61 research outputs found
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
Learning Rays via Deep Neural Network in a Ray-based IPDG Method for High-Frequency Helmholtz Equations in Inhomogeneous Media
We develop a deep learning approach to extract ray directions at discrete
locations by analyzing highly oscillatory wave fields. A deep neural network is
trained on a set of local plane-wave fields to predict ray directions at
discrete locations. The resulting deep neural network is then applied to a
reduced-frequency Helmholtz solution to extract the directions, which are
further incorporated into a ray-based interior-penalty discontinuous Galerkin
(IPDG) method to solve the Helmholtz equations at higher frequencies. In this
way, we observe no apparent pollution effects in the resulting Helmholtz
solutions in inhomogeneous media. Our 2D and 3D numerical results show that the
proposed scheme is very efficient and yields highly accurate solutions.Comment: 30 page
Low Regularity Ray Tracing for Wave Equations with Gaussian beams
We prove observability estimates for oscillatory Cauchy data modulo a small
kernel for -dimensional wave equations with space and time dependent
and coefficients using Gaussian beams. We assume the domains and
observability regions are in , and the GCC applies. This work
generalizes previous observability estimates to higher dimensions and time
dependent coefficients. The construction for the Gaussian beamlets solving
wave equations represents an improvement and simplification over
Waters (2011).Comment: this version shortens and changes the previous construction and
contains an extension to space time dependent coefficient
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