Thickness and structure of the martian crust from InSight seismic data.

A planet's crust bears witness to the history of planetary formation and evolution, but for Mars, no absolute measurement of crustal thickness has been available. Here, we determine the structure of the crust beneath the InSight landing site on Mars using both marsquake recordings and the ambient wavefield. By analyzing seismic phases that are reflected and converted at subsurface interfaces, we find that the observations are consistent with models with at least two and possibly three interfaces. If the second interface is the boundary of the crust, the thickness is 20 ± 5 kilometers, whereas if the third interface is the boundary, the thickness is 39 ± 8 kilometers. Global maps of gravity and topography allow extrapolation of this point measurement to the whole planet, showing that the average thickness of the martian crust lies between 24 and 72 kilometers. Independent bulk composition and geodynamic constraints show that the thicker model is consistent with the abundances of crustal heat-producing elements observed for the shallow surface, whereas the thinner model requires greater concentration at depth.

Scattering Attenuation of the Martian Interior through Coda Wave Analysis.

We investigate the scattering attenuation characteristics of the Martian crust and uppermost mantle to understand the structure of the Martian interior. We examine the energy decay of the spectral envelopes for 21 high-quality Martian seismic events from Sol 128 to Sol 500 of InSight operations. We use the model of Dainty et al. (1974b) to approximate the behavior of energy envelopes resulting from scattered wave propagation through a single diffusive layer over an elastic half-space. Using a grid search, we mapped the layer parameters that fit the observed InSight data envelopes. The single diffusive layer model provided better fits to the observed energy envelopes for High Frequency (HF) and Very High Frequency (VF) than for the Low Frequency (LF) and Broadband (BB) events. This result is consistent with the suggested source depths (Giardini et al., 2020) for these families of events and their expected interaction with a shallow scattering layer. The shapes of the observed data envelopes do not show a consistent pattern with event distance, suggesting that the diffusivity and scattering layer thickness is non-uniform in the vicinity of InSight at Mars. Given the consistency in the envelope shapes between HF and VF events across epicentral distances and the tradeoffs between the parameters that control scattering, the dimensions of the scattering layer remain unconstrained but require that scattering strength decreases with depth and that the rate of decay in scattering strength is fastest near the surface. This is generally consistent with the processes that would form scattering structures in planetary lithospheres.

Imaging multiple local changes in heterogeneous media with diffuse waves.

This study focuses on imaging local changes in heterogeneous media. The method employed is demonstrated and validated using numerical experiments of acoustic wave propagation in a multiple scattering medium. Changes are simulated by adding new scatterers of different sizes at various positions in the medium, and the induced decorrelation of the diffuse (coda) waveforms is measured for different pairs of sensors. The spatial and temporal dependences of the decorrelation are modeled through a diffuse sensitivity kernel, based on the intensity transport in the medium. The inverse problem is then solved with a linear least square algorithm, which leads to a map of scattering cross section density of the changes.

Velocity and attenuation of scalar and elastic waves in random media: a spectral function approach.

This paper investigates the scattering of scalar and elastic waves in two-phase materials and single-mineral-cubic, hexagonal, orthorhombic-polycrystalline aggregates with randomly oriented grains. Based on the Dyson equation for the mean field, explicit expressions for the imaginary part of Green's function in the frequency-wavenumber domain (ω, p), also known as the spectral function, are derived. This approach allows the identification of propagating modes with their relative contribution, and the computation of both attenuation and phase velocity for each mode. The results should be valid from the Rayleigh (low-frequency) to the geometrical optics (high-frequency) regime. Comparisons with other approaches are presented for both scalar and elastic waves.

Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium.

This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation-the resolvent formula-Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to generalized forms of optical theorem involving the off-shell T-matrix of elastic waves, which describes scattering in the near-field. The role of temporal absorption in the formulation of the theorem is discussed. Previously established symmetry and reciprocity relations involving the on-shell T-matrix are recovered in the usual far-field and infinitesimal absorption limits. The theory is applied to a point scattering model for elastic waves. The T-matrix of the point scatterer incorporating all recurrent scattering loops is obtained by a regularization procedure. The physical significance of the point scatterer is discussed. In particular this model satisfies the off-shell version of the generalized optical theorem. The link between equipartition and Green's function reconstruction in a scattering medium is discussed.

Lopsided growth of Earth's inner core.

Hemispherical asymmetry is a prominent feature of Earth's inner core, but how this asymmetry relates to core growth is unknown. Based on multiple-scattering modeling of seismic velocity and attenuation measurements sampling the whole uppermost inner core, we propose that the growth of the solid core implies an eastward drift of the material, driven by crystallization in the Western Hemisphere and melting in the Eastern Hemisphere. This self-sustained translational motion generates an asymmetric distribution of sizes of iron crystals, which grow during their translation. The invoked dynamical process is still active today, which supports the idea of a young inner core.

Nonparametric estimation of the heterogeneity of a random medium using compound Poisson process modeling of wave multiple scattering.

In this paper, we present a nonparametric method to estimate the heterogeneity of a random medium from the angular distribution of intensity of waves transmitted through a slab of random material. Our approach is based on the modeling of forward multiple scattering using compound Poisson processes on compact Lie groups. The estimation technique is validated through numerical simulations based on radiative transfer theory.

Generalized eigenfunctions of layered elastic media and application to diffuse fields.

The spectral decomposition of the elastic wave operator in a layered isotropic half-space is derived by means of standard functional analysis methods. Particular attention is paid to the coupled P-SV waves. The problem is formulated directly in terms of displacements which leads to a 2 x 2 Sturm-Liouville system. The resolvent kernel (Green's function) is expressed in terms of simple plane-wave solutions. Application of Stone's formula leads naturally to eigenfunction expansions in terms of generalized eigenvectors with oscillatory behavior at infinity. The generalized eigenfunction expansion is employed to define a diffuse field as a white noise process in modal space. By means of a Wigner transform, we calculate vertical to horizontal kinetic energy ratios in layered media, as a function of depth and frequency. Several illustrative examples are considered including energy ratios near a free surface, in the presence of a soft layer. Numerical comparisons between the generalized eigenfunction summation and a classical locked-mode approximation demonstrate the validity of the approach. The impact of the local velocity structure on the energy partitioning of a diffuse field is illustrated.

Observation of multiple scattering of kHz vibrations in a concrete structure and application to monitoring weak changes.

In this paper, we present two experimental studies of mechanical wave propagation in a concrete building around 1 kHz. The first experiment is devoted to the observation of the coherent backscattering enhancement, which demonstrates the presence of multiple diffractions in the late part of the wave records. An application of multiple diffraction and reverberations is proposed in a second experiment. Thanks to their sensitivity to weak changes of the medium, the late records are used to monitor weak change in concrete wave velocity induced by thermal variations. The velocity change measurements have a precision of deltac/c=10(-4). Such a precision is difficult to obtain with direct waves. This experiment is the first step to other applications like stress, damage, aging, or crack monitoring in concrete structures.

Passive retrieval of Rayleigh waves in disordered elastic media.

When averaged over sources or disorder, cross correlation of diffuse fields yields the Green's function between two passive sensors. This technique is applied to elastic ultrasonic waves in an open scattering slab mimicking seismic waves in the Earth's crust. It appears that the Rayleigh wave reconstruction depends on the scattering properties of the elastic slab. Special attention is paid to the specific role of bulk to Rayleigh wave coupling, which may result in unexpected phenomena, such as a persistent time asymmetry in the diffuse regime.