses without direct measurement of the input forces, relying commonly on the simplifying assumption that excitations behave as broadband (near white‑noise) inputs so that recorded signals principally reflect the structure’s inherent dynamics.
Excitation sources include external agents (wind, ground vibrations) and internal agents (machinery, foot traffic). In practice, internal sources are seldom exploited for system identification, and ground‑borne excitation is frequently treated as the dominant input when transfer‑based schemes are applied. Measured vibration signatures, however, are the integrated outcome of the entire built system: the primary load‑bearing elements, stiff or heavy non‑structural components (e.g., masonry infill), light finish elements (e.g., windows, cladding) and the foundation interaction with the supporting soil. Soil–structure interaction (SSI) in particular breaks the idealization of a rigidly fixed base and complicates forward modelling and interpretation of observed dynamics.
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A spectrum of practical identification techniques is used depending on objectives and data availability. Single‑station methods extract power spectral estimates from recordings at one location (often the roof or top floor) to identify dominant resonance peaks and provide a first estimate of damping. Transfer‑function approaches compute the frequency response between recordings at the base and higher levels to compensate for non‑white inputs and improve detection under low signal‑to‑noise conditions, although they typically cannot fully remove SSI effects. Multi‑sensor array deployments aim to recover global modal parameters (natural frequencies, damping ratios, mode shapes) across the structure; without knowledge of the excitation, however, modal participation factors generally remain indeterminate, and the use of a common reference sensor facilitates combining results from separate arrays.
Correlation‑based methods form cross‑spectral (power spectral density) matrices from simultaneous recordings and enable modal extraction via peak‑picking or decomposition algorithms such as Frequency Domain Decomposition (FDD), which can distinguish closely spaced or coupled modes. Beyond these categories, a broad suite of system‑identification techniques exists in the literature and can be applied to ambient vibration datasets; their relative suitability depends on sensor geometry, record quality, the degree of SSI and the specific parameters sought. Method selection therefore requires balancing available data, expected noise characteristics and the influence of non‑structural elements and foundation interaction on the measured response.
The global shutdowns during the COVID‑19 pandemic produced a simultaneous, large‑scale diminution of anthropogenic surface processes that generate seismic waves, yielding an unprecedented perturbation of ambient seismic noise. Reductions were strongest in densely populated corridors with concentrated transport and industrial infrastructure, so the spatial pattern of diminished ground vibration closely mirrored urban and metropolitan activity footprints rather than being uniform across regions.
Spectral analyses of continuous recordings show that the decline was concentrated in the high‑frequency band of ambient seismic energy—frequencies typically attributable to shallow, short‑period sources such as road, rail and airport traffic and numerous industrial machines—supporting the interpretation that curtailed human mobility and operations were the primary drivers. The magnitude, synchronicity and duration of these reductions make the pandemic interval the most prolonged and globally coherent attenuation of anthropogenic seismic noise documented to date.
Because short‑period seismic energy correlates with patterns of movement and throughput, researchers have investigated pandemic‑era seismic observations as a near‑continuous, spatially resolved indicator of economic and behavioral change. The interval also had immediate geophysical benefits: lower anthropogenic masking improved detection of small natural earthquakes in some locales and provides a rare baseline for disentangling human and natural sources in urban and regional seismology.
However, employing seismic noise as a proxy for economic activity demands careful geographic calibration and attention to confounding influences. Robust inference requires accounting for instrument distribution and siting, local site effects and geology, seasonal and meteorological cycles, and other non‑human noise contributors; without such controls, comparisons of relative economic performance across cities or countries can be misleading.
Inversion, model updating and multi-model approach
Ambient-seismic observations such as amplitudes, spectral content, dispersion curves and modal shapes do not directly specify subsurface properties because wave propagation and structural response mediate the relationship between physical parameters (e.g. S‑wave velocity, density, stiffness, damping) and the measured noise signatures. Consequently, quantitative interpretation requires a forward model that predicts observable quantities from a hypothesized physical description; this forward problem embeds the governing physics (wave propagation, boundary conditions, material behaviour) and produces synthetic dispersion curves, mode shapes or other noise-derived observables that can be compared with measurements.
The inverse task is to identify model parameters whose forward-modelled observables best match the data, casting estimation as an optimisation or statistical inference problem. Practical formulations therefore specify a misfit or likelihood function, choose a model parameterisation (layered profiles, finite‑element meshes, modal bases, etc.), and adopt numerical solution strategies such as gradient-based optimisation, Monte Carlo sampling or regularized least squares. Because the mapping from parameters to observables is typically non‑unique and ill‑posed, inversion requires regularisation (e.g. smoothing, bounds, damping), incorporation of prior geological or engineering information, and constraints from independent measurements to produce physically plausible solutions.
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Sensitivity and resolution analysis—via the forward-model Jacobian or sensitivity kernels—identifies which aspects of the model (for example shallow versus deep S‑wave velocity, layer thicknesses or stiffness contrasts) are most responsible for features in dispersion and modal data; these diagnostics inform parameterisation, survey design and uncertainty assessment. Equally important are data‑processing and observational choices: frequency bandwidth, spatial sampling of arrays, signal‑to‑noise ratio and the particular observables extracted (complete dispersion branches versus isolated picks, quality of modal‑shape estimation) determine the information content available to the inversion and hence the achievable resolution of S‑wave velocity and stiffness.
Robust interpretation therefore couples inversion with explicit uncertainty quantification and validation. Synthetic tests, posterior parameter distributions or trade‑off curves, comparison with independent borehole, geotechnical or structural measurements, and testing model predictions against withheld or cross‑validated noise data help to reveal non‑uniqueness, quantify confidence, and ensure that updated models are reliable and useful for ground‑motion and civil‑engineering applications.
Material needed
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Seismic acquisition for ambient-noise surveys is fundamentally simple in hardware: a ground-motion sensor coupled to a digitizer that converts analog motion into time‑stamped digital records suitable for analysis. The number and arrangement of sensors depend on the method — single‑station deployments suffice for spectral and HVSR analyses, whereas array techniques require multiple, often three or more, colocated sensors arranged to sample wavefield coherence. Three‑component (3C) sensors, recording one vertical and two orthogonal horizontal channels, are the norm because they capture the full vector motion; single‑component instruments are used only in specific, limited applications.
Instrument selection must be driven by the target frequency band and expected amplitudes. Near‑surface ambient noise typically contains very small amplitudes at low frequencies, so velocimeters with low corner frequencies are preferred; field practice commonly employs sensors with corner frequencies below ≈0.2 Hz for such ground measurements. Conventional geophones (typical corner ≈4.5 Hz) and many accelerometers lack the sensitivity at these low frequencies and are therefore inadequate when energy below ~0.2 Hz is important. By contrast, measurements on built structures generally involve larger amplitudes and higher frequencies, allowing the use of accelerometers or velocimeters with higher corner frequencies; nevertheless, simultaneous ground reference recordings at selected points may still require more sensitive, lower‑corner instruments.
For coherent multi‑station analysis, all recording channels must share a common time base except in single‑station experiments. Practical synchronization approaches include a GPS clock at each station, issuing a common remote start signal, or using a single digitizer that records multiple sensors simultaneously. Finally, accurate knowledge of sensor positions is necessary to the degree demanded by the chosen technique: coarse geometries can be recorded by manual distance measurements, while rigorous spatial registration requires differential GPS or equivalent high‑precision positioning.
Ambient vibration (seismic noise) methods provide a cost-effective, non-destructive means of site characterization that is particularly well suited to densely built or otherwise sensitive areas because they do not require active sources or boreholes. Even very small datasets can yield valuable constraints: single three-component recordings analyzed with Horizontal-to-Vertical Spectral Ratio (HVSR) methods rapidly indicate site resonance frequencies and relative amplification, while array-based surface-wave analyses commonly recover Rayleigh-wave dispersion curves that supply frequency-dependent phase velocities for constraining shear‑wave velocity profiles. These approaches are routinely used to estimate engineering parameters such as Vs30, which are central to seismic site classification and ground‑motion prediction.
However, the method suite has clear limitations. The maximum investigation depth is not intrinsic to the technique but is governed by array aperture and by the spectral content and signal-to-noise ratio of ambient energy; a lack of long‑period noise precludes imaging of deeper structure. Spatial resolution and the onset of aliasing are controlled by sensor spacing and array geometry: inadequate sampling or poorly designed layouts reduce the range of unaliased wavenumbers and thus the resolvable wavelengths and depths. Interpretation is further complicated by the heterogeneous nature of the ambient wavefield—coexisting Rayleigh and Love waves, higher surface‑wave modes, body‑wave contamination and local sources can obscure modal identification and require multi‑component processing or modal separation.
Many processing algorithms additionally assume planar wavefronts and/or horizontally layered (1D) structure. These simplifications break down when energy originates within the array, when azimuthal energy distributions are strongly heterogeneous, or when lateral velocity contrasts are significant; in such cases plane‑wave or 1D inversions can produce biased phase velocities and misleading velocity–depth models. Finally, ambient‑noise inversions are subject to the usual non‑uniqueness and trade‑offs of geophysical inverse problems, limited vertical resolution, and sensitivity to starting models and regularization. Robust interpretations therefore typically rely on auxiliary constraints, joint inversion strategies, or independent borehole/active‑source data to reduce ambiguity.