ALBERT

Description: Scattered seismic coda waves are frequently used to characterize small scale medium heterogeneities, intrinsic attenuation or temporal changes of wave velocity. Spatial variability of these properties raises questions about the spatial sensitivity of seismic coda waves. Especially the continuous monitoring of medium perturbations using ambient seismic noise led to a demand for approaches to image perturbations observed with coda waves. An efficient approach to localize spatial and temporal variations of medium properties is to invert the observations from different source–receiver combinations and different lapse times in the coda for the location of the perturbations. For such an inversion, it is key to calculate the coda-wave sensitivity kernels which describe the connection between observations and the perturbation. Most discussions of sensitivity kernels use the acoustic approximation in a spatially uniform medium and often assume wave propagation in the diffusion regime. We model 2-D multiple non-isotropic scattering in a random elastic medium with spatially variable heterogeneity and attenuation using the radiative transfer equations which we solve with the Monte Carlo method. Recording of the specific energy density of the wavefield that contains the complete information about the energy density at a given position, time and propagation direction allows us to calculate sensitivity kernels according to rigorous theoretical derivations. The practical calculation of the kernels involves the solution of the adjoint radiative transport equations. We investigate sensitivity kernels that describe the relationships between changes of the model in P- and S-wave velocity, P- and S-wave attenuation and the strength of fluctuation on the one hand and seismogram envelope, traveltime changes and waveform decorrelation as observables on the other hand. These sensitivity kernels reflect the effect of the spatial variations of medium properties on the wavefield and constitute the first step in the development of a tomographic inversion approach for the distribution of small-scale heterogeneity based on scattered waves.

Description: Following its deployment at the surface of Mars, the seismometer SEIS of the InSIght – NASA Mission has detected tens of very high-frequency (VF) seismic events (〉 1 Hz). In this work, we constrain the regional attenuation properties of the Martian lithosphere using both impacts and VF data to characterize the heterogeneities and volatile content as a function of depth. To carry out this task, we model the high-frequency energy envelopes of the seismic events using a multiple-scattering approach, considering a stratification of velocity and attenuation in the medium. In a first approximation, we consider a simple attenuation structure composed of a heterogenous crust overlying a weakly inhomogeneous mantle. Our inversion results show that a strongly diffusive and globally dry layer of about 20 km thickness in the vicinity of the InSight landing site (northern plains) suffices to retrieve the shape of near impacts, but the thickness has to be increased to at least 60 km to recover the shape of distant VF events. The observed correlation between the depth extent of the diffusive layer and the thickness of the crust indicates that the main cause of scattering is the lithological heterogeneity. Furthermore, our model suggests that the sources of a number of distant VF seismic events are shallow and located in the southern highlands or in close vicinity of the Martian dichotomy.

Description: Following its deployment at the surface of Mars, the SEIS seismometer of the NASA-InSight mission recorded tens of high-frequency Martian seismic events (〉 1Hz) which we analyzed to characterize the attenuation properties of the Martian lithosphere from an Earth-Moon-Mars comparison perspective. The Martian waveforms are generally depolarized and show P and S arrivals with a gradual beginning, a broad maximum and a very long coda decay. These characteristics are reminiscent of the seismic wavefield in the terrestrial oceanic lithosphere at high frequency (Po and So above 2Hz). To constrain the attenuation properties on Mars, we modeled the energy envelopes of very-high frequency events (〉2Hz) using a multiple-scattering approach, in which we considered a stratification of velocity and attenuation in the medium. We found that a simple model composed of a highly scattering crust overlying a weakly inhomogeneous mantle is sufficient to explain the main features of Martian events. We found that the Martian crustal diffusivity (10-12 km2/s) is similar to the estimation obtained in the lithosphere of the Atlantic Ocean (15–60 km2/s, Hannemann et al. 2022), but higher than the Lunar crust value (2 km2/s). The absorption attenuation results indicate that the Martian crust is globally dry (Q subscript mu superscript negative 1 end superscript~ 10-4) compared to the terrestrial crust (~ 10-3). Our results suggest that the basaltic nature and the heterogeneities of the crust are the main source of the scattering in the Martian and oceanic lithospheres. By contrast, the extreme strength of the scattering on the Moon suggests a predominant role of fractures.

Description: At high frequency (f〉0.5Hz), spatial variations of seismic attenuation parameters -scattering and absorption- control to a large extent the variability of observed ground motions at the regional scale. Hence, our ability to predict seismic hazard depends critically on mapping frequency-dependent attenuation. To address this issue, we developed a hybrid inversion method to separate attenuation parameters (scattering and intrinsic absorption) in 6 frequency bands covering the 0.75 – 24 Hz range from the modeling of the S-wave energy envelopes. Synthetic envelopes and their partial derivatives with respect to attenuation parameters are calculated using the Monte-Carlo method for elastic waves in a simple but realistic model of the Earth's lithosphere. The hybrid inversion method combines a grid-search with an iterative optimization using the Levenberg-Marquardt algorithm, which respectively test different models of random heterogeneities and constrain the level of scattering and absorption. The inversion procedure has been applied to more than 10000 waveforms retrieved from the database of the French seismological and geodetic network RESIF. The obtained attenuation maps show the extreme variability of frequency-dependent attenuation parameters (scattering and intrinsic absorption) at the regional scale. In particular, we find zones of strong scattering in the Western Pyrenees at all frequencies and in young sedimentary basins below 3 Hz. Absorption is stronger in the Paris Basin at low frequency and in the French Alps above 3-6 Hz. Western France is characterized by weak scattering and absorption. We also find that scattering generally dominates absorption below 1-2 Hz while the opposite is true at higher frequency.

Description: An accurate magnitude estimation is necessary to properly evaluate seismic hazard. Unfortunately, magnitudes of small earthquakes are subject to large uncertainties due to high-frequency propagation effects which are generally not properly considered. To address this issue, we developed a method to separate source, attenuation and site parameters from the elastic radiative transfer modeling of the full energy envelopes of seismograms. The key feature of our approach is the treatment of attenuation -both scattering and absorption- in a simple but realistic velocity model of the Earth's lithosphere, including a velocity discontinuity at the Moho. Our separation method is based on a 2-steps inversion procedure. First, for each source-station pair, we retrieve optimal frequency-dependent attenuation parameters from the fitting of observed energy envelopes in the 0.375-24Hz band. In a second step, we correct for regional propagation effects to determine site amplification and source displacement spectra. From the latter, we estimate the moment magnitude Mw. The inversion procedure is applied to the 2019 ML 5.2 Le Teil and 2014 ML 4.5 Lourdes earthquakes, which both occurred in Southern France. The inversion results confirm a significant variability in the attenuation parameters (scattering and intrinsic absorption) at regional scale and a strong frequency dependence. We determine moment magnitudes Mw 5.07±0.17 for the Le Teil earthquake and 4.13±0.13 for the Lourdes earthquake, in good agreement with previous estimates. In the future, we intend to automate our method and apply it routinely to smaller earthquakes for which traditional methods are not readily applicable due to the complexity of waveforms.