# The physics of seismic noise: A revolution in Earth imaging and monitoring

J. Starke, I. Wienk, N. Bontemps, L. Moreau, E. Larose, Romain Rousseau

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J. Starke, I. Wienk, N. Bontemps, L. Moreau, E. Larose, et al. The physics of seismic noise: A revolution in Earth imaging and monitoring. EPL - Europhysics Letters, 2025, 150 (3), pp.30001. 10.1209/0295-5075/adcbd1. hal-05184049

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# The physics of seismic noise: A revolution in Earth imaging and monitoring

J. STARKE, I. WIENK, R. ROUSSEAU, N. BONTEMPS, L. MOREAU and E. LAROSE

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# The physics of seismic noise: A revolution in Earth imaging and monitoring

J. STARKE, I. WIENK, R. ROUSSEAU, N. BONTEMPS, L. MOREAU and E. LAROSE(a)

Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IRD, UGE, INP, ISTerre - 38000 Grenoble, France

received 24 February 2025; accepted in final form 11 April 2025
published online 12 May 2025

**Abstract** – Ambient seismic noise consists of continuous vibrations randomly excited in time and space, mostly at the Earth's surface, by natural and anthropogenic dynamic phenomena. Noise has long been considered a contaminant of seismic impulse responses from earthquakes or man-made explosions. The deterministic nature of the wave equation, together with the temporal and spatial coherence of seismic waves and the development of massive computing infrastructures, have enabled our ability to turn “noise into signal” and to obtain deterministic images of the Earth's subsurface and its mechanical evolution from these random-like noise records.

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**Introduction.** — Any experimental measurement, or record, of a physical phenomenon, say the response of a system to an excitation, is polluted by unwanted contributions called “noise”. A first family of contributions comes from the measurement apparatus, including at least the electronic noise that naturally results from thermal fluctuations and excitation of atoms and electrons. A second family of “noise” contributions comes from the system itself, either because the system naturally fluctuates (the parameter to read is not constant), or because the system cannot be totally isolated from the environment. In that last case, the system does not only respond to the single controlled excitation but also to a series of external solicitations. For both families, we generally hope that the “signal” that results from the solicited and controlled excitation is much larger than the “noise”, and the “noise” is generally considered as a pollution to the “signal”. The second family of “noise” originating from internal fluctuations or from external excitations may nevertheless reveal extremely informative and valuable insights.

As a simple example, photons coming from the Sun im-
pact surrounding objects randomly in time, space and en-
ergy. They are known to constitute a pollution to many
optical experiments: laser- or astro-physicists are taught
to work in dark rooms. Nevertheless, photons are partially

reflected at the surface of the objects surrounding us, to
finally reach our eyes. Those eyes have not only the abil-
ity to sharply focus on each surface emission detail, but
also average the energy on timescales where intensity is al-
most constant. In this way, random photons are no longer
“noise” but constitute a series of “signals” that allow us
to see.

In acoustics, seismology, and more generally in the physics of mechanical waves, where we have easy access to the phase and amplitude of the wave field in both the time and frequency domains, we will see that similar concepts allow “noise” to be transformed into “signals” that can be used to image and monitor various objects and materials.

**Noise source, source identification, noise propagation.** — Seismic ambient noise is very rich because it results from the convolution between noise sources and the Green’s function of the medium, both of which can exhibit a high degree of complexity. As it propagates, it accumulates information about the geometry and mechanical properties of the Earth’s structure that can be used to image the Earth [1], providing significant knowledge, or at least assumptions, about the different types of noise sources. The study of noise sources also provides insight into the nature and origin of natural and anthropogenic forcing. Noise can be impulsive, transient, or stationary. Depending on their characteristics, noise sources can be used for a variety of applications. For example,

<footnote>(a)E-mail: eric.larose@univ-grenoble-alpes.fr (corresponding author)</footnote>
determining the spatial distribution of impulsive sources provides information about the geometry of geological structures, while monitoring the temporal occurrence of noise provides information about its evolution. Stationary noise, such as primary and secondary microseisms, has been used mainly for noise interferometry to retrieve the Green's function between pairs of sensors (see related section). Other applications include tracking storms and using them to extract bulk seismic waves for imaging the deep Earth [2], tracking anthropogenic activities [3] or using them as an additional way to monitor fault zones [4,5].

The development of noise seismology has coincided with technological advances that have allowed the proliferation of seismic arrays from large global scales to regional (100 km) and local (km) scales. With special array processing [6], noise sources can be studied with high resolution in time and space. Three types of processing families can be distinguished.

- Beamforming-like approaches consist of combining the recordings of an array using delay and sum algorithms. Such algorithms work by scanning through combinations of phase velocities and azimuths and applying the corresponding delays to the signals. The azimuth and velocity that give maximum coherence through the array correspond to the directionality and phase velocity of the seismic noise.

- Waveform inversion approaches consist of generating synthetic waveforms with a numerical model and adjusting the model parameters to minimize a cost function between the synthetics and the data, yielding very fine resolution in geological structures but requiring high computational power (see for instance the recent high-resolution tomography of the Alps [7]).

- Artificial Intelligence (AI) approaches train convolutional neural networks to identify patterns and analyze continuous recordings to extract hidden information. Convolutional neural networks have dramatically improved earthquake catalogs, revealing fault zone structures with much greater clarity [8]. Another example comes from seismology in ice (cryo-seismology), where it is possible to extract thousands of microseismic signals from sea ice and invert their waveforms to monitor ice thickness while simultaneously inverting the position of the sources [9], revealing geophysical forcing associated with tidal effects.

**Stationary waves and resonant effects to reveal the Earth structure and furthermore elastic nonlinearities.** – In the study of seismic noise, stationary waves and resonance effects provide insight into subsurface properties, including layer thickness and material stiffness. Resonance effects occur when the vibrations of ambient noise interact with geological structures, especially boundaries with strong impedance contrasts, to produce standing wave patterns at specific frequencies.

<figure><img src="image_12.png" /><figcaption>Fig. 1: Different experimental settings for monitoring resonance effects. Seismometers S1–S3 enable the use of the H/V-method (see section *The H/V-method*) to track the thickness of sediment layers (S1) or ice layers (S2, S3). At location S3, an underlying cavity modifies the seismic noise wave field, causing an anomalous H/V curve (the vertical vibrations dominate, see section *Resonance frequencies of glaciers*). Seismometer S4 is positioned on a gravitational instability, where the resonance frequencies can be used to monitor structural changes (see section *Resonance frequencies of gravitational instabilities*).</figcaption></figure>

Analyzing these frequencies is critical for imaging the structure of the subsurface: researchers and engineers can characterize features such as sediment layer thickness, water table depth, and glacier thickness using the horizontal-to-vertical (H/V) spectral ratio [10–13]. In addition, monitoring resonant frequency is useful for assessing unstable geologic and man-made structures because changes in stiffness can indicate potential failure risks and resonant effects can reveal how materials respond to stress variations and environmental factors [14–16]. Figure 1 shows various settings in which resonant effects can reveal material properties and geometries.

Standing wave patterns, defined by nodes and antinodes, result from the interference of seismic waves within geologic layers. Their resonant frequencies are determined by the material properties, geometry, and boundary conditions of these layers. In earthquake engineering, for example, structures are designed to account for resonance effects by avoiding alignment with the seismic frequencies of sedimentary basins or by incorporating systems to dissipate energy efficiently [17].

Changes in resonant frequencies can reflect variations in material stiffness or rigidity, often associated with external factors such as increased pore pressure or temperature variations, as well as geometric changes in boundaries (including crack development) [18].

**The H/V-method.** The horizontal-to-vertical spectral ratio (HVSR or H/V) method [19] is a powerful technique for exploring shallow subsurface seismic properties using data from a single 3-component seismic station. In this method, the ratio of the horizontal and vertical Fourier
spectra is calculated, resulting in what is known as the HVSR or H/V curve. Typically, the spectra from the two horizontal components are combined into a single horizontal spectrum by using the arithmetic or geometric mean, or vector summation [20].

If the impedance contrast between successive layers is sufficiently strong, the H/V curve will show a prominent peak, indicating the (first) resonance frequency $f_{n=0}$ for the site. Without absorption, the resonant frequency $f_n$ is related to the thickness of the overlying layer as $f_n = (2n+1)(\frac{v_{S,0}}{4h})$, ($n = 0, 1, 2, ...$), where $v_{S,0}$ is the shear wave velocity of the overlying layer, $h$ is the layer thickness, and $n$ is the mode number [19].

However, the peaks in the H/V curve are often difficult to interpret due to the complex composition of the wave field: 1) both body and surface waves contribute to the signal, 2) attenuation reduces and enlarges the peaks, and 3) 3D effects generate additional secondary peaks. It is therefore sometimes difficult to accurately attribute the resonance to specific subsurface features [19].

*Resonance frequencies of glaciers.* The seismic resonance frequency technique has also proven effective for estimating glacier thickness [18,19]. However, this approach faces a limitation specific to glaciers: the difficulty of coupling seismic sensors to the ice [21]. Recent studies have highlighted another application: when a sublayer has a lower impedance (e.g., air, water, or soft soil) than the overlying ice, the seismic noise amplitude is anomalously higher in the vertical component, similar to the behavior of a bridge. This results in a peak in the vertical-to-horizontal spectral ratio (the inverse of the HVSR) [22].

*Resonance frequencies of gravitational instabilities.* The resonant frequencies of gravitational unstable bodies, such as rock slopes or cliffs (see fig. 2), are highly sensitive to the stiffness $K$ and mass $M$ of the material. The first resonant frequency $f_1$ (fig. 2(b)) is proportional to $f_1 \propto A\sqrt{\frac{K}{M}}$, where $A$ is a geometric factor that depends on the 3D geometry and boundary conditions [17]. Monitoring these resonance frequencies helps to track the stability of such structures. Prior to failure, a decrease in $f$ is expected, as these unstable bodies may lose stiffness due to bulk damage or increase the depth of rear cracks [16,23]. For example, a study by Lévy et al. found a 30% reduction in $f_1$ in a limestone cliff weeks before it collapsed, indicating a critical reduction in stiffness [24].

The seismic resonant frequency $f$ of an unstable compartment can be determined by noise spectrum analysis, with frequencies appearing clearly in spectrograms from seismic stations placed on the instability (fig. 2(a) and (c)). Daily and seasonal shifts in $f$ reflect a combination of environmental effects. In particular, changes in the stiffness of a posterior crack (between the unstable and stable sections) can significantly affect $f$: temperature variations can alter the crack opening and contact area, reducing stiffness and lowering $f$, which may indi-

<figure><img src="image_13.png" /><figcaption>Fig. 2: Left: spectrograms of the two horizontal components (N and E directions) of the velocity measured by a seismometer placed on an unstable rock column. The orange/red areas correspond to the resonance frequencies of the instability. The first and second frequencies are clearly visible on the North (N) component, while the second and third frequencies are more visible on the East (E) component. The resonance frequencies show seasonal behavior, with higher values in summer and lower values in winter, due to changes in thermal stress in the rock. Right: schematic views of the mode displacement, for the first and second modes. The first resonant frequency is not visible on the E component because it is only a N-S bending mode with almost no displacement in the E direction.</figcaption></figure>

cate potential failure. Environmental variations in frequency are attributed to thermo-acousto-elasticity, where thermal variations affect both the acoustic properties and the elasticity of rocks [25]. The nonlinear elasticity of the rock is critical; as it warms, expansion increases internal stresses, increases wave velocities, and closes surface fractures. The acousto-elastic factor, which relates stress to stiffness, can vary by several orders of magnitude depending on the damage state of the material, making this parameter an ideal proxy for rock damage [12,26].

Environmental effects such as ice and water infiltration further modify resonance. Ice increases fracture and contact stiffness, raising $f$ [27], while water infiltration slightly increases mass and reduces stiffness by filling pore spaces [28], leading to a drop in frequency. Long-term monitoring of these fluctuations —distinguishing between reversible and irreversible changes— may therefore indicate ongoing erosion or warn of impending failure [16,29].

**Ambient noise cross-correlation.** — An alternative method of using seismic noise to study the Earth's subsurface is passive seismic interferometry, also called passive imaging, a method of extracting coherent signals from records of random seismic noise. The foundations for this method were made in the early 1950s, when the groundwork for understanding ambient seismic noise was laid [30–32]. Seismic interferometry computes cross-correlations $C_{AB}(\tau)$ between continuous background noise
<figure><img src="image_14.png" /><figcaption>Fig. 3: (a) Reconstruction of the causal $G(-τ)$ and acausal $G(-τ)$ Green's function when the medium is filled with noise sources, or at least if noise sources are distributed along a continuous line $Γ$ enclosing the receivers. (b) Earth's heterogeneities act as scatterers that are similar to secondary sources, and can compensate for the incomplete noise distribution.</figcaption></figure>

measured simultaneously at two receivers ($\varphi_A, \varphi_B$) [12,33]:

$$ \partial_{\tau} C_{AB}(\tau) = \partial_{\tau} \int \varphi_A(t) \varphi_B(t + \tau) dt \\ \propto G(A, B, \tau) - G(A, B, -\tau). \quad (1) $$

The result of the cross-correlation is an estimate of the Green's function ($G(A, B, \tau)$) between the two receivers. The Green's function gives the seismic response recorded at one receiver due to an impulsive energy source at the other [33]. The cross-correlation is a two-sided function consisting of both the causal $G(-τ)$ and acausal $G(-τ)$ Green's functions: positive times represent the signal as if the first receiver were a virtual source, while negative times represent the second receiver acting as a virtual source (fig. 3). The ability to create virtual sources where there are only receivers and the lack of active sources make this technique particularly useful in seismically inactive areas.

Theoretically, the cross-correlation of continuous seismic noise records converges to the complete Green's function between the receivers, including all reflection, scattering, and propagation modes [34]. To extract the complete Green's function, the sources must be uncorrelated in time and uniformly distributed around the receivers [35], or at least along a line $Γ$ enclosing the receivers (see fig. 3). In the case of the Earth, these conditions are rarely met. As a result, cross-correlation of ambient seismic noise provides an approximation of the Green's function between the two receivers. Since most sources of ambient seismic noise are at the surface, the surface wave portion of the Green's function is most easily extracted. To improve the quality of Green's function estimation, cross-correlations are often stacked over long time periods, such as days to years, because the distribution of noise sources randomizes when averaged over sufficient time [36]. In addition, seismic noise also consists of waves scattered within the Earth's crust, which increases the azimuthal distribution of the noise field [37], furthermore increasing the convergence toward the Green's function.

**Applications.** The use of seismic interferometry has seen considerable growth and development over the last twenty years. Ambient noise cross-correlation was first

used in the field of helioseismology [38]. Experiments in ultrasound showed that diffuse thermal noise recorded and cross-correlated at two ultrasound receivers provided the complete Green's function between these two points [33]. In seismology, Shapiro and Campillo reconstructed intermediate and long-period surface waves by correlating seismic noise at stations up to thousands of kilometers apart, paving the way for imaging the Earth's lithosphere with ambient noise [1]. The ability to reconstruct surface waves from ambient seismic noise led to the development of ambient noise surface wave tomography, where surface wave dispersion curves are measured from cross-correlations and inverted to obtain the distribution of shear velocities in the subsurface. Shapiro et al. constructed such tomographic images from ambient seismic noise and showed that they broadly correspond to the major geologic units in California [36]. Since its introduction, ambient noise tomography has expanded rapidly at various scales [39–41].

Because surface waves have limited depth resolution, several studies have also attempted to recover body waves from the seismic noise. This is more challenging because of the dominance of Rayleigh waves in the cross-correlations, but also because body wave amplitudes decay more rapidly with distance. However, the use of dense seismic arrays and appropriate stacking strategies has made it possible to observe body waves in cross-correlations at multiple scales. Using one month of continuous seismic noise data for 30 receivers located in an 11 km square, it was possible to detect P-waves in cross-correlations on a local scale [42]. Body waves were then also observed in crustal scale noise correlations [43]. Poli et al. were the first to observe P-waves propagating through the deep Earth. Their study revealed that P-waves reflected from the 410 km and 660 km mantle discontinuities in cross-correlations computed from ambient seismic noise recordings in Scandinavia [44]. Their study showed that it is possible to map the mantle transition zone without using earthquake sources. Several other studies have since succeeded in extracting body waves from the deep Earth [45–48].

Ambient seismic noise is continuously available and can therefore be used to continuously monitor temporal changes in seismic velocities in the subsurface. This application is discussed in the following sections.

## Noise, scattering, coda waves and Earth monitoring. –

*Wave propagation regimes and coda waves.* Three wave propagation regimes can be identified in heterogeneous media: the direct propagation regime, the single scattering regime, and the multiple scattering regime (we leave aside the strong localization regime or the Anderson localization regime [49]). To identify them, several characteristic times must be introduced: $t_s$ is the scattering mean free time, which corresponds to the mean time between two scattering events. $t^*$, the transport mean free time, is sometimes introduced and corresponds to the
mean time during which the wave keeps the memory of its incident propagation direction, it can sometimes deviate from $t_s$. $t_a$ is the absorption time, $t_t$ is the (direct) travel time.

In the single-scattering regime, where conventional imaging techniques are used, $t_a < t_s$. The wave is scattered at most once before it is attenuated. If $t_t$ is not much larger than $t_a$, the travel time of the wave can be followed and the usual techniques for imaging the Earth can be used: travel time tomography, seismic reflection, receiver functions, surface wave dispersion.... On Earth, this regime is widespread and corresponds to early times in the seismic record, including direct waves and the early coda waves.

As the degree of heterogeneity increases, reaching the condition $t_s < t_a$, or if the observation time is longer than the scattering times $t_s < t_{obs}$, the waves enter the multiple scattering regime: they are scattered several times before being attenuated or reaching the receiver. Seismographs then show a long lasting wave tail, called coda, where the memory of the initial wave direction is lost and the propagation paths cannot be traced back. This feature renders conventional imaging techniques useless, but allows the mean intensity of the seismograms to be described statistically with the radiative transfer equation or even the diffusion equation. This regime is observed for seismic waves on the Moon [50], on volcanoes [51], but also corresponds to a wide variety of observed seismograms if the frequency is high enough (generally > 1 Hz) and the observation time is long enough (generally the late coda). These waveforms were long thought to be useless noise, like low-amplitude wiggles, but eventually turned out to be very useful for detecting and imaging tiny mechanical changes in the Earth. In addition, the late coda shares several characteristics with ambient noise, including equipartition [52], a property that causes waves to propagate everywhere, in all directions and polarizations, at all times. The next section will show how to monitor and image mechanical changes in this multiple scattering regime and/or in the late coda.

**Coda Wave Interferometry and Coda Wave Correlation.** In the 1980s, Poupinet et al. [53] showed that the coda obtained from reproducible earthquakes (so-called doublets) is more sensitive to weak changes than the ballistic wave. The general idea is to collect similar Green's functions $G_{1,2}(t)$ from the same source and receiver at different dates 1 and 2, as visualized in fig. 4. The relative velocity change $dV/V$ of the material can then be derived from the phase shifts in the Fourier transforms of the waveforms, or from the time shifts of the waveforms in the coda. This approach was later referred to as Coda Wave Interferometry [54]. In the time domain, the stretching approach [55] proposes to determine $dV/V$ as the stretching factor $\epsilon$ that maximizes the waveform

<figure><img src="image_15.png" /><figcaption>Fig. 4: Two simulated seismic traces illustrating waveform changes due to variations in material properties. The initial state (solid blue) and the modified state (dashed red) show phase shifts resulting from these changes. The left zoom shows the ballistic wave and the right zoom shows the coda waves.</figcaption></figure>

correlation in the coda around time $t_0$:

$$CC = \max \left\{ \frac{\int_{t_0-T}^{t_0+T} G_1(t)G_2(t(1-\epsilon))dt}{\int_{t_0-T}^{t_0+T} G_1^2(t)dt \int_{t_0-T}^{t_0+T} G_2^2(t(1-\epsilon))dt} \right\}_\epsilon . \quad (2)$$

Except for water table changes [56], where local density is modified, most relative velocity changes are associated with underground stiffness changes, providing a new way to monitor the Earth material stiffness and damage. As a powerful tool in many geophysical applications, the method has been applied in various geophysical settings, including volcano monitoring [55,57], crustal response to earthquakes [58,59], slow slip events [60], groundwater monitoring [3,61], landslides [62,63] and rocky glaciers [64,65].

In optics and ultrasound, another approach has been proposed to exploit waveform decorrelation, coda waves decorrelate when a structural change (such as a scatterer position) occurs in the material:

$$DC = 1 - \frac{\int_{t_0-T}^{t_0+T} G_1(t)G_2(t)dt}{\int_{t_0-T}^{t_0+T} G_1^2(t)dt \int_{t_0-T}^{t_0+T} G_2^2(t)dt} . \quad (3)$$

This concept was initially introduced in optics through Diffusing Wave Spectroscopy [66], which allows the detection of changes in the medium by analyzing variations in the intensity of speckle patterns. Later, diffuse acoustic wave spectroscopy [67] was developed in the ultrasonic domain, demonstrating the capability to track the motion of scatterers, even when displacements are smaller than the wavelength. Using Coda Wave Decorrelation measurements, we will show that it is possible to image structural changes in the material under test.

**Locadiff:** imaging weak changes in heterogeneous media. In order to locate weak changes of velocity and of scatter position in the medium, the technique called Locadiff was subsequently developed [68–70] and proposed to describe the wave trajectory in a statistical and probabilistic sense. This technique is based on the inversion
of a direct problem that links experimental relative ve- locity changes (measured for instance from Coda Wave Interferometry) and waveform decorrelation (also named Coda Wave Decorrelation) to the sensitivity kernel of dif- fuse waves for the given source and receiver positions. This sensitivity kernel [71] represents the probability that the wave passes through x given that it was emitted at s₁ and received at s₂ after a propagation time t, and is given by

$$K(s_1, s_2, t, x) = \frac{\int_{0}^{t} I(s_1, x, u)I(x, s_2, t-u) du}{I(s_1, s_2, t)}, \quad (4)$$

where I(s₁, s₂, t) represents the probability that the wave travels from s₁ to s₂ during the time t. This probability can be approximated, in the multiple scattering regime, by the wave intensity obtained from the diffusion equation, which is easily solved either analytically for infinite and semi-infinite media or numerically [72] for media with an irregular shape.

Based on the previous sensitivity kernel, a linear direct problem linking the experimental data (denoted by d) to the local property changes m(x) through the sensitivity term S is proposed:

$$d = \int_{\Omega} S(x)m(x)dx, \quad (5)$$

where Ω represents the propagation medium (see [73,74] for a full derivation). In the case of the Coda Wave Interferometry, ϵ is linked to the apparent velocity change. Then eq. (5) becomes

$$d = \epsilon, \quad S(x) = \frac{K(x)}{t}, \quad m(x) = \frac{dv}{v}(x). \quad (6)$$

In the case of Coda Wave Decorrelation, DC is linked to the spatial density of effective scattering cross-section (σ(x)). Then eq. (5) becomes

$$d = DC, \quad S(x) = \frac{c_0K(x)}{2}, \quad m(x) = \sigma(x). \quad (7)$$

The velocity variation or the scattering cross-section can then be imaged by inverting the linear problem (5) to estimate m(x).

*Locadiff applications.* Locadiff was first used and developed with ultrasonic experiments that led to several applications in the nondestructive field in particular to detect structural changes in concrete [75,76] as well as stress variation [74,77].

Furthermore, Locadiff has also been used with ambient seismic noise cross-correlations to detect and locate preeruptive phenomena in volcanoes [78,79]. These authors found both a decrease in wave velocity at the eruption site up to a few weeks before the eruption, and a structural change at the eruption site with an even better spatial resolution.

The use of Locadiff with ambient seismic noise also demonstrates the potential to prevent gas kick in geothermal sites [80] by imaging the waveforms decoherence in 2D. Once again, the zone of the structural change was located, even with only seven seismic stations. A final application of Locadiff with seismic ambient noise is shown in [81–83] where structural and mechanical changes due to earthquake and monsoon were detected and localized.

**Summary and perspectives.** – In this article, we have reviewed various applications of ambient seismic noise to image and monitor the Earth’s subsurface. Seismic noise comes from a variety of sources that are mostly decorrelated in space and time. Nevertheless, anthropic and meteorological sources can develop spatial or temporal coherence features that must be accounted for in noise-derived models. Since wave propagation remains deterministic, we can extract a variety of information from this noise, including the location of the sources (e.g., using array processing), the local geological structure around the sensors (e.g., by analyzing peaks in the vertical and horizontal components of the Fourier spectra), or even the medium between two sensors (e.g., using ambient noise cross-correlations). Other approaches that can simultaneously invert the noise source positions, the noise source waveform, and the structure of the media are under investigation [84]. The deployment of new sensors, including fiber optic distributed acoustic sensing (DAS) will offer seismic wave field, opening new data processing approaches. The sensitivity of surface waves to local perturbations at depth is currently the focus of much attention. In addition, weak nonlinearities of the Earth’s materials can also be tracked by ambient noise [25,85], opening a new avenue for monitoring nonlinear elastic parameters, which are known to play a key role in damage development, with applications to earthquake nucleation, earthquake recovery, and landslide triggering.

***

We acknowledge the support of the European Research Council (ERC) under the grant agreement No. 101142154 (Crack The Rock). This work was also partially funded by Horizon Europe MSCA Doctoral Network EnvSeis (grant agreement No. 101073148), and is part of the Labex OSUG Habitability.

*Data availability statement:* No new data were created or analysed in this study.

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