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Seismic noise

Seismic noise refers to the continuous, low-amplitude vibrations of the Earth's surface generated by a diverse array of natural and anthropogenic sources, often interfering with the detection of targeted seismic signals such as those from earthquakes or controlled surveys.^[1] These vibrations, typically ranging from millihertz to several hertz in frequency, arise persistently across the globe and can be impulsive, transient, or stationary in nature.^[2] Natural sources dominate much of the seismic noise spectrum, including ocean waves that produce primary microseisms (0.04–0.17 Hz) through direct seafloor interactions and secondary microseisms (0.08–0.34 Hz) via nonlinear wave interactions, as well as atmospheric phenomena like storms, wind, and thunderstorms that generate lower-frequency hums (0.3–20 mHz) and higher-frequency disturbances (0.02–2.5 Hz). Volcanic activity contributes tremors (1–9 Hz) and eruption-related signals (0.01–3 Hz), while other terrestrial events such as mass movements like landslides (>10 Hz) and icequakes (1–20 Hz) add to the background. Anthropogenic sources, often termed cultural noise, include traffic and industrial activities (>1 Hz), explosions such as mining blasts (>10 Hz), and controlled operations like airguns (10–200 Hz) or wind turbines (0.9–6.9 Hz onshore, 30–1000 Hz offshore). Although traditionally viewed as a contaminant in active seismic exploration, seismic noise has revolutionized passive seismology by serving as a natural illumination source for subsurface imaging and monitoring. Techniques like ambient noise tomography use cross-correlations of noise recordings to retrieve Green's functions and map shear-wave velocities, revealing structures from crustal depths to mantle discontinuities (e.g., at 410 km and 660 km).^[1] Other methods, such as the horizontal-to-vertical spectral ratio (HVSR), exploit noise to estimate overburden thickness and site resonance, aiding in earthquake hazard assessment and geothermal exploration.^[4] Coda wave interferometry further enables real-time monitoring of velocity changes in dynamic environments like volcanoes and landslides, detecting precursors to events such as pre-eruptive inflation or structural collapses.^[1]

Fundamentals

Definition and Overview

Seismic noise, often referred to as ambient seismic noise, encompasses the continuous, low-amplitude ground motions arising from a variety of natural and anthropogenic processes, excluding targeted seismic signals from sources such as earthquakes, explosions, or active seismic surveys. These vibrations represent the background seismic field recorded by seismometers worldwide, providing a persistent signal that permeates the Earth's crust and upper mantle. Unlike the transient signals from active seismology, seismic noise offers a passive, omnipresent resource for probing subsurface structures. A critical distinction exists between seismic noise, which comprises actual geophysical waves propagating through the Earth due to external excitations, and instrumental or processing noise, which originates from the inherent limitations of recording equipment, such as thermal fluctuations in sensors or electronic artifacts in data handling. Ambient seismic noise is characterized by its random, stochastic nature and can be quantified using models like the New High Noise Model and New Low Noise Model developed by the U.S. Geological Survey, which delineate the global range of background levels across frequencies. This separation is essential for accurate data interpretation, as instrumental noise dominates in ultra-quiet environments or at extreme frequencies, potentially masking true geophysical signals.^[5] At the heart of exploiting seismic noise lies ambient noise interferometry, a technique that reconstructs the Green's function—the response to an impulsive source—by cross-correlating prolonged recordings of noise between pairs of stations. This method leverages the principle that noise fields, under certain conditions of equipartitioning, approximate a diffuse wavefield, allowing the emergence of coherent wave propagation information akin to active-source surveys. Seminal demonstrations showed that broadband Rayleigh waves could be retrieved from such correlations, even without knowledge of noise sources.^[6] Building on this, noise tomography utilizes the interferometrically retrieved Green's functions to image the Earth's interior passively, inverting phase or group velocities of surface waves to map shear-wave speed variations in the crust and uppermost mantle. This approach has enabled high-resolution crustal models, particularly in regions with dense seismic networks, bypassing the logistical challenges of active-source experiments. By the mid-2000s, noise tomography had transitioned from theoretical concept to practical tool, revolutionizing passive seismology.^[7] The perception of seismic noise has undergone a profound shift since the late 20th century. Initially regarded as mere interference to be filtered out in exploration geophysics—as articulated in early interferometry theories from the 1960s—it was reconceptualized post-2000 as a exploitable resource through advances in correlation techniques. This evolution, driven by computational power and array deployments, marked the 2000s as a turning point, with noise-based methods now integral to global Earth imaging and monitoring efforts.

Sources

Seismic noise arises from a variety of natural and anthropogenic sources that generate vibrations in the Earth's crust through different physical mechanisms. Natural sources dominate the low-frequency spectrum, primarily through interactions between the ocean, atmosphere, and solid Earth. The primary microseism is generated by the direct pressure exerted by ocean waves on the seafloor, particularly near coastal regions where waves interact with shallow bathymetry, producing seismic waves in the frequency range of approximately 0.05–0.12 Hz.^[8] The secondary microseism, the most energetic component of ambient seismic noise, results from nonlinear interactions between opposing ocean waves of similar frequencies, often along coastlines or in deep ocean areas during storms, leading to body force excitations at roughly double the ocean wave frequency, around 0.1–0.25 Hz.^[2] Additional natural contributions include the infrasound hum, caused by long-period ocean infragravity waves and atmospheric pressure fluctuations that couple into the solid Earth, manifesting in the 0.003–0.03 Hz band.^[2] Wind-induced tilts, arising from atmospheric pressure variations that deform the ground surface, further contribute to noise at very low frequencies, typically 0.01–0.05 Hz, with high coherence to local wind patterns.^[2] Anthropogenic, or cultural, sources of seismic noise primarily stem from human activities and are most prominent in the 1–10 Hz frequency range. These include vibrations from traffic on roads and railways, operations of industrial machinery, urban construction activities, and controlled explosions such as those used in mining or demolition, which transmit elastic waves through the ground via surface coupling or direct impact.^[9] Such sources are localized and intermittent but can significantly elevate noise levels in populated or industrial areas, often exceeding natural background in urban environments.^[10] Ocean-atmosphere interactions represent the dominant global sources of seismic noise, particularly the microseisms, as storm-generated ocean waves provide the primary excitation mechanism across much of the planet. These interactions exhibit clear seasonal variations, with microseism amplitudes strengthening during winter months in each hemisphere due to increased storm activity and wave heights in the respective stormy seasons. Rare natural sources, such as volcanic tremors from fluid movement within magmatic systems or glacial quakes triggered by iceberg calving and ice fracturing, can also produce persistent, noise-like seismic signals, though these are site-specific and less ubiquitous than oceanic origins.^[11] A notable quantitative example of secondary microseism dominance occurs during major storms, where amplitudes can peak dramatically, contributing up to 90% of the global seismic noise in the 0.1–0.25 Hz band due to enhanced wave interference.

Physical Characteristics

Frequency Content and Amplitude

Seismic noise spans a wide frequency range, from infrasonic millihertz levels to tens of hertz, with distinct bands reflecting different dominant contributions. The long-period band, known as seismic hum, covers frequencies below approximately 30 mHz and arises from large-scale ocean and atmospheric disturbances. The microseism band extends from 0.05 to 0.5 Hz, primarily driven by ocean wave interactions that generate body and surface waves. Cultural noise dominates the 1–20 Hz range, stemming from anthropogenic activities like transportation and machinery, while high-frequency noise above 20 Hz originates from localized sources such as nearby traffic or industrial vibrations.^[2]^[12] The amplitude of seismic noise, expressed as ground velocity, generally falls within 10^{-9} to 10^{-4} m/s, encompassing root-mean-square or peak values across typical recording conditions. This range reflects the weak, persistent nature of background vibrations, with lower values (around 1 nm/s) common in quiet long-period bands and higher values (up to 100 μm/s) in energetic microseism or cultural noise intervals. Amplitudes are notably elevated in coastal regions compared to inland areas, particularly in the microseism band, due to stronger coupling with ocean-generated waves near shorelines.^[13]^[14] A fundamental metric for quantifying seismic noise is the power spectral density (PSD), which describes the distribution of energy as a function of frequency. For displacement records, the PSD is computed as

\mathrm{PSD}(f) = \frac{|U(f)|^2}{T},

where U(f) is the Fourier transform of the displacement time series u(t) and T is the duration of the record. This one-sided PSD provides a stable estimate of noise power in units of (m)^2/Hz, enabling comparisons of spectral characteristics across stations and conditions.^[15] To standardize noise assessments, global reference models were established by Peterson in 1993 using data from over 2,000 stations worldwide. The New High Noise Model (NHNM) outlines the upper envelope of observed noise, capturing maximum levels from cultural and microseismic sources, while the New Low Noise Model (NLNM) defines the quietest conditions, often achieved at remote sites with optimal vaults. These models, plotted as acceleration PSD in dB relative to 1 (m/s²)²/Hz, span from 0.001 to 100 Hz and serve as benchmarks for evaluating seismograph site quality and instrument self-noise.^[16] Noise levels are conventionally reported in decibels (dB) with respect to acceleration to facilitate instrument-independent comparisons. The conversion from displacement PSD to this scale uses the relation

\mathrm{NL} = 10 \log_{10} \left( \mathrm{PSD}(f) \cdot \frac{f^4}{(2\pi)^4} \right),

where PSD(f) is in (m)²/Hz and f is frequency in Hz; the f^4 / (2\pi)^4 term accounts for the double differentiation to acceleration in the frequency domain. This formulation aligns with Peterson's models, where NLNM values range from about -200 dB at 0.1 Hz to -120 dB at 10 Hz, providing a quantitative framework for noise analysis.^[13]^[16]

Spatial and Temporal Variations

Seismic noise exhibits significant spatial variations influenced by local environmental and anthropogenic factors. In urban areas, noise levels are markedly higher, particularly in the 1–20 Hz range, due to cultural sources such as traffic and industrial activities, with root-mean-square values often exceeding 50 dB compared to non-urban sites.^[17] Coastal regions experience elevated microseismic noise from ocean wave interactions, showing increased power at periods around 1 s relative to inland areas.^[18] In contrast, quiet sites in arid or remote regions, such as the Intermountain West of the United States with crystalline bedrock and low population density, record the lowest noise levels, particularly at short periods (0.2–1 s), benefiting from minimal anthropogenic interference.^[18] Additionally, noise displays azimuthal dependence, as directional ocean swells generate microseisms with propagation patterns aligned to swell azimuths, leading to anisotropic noise fields observable in ocean-bottom recordings.^[19] Temporal variations in seismic noise occur across multiple scales, driven by periodic human and natural forcings. Diurnal cycles are prominent in populated regions, where short-period noise (0.1–1 s) peaks during daytime hours by up to 15 dB due to heightened human activity, such as traffic, while remote sites show negligible daily fluctuations.^[20] Seasonal patterns are dominated by microseismic enhancements from storm activity, with noise power increasing by 10–20 dB during winter months in the Northern Hemisphere, as extratropical cyclones generate stronger ocean waves.^[21] Over longer timescales, climate trends contribute to gradual increases in microseismic intensity, linked to rising ocean wave energy from global warming, with observed multi-decadal amplifications in secondary microseism power.^[22] Local site effects further modulate noise levels through geological amplification. Soft, unconsolidated sediments, such as those in coastal plains or sedimentary basins, can increase low-frequency noise (periods <5 s) by over 20 dB via impedance contrasts and resonance, exacerbating signal-to-noise ratios compared to bedrock sites.^[18] This amplification is particularly pronounced in water-saturated layers, where pressure-induced deformations enhance horizontal components.^[23] Global models from networks like the Incorporated Research Institutions for Seismology (IRIS) and the United States Geological Survey (USGS) reveal latitude-dependent microseism peaks, with higher amplitudes at mid-to-high latitudes due to intensified storm tracks in winter seasons.^[18] These maps, derived from broadband station data, highlight equatorial stability contrasted with polar enhancements from cryospheric interactions, such as sea ice modulation delaying microseism peaks by 1–2 months post-minimum ice extent.^[24] Statistical measures, including probability density functions (PDFs) of power spectral densities, quantify noise variability, often revealing log-normal distributions for microseismic amplitudes that reflect the stochastic nature of wave interactions and site-specific influences.^[25] These PDFs enable assessment of noise percentiles, showing tighter distributions at quiet sites (e.g., 4–5 dB spread between 10th and 90th percentiles in microseism bands) versus broader variability in noisy environments.^[15]

Historical Development

Early Observations and Civil Engineering Applications

Early observations of seismic noise trace back to the late 19th and early 20th centuries, when seismologists began documenting persistent low-amplitude ground vibrations unrelated to earthquakes. In the 1910s, Beno Gutenberg conducted pioneering studies linking microseisms—small, continuous seismic tremors—to ocean wave activity, notably correlating surf noise along the Norwegian coast with recordings at the Göttingen observatory in 1910.^[26] These microseisms, typically in the 0.05–0.3 Hz range, were recognized as natural background signals originating from storm-generated sea waves interacting with coastlines. By the 1920s, advancements in instrumentation, such as those developed by Hugo Benioff, enabled the recording of anthropogenic or "cultural" noise in urban environments, including vibrations from traffic, machinery, and industrial activities that contaminated seismic traces in city-based observatories.^[27] In civil engineering contexts, seismic noise transitioned from a mere observational curiosity to a practical tool for vibration monitoring during the 1960s and 1970s, particularly for large infrastructure like dams and bridges. Engineers deployed accelerometers to assess ambient and operational vibrations at sites such as Hoover Dam, where early strong-motion installations from the 1930s were expanded to capture noise-induced responses, aiding in the evaluation of structural stability under everyday loads.^[28] Array-based methods emerged around this time for site response assessment, using multiple seismometers to analyze noise propagation and estimate soil amplification effects at construction sites, helping to predict how local geology might exacerbate vibrations during dynamic events.^[29] These techniques prioritized passive recordings to avoid the disruptions of active sources like explosives. A key milestone in this era was the development of the horizontal-to-vertical spectral ratio (HVSR) technique during the 1970s to 1980s, initially proposed by Nogoshi and Igarashi in the early 1970s and popularized by Nakamura in the late 1980s, for estimating resonance frequencies in building foundations using ambient noise.^[30] HVSR involves computing the ratio of horizontal to vertical components of noise spectra to identify site-specific fundamental frequencies, typically 0.5–10 Hz, which inform foundation design to mitigate resonance with expected vibrations. Early applications focused on urban sites where cultural noise dominated, providing a cost-effective alternative to invasive testing. Post-World War II, engineers recognized seismic noise primarily as interference in active geophysical surveys, yet began leveraging passive noise recordings for structural integrity checks. The 1971 San Fernando earthquake (magnitude 6.6) marked a pivotal event, spurring the use of noise-based assessments for post-event damage evaluation in affected structures. Ambient vibration surveys of buildings revealed shifts in modal frequencies attributable to cracking and stiffness loss, guiding retrofit decisions and highlighting noise's utility in non-destructive integrity monitoring.^[31] This event underscored the dual role of seismic noise—as both a challenge in signal detection and a resource for engineering diagnostics—shaping subsequent practices in vibration control for civil infrastructure.

Scientific Advancements in Geophysics

During the 1980s and 1990s, foundational concepts from earlier decades were adapted to transform seismic noise from an interference into a geophysical asset, particularly through spatial autocorrelation techniques for surface-wave analysis. Keiiti Aki's 1957 spatial autocorrelation (SPAC) method, which estimates phase velocities of surface waves by correlating ambient noise records from an array of stations, saw renewed application in these periods for shallow crustal imaging and site characterization.^[32] Complementing this, Jon Claerbout's 1968 conjecture posited that ambient noise could serve as virtual sources, with the autocorrelation of transmission responses approximating the impulse reflection response of a layered medium, laying theoretical groundwork for noise-based wavefield reconstruction. These ideas gained traction in geophysics during the late 20th century, enabling passive monitoring without active sources and shifting perceptions of noise toward its utility in deriving velocity structures. The 2000s marked a revolutionary advancement with empirical demonstrations and theoretical formalizations that established ambient noise as a reliable tool for global-scale imaging. Nikolai Shapiro and Michel Campillo's 2004 study demonstrated the extraction of coherent broadband Rayleigh waves (periods 7–60 s) from cross-correlations of one month of continuous seismic noise recorded across southern California, revealing dispersion characteristics comparable to earthquake-based measurements.^[33] This breakthrough spurred the development of ambient noise tomography (ANT), a technique for mapping crustal and upper-mantle shear velocities by inverting noise-derived Green's functions. Kees Wapenaar's 2004 interferometry theory provided a rigorous elastodynamic framework, showing that the Green's function between two receivers could be retrieved exactly from cross-correlations under diffuse noise illumination, unifying prior acoustic approximations. Building on this, Gideon Bensen and colleagues in 2007 processed two years of USArray Transportable Array data to generate the first continent-scale ANT model, yielding high-resolution group velocity maps (8–30 s) that illuminated tectonic features like the North American craton.^[34] In the 2010s, advancements extended noise interferometry to body waves, enhancing resolution for deeper Earth structures and integrating it with traditional seismology. A pivotal 2012 study by Piero Poli and co-authors retrieved P- and S-body waves from short-period (1–10 s) noise correlations over interstation distances up to 3000 km in Europe, demonstrating emergence of causal body-wave signals despite surface-wave dominance.^[35] This body-wave interferometry enabled probing of the upper mantle and core-mantle boundary, complementing surface-wave ANT for full waveform inversion. Further progress involved hybrid approaches combining noise-derived paths with earthquake data, improving global tomography models by filling coverage gaps in passive arrays. By the 2020s, machine learning innovations have refined noise utilization, particularly for source separation in complex environments. Recent 2023 research applied convolutional autoencoders—unsupervised neural networks trained to reconstruct clean signals from noisy inputs—to denoise mine microseismic events in low-amplitude recordings dominated by cultural and oceanic noise.^[36] These methods automate microseism filtering, enhancing ANT reliability in urban or industrial settings and paving the way for real-time geophysical monitoring. As of 2025, further advancements include hybrid AI-seismic models for improved real-time velocity change detection in volcanic regions.^[37]

Methods and Techniques

Data Acquisition and Equipment

Data acquisition for seismic noise relies on sensitive instruments capable of capturing low-amplitude ambient vibrations across a wide frequency range. Broadband seismometers, such as the Streckeisen STS-1, are commonly used for low-frequency components (typically 0.005–50 Hz), providing high sensitivity to microseisms and other long-period noise sources with self-noise levels below the new low-noise model (NLNM) in the 0.1–10 Hz band.^[38]^[39] Short-period geophones (e.g., 4.5–10 Hz natural frequency) complement these for higher-frequency cultural noise, while micro-electro-mechanical systems (MEMS) accelerometers enable dense urban deployments due to their low cost (under $150 per unit) and compact size.^[40]^[41] Deployment strategies vary by objective: single-station setups using a three-component broadband seismometer are standard for horizontal-to-vertical spectral ratio (HVSR) analysis of site resonance, requiring minimal infrastructure.^[4] For array-based tomography, configurations typically involve 10–100 stations spaced 1–10 km apart to resolve subsurface structure, with recording durations of 1–30 days ensuring stable noise correlations. Essential equipment includes geophones or accelerometers connected to 24-bit analog-to-digital converters (ADCs) for high dynamic range (up to 144 dB), GPS receivers for precise timing synchronization (<1 μs accuracy), and solar power systems for remote sites to support continuous operation.^[42]^[43] Noise floors of modern sensors are targeted below 1 ng/√Hz to detect ambient signals above instrumental limits.^[38] Best practices emphasize site selection in low-noise environments, such as away from roads, railways, or industrial areas to minimize cultural interference, often guided by preliminary noise surveys.^[44]^[45] GPS synchronization ensures accurate cross-correlation across arrays, while data are stored in standardized formats like SEED or MiniSEED for interoperability and metadata inclusion.^[46]^[47] Recent advances include distributed acoustic sensing (DAS), which repurposes existing fiber-optic cables as dense sensor arrays spanning kilometers, sampling seismic noise every 2–10 m without deploying individual sensors.^[48] This technology that emerged in the 2010s with significant advancements in the 2020s reduces deployment costs by leveraging "dark" fibers, enabling km-scale monitoring at a fraction of traditional array expenses while maintaining broadband sensitivity for ambient noise interferometry.^[49]^[50]

Processing and Interferometry

Processing seismic noise data involves several key steps to transform raw recordings into empirical Green's functions that approximate wave propagation between receiver pairs. Preprocessing begins with removing the instrument response to convert digital counts into physical units such as velocity or displacement, typically using metadata from formats like SEED or StationXML.^[34] This step ensures that the recorded signals reflect true ground motion rather than sensor artifacts. Temporal normalization follows to mitigate amplitude variations and suppress outliers; common techniques include one-bit clipping, which signs the waveform to ±1, and phase-weighted stacking, which emphasizes coherent arrivals by weighting based on phase coherence across multiple correlations.^[34] The core of noise interferometry is computing the cross-correlation function (CCF) between pairs of noise recordings from stations i and j. The CCF is defined as

\text{CCF}(\tau) = \int u_i(t) u_j(t + \tau) \, dt,

where u_i(t) and u_j(t) are the preprocessed velocity records, and \tau is the lag time. Under suitable conditions, this CCF approximates the Green's function, treating one station as a virtual source for the other.^[33] To enhance signal-to-noise ratio, correlations are stacked over extended periods, such as daily or monthly intervals comprising 100 to 1000 individual correlations, which averages out incoherent noise while reinforcing deterministic arrivals.^[34] Frequency-time analysis (FTAN) is then applied to the stacked CCFs to extract dispersion curves, identifying group or phase velocities as a function of frequency by measuring the energy maxima in the frequency-time domain.^[34] The theoretical foundation of noise interferometry relies on the equipartitioning assumption, where the ambient noise field is isotropic, meaning energy is equally distributed across all propagation directions and wave modes. This condition allows retrieval of surface waves, particularly Rayleigh waves, from the causal and acausal parts of the CCF, enabling the reconstruction of inter-station wave propagation without active sources.^[33] Seminal demonstrations showed that broadband Rayleigh waves emerge from correlations of global seismic noise across distances of 100 to 2000 km, validating the approach for crustal-scale imaging.^[33] Recent advancements address limitations in traditional processing, such as coherent noise from directional sources. Machine learning techniques, including generative adversarial networks (GANs), have been developed for denoising, where a generator produces clean seismograms from noisy inputs and a discriminator evaluates realism, effectively removing coherent noise like cultural interference while preserving signal integrity.^[51] For handling directional noise, beamforming methods estimate noise source distributions by scanning plane-wave arrivals across possible back-azimuths and slownesses, allowing selective stacking of correlations from desired directions to mitigate anisotropy effects.^[52]

Inversion and Modeling Approaches

Inversion approaches for seismic noise data primarily aim to derive subsurface models, such as shear-wave velocity (Vs) profiles, from processed observables like surface wave dispersion curves extracted via interferometry. Linear inversion techniques are commonly employed for their computational efficiency in obtaining 1D Vs models from Rayleigh or Love wave dispersion data. These methods assume a linearized relationship between model parameters and data, often using least-squares optimization to fit observed dispersion curves to synthetic ones generated via forward modeling. A widely used tool is the Surf96 code, which performs linear least-squares inversion to estimate layered Vs profiles, incorporating constraints on layer thicknesses and velocities to stabilize solutions. For instance, Surf96 has been applied to ambient noise-derived dispersion data to resolve near-surface Vs structures in sedimentary basins. To address uncertainties inherent in these linear approximations, Bayesian frameworks integrate prior information on model parameters, enabling probabilistic quantification of posterior distributions and resolution of non-uniqueness through Markov chain Monte Carlo sampling. Such approaches have been used to invert ambient noise surface wave dispersion maps, yielding uncertainty estimates for crustal Vs models across continental scales. Nonlinear inversion methods extend these capabilities to handle more complex, full-waveform fitting problems where linear assumptions fail, particularly for 3D structures or multimodal wave propagation. The neighborhood algorithm, a derivative-free global optimization technique, explores the model space by sampling Voronoi cells to identify ensembles of good-fitting models, mitigating local minima traps in highly nonlinear problems. It has been applied to invert phase velocity maps from ambient noise tomography into depth-dependent Vs profiles, revealing shallow crustal anomalies. Similarly, Monte Carlo methods, including Markov chain Monte Carlo variants, stochastically sample the posterior distribution to fit full waveforms from noise correlations, providing robust uncertainty quantification for 1D to 3D Vs models. For large-scale 3D imaging, adjoint tomography iteratively updates models by minimizing waveform misfits using adjoint-state methods, which compute sensitivity kernels for efficient gradient-based optimization; this has been adapted to ambient noise data to resolve fine-scale lithospheric structures, such as fluid-bearing fractures, by leveraging differential misfits between observed and predicted correlations. Multi-model strategies, such as ensemble modeling, combine outputs from deterministic linear inversions with stochastic nonlinear ones to produce comprehensive representations of subsurface variability, often integrating ambient noise data with active-source observations for enhanced resolution. These approaches generate large ensembles of plausible models, weighted by data fit and prior constraints, to capture epistemic uncertainties and improve reliability in heterogeneous media. Recent studies have demonstrated this by jointly inverting noise-derived dispersion curves with active-source data such as MASW, yielding hybrid Vs models that resolve near-surface layering with reduced trade-offs between parameters.^[53] Model updating in these inversions involves iterative refinement to align predicted Green's functions—approximated from noise cross-correlations—with observations, ensuring progressive improvement in data fit while addressing inherent non-uniqueness. Regularization techniques, such as Occam's inversion, enforce smoothness by minimizing a combined data misfit and model norm, favoring the simplest model consistent with the data. This is formalized through an objective function that balances fidelity to observations and model complexity:

J(\mathbf{m}) = \|\mathbf{d}_\mathrm{obs} - \mathbf{G}(\mathbf{m})\|^2 + \lambda \|\mathbf{m}\|^2

where \mathbf{d}_\mathrm{obs} are the observed dispersion data, \mathbf{G}(\mathbf{m}) is the forward operator modeling synthetic data for model parameters \mathbf{m}, and \lambda is a regularization parameter controlling the trade-off. Such iterative schemes have been pivotal in updating 1D profiles to 3D crustal models from noise data, incorporating damping to stabilize against noise artifacts.

Applications

Subsurface Characterization

Seismic noise tomography, particularly ambient noise tomography (ANT), enables the construction of velocity models by extracting empirical Green's functions from continuous noise recordings to image shear-wave velocity (Vs) profiles in the crust. This approach has been applied to resolve crustal structures at depths of 10-50 km, providing insights into lithospheric variations without active sources. For instance, probabilistic ANT has revealed detailed Vs anomalies in the Eastern European crust, highlighting tectonic boundaries and sediment-basement interfaces.^[54] In site characterization, the horizontal-to-vertical spectral ratio (HVSR) method analyzes ambient noise to estimate sediment thickness overlying bedrock, typically ranging from 1 to 500 m, by identifying resonance frequencies associated with impedance contrasts. This technique is widely used for local Vs profiling in sedimentary basins, aiding in the assessment of site amplification effects. Geological applications of seismic noise include fault mapping through reflected surface-wave analysis from dense arrays, which delineates shallow fault zones, and basin delineation via noise-derived velocity models that outline sediment fill geometries. A notable case study is the 2024 probabilistic ANT model of the Eastern European crust, derived from noise arrays across multiple stations, which mapped crustal thickness variations and fault-related discontinuities with enhanced resolution.^[55]^[56]^[54] In hydrogeology, low-frequency ambient noise (below 1 Hz) facilitates imaging of aquifers by monitoring velocity perturbations linked to groundwater storage and flow, with cross-correlations revealing Vs changes indicative of saturation levels. This has been demonstrated in characterizing the Floridan aquifer system, where noise interferometry mapped hydraulic boundaries and inferred permeability contrasts from velocity gradients. For mineral exploration, passive ANT detects ore bodies by imaging Vs anomalies associated with mineralization, as shown in skarn-type Cu-Fe deposits where noise tomography outlined low-velocity zones corresponding to ore extents.^[57]^[58] Resolution in seismic noise imaging is fundamentally wavelength-dependent, limited to approximately λ/2, where λ = Vs / f, with Vs as shear-wave velocity and f as frequency; for example, at 0.1 Hz and Vs = 3 km/s, this yields a horizontal resolution of about 15 km in crustal applications. This constraint arises from the diffusive nature of noise-derived surface waves, emphasizing the need for low-frequency content to probe deeper structures while dense arrays improve lateral detail.^[59]

Structural Health Monitoring

Seismic noise, encompassing ambient vibrations from sources such as traffic, wind, and microseisms, enables operational modal analysis (OMA) for identifying key dynamic properties of civil infrastructure like bridges and towers. In OMA, sensors capture these natural excitations to estimate modal parameters, including natural frequencies and damping ratios, without requiring artificial forcing, allowing continuous assessment under normal operating conditions. For instance, studies on highway bridges have demonstrated that ambient noise correlations can reconstruct Green's functions akin to active seismic surveys, facilitating precise modal identification that aligns closely with finite element predictions. This approach has been applied to structures like the Z24 Bridge in Switzerland, where noise-based OMA revealed frequency shifts indicative of progressive damage from environmental factors. Damage detection leverages variations in seismic noise correlations before and after seismic events to pinpoint structural alterations. By comparing pre- and post-event noise interferograms, researchers can quantify velocity changes or decorrelation times that signal cracks or stiffness reductions, often using coda wave interferometry to enhance sensitivity to subtle damages. Such methods provide early warnings for maintenance, as seen in European bridge networks where noise-based monitoring detected event-induced changes in modal damping. In urban settings, dense sensor arrays exploit seismic noise for real-time monitoring of high-rise structures, particularly for wind-induced responses in cities like Tokyo. For example, ambient vibration tests on a 15-story office building in Tokyo identified fundamental frequencies around 0.5-1 Hz, correlating wind loads with sway modes to validate damping systems and ensure occupant comfort during gusts. These networks enable city-scale deployments, integrating data from multiple skyscrapers to model collective responses under varying environmental loads. Advanced techniques, such as time-frequency analysis of noise signals, further support crack detection by isolating non-stationary features like frequency modulations associated with damage propagation. The smoothed pseudo-Wigner-Ville distribution (SPWVD), applied to high-rise buildings, has resolved resonance shifts as small as 0.1 Hz, linking them to localized cracks via wavelet transforms. Integration with finite element models enhances this by updating parameters like stiffness matrices to match observed noise-derived modes, as demonstrated in girder bridge studies where model errors were reduced by over 20% post-calibration. This hybrid approach refines predictive simulations for long-term health assessment. The practical benefits of seismic noise in structural health monitoring include non-invasive testing during full operation, minimizing disruptions and costs compared to traditional methods that require closures. By enabling continuous data collection, it reduces downtime for infrastructure like bridges, potentially extending service life through proactive interventions.

Emerging and Interdisciplinary Uses

Recent advancements in machine learning have integrated ambient seismic noise analysis to detect precursors for earthquake forecasting. In 2024, bio-inspired models mimicking otolith sensitivity in fish were applied to filter ambient seismic noise, identifying subtle pre-seismic shifts with 98% accuracy in predicting events 6 to 45 days in advance.^[60] These models distinguish anomalous vibrations from background noise, enabling real-time fault monitoring by processing long-term datasets spanning 12 to 15 years. Additionally, waveform envelope techniques have enhanced recognition of foreshock patterns in seismic sequences, where sawtooth anomalies in ground velocity envelopes precede major events, with 91% of analyzed foreshocks showing distinct signatures compared to non-foreshocks.^[61] Such approaches leverage noise interferometry to isolate precursors, improving probabilistic forecasts in regions with frequent seismicity. In environmental monitoring, seismic noise generated by ocean waves has enabled forecasting of wave conditions and associated storm impacts. A 2024 study demonstrated that mid-frequency seismic noise spectra (0.15–2 Hz) at underground sites can be predicted up to 16 days ahead using sea weather forecasts from nearby buoys, achieving strong correlations with wave height and period during events like Storm Bella in December 2020.^[62] This method employs multivariate linear regression on noise data to anticipate elevated noise levels from intensifying storms, aiding in the planning of noise-sensitive operations such as gravitational wave detection. For volcanic unrest, ambient noise tomography has illuminated subsurface dynamics at sites like Campi Flegrei, Italy. In a 2024 analysis, joint interpretation of ambient noise and earthquake tomography revealed a high-velocity body at 3 km depth beneath Pozzuoli and Solfatara, rich in fluids and controlling ongoing uplift and seismicity since 2022, with low-velocity zones indicating migration pathways along resurgent block edges.^[63] Applications in social sciences extend seismic noise to urban planning and health assessments. Urban seismic networks map ground vibrations from anthropogenic sources, aiding in urban planning and seismic risk assessment in densely populated areas.^[64] In archaeology, shallow ambient noise tomography detects near-surface cavities and structures without invasive methods. Links to climate science utilize long-term seismic noise trends to track cryospheric changes. Global microseismic hum studies from 2023 show increasing ocean wave energy at 0.27% per year since the late 20th century, reflecting storm intensification tied to warming oceans and contributing to sea-level rise projections.^[65] In Greenland, seismic noise autocorrelations monitor ice sheet mass balance, revealing seasonal velocity changes lagging surface melt by 3 months and a 2013 transition from rapid loss (345 Gt/year) to stabilization (222 Gt/year), informing sea-level contributions from ice dynamics.^[66] Space applications reinterpret planetary seismic data through noise analogs. A 2024 study of InSight mission recordings on Mars analyzed ambient noise autocorrelations over 966 sols, identifying potential peaks in the 2–4 mHz band consistent with atmosphere-induced free oscillations, though limited by glitches, offering new insights into martian interior structure and noise sources.^[67]

Advantages and Limitations

Key Benefits

Seismic noise methods offer significant cost-effectiveness compared to traditional active seismic techniques, as they rely on passive recording of ambient vibrations without the need for artificial sources like explosives or vibrators, thereby eliminating substantial logistical and material expenses. Studies indicate that this approach can reduce overall survey costs dramatically, often by orders of magnitude, making it particularly viable for large-scale or resource-limited explorations.^[68]^[69] The non-invasiveness of seismic noise acquisition enhances its suitability for sensitive or populated areas, allowing deployment of sensors without ground disruption, heavy machinery, or potential environmental hazards associated with active sources. This enables safe, continuous monitoring in urban settings, protected ecosystems, or infrastructure sites, where traditional methods might be restricted or impractical. Furthermore, the technique's accessibility stems from its ability to operate effectively in inherently noisy environments, leveraging background vibrations from natural or anthropogenic sources to generate usable data year-round, providing persistent baseline information for long-term studies.^[69]^[70] Seismic noise excels in resolving low-frequency structures, offering high-resolution imaging of deep subsurface features up to 100 km or more, where active sources typically attenuate rapidly and fail to penetrate effectively. This capability is crucial for probing crustal and upper mantle dynamics that influence tectonic and volcanic processes. Additionally, the environmental friendliness of these methods contributes to their growing adoption, with a minimal carbon footprint due to reduced energy use and no emissions from source generation, facilitating sustainable global investigations such as the analysis of firn structure in East Antarctica using ambient seismic noise from a 2022–2023 deployment.^[71]

Challenges and Constraints

One major challenge in seismic noise studies arises from data quality issues, particularly due to inhomogeneous noise fields that lead to biased retrieval of Green's functions through cross-correlation. Inhomogeneous distributions of noise sources can distort the estimated empirical Green's functions, resulting in anisotropic retrieval and reduced accuracy for isotropic approximations, as demonstrated in analyses of global noise source distributions. To achieve stable and reliable correlations, long recording durations—often spanning several months—are typically required to ensure convergence of the interferometric signals, mitigating the effects of temporal variability in noise excitation.^[52]^[72] Resolution limits further constrain the applicability of seismic noise methods, with particularly poor performance in imaging body waves or in anisotropic media where directional dependencies complicate wave propagation retrieval. Seasonal variability in microseism amplitudes significantly impacts repeatability, as noise levels in the 1-20 s period band can fluctuate by 10-20 dB between northern hemisphere winter and summer, driven by changes in ocean storm activity and wave generation. These variations introduce inconsistencies in baseline noise models, affecting the robustness of long-term monitoring efforts.^[73]^[21] Computational demands pose substantial logistical barriers, especially for stacking and inversion processes involving large seismic arrays. Processing data from arrays exceeding 1000 stations, such as those in the EarthScope USArray, requires high-performance computing resources to handle the petabyte-scale datasets and perform extensive cross-correlations and tomographic inversions without prohibitive delays. These demands escalate with array density, limiting accessibility for resource-constrained research groups and necessitating advanced parallel computing infrastructures.^[74]^[75] Interpretive uncertainties remain a core limitation, primarily stemming from the non-uniqueness inherent in inversion procedures for surface wave data derived from noise correlations. Multiple velocity models can fit the observed dispersion curves equally well, leading to ambiguities in subsurface structure delineation without additional constraints like well logs or active source data. In urban environments, cultural noise—generated by human activities such as traffic and industry—frequently masks natural seismic signals, dominating the high-frequency band (>1 Hz) at a majority of sites and complicating the isolation of ambient noise for interferometry.^[76]^[77] Emerging challenges are exacerbated by climate change, which alters the spatial and temporal characteristics of noise sources through intensified storm patterns and shifting ocean wave climates. Forecasts indicate that increased storm frequency and severity, particularly in the North Atlantic and Pacific, will elevate microseism amplitudes, potentially disrupting established noise baselines and requiring adaptive recalibration of processing workflows.^[65]^[78]

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