Bernard Valette

Spectral Element Analysis in Seismology

We present a review of the application of the spectral-element method to regional and global seismology. This technique is a high-order variational method that allows one to compute accurate synthetic seismograms in three-dimensional heterogeneous Earth models with deformed geometry. We first recall the strong and weak forms of the seismic wave equation with a particular emphasis set on fluid regions. We then discuss in detail how the conditions that hold on the boundaries, including coupling boundaries, are honored. We briefly outline the spectral-element discretization procedure and present the time-marching algorithm that makes use of the diagonal structure of the mass matrix. We show examples that illustrate the capabilities of the method and its interest in the context of the computation of three-dimensional synthetic seismograms.

3D maps of the local ISM from inversion of individual color excess measurements

Three-dimensional (3D) maps of the Galactic interstellar matter (ISM) are a potential tool of wide use, however accurate and detailed maps are still lacking. One of the ways to construct the maps is to invert individual distance-limited ISM measurements, a method we have here applied to measurements of stellar color excess in the optical. We have assembled color excess data together with the associated parallax or photometric distances to constitute a catalog of ~ 23,000 sightlines for stars within 2.5 kpc. The photometric data are taken from Stromgren catalogs, the Geneva photometric database, and the Geneva-Copenhagen survey. We also included extinctions derived towards open clusters. We applied, to this color excess dataset, an inversion method based on a regularized Bayesian approach, previously used for mapping at closer distances. We show the dust spatial distribution resulting from the inversion by means of planar cuts through the differential opacity 3D distribution, and by means of 2D maps of the integrated opacity from the Sun up to various distances. The mapping assigns locations to the nearby dense clouds and represents their distribution at the spatial resolution that is allowed by the dataset properties, i.e. of the order of ~10 pc close to the Sun and increasing to ~100 pc beyond 1 kpc. Biases towards nearby and/or weakly extincted stars make this dataset particularly appropriate to map the local and neighboring cavities, and to locate faint, extended nearby clouds, both goals that are difficult or impossible with other mapping methods. The new maps reveal a ~1 kpc wide empty region in the third quadrant in the continuation of the so-called CMa tunnel of the Local Cavity, a cavity that we identify as the Superbubble GSH238+00+09 detected in radio emission maps and that is found to be bounded by the Orion and Vela clouds.

Spectral element modelling of three-dimensional wave propagation in a self-gravitating Earth with an arbitrarily stratified outer core

SUMMARY This paper deals with the spectral element modelling of seismic wave propagation on a global scale. Two aspects relevant to low-frequency studies are particularly emphasized. First, the method is generalized beyond the Cowling approximation in order to fully account for the effects of self-gravitation. In particular, the perturbation of the gravity field outside the Earth is handled by a projection of the spectral element solution onto the basis of spherical harmonics. Second, we propose a new formulation inside the fluid which allows us to account for an arbitrary density stratification. It is based upon a decomposition of the displacement into two scalar potentials, and results in a fully explicit fluid–solid coupling strategy. The implementation of the method is carefully detailed and its accuracy is demonstrated through a series of benchmark tests.

Spatial distribution of interstellar dust in the Sun's vicinity Comparison with neutral sodium-bearing gas

Aims. 3D tomography of the interstellar dust and gas may be useful in many respects, from the physical and chemical evolution of the interstellar medium itself to foreground decontamination of the cosmic microwave background, or various studies of the environments of specific objects. However, while spectral data cubes of the galactic emission become increasingly precise, the information on the distance to the emitting regions has not progressed as well and relies essentially on the galactic rotation curve. Our goal here is to bring more precise information on the distance to nearby interstellar dust and gas clouds within 250 pc. Methods. We apply the best available calibration methods to a carefully screened set of stellar Stromgren photometry data for targets possessing a Hipparcos parallax and spectral type classification. We combine the derived interstellar extinctions and the parallax distances for about 6000 stars to build a 3D tomography of the local dust. We use an inversion method based on a regularized Bayesian approach and a least squares criterion, optimized for this specific data set. We apply the same inversion technique to a totally independent set of neutral sodium absorption data available for about 1700 target stars. Results. We obtain 3D maps of the opacity and the distance to the main dust-bearing clouds within 250 pc and identify in those maps well-known dark clouds and high galactic more diffuse entities. We calculate the integrated extinction between the Sun and the cube boundary and compare this with the total galactic extinction derived from infrared 2D maps. The two quantities reach similar values at high latitudes, as expected if the local dust content is satisfyingly reproduced and the dust is closer than 250 pc. Those maps show a larger high latitude dust opacity in the North compared to the South, reinforcing earlier evidences. Interestingly the gas maps do not show the same asymmetry, suggesting a polar asymmetry of the dust to gas ratio at small distances. We compare the opacity distribution with the 3D distribution of interstellar neutral sodium resulting from the inversion of sodium columns. We discuss the similarities and discrepancies and the influence of data set limitations. Finally we discuss the potential improvements of those 3D maps.

Seismic noise correlations to image structural and mechanical changes associated with the Mw 7.9 2008 Wenchuan earthquake

We locate temporal changes of seismic wave speed and scattering properties of the crust associated with the 2008 Mw7.9 Wenchuan earthquake. To that end, we analyze ambient seismic noise records from 2007 until the end of 2008 in the 1–3 s period band and in the 12–20 s period band measured in a region that covers the southern two thirds of the fault activated during the earthquake. To locate the changes, we use a refined imaging procedure based on the sensitivity of scattered waves to weak perturbations. This inverse method uses the radiative transfer approximation to describe the intensity of the noise correlation coda. Our results show that the largest structural changes are observed northeast of the Wenchuan epicenter, around the fault zone where aftershocks are distributed. The spatial and temporal characteristics of the behavior of the crust at depth around the Wenchuan earthquake suggest a postseismic and geology-dependent signature of the middle crust. We also observe a clear seasonal signature within the Sichuan basin at depth that we relate to the heavy rainfalls during the monsoon season. This seasonality can also be observed at the surface in form of a waveform decoherence. Our study highlights that seismic velocity changes, and waveform decoherence are independent measurements that are sensitive to different parameters and can thus give complementary information. In our study we also point out the value of studying the evolution of the changes at different times in the coda.

NaI and HI 3-D density distribution in the solar neighbourhood

A study of the local interstellar medium (LISM) using a robust inversion method, similar to current tomography techniques, is applied to compiled data on neutral interstellar absorbers and Hipparcos parallaxes. We present here the 3-D distribution of two neutral species, NaI and HI. Our analysis enables us to obtain a reliable 3-D density distribution of the IS matter in the solar neighbourhood, providing a new basis for the discussion of origin, present state and evolution of the LISM. We show that neutral IS matter is distributed in compact clouds or in cloud complexes with cavities between them. It is now easy to distinguish the so-called Local Bubble and the Loop I cavities and also two tunnels linking the Local Bubble to the outer regions of the galaxy, away from the galactic plane. Better accuracy is achieved for NaI, as to a larger number of lines-of-sight and target stars than are available for HI. A rather detailed NaI 3-D density distribution is obtained with a 40 pc smoothing length. The extended high-density regions in the NaI and HI maps are correlated which is not the case for the diffuse regions. The density ratio

Bornes des moments de la densité à l'intérieur de la Terre ou d'une planète

\rho_{\rm HI}/\rho_{\rm NaI}

Inversion of field data in fault tectonics to obtain the regional stress — I. Single phase fault populations: a new method of computing the stress tensor

is lower or equal to

Spatial and temporal evolution of a long term slow slip event: the 2006 Guerrero Slow Slip Event

9.1.10^{8} \pm 3.10^{8}

Flattening of the Earth: further from hydrostaticity than previously estimated

for extended high density clouds.