|
The group is located in the Institut de Physique du Globe de Paris (IPGP) on the campus of Jussieu. The experimental part is located on the site of the IPGP at Saint-Maur east of Paris.
The administrative address of the group is:
|
Institut de Physique du Globe de Paris
Tour 24, Couloir 24-25, 4 ème étage 4 Place Jussieu 75252 - Paris cedex 05 (France) |
The Modelisation and Tomography (ModTom) group is part of the Seismological Laboratory (UMR 7580) of IPGP and an active component of the Physical Modelling and Numerical Department.
| Team members | ||
| Jean-Pierre Vilotte | Physicist | vilotte@ipgp.jussieu.fr |
| Albert Tarantola | Physicist | tarantola@ipgp.jussieu.fr |
| Eric Lajeunesse | Lecturer IPG | lajeunes@ipgp.jussieu.fr |
| Anne Mangeney | Lecturer Paris VII | mangeney@ipgp.jussieu.fr |
| G. Moguilny | System engineer | moguilny@ipgp.jussieu.fr |
| Jean-Paul Ampuero | Ph.D. student | ampuero@ipgp.jussieu.fr |
| Lydie Staron, | Ph.D. student | staron@ipgp.jussieu.fr |
| Julien Couder | Ph.D. student | couder@ipgp.jussieu.fr |
| Sudhakar Yerneni | PostDoc | sudhakar@ipgp.jussieu.fr |
The research activities of the Modelisation and Tomography group are focused on the physics of disordered geological systems. The modelisation in this field requires an original approach combining numerical and experimental studies.
The main objectives of our research are:
The physics of a number of geological systems has still to be formulated. A major difficulty is the analysis and the integration at the geological scales of the physical information obtained at small scales. This work implies close collaborations with other fields like physics, mechanics and numerical analysis.
Propagation of seismic waves in 3D heterogeneous media is an important problem in geophysics which is still not well understood and difficult to model. The modelisation in this field has important implications for seismic risk and site effects, regional and exploration tomography.
At scales of a fault zone, a geological basin or the lithosphere, the variations of the seismic wave velocities are quite strong, exceeding often 15%. Moreover, the structures are generally complex and anisotropic. The wave propagation are then associated with localisation phenomena resulting on the seismograms, behind the first coherent arrivals, in an incoherent signal, or coda, associated with multiple diffractions. Mode conversion, i.e. the energy transfer between compressive and shear waves, is a characteristic signature of heterogeneous media. In these media, the wavenumber polarization can rapidly disappear. The way it disappears contain important informations on the underlying structures. Theoretically, it is important to develop models that can take into account the multi-scales spectrum of the heterogeneities in the propagation and the diffraction of the wavefield as well as the diffraction by surface topography.
We develop direct numerical simulation (DNS) methods which can take into account the heterogeneities and the geometrical complexity of geological media. Classical methods in seismology faces today serious limit. One important problem is free surface and interface boundary conditions. We have developed a spectral element method combining the geometrical flexibility of finite element methods with the high precision of spectral methods. This variational method, in space, leads to an accurate resolution of surface and interface waves in strongly heterogeneous media. This theoretical formulation has allowed us to simulate the response of geological basins and site effects. A multi-scale resolution can be achieved using variational mortar methods with non conforming meshes.
Even though the advent of parallel architectures allows more and more advanced direct numerical simulations of wave propagation in heterogeneous media, a number of theoretical and observational difficulties make this approach difficult. In particular, for large propagation distances, compared to characteristic wavelengths of the propagative signal and correlation lengths of the heterogeneities, the seismic energy becomes essentially incoherent. For realistic 3D geometries, it is quite difficult to generate, with DNS methods, long duration synthetic seismograms. Moreover, comparison with observations can only been made statistically. In this regime, the development of physical approximations like radiative transport coupled with Monte-Carlo methods is a promising approach. We start to work in this direction. One goal here is, through a direct comparison between DNS and radiative transport methods, to get a better understanding of the validity domain of such approximations and of the transition between radiative and localisation regimes in heterogeneous media.
At global scale, imaging the internal structures of the earth and understanding their links with geodynamics is a difficult problem due the wide range of scales of the heterogeneities: in the crust and the lithosphere (ocean-continents, earth topography, ...); in the mantle (subduction zones, plumes, topography of the main discontinuities, ...); as well as in the vicinity of some main interfaces (D" transition zone at the core-mantle boundary). In this problem, seismology is a fundamental tool which relies on: in one hand, the recording at the surface of broad-band seismograms, via the rapid deployment of global networks like the GEOSCOPE network; on the other hand, the physical understanding of the wavefield propagation within laterally heterogeneous earth models. The energy sources are here the earthquakes with a spatial repartition that is far from being uniform and strongly correlated with plate dynamics. Global seismology makes use essentially of the coherent part of the seismograms: arrival times of various phases of surface and body waves, differential time arrivals, eigenfrequencies of normal modes of the earth and more recently waveforms.
Since the first spherically symmetric ``mean'' earth models with only radial variations of seismic properties (density, wave velocities), seismologists try to characterize the perturbations with respect to these mean reference models, i.e. long wavelengths lateral variations, and to correlate them with plate tectonics and mantle convection. All these studies suggest 3D structures over a wide range of scales. Improving the resolution of the global tomographic models requires now a deeper physical understanding of potential signatures of small scale heterogeneities in the seismic observations recorded at the surface.
The traditional approach, based on inversion techniques, faces serious limitations that come in part from the use of restrictive approximations of the elastodynamics equations. The direct computation of body waves travel time is based on various ray approximations, while surface waves modelisation relies on various Born and asymptotic approximations. Up to now, the computation of synthetic seismograms makes use of normal mode summation methods. A reference basis of normal modes is computed for a spherically symmetric elastic, or anelastic, non rotating reference earth model and is expanded into generalized spherical harmonics basis. The ellipticity, the rotation and the lateral variations are then computed as small perturbations with respect to the reference solution and expressed in the same basis. The solution of the perturbed problem requires to take into account the coupling between modes and a second order, or higher, perturbation analysis. This limits the feasibility of such an approach. For this reason, waveform modeling is generally limited, for laterally heterogeneous aspherical earth models, to surface waves.
We have started to develop direct numerical simulation methods for wavefield propagation, in space and time, at global scales to improve our physical understanding of wave propagation in realistic earth models and of the signatures of lateral heterogeneities in the seismograms recorded at the surface. This approach is complementary to traditional inversion approaches, and should allow the quantification of the actual limits of the various approximations used in the direct problem of the inversion methods and suggest new approximations. The main difficulties are here: the geometrical discretization; the accurate computation of surface and interface waves; the solid-liquid coupling at the core-mantle interface; the computational cost.
The extension of the spectral element method to global earth models is based on: on one hand, the use of geometrical transformations, based on a gnomonic projection, allowing the discretization of the sphere in hexahedra and of surface and interfaces topography; on the other hand, variational mortar techniques allowing, via non conforming meshes, an optimal resolution of the radial variations of the elastic parameters and of the interface discontinuities as well as local mesh refinement. Moreover, in order to reduce the computational cost, we also developed a method allowing to couple the spectral element method, formulated in space and time, with a modal summation method, formulated in frequency and wavenumber, via a DtN (Dirichlet-to-Nemann) interface operator. Lateral heterogeneities are then limited to the spectral element domain, an outer shell which can be mapped to the whole mantle, while only radial heterogeneities are assumed in the modal summation domain defined as an inner sphere.
This leads to interesting perspectives for the study of lithospheric heterogeneities or the D" transition zone at the core-mantle boundary. These theoretical developments have allowed us to simulate for the first time the complete wavefield propagation in laterally heterogeneous spherical earth models like SAW12D (smooth heterogeneities), down to a corner period of 30 seconds, as well as the diffraction by spatially localized heterogeneities like plumes.
The research directions are now to introduce the earth topography and the ocean-continent transitions as well as, for low frequency, the mass redistribution. An open theoretical problem is to take into account a non stratified liquid core.
The acquisition of increasingly accurate near-field observations, with the help of broad-band borehole instruments and GPS or interferometric measurements, allows today better constrains on the spectral content of the seismic source, on the slip and slip-rate fields distributions during an earthquake as well as on the resolution of precursor mechanisms during the rupture nucleation. These new observations, and the one to come with the project in the Gulf of Corinth, suggest a need for upstream theoretical investigations of dynamic rupture modelling in order to better understand the physics of the nucleation and of the dynamic propagation of a seismic rupture; to predict pertinent observations and to suggest new data acquisition programs. Rupture modelling must integrate several scales in order to resolve: the dynamics of the nucleation phase and of the propagating rupture front; the associated radiation field and its propagation within realistic geological media. In the same time, the internal structures of the fault zones has to be taken into account as well as the competing interactions between volumetric dissipation (damage) and surface dissipation (friction). These points are essential to understand physically the influence of the various parameters and to control the models by seismic and accelerometric observations, in the vicinity of faults, as well as by co-seismic geodesic observations.
From a theoretical point of view, we are working on the seismic nucleation phase. The goal here is to precise the scaling laws that may correlate the spatial extension and the duration of the nucleation process to the physical parameters of the effective friction constitutive laws, the size and the distribution of the asperities along the fault, and the size of the fault. This work has been extended to damaged fault zones and systems of parallel faults. We are also studying the dynamics of propagating rupture front along heterogeneous faults, described by a random distribution of asperities. We have characterized the spatio-temporal correlations of the slip-field, induced by the interaction between the rupture dynamics and the disorder of the interface. Recently, we have characterized the inertial effects on the long term dynamics of heterogeneous fault interfaces. This study is based on an original perturbation analysis that has allowed us to identify a cross-over transition between a seismically weakly coupled regime, characterized by a recurrent activity on a small number of asperities, and a strongly coupled regime, characterized by an algebraic spatio-temporal distribution of the seismic activity. This work has some interesting implications in term of the analysis of co-seismic geodesic observations.
We are developing in parallel variational methods for the direct numerical simulation of the seismic rupture which can take into account more realistic fault zones and more accurate approximations of the contact and friction conditions retaining small dispersion errors. This type of formulation, combined with variational mortar techniques for non conforming discretizations provide the possibility of a consistent coupling between domains with high frequency resolution, in the immediate vicinity of the fault zone, and domains of lower frequency resolution for the 3D propagation of the radiated wavefield within realistic geological structures. High frequency resolution is required in the vicinity of the fault zone to resolve the scales associated with the dynamic rupture front propagation. Such a high resolution should allow new insights on phenomena like supershear front propagation and direct comparisons between broad-band kinematic models and dynamic models. Applications are here the simulation of earthquake events along strike or subduction faults.
Today, the nature of the physical processes that trigger the instability and the gravitational flow of rock masses is poorly understood. This flows, intrinsically transient and non uniform, exhibit a striking mobility of controversial origin. In the lack of a clear physical basis, the phenomenological models of transport for these flows are difficult to constrain and are far from being predictive.
If natural avalanches can not generally be reduced to ``simple'' dry avalanches, it is of interest, taking into account the complexity of the underlying physical mechanisms, to first study simple physical models at the scale of the particles. Analysis at this scale, and its implications for macroscopic formulations through pertinent internal variables, is far from being an easy problem due to subtle interactions between the geometrical evolution of the underlying structures and the non smooth frictional and contact particle interactions as well as possible cohesive interactions.
The study of rock avalanches requires the physical analysis of two regimes: quasi-static and dynamic, as well as the transition between them. In the static regime, the system evolves under external sollicitations, local or gravity forces, toward a stability threshold which trigger the inset of motion of a more or less important volume of material. Understanding this regime is of importance in view of the risk assessment associated with avalanches in volcanic and mountains area since these instabilities are still today quite unpredictable. The evolution, during the quasi-static phase, of the force and the contact networks, of the density controls the stability limit and the importance of the volume of material actually mobilized. The problem here is to understand possible correlations between the initial texture, its progressive reorganization and the dynamic angle of stability. Another important issue is to identify possible precursors and to study their signatures on recorded signals at the surface. In the dynamic regime, the inertial flow mobilizes the system at various depths and is triggered by complex convection/diffusion, segregation and erosion processes over long distances. Analysis of the velocity fluctuations and of the thickness of the mobilized layer should allow better constrains on the validity limits and the pertinence of the phenomenological models that are usually formulated in terms of coupled hydrodynamic variables.
Our research is based on a combined numerical and experimental approach. These studies require measurements of physical variables at both local and global scales during the quasi-static and the dynamic phases. Discrete numerical simulation is in that respect quite attractive, specially with the continuously increase of computational resources which allow now 3D simulations. The method that we are using is the non-smooth contact dynamics method, developed by J.J. Moreau and M. Jean in the LGMC (Montpellier). The method allows the statistical analysis of the evolution of the texture, of the force network, of the velocity and the strain rates as well as of the kinetic and the dissipative energies. Numerical experiments allow to identify the pertinent variables, and their characteristic fluctuation scales, that must be taken into account in a phenomenological formulation. In parallel, we develop continuous numerical models for the dynamic phase based on shallow-water approximations. These models are required for actual studies at geological scales. However, their formulation and validity have to be evaluated with regard to the discrete numerical experiments. The characteristic regimes of natural avalanches are still today a numerical and a physical challenge.
Our experimental approach is at the moment bidimensional. A first type of experiments involves simple physical configuration: a bi-dimensional channel, between two thick glass plates, in which we can study the destabilization and the flow of a granular mass made of weakly polydisperse disks or spheres. The avalanches are triggered by an external driving force: either a local perturbation or a rotation of experimental set-up (gravitational perturbation). The configuration allows us to study the quasi-static evolution toward the stability threshold and the avalanche flow and its arrest phase. Latter, we consider the possibility of more complex configurations. One of these includes having a rough basal topography. When the bottom is made of a weakly cohesive material, erosion and deposition processes can take place modifying the dynamics and the runout of the avalanches. The acquisition techniques that we use are: digital ultra-speed camera with high resolution (CCD camera) allowing image and particle tracking analysis; pressure sensors; and ultrasonor measurements.
Among natural hazards, debris flows are fast gravitational particulate flows
involving multi-phase media. The physical understanding of the mechanisms that
trigger the stability, the mobilization, the flow and the arrest of these
saturated and weakly consolidated sediment masses is a scientific challenge
with important implications in the domains of the geomorphology, the
environment, and the rock mechanics.
While the physics of rock avalanches is mainly controlled by solid interactions
between particles and mud flows are mainly dominated by fluid forces, debris
flow involve complex interactions between the solid and the fluid phases. These
transient flows, mobilize important volumes, occur in very short time scales,
less than 10 000 seconds, with velocities that can be as fast as 10 meters per
second, imply strong inertial forces, and exhibit a remarkable mobility which
remains unexplained. The solid phase concentrations are not that different
from those of the static sediment masses and can exceed 60 %. While these
materials can sustain shear stresses up to a certain threshold, during the
flow they behave like a multiphase fluid over characteristic time scales of
several seconds. This fluid behaviour implies: for slow flows,
competing effects between volumetric dissipation, associated with the viscosity
of the interstitial fluids, and surface dissipation, associated with contacts
between solid particles, as well as segregation and sedimentation processes;
for fast flows, turbulent scales of dissipation, and dynamic
collisions between solid particles, associated with the notion of granular
temperature, as well as non local interactions between the fluid and the solid
phases that can trigger density waves phenomena.
The modelisation requires to take into account the multiphase nature of these flows. Unfortunately, we do not have today clear physical models for such inertial regimes. A better physical understanding of the dynamics of debris flows should allow the evaluation of the runout distances and of the capacity for the flow to over pass local topography. An important aspect here is to characterize the dynamics at both local and global scales. This requires the analysis of velocity fluctuations and their correlations; of the fluid-solid interactions like viscous drag and non-local hydrodynamic interactions; of the thickness fluctuations of the mobilized layer during the flow.
The aim of our current research is to get new physical insights in the dynamics of debris flows from a combined experimental and numerical approach. This especially since the violence of debris flow phenomena makes field measurements quite difficult even though textures of the deposit are useful observations. In view of the complexity of the mechanisms involved in debris flows, it is important to first consider simple physical models at the scale of the particles even if such analysis and its integration into phenomenological models through internal variables remains a challenging problem. Experimental and numerical analysis require measurements of physical variables at both local and global scales.
In the experimental approach, we are considering a bidimensional set-up, an inclined Hele-Shaw cell, and a tridimensional set-up, an inclined plane channel, for dense polydisperse suspensions. By controlling the viscosity of the interstitial fluid, different flow regimes can be studied. Segregation and sedimentation mechanisms can also be quantified during experiments. The experimental analysis will make use of ultrasonor and light measurements, of pressure sensors and digital camera visualisation.
In the numerical approach, we are developing direct simulation methods, in 2D and 3D, at both the discrete and the continuous scales. At the discrete scale, the method takes into account a continuous fluid phase, with viscous and inertia effects, and a solid phase made of discrete particles in which interactions between particles and fluid as well as particle collisions are explicitly formulated. This allows to study the complex interactions between fluid pressure and granular temperature. At the continuous scale, we try to develop models that take into account inertia effects and solid-fluid phase interactions within a shallow-water approximation.
Le document d'Albert est mis a part dans un directory propre (GeoTheo)
The group has active collaborations with the following teams.
We are also part of the new GDR ``Milieux Divisés'' of the CNRS.
The group has a dual approach experimental and numerical