Seismological studies are traditionally based on the observation of ground motions recorded by translation sensors. However, to assess a comprehensive description of any wavefield produced by seismic sources, the three components of rotation are as important as the three translation components. Due to improvements in instrumentation through the last two decades, the ground rotational motion is now an observable. Several recent publications show that 6 degrees of freedom (-dof) seismic station, recording the 3 translation and 3 rotation components of the ground motion, provides valuable information to locate events or to infer their source mechanism.Rotation motions can be recorded directly via dedicated sensors, or numerically derived via a dense array of seismometers. The formers primarily use technologies based on fiber optic gyroscopes, liquid-based systems, or mechanical principles. However, these broadband instruments do not have the high sensitivity required to detect "weak" ground movements. Conventional sensor arrays, on the other hand, use finite differences techniques to estimate reliable indirect rotation measurements, but these are limited at high frequencies (wavelength > 4 × array aperture).Since the end of 2025, a temporary experimental campaign is set at the Low Noise Underground Laboratory (LSBB) in Rustrel, France. Two rotational rate sensors, namely a BlueSeis 3A and a Eentec R3, are deployed in the underground galleries, jointly with five seismometers which complete the permanent seismic array. The dense seismic array co-located around the rotation sensors is used to compute array derived rotations (ADR), and validate the direct observations of rotational ground motions. Furthermore, six seismometers are deployed at the surface to form an array with an aperture of around fifty kilometers. It has been designed for long-term observations of regional and global seismicity and array processing analysis, such as beamforming techniques. This campaign allows to compare the performance of classical seismic array processing with innovative gradiometric approaches based on a single 6-dof station, focusing on detection, location, and characterization of seismic events within a common frequency band. A sensitivity study on rotation signals, in terms of instrumental conditions (array geometry, station quality) and processing parameters (signal duration, filtering), is carried out with the help of numerical full waveform modelling in order to quantify the uncertainty of the estimated source parameters. We present the benefit of such multi-component seismic wavefield recording, illustrated on several events of interest such as the recent (2025/07/29) Kamchatka event (Mw 8.8).

There is a growing interest in applying ambient noise processing techniques to fiber-optic arrays, which are now a mainstream tool in seismology. Traditionally applied to geophone arrays, noise-based interferometry methods have been widely used for subsurface imaging and monitoring over the last two decades. In this study, we retrieve surface wave phase velocities by cross-correlation of DAS-recorded ambient noise data to monitor the subsurface of a quiet brackish marsh site of the Loire estuary. Seasonal recordings were obtained from a DAS array consisting of multiple linear and a spiral cable layout, capturing the ambient seismic wavefield mainly influenced by natural forcing, for example, tidal activity in the river and streams (below 15 Hz), but also by anthropogenic sources. We use time-frequency weighted Phase Cross-Correlation (PCC) technique, which in addition to being efficient, reduces sensitivity to amplitude variations and emphasizes phase coherence. We observe diurnal and seasonal variation in ground water level and in noise characteristics, like amplitude and directionality. Such temporal variations provide an opportunity to monitor both (a) the changes in the subsurface medium itself, and (b) the impact of noise characteristics on surface wave retrieval. We also observe a pronounced lateral contrast of surface wave phase velocity across the marsh site, highlighting the extent of spatial variability of the subsurface in complex natural environments.

Volcanic activity encompasses a wide range of seismogenic phenomena occurring from the deep magmatic conduit to the surface of volcanic flanks. Volcanic tremor, long period (LP), and very long period (VLP) seismic signals are commonly associated with magma and fluid movement within the conduit, whereas sliding mass and density currents along the flanks typically produce minute-long, cigar-shaped seismic traces.Characterising these phenomena through seismic analysis requires high measurement accuracy over a broad frequency range, together with high spatial and temporal resolution. Meeting these requirements in complex volcanic environments can be particularly challenging because the deployment and the maintenance of dense seismic networks involves considerable logistical effort. Distributed Acoustic Sensing (DAS) offers the opportunity to bridge the gap between sparse seismic networks and denser arrays, enabling continuous strain measurements along fibre-optic cables at comparatively low operational costs.Here, we investigate several different volcanic processes at Stromboli volcano (Italy) through DAS observations acquired along a 6 km fibre-optic cable integrated within a permanent multiparameter monitoring network comprising broadband seismometers, thermal and visible cameras, and infrasonic pressure sensors. The fibre was deployed on the volcanic flanks between 2020 and 2023 and interrogated during several month-long campaigns using a Febus A1-R. The dataset includes signals generated by ordinary Strombolian explosions, major explosions, lava flows, partial crater collapses and pyroclastic density currents (PDCs), which were analysed using different analytical approaches.Array-processing techniques in the 1–5 Hz frequency range were used to track the source of volcanic tremor, explosions, and PDCs with DAS strain-rate signals. Tremor and explosion signals are consistently located near the crater area, whereas PDCs propagate along the volcanic flanks. Moreover, by combining visible imagery with seismic energy recorded by DAS and inertial seismometers, we estimate the flow velocities and volumes of the PDCs and derive empirical, volume-dependent friction angles that provide insight into flow dynamics.Additionally, we exploit the distributed nature of DAS measurements to reconstruct the axisymmetric principal strain axes of VLP strain signals (between 0.04–0.2 Hz) associated with each explosion. The VLP strain signals recorded along the fibre nicely fit a deformation point-source (Mogi) located beneath the active craters, with an estimated volumetric change of ~30 m³.Our results demonstrate the capability of DAS measurements to characterise the dynamics of volcanic processes and to resolve the VLP strain distribution with enhanced spatial resolution. Overall, these findings highlight the significant potential of DAS as an innovative tool for analysing and monitoring a wide range of volcanic phenomena across different spatial and temporal scales.

Distributed Acoustic Sensing (DAS), a photonic technology that converts a fibre-optic cable into a long (tens of kilometres) high-linear-density (every few metres) array of seismo-acoustic sensors, can provide high-density, high-resolution strain measurements along the entire cable. The potential of such a distributed measurement has gained increasing attention in the seismology community for a wide range of applications. It has been shown that DAS has a subwavelength sensitivity to heterogeneities near the fibre-optic cable. This sensitivity is linked to the fact that the DAS measures deformation, as opposed to the displacements that seismometers measure. However, this sensitivity can create difficulties for many DAS applications, such as source location or distant imaging. Regardless, it can be advantageous in obtaining information about the subsurface near the cable. Here we present a method to locate small heterogeneities near the fibre-optic cable by inverting an indicator of the small-scale heterogeneities: the homogenized first-order corrector. We show that this first-order corrector can be used to locate heterogeneities near the fibre-optic cable at the gauge length precision, independent of the wavelength.

Very long period (VLP; 0.01-0.2 Hz) seismicity is observed at many volcanoes worldwide, and provides key insights into magma and fluid dynamics within volcanic structures. VLPs are typically recorded by sparse networks of seismometers, which limits the ability to resolve the resulting displacement (or deformation) at fine spatial scales. Distributed acoustic sensing (DAS) may help overcome this limitation by densely sampling the projection of the strain tensor along fibre-optic cables with high spatial and temporal resolution, enabling a more complete view of VLP-induced deformation. Here, we analyse VLP strain signals recorded by DAS at Stromboli volcano (Italy) in November 2022 along a 6-km dedicated fibre-optic cable. We designed the cable geometry to provide broad coverage of the craters and to sample the strain at multiple locations and along different directions. We focus on a dataset of approximately 200 VLP events recorded between November 13 and 14, 2022. The VLP strain signals correlate with explosive activity and show consistent features across multiple events, indicating a persistent, non-destructive source. Leveraging the distributed nature of DAS measurements, we recover the principal strain axes of VLPs and estimate both the location and the volumetric change of the source using a quasi-static deformation model. We retrieve the principal horizontal strains for each VLP by inverting strain amplitudes measured along three different fibre directions and at multiple locations along the cable, allowing us to resolve their spatial distribution. The resulting principal VLP strains exhibit radial and tangential orientations with respect to the craters, consistent with observed seismic particle motions and an axisymmetric source. We then model the VLP strain along the fibre using a point-like deformation source (Mogi). The optimal agreement between modeled and observed VLP strain averaged over the 200 events is for a point source located ~500 m beneath the active craters, with an estimated volumetric change of ~30 m³. Under the assumption of a spherical source with a radius of 87 m, the inferred volumetric change corresponds to a pressure change of ~19 kPa. These results are consistent with previous studies and highlight the capability of DAS to investigate volcano deformation at long periods.

In seismic tomography, only waveforms up to a minimum period are observed, preventing to resolve scales smaller than a minimum wavelength. As a result, seismic tomography is only able to recover effective mediums, which are smoothed versions of the studied structures. A true small-scale structure can be related to its corresponding effective medium through the homogenization theory of wave propagation. Geodynamics is able to model small-scales structures, providing useful a priori information about the Earth structures. In this study, we aim to combine small-scale a priori information and the homogenization theory to downscale tomographic images, i.e. find the small-scale realistic models equivalent to the observed smooth images. It requires an appropriate parametrization of the small-scale models, that takes into account the a priori information. We propose to carry out this parametrization with a Generative Neural Network. After the training, the network can generate models that are statistically similar to the training set – in this context, a set of small-scale models, corresponding to the a priori structures. This parameterization integrates the prior, as it is learned during the training. It also has the advantages to be low-dimensional, computationally quick, and avoid strong non-linearities relationships between parameters and the data. The network is then utilized in an inverse framework to dowscale a given tomographic image. To test this methodology, we train the network on geodynamical simulations of the mantle, the marble-cake models. For a given synthetic smoothed effective tomographic image, we plug the network into a Bayesian framework, using a McMC to explore the space of marble-cake models that are equivalent to the tomographic image for long period waves.

Seismic anisotropy mainly originates from the crystallographic preferred orientation (CPO) of minerals deformed in the convective mantle flow. While fabric transitions have been previously observed in experiments, their influence on large‐scale anisotropy is not well‐documented. Here, we implement 2D geodynamic models of intra‐oceanic subduction coupled with mantle fabric modeling to investigate the combined effect of pressure ‐and water‐dependent microscopic flow properties of upper mantle and upper transition zone (UTZ) minerals, respectively, on large‐scale anisotropy. We then compare our anisotropy models with anisotropic tomography observations across the Honshu subduction zone. Our results for the upper mantle correlate well with observations, implying that the ‐dependence of olivine fabrics is sufficient to explain the variability of anisotropy. Meanwhile, a dry UTZ tends to be near‐isotropic whereas a relatively wet UTZ could produce up to azimuthal and radial anisotropy. Because water facilitates CPO development, it is therefore likely a requirement to explain the presence of anisotropy in the transition zone close to subducting slabs.

Pyroclastic flows are highly hazardous phenomena demanding precise detection, localization, and comprehensive characterization for effective volcanic risk management. During October and December 2022, the volcanic activity of Stromboli produced more than 60 pyroclastic flows. The flows propagated from the craters (~700 m a.s.l.) to the sea, resulting in tsunami waves ranging from centimetres to meters in height. These events coincided with an experiment involving distributed acoustic sensing (DAS) data acquisition with a dedicated 4-kilometer-long fibre-optic cable. A 3-component array consisting of 27 geophones and the multi-parameter monitoring network managed by the Laboratory of Experimental Geophysics (LGS) at the University of Florence were active simultaneously. We study two distinct pyroclastic flows of varying intensities. Using array processing techniques applied to DAS, seismic, and infrasonic measurements, we estimate back-azimuths that consistently track flows moving at velocities between 40 and 50 m/s from the craters to the shoreline. Validation of these measurements was accomplished through georeferenced images obtained by a visible camera, affirming their accuracy. These results demonstrate the effectiveness of the three datasets in monitoring pyroclastic flows and the need for multi-parametric observations for a better interpretation of volcanic phenomena.

SUMMARY Inverse problems occur in many fields of geophysics, wherein surface observations are used to infer the internal structure of the Earth. Given the non-linearity and non-uniqueness inherent in these problems, a standard strategy is to incorporate a priori information regarding the unknown model. Sometimes a solution is obtained by imposing that the inverted model remains close to a reference model and with smooth lateral variations (e.g. a correlation length or a minimal wavelength are imposed). This approach forbids the presence of strong gradients or discontinuities in the recovered model. Admittedly, discontinuities, such as interfaces between layers, or shapes of geological provinces or of geological objects such as slabs can be a priori imposed or even suggested by the data themselves. This is however limited to a small set of possible constraints. For example, it would be very challenging and computationally expensive to perform a tomographic inversion where the subducting slabs would have possible top discontinuities with unknown shapes. The problem seems formidable because one cannot even imagine how to sample the prior space: is each specific slab continuous or broken into different portions having their own interfaces? No continuous set of parameters seems to describe all the possible interfaces that we could consider. To circumvent these questions, we propose to train a Generative Adversarial neural Network (GAN) to generate models from a geologically plausible prior distribution obtained from geodynamic simulations. In a Bayesian framework, a Markov chain Monte Carlo algorithm is used to sample the low-dimensional model space depicting the ensemble of potential geological models. This enables the integration of intricate a priori information, parametrized within a low-dimensional model space conducive to efficient sampling. The application of this approach is demonstrated in the context of a downscaling problem, where the objective is to infer small-scale geological structures from a smooth seismic tomographic image.

SUMMARY Modelling seismic wavefields in complex 3-D elastic media is the key in many fields of Earth Science: seismology, seismic imaging, seismic hazard assessment and earthquake source mechanism reconstruction. This modelling operation can incur significant computational cost, and its accuracy depends on the ability to take into account the scales of the subsurface heterogeneities varying. The theory of homogenization describes how the small-scale heterogeneities interact with the seismic waves and allows to upscale elastic media consistently with the wave equation. In this study, an efficient and scalable numerical homogenization tool is developed, relying on the similarity between the equations describing the propagation of elastic waves and the homogenization process. By exploiting the optimized implementation of an elastic modelling kernel based on a spectral-element discretization and domain decomposition, a fully scalable homogenization process, working directly on the spectral-element mesh, is presented. Numerical experiments on the entire SEAM II foothill model and a 3-D version of the Marmousi II model illustrate the efficiency and flexibility of this approach. A reduction of two orders of magnitude in terms of absolute computational cost is observed on the elastic wave modelling of the entire SEAM II model at a controlled accuracy.

Distributed Acoustic Sensing (DAS) is a photonic technology allowing toconvert fiber-optics into long (tens of kilometers) and dense (every few meters) arrays of seismo-acoustic sensors which are basically measuring the strain of the cable all along the cable. The potential of such a distributed measurement is very important and has triggered strong attention in the seismology community for a wide range of applications. In this work, we focus on the interaction of such measurements with heterogeneities of scale much smaller than the wavefield minimum wavelength. With a simple 2-D numerical modeling, we first show that the effect of such small-scale heterogeneities, when located in the vicinity of the instruments, is very different depending on whether we measure particle velocity or strain rate: in the case of velocity, this effect is small but becomes very strong in the case of the strain rate. We then provide a physical explanation of these observations based on the homogenization method showing that indeed, the strain sensitivity to nearby heterogeneities is strong, which is not the case for more traditional velocity measurements. This effect appears as a coupling of the strain components to the DAS measurement. Such effects can be seen as a curse or an advantage depending on the applications.

Continuous seismic monitoring of volcanoes is challenging due to harsh environments and associated hazards. However, investigating volcanic phenomena near their sources is essential for eruption forecasting. In seismo-volcanic applications, Distributed Acoustic Sensing (DAS) offers new possibilities for long-duration surveys. We analyse DAS strain rate signals generated by volcanic tremor, explosions and pyroclastic flows at Stromboli volcano (Italy) recorded along 4 km of a dedicated fibre-optic cable installed between 2020 and 2022. We buried the fibre-optic cable at a depth of 30 cm and designed the layout geometry to provide broad coverage on the active craters. We compared DAS recordings with the data provided by the monitoring network of the University of Firenze (Italy) comprising broadband seismic stations, tiltmeters, infrasonic sensors, tsunami gauges and visible and thermal cameras. We also installed nodal seismometers along the fibre to calibrate the recordings together with an innovative optical strainmeter. The inversion of time delays between DAS strain rate waveforms provides back-azimuths indicating a dominant and persistent seismic source in the proximity of active craters during tremor and explosions. We analysed two pyroclastic flows of varying intensity that occurred in October and December 2022. The two flows propagated from the craters to the shore, generating centimetre-scale tsunami waves. The back-azimuths estimated with the DAS array enabled us to track the downslope movement of the seismic source with a timing consistent with what is observed with monitoring cameras and with seismic and infrasonic observations. These results demonstrate the potential of DAS in monitoring volcanic areas.

SUMMARY We present a time-domain distributional finite-difference scheme based on the Lebedev staggered grid for the numerical simulation of wave propagation in acoustic and elastic media. The central aspect of the proposed method is the representation of the stresses and displacements with different sets of B-splines functions organized according to the staggered grid. The distributional finite-difference approach allows domain-decomposition, heterogeneity of the medium, curvilinear mesh, anisotropy, non-conformal interfaces, discontinuous grid and fluid–solid interfaces. Numerical examples show that the proposed scheme is suitable to model wave propagation through the Earth, where sharp interfaces separate large, relatively homogeneous layers. A few domains or elements are sufficient to represent the Earth’s internal structure without relying on advanced meshing techniques. We compare seismograms obtained with the proposed scheme and the spectral element method, and we show that our approach offers superior accuracy, reduced memory usage, and comparable efficiency.

ABSTRACT To enhance the local resolution of global waveform tomography models, particularly in areas of interest within the Earth’s deep structures, a higher resolution localized tomography approach (referred to as “box tomography”) is crucial for a more detailed understanding of the Earth’s internal structure and geodynamics. Because the small-scale features targeted by box tomography are finer than those in global reference models, distinct spatial meshes are necessary for global and local (hybrid) forward simulations. Within the spectral element method (SEM) framework, we employ the intrinsic Lagrangian spatial interpolation to compute and store hybrid inputs (displacement/potential) in the global numerical simulation. These hybrid inputs are subsequently imposed into the localized domain during the iterative box tomography. However, inaccurate spatial Lagrange interpolation can lead to imprecise hybrid inputs, and this error can propagate from the global simulation to the hybrid simulation. It is essential to quantitatively analyze this error propagation and control it to ensure the credibility of box tomography. We introduce a unique spatial window function into the conventional “direct discrete differentiation” hybrid method. When the local mesh and structure align with those in the global simulation, the synthetic hybrid waveforms match the global ones, serving as a reference for quantitatively assessing error propagation stemming from changes in the local spatial mesh during hybrid simulation. Significantly, the relative waveform error arising due to spatial Lagrange interpolation is around 5% when employing the traditional SEM with five Gauss–Lobatto–Legendre points per minimum wavelength in the 3D global simulation through SPECFEM3D_GLOBE. Ultimately, we achieve hybrid waveforms with an accuracy of about 1.5% by increasing the spectral elements by about 1.5 times in the standard global simulation.

SUMMARY Observations of large-scale seismic anisotropy can be used as a marker for past and current deformation in the Earth’s mantle. Nonetheless, global features such as the decrease of the strength of anisotropy between ∼150 and 410 km in the upper mantle and weaker anisotropy observations in the transition zone remain ill-understood. Here, we report a proof of concept method that can help understand anisotropy observations by integrating pressure-dependent microscopic flow properties in mantle minerals particularly olivine and wadsleyite into geodynamic simulations. The model is built against a plate-driven semi-analytical corner flow solution underneath the oceanic plate in a subduction setting spanning down to 660 km depth with a non-Newtonian n = 3 rheology. We then compute the crystallographic preferred orientation (CPO) of olivine aggregates in the upper mantle (UM), and wadsleyite aggregates in the upper transition zone (UTZ) using a viscoplastic self-consistent (VPSC) method, with the lower transition zone (LTZ, below 520 km) assumed isotropic. Finally, we apply a tomographic filter that accounts for finite-frequency seismic data using a fast-Fourier homogenization algorithm, with the aim of providing mantle models comparable with seismic tomography observations. Our results show that anisotropy observations in the UM can be well understood by introducing gradual shifts in strain accommodation mechanism with increasing depths induced by a pressure-dependent plasticity model in olivine, in contrast with simple A-type olivine fabric that fails to reproduce the decrease in anisotropy strength observed in the UM. Across the UTZ, recent mineral physics studies highlight the strong effect of water content on both wadsleyite plastic and elastic properties. Both dry and hydrous wadsleyite models predict reasonably low anisotropy in the UTZ, in agreement with observations, with a slightly better match for the dry wadsleyite models. Our calculations show that, despite the relatively primitive geodynamic setup, models of plate-driven corner flows can be sufficient in explaining first-order observations of mantle seismic anisotropy. This requires, however, incorporating the effect of pressure on mineralogy and mineral plasticity models.

SUMMARY Seismic gradient measurements from distributed acoustic sensors and rotational sensors are becoming increasingly available for field surveys. These measurements provide a wealth of information and are currently being considered for many applications such as earthquake detection and subsurface characterizations. In this work, using a simple 2-D numerical approach, we tackle the implications of such wavefield gradient measurements on full waveform inversion (FWI) techniques using a simple 2-D numerical test. In particular, we study the impact of the wavefield gradient measurement sensitivity to heterogeneities that are much smaller than the minimum wavelength. Indeed, as shown through the homogenization theory, small-scale heterogeneities induce an unexpected coupling of the strain components to the wavefield gradient measurement. We further show that this coupling introduces a potential limitation to the FWI results if it is not taken into account. We demonstrate that a gradient measurement-based FWI can only reach the accuracy of a classical displacement field-based FWI if the coupling coefficients are also inverted. Furthermore, there appears to be no specific gain in using gradient measurements instead of conventional displacement (or velocity, acceleration) measurements to image structures. Nevertheless, the inverted correctors contain fine-scale heterogeneities information that could be exploited to reach an unprecedented resolution, particularly if an array of receivers is used.

<p>Volcano seismology is essential for understanding, monitoring, and forecasting eruptive events. The use of distributed acoustic sensing (DAS) technology can be particularly useful for this purpose because of its high temporal and spatial resolution, which may help to overcome the challenges of deploying and maintaining seismic arrays on volcanoes.</p> <p>Between 2020 and 2022, we installed 4 km of optical fibre on Stromboli volcano, Italy, whose persistent activity is well-suited for investigating the related dynamic strain rate. The cable was buried at a depth of 30 cm and the layout geometry was designed to provide wide coverage while being constrained by natural obstacles and topographical features. Seismometers were also installed along the fibre. DAS data were collected using a Febus A1-R interrogator, and the acquisition period increased from one week in 2020 to over four months in 2022. We recorded volcanic tremor, ordinary explosions (several per hour), two major explosions in 2021 and 2022, and the entire sequence of a pyroclastic flow in 2022. </p> <p>DAS and seismic data show good agreement in both time and frequency domains after converting strain rate to velocity and vice versa using different methodologies. Beamforming of DAS data shows a dominant signal in the 3-5 Hz frequency band coming from the active craters. We will also present preliminary results of major explosions and pyroclastic flow. This experiment demonstrates that DAS can be used for monitoring volcanic activity.</p>

Abstract Tremors are a type of slow earthquake with long‐duration signals compared to ordinary earthquakes. The long signals have been considered to solely reflect their long source process. However, here, we provide evidence suggesting that the source processes of tremors are not always long. We refer to these observations as short‐duration tremors. They were recorded by ocean‐bottom seismometers placed very close to the source. Although these tremors exhibit a short‐duration signal when recorded near the source, they exhibit a typical long‐duration signal elsewhere. Our numerical simulations demonstrate that the features can be captured by considering a strongly scattering medium around their source. One such structure could be small low‐velocity inclusions distributed around the seismic source. The inclusions may represent the seismic expression of geologically detected aquifers in tremor source regions. Furthermore, this medium could be embedded along the slow earthquake fault zone and play a critical role in their source process.

Summary Full waveform modelling and inversion are essential tools commonly used in seismic imaging. Due to the restrictions from instruments and computing resources, the seismic data are usually frequency-band limited. Thus, the resulting imaging result is a smooth version of the true Earth with the lack of scales smaller than the minimum propagating wavelength. The non-periodic homogenization technique allows for building a long-wave equivalent medium to account for wave interactions with small geological structures and producing similar waveforms as for the original medium at a controlled accuracy. The current non-periodic homogenization implementation is memory and time consuming even with parallel computing techniques. To boost its applicability on large-scale 3D problems, we propose a fully scalable non-periodic homogenization implementation. As the core of the homogenization process, the solution of elastostatic equations and the low-pass filtering operations are formulated as the linear system solution with a matrix-free conjugate-gradient algorithm to exploit highly optimized matrix-vector-product routines developed in our elastic wave modelling and inversion parallel code SEM46. For the algorithm consistency, an approximated Gaussian low-pass filtering is introduced by a cascade of PDE-defined Bessel filters without sacrificing the effectiveness. All these improvements enhance the efficiency, scalability and robustness of the non-periodic homogenization process.

SUMMARYThe time reversal method is based on the backpropagation of seismic waveforms recorded at a set of receivers. When this set forms a closed surface and the elastic properties of the medium are correct, the seismic energy focuses at the source location, creating a focal spot. Such a spot is smooth in space, whereas the original wavefield usually shows a displacement discontinuity at the source. The goal of this paper is to discuss the link between the focal spot and the original source using the concept of homogenized point source. We show that the backpropagated wavefield is equivalent to the sum of two low-wavenumber fields resulting from the homogenization of the original point source. In other words, the homogenized point source is the equivalent force for producing the focal spot. In addition to the demonstration in the general 3-D heterogeneous case, we present some numerical examples in 2-D.