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A variational formulation of a stabilized unsplit convolutional perfectly matched layer for the isotropic or anisotropic seismic wave equation
 CMES
, 2008
"... In the context of the numerical simulation of seismic wave propagation, the perfectly matched layer (PML) absorbing boundary condition has proven to be efficient to absorb surface waves as well as body waves with non grazing incidence. But unfortunately the classical discrete PML generates spurious ..."
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Cited by 16 (7 self)
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In the context of the numerical simulation of seismic wave propagation, the perfectly matched layer (PML) absorbing boundary condition has proven to be efficient to absorb surface waves as well as body waves with non grazing incidence. But unfortunately the classical discrete PML generates spurious modes traveling and growing along the absorbing layers in the case of waves impinging the boundary at grazing incidence. This is significant in the case of thin mesh slices, or in the case of sources located close to the absorbing boundaries or receivers located at large offset. In previous work we derived an unsplit convolutional PML (CPML) for staggeredgrid finitedifference integration schemes to improve the efficiency of the PML at grazing incidence for seismic wave propagation. In this article we derive a variational formulation of this CPML method for the seismic wave equation and validate it using the spectralelement method based on a hybrid first/secondorder time integration scheme. Using the Newmark time marching scheme, we underline the fact that a velocitystress formulation in the PML and a secondorder displacement formulation in the inner computational domain match perfectly at the entrance of the absorbing layer. The main difference between our unsplit CPML and the split GFPML formulation of Festa and Vilotte (2005) lies in the fact that memory storage of CPML is reduced by 35 % in 2D and 44 % in 3D. Furthermore the CPML can be stabilized by correcting the damping profiles in the PML layer in the anisotropic case. We show benchmarks for 2D heterogeneous thin slices in the presence of a free surface and in anisotropic cases that are intrinsically unstable if no stabilization of the PML is used.
Accelerating a threedimensional finitedifference wave propagation code using GPU graphics cards
, 2010
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Exploiting Intensive Multithreading for the Efficient Simulation of 3D Seismic Wave Propagation
 in CSE ’08: Proceedings of the 11th International Conference on Computational Science and Engineerin, Sao
, 2008
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A HighOrder Time and Space Formulation of the Unsplit Perfectly Matched Layer for the Seismic Wave Equation Using Auxiliary Differential Equations (ADEPML)
 CMES
, 2010
"... Unsplit convolutional perfectly matched layers (CPML) for the velocity and stress formulation of the seismic wave equation are classically computed based on a secondorder finitedifference time scheme. However it is often of interest to increase the order of the timestepping scheme in order to i ..."
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Cited by 7 (2 self)
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Unsplit convolutional perfectly matched layers (CPML) for the velocity and stress formulation of the seismic wave equation are classically computed based on a secondorder finitedifference time scheme. However it is often of interest to increase the order of the timestepping scheme in order to increase the accuracy of the algorithm. This is important for instance in the case of very long simulations. We study how to define and implement a new unsplit nonconvolutional PML called the Auxiliary Differential Equation PML (ADEPML), based on a highorder RungeKutta timestepping scheme and optimized at grazing incidence. We demonstrate that when a secondorder timestepping scheme is used the convolutional PML can be derived from that more general nonconvolutional ADEPML formulation, but that this new approach can be generalized to highorder schemes in time, which implies that it can be made more accurate. We also show that the ADEPML formulation is numerically stable up to 100,000 time steps.
Energyconserving local time stepping based on highorder finite elements for seismic wave propagation across a fluidsolid interface
, 2009
"... When studying seismic wave propagation in fluidsolid models based on a numerical technique in the time domain with an explicit time scheme it is often of interest to resort to time substepping because the stability condition in the solid part of the medium can be more stringent than in the fluid. ..."
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Cited by 4 (0 self)
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When studying seismic wave propagation in fluidsolid models based on a numerical technique in the time domain with an explicit time scheme it is often of interest to resort to time substepping because the stability condition in the solid part of the medium can be more stringent than in the fluid. In such a case, one should enforce the conservation of energy along the fluidsolid interface in the time matching algorithm in order to ensure the accuracy and the stability of the time scheme. This is often not done in the available literature and approximate techniques that do not enforce the conservation of energy are used instead. We introduce such an energyconserving local time stepping method, in which we need to solve a linear system along the fluidsolid interface. We validate it based on numerical experiments performed using highorder finite elements. This scheme can be used in any other numerical method with a diagonal mass matrix.
WAVE ACOUSTIC PROPAGATION FOR GEOPHYSICS IMAGING, FINITE DIFFERENCE vs FINITE ELEMENT METHODS COMPARISON AND BOUNDARY CONDITION TREATMENT
, 2008
"... Imaging techniques for geophysic prospection of sea bottom are extremely demanding in terms of mathematical methods and computational resources [8]. This is because the measurements are going deeper than before, thus making the structures identification a hard task, and the datasets to be computed ..."
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Cited by 3 (1 self)
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Imaging techniques for geophysic prospection of sea bottom are extremely demanding in terms of mathematical methods and computational resources [8]. This is because the measurements are going deeper than before, thus making the structures identification a hard task, and the datasets to be computed huge. Besides, the current trend is to analyze the images in three dimensions (3D) [4], adding an extra difficulty to the process. Currently, the prospection process is highly automatized by computer programs, where these programs not only implement and solve the mathematical model, but also carry the burden of the datasets manipulation, particularly in pre and post processing. All of these demands (complex mathematical models to be solved and huge datasets to be manipulated) lead us to high performance computing (HPC) environments, which are mainly available by supercomputers composed by thousands of computational nodes, thus efficient parallelization of those computer programs is required. Figure 1: Marmousi test case. Impulse response test at t = 0.36s on a 2D cut Geophysic prospection of the sea bottom widely and recently use isotropic acoustic wave propagation [4]. From the mathematical modeling point of view two crucial points have to be considered. The first point is the numerical method used to solve the particular PDE of acoustic. In this paper, we
R delâ s b a s n t i r T m e
"... In Komatitsch and Martin 2007, we presented an improved aborbing boundary technique for the purely elastic wave equation ased on an unsplit convolutional perfectly matched layer CPML nd applied it to the seismic wave equation, written as a firstorder ystem in velocity and stress, discretized based ..."
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In Komatitsch and Martin 2007, we presented an improved aborbing boundary technique for the purely elastic wave equation ased on an unsplit convolutional perfectly matched layer CPML nd applied it to the seismic wave equation, written as a firstorder ystem in velocity and stress, discretized based on a secondorder fiitedifference technique in space and time. We showed that this echnique is more efficient than the classical perfectly matched layer Goode et al., 2005. In addition to viscous fluid dissipation, the Hickey model introduces thermomechanical coupling and involves porosity and massdensity perturbations as the porous medium is submitted locally to pressure variations. In spite of all these improvements, some authors consider that the Biot and Hickey theories lead to similar waveforms QuirogaGoode et al., 2005. For this reason, we focus on Biot equations in this article. In terms of numerical simulation of wave propagation, as ex
GJI Seismology Linesource simulation for shallowseismic data. Part 1: theoretical background
"... Equivalent linesource seismograms can be obtained from shallow seismic field recordings by (1) convolving the waveforms with t−1, (2) applying a t−1 timedomain taper, where t is traveltime and (3) scaling the waveform with roffset 2, where roffset is sourcetoreceiver offset. We require such a pr ..."
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Equivalent linesource seismograms can be obtained from shallow seismic field recordings by (1) convolving the waveforms with t−1, (2) applying a t−1 timedomain taper, where t is traveltime and (3) scaling the waveform with roffset 2, where roffset is sourcetoreceiver offset. We require such a procedure when applying algorithms of 2D adjoint fullwaveform inversion (FWI) to shallowseismic data. Although derived from solutions for acoustic waves in homogeneous full space this simple procedure performs surprisingly well when applied to vertical and radial components of shallowseismic recordings from hammer blows or explosions. This is the case even in the near field of the force, although the procedure is derived from a farfield approximation. Similar approximative procedures recommended in literature are optimized for reflected waves and do not convert the amplitudes of all shallow seismic wavefield constituents equally well. We demonstrate the suitability of the proposed method for the viscoelastic case by numerical examples as well as analytical considerations. In con