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ISBN 978-952-5726-09-1 (Print)
Proceedings of the Second International Symposium on Networking and Network Security (ISNNS ’10)
Jinggangshan, P. R. China, 2-4, April. 2010, pp. 129-132
Modeling Seismic Wave Propagation Using
Graphics Processor Units (GPU)
Zhangang Wang 1 , Suping Peng 1 , and Tao Liu 2
1 State Key Laboratory of Coal Resources and Mine Safety, China University of Mining and Technology, Beijing, China
Email: millwzg@163.com
2 School of Earth and Space Sciences, Peking University, Beijing, China
Email: liuluot@126.com
Abstract—The main drawback of the seismic modeling in
2D viscoelastic media on a single PC is that simulations
with large gridsizes require a tremendous amount of
floating point calculations. To improve computation
speedup, a graphic processing units (GPUs) accelerated
method was proposed using the staggered-grid finite
difference (FD) method. The geophysical model is
decomposed into subdomains for PML absorbing
conditions. The vertex and fragment processing are fully
used to solve FD schemes in parallel and the latest updated
frames are swapped in Framebuffer Object (FBO)
attachments as inputs for the next simulation step. The
simulation program running on modern PCs provides
significant speedup over a CPU implementation, which
makes it possible to simulate realtime complex seismic
propagation in high resolution of 2048*2048 gridsizes on
low-cost PCs.
Index Terms—seismic, wave propagation, finite difference,
viscoelastic media, model, GPU
I. INTRODUCTION
The main drawback of the FD method is that
simulations with large model spaces or long
nonsinusoidal waveforms can require a tremendous
amount of floating point calculations and run times. In
recent years the spatial parallelism on high-performance
PC clusters makes it a promising method for seismic
numerical computing in realistic (complex) media [1, 2].
Modern GPUs have now become ubiquitous in
desktop computers and offer an excellent cost-toperformance-ratio,
exceeding the performance of general
purpose CPU by many times, due to their powerful and
fully programmable parallel processing architectures. In
the past few years, programmability of GPU and
increased floating point precision has allowed GPU to
perform general purpose computations [3, 4].
In this article, we have proposed a new
implementation under the current GPU architecture to
improve the real-time FD simulation of wave
propagation in viscoelastic media, including domain
decomposition and processing techniques.
II. THEORY
Early researches on FDM for elastic wave modeling in
complex media gradually formulated finite difference
schemes based on a system of high-order coupled elastic
equations [5-8]. In such studies, however, the earth’s
viscosity has been ignored and synthetic seismograms
fail to model attenuation and dispersion of seismic waves.
Day and Minster [9] made the first attempt to incorporate
anelasticity into a 2-D time-domain modeling methods
by applying a Pade approximant method. An efficient
approach [10] was proposed based on the rheological
model called “generalized standard linear solid” (GSLS),
which was shown to explain experimental observations
of wave propagation through earth materials [11]. Then a
staggered grid finite difference technique was proposed
based on the GSLS to model the propagation of seismic
waves in 2D/3D viscoelastic media [12], for staggeredgrid
operators are more accurate than standard grid to
perform first derivatives for high frequencies close to the
Nyquist limit [8].
A. Staggered-grid Finite difference formulation
The first-order velocity-stress equations of viscoelastic
wave propagation are given by
s
⎧∂σ
xy τ v
ε
∂v
∂
x y
⎪ = μ ( + ) + γ
xy
⎪ ∂t τσ
∂y ∂x
⎪
p
s
∂σxx
τ v
x y
v
ε
∂v
∂ τ ∂
ε y
⎪ = π ( + ) −2μ ⋅ + γxx
⎪ ∂t τσ
∂x ∂y τσ
∂y
⎪
p
s
⎪
∂σ yy τ v v
ε
∂ ∂
x y τε
∂vx
= π ( + ) −2μ ⋅ + γ
yy
⎪ ∂t τσ
∂x ∂y τσ
∂x
⎪
p
s
⎪∂γ xx
1 τ v vy
vy
[ (
ε
∂ ∂ 1)(
x
τ ∂
xx
) 2 (
ε
=− γ + π − + − μ − 1) ⋅ ]
⎪ ∂t τσ τσ ∂x ∂y τσ
∂y
⎨
p
s
⎪∂γ
yy 1 τ [
yy (
ε
∂v
∂v
x y τε
∂vx
⎪
=− γ + π −1)( + ) −2 μ( −1) ⋅ ]
∂t
τσ
τσ
∂x ∂y τ
σ
∂x
⎪
⎪∂
s
γ
xy 1 τ v vy
[ (
ε ∂ 1)(
x ∂
⎪ =− γ
xy
+ μ − + )]
⎪ ∂ t τσ
τσ
∂ y ∂ x
⎪∂vx
1 ∂σ
∂σ
xy
[
xx
⎪ = + + fx
]
⎪ ∂t ρ ∂x ∂y
⎪ ∂ vy 1 ∂ σxy ∂ σ
⎪
yy
= [ + + f
y ]
⎪⎩
∂t ρ ∂x ∂y
The moduli π, μ can be expressed as
π = v
ρR
2 2
p0
1 ,
iw0τ
σ p
+ τε
+ iw0τ
σ
1 1
μ = v
ρR
2 2
s0
1
(1)
(2)
iw0τ
σ s
+ τ
ε
+ iw0τ
σ
1 1
Where v P0 , v S0 denote the phase velocity at the centre
frequency of the source(w 0 ) for P- and S-waves,
respectively. The symbol R denotes the real part of the
complex variable. The constants of stress relaxation
times for both P-and S-waves, can be calculated by
quality factor Q and angular frequency w.
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