523 research outputs found
Structural uncertainty of time-migrated seismic images
AbstractStructural information in seismic images is uncertain. The main cause of this uncertainty is uncertainty in velocity estimation. We adopt the technique of velocity continuation for estimating velocity uncertainties and corresponding structural uncertainties in time-migrated images. Data experiments indicate that structural uncertainties can be significant even when both structure and velocity variations are mild
A fast butterfly algorithm for the hyperbolic Radon transform
We introduce a fast butterfly algorithm for the hyperbolic Radon transform commonly used in seismic data processing. For two-dimensional data, the algorithm runs in complexity O(N[superscript 2] logN), where N is representative of the number of points in either dimension of data space or model space. Using a series of examples, we show that the proposed algorithm is significantly more efficient than conventional integration
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
Azimuthally Anisotropic 3D Velocity Continuation
We extend time-domain velocity continuation to the zero-offset 3D azimuthally anisotropic
case. Velocity continuation describes how a seismic image changes given a change in migration
velocity. This description turns out to be of a wave propagation process, in which images
change along a velocity axis. In the anisotropic case, the velocity model is multiparameter.
Therefore, anisotropic image propagation is multidimensional. We use a three-parameter
slowness model, which is related to azimuthal variations in velocity, as well as their principal
directions. This information is useful for fracture and reservoir characterization from
seismic data. We provide synthetic diffraction imaging examples to illustrate the concept
and potential applications of azimuthal velocity continuation and to analyze the impulse
response of the 3D velocity continuation operator
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
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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
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