Seismic modeling using the frozen Gaussian approximation

We adopt the frozen Gaussian approximation (FGA) for modeling seismic waves. The method belongs to the category of ray-based beam methods. It decomposes seismic wavefield into a set of Gaussian functions and propagates these Gaussian functions along appropriate ray paths. As opposed to the classic Gaussian-beam method, FGA keeps the Gaussians frozen (at a fixed width) during the propagation process and adjusts their amplitudes to produce an accurate approximation after summation. We perform the initial decomposition of seismic data using a fast version of the Fourier-Bros-Iagolnitzer (FBI) transform and propagate the frozen Gaussian beams numerically using ray tracing. A test using a smoothed Marmousi model confirms the validity of FGA for accurate modeling of seismic wavefields.Comment: 5 pages, 8 figure

Analysis and algorithms for a regularized Cauchy problem arising from a non-linear elliptic PDE for seismic velocity estimation

In the present work we derive and study a nonlinear elliptic PDE coming from the problem of estimation of sound speed inside the Earth. The physical setting of the PDE allows us to pose only a Cauchy problem, and hence is ill-posed. However we are still able to solve it numerically on a long enough time interval to be of practical use. We used two approaches. The first approach is a finite difference time-marching numerical scheme inspired by the Lax-Friedrichs method. The key features of this scheme is the Lax-Friedrichs averaging and the wide stencil in space. The second approach is a spectral Chebyshev method with truncated series. We show that our schemes work because of (1) the special input corresponding to a positive finite seismic velocity, (2) special initial conditions corresponding to the image rays, (3) the fact that our finite-difference scheme contains small error terms which damp the high harmonics; truncation of the Chebyshev series, and (4) the need to compute the solution only for a short interval of time. We test our numerical scheme on a collection of analytic examples and demonstrate a dramatic improvement in accuracy in the estimation of the sound speed inside the Earth in comparison with the conventional Dix inversion. Our test on the Marmousi example confirms the effectiveness of the proposed approach

Modelling the evaporation of thin films of colloidal suspensions using Dynamical Density Functional Theory

Recent experiments have shown that various structures may be formed during the evaporative dewetting of thin films of colloidal suspensions. Nano-particle deposits of strongly branched `flower-like', labyrinthine and network structures are observed. They are caused by the different transport processes and the rich phase behaviour of the system. We develop a model for the system, based on a dynamical density functional theory, which reproduces these structures. The model is employed to determine the influences of the solvent evaporation and of the diffusion of the colloidal particles and of the liquid over the surface. Finally, we investigate the conditions needed for `liquid-particle' phase separation to occur and discuss its effect on the self-organised nano-structures

Commande numérique d'axe avec compensation du couple résistant

A PWM fed synchronous motor drive with high performances is achieved by utilization of a state space control with load torque compensation. With a simple model, a state space load torque observer is studied and implemented. This control law, applied to a synchronous motor, results in a low sensitive position control system.La réalisation d'un variateur de position de haute performance, constitué d'une machine synchrone associée à un onduleur de tension MLI, peut s'obtenir en utilisant des techniques d'état associées à la compensation du couple résistant. Nous avons, dans ce travail, développé un observateur dynamique de couple, élaboré à partir d'un modèle simple assurant une bonne évaluation de la charge entrainée. L'utilisation d'un tel dispositif, nous permet d'obtenir un servomoteur synchrone doué de caractéristiques indépendantes de la charge

Characterizing Marine Gas-Hydrate Reservoirs and Determining Mechanical Properties of Marine Gas-Hydrate Strata With 4-Component Ocean-Bottom-Cable Seismic Data

The technical approach taken in this gas-hydrate research is unique because it is based on applying large-scale, 3-D, multi-component seismic surveys to improve the understanding of marine gas-hydrate systems. Other gas-hydrate research uses only single-component seismic technology. In those rare instances when multi-component seismic data have been acquired for gas-hydrate research, the data acquisition has involved only a few receiver stations and a few source stations, sometimes only three or four of each. In contrast, the four-component, 3-D, ocean-bottom-cable (4C3D OBC) data used in this study were acquired at thousands of receiver stations spaced 50 m apart over an area of approximately 1,000 km{sup 2} using wavefields generated at thousands of source stations spaced 75 m apart over this same survey area. The reason for focusing research attention on marine multi-component seismic data is that 4C3D OBC will provide a converted-SV image of gas-hydrate systems in addition to an improved P-wave image. Because P and SV reflectivities differ at some stratal surfaces, P and SV data provide two independent, and different, images of subsurface geology. The existence of these two independent seismic images and the availability of facies-sensitive SV seismic attributes, which can be combined with conventional facies-sensitive, P-wave seismic attributes, means that marine gas-hydrate systems should be better evaluated using multi-component seismic data than using conventional single-component seismic data. Conventional seismic attributes, such as instantaneous reflection amplitude and reflection coherency, have been extracted from the P and SV data volumes created from the 4C3D OBC data used in this research. Comparisons of these attributes and comparisons of P and SV time slices and vertical slices show that SV data provide a more reliable image of stratigraphy and structure associated with gas-invaded strata than do P-wave data. This finding confirms that multi-component seismic data will be more valuable than conventional P-wave seismic data for exploiting gas-hydrate reservoirs that cause gas invasion into surrounding strata. Published laboratory studies have shown that the ratio of P-wave velocity (V{sub p}) and SV velocity (V{sub s}) is an important parameter for identifying lithofacies. (In this report, the subscript S that accompanies a parameter can be replaced with the subscript SV to more accurately define the type of shear wave data used in this study.) Seismic estimates of V{sub p}/V{sub s} can be made when multi-component seismic data are acquired. Seismic-based V{sub p}/V{sub s} ratios are being analyzed across the research study area to determine what types of shallow lithofacies can be distinguished by this velocity parameter. These research findings will be summarized in the final project report