Correlation Functions of Random Media

Klimeš, Luděk

doi:10.1007/s00024-002-8710-2

Cited by 93 publications

(40 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many earth scientists (e.g., [17][18][19]) believe that a reasonable stochastic model for earth materials is self-affine structure in the physical properties with ÿ1=2 < H < 0 (property fluctuations decreasing with increasing scale). We encourage laboratory (or field) experimentalists to look for the power-law relation Q ÿ1…”

Section: Prl 97 184301 (2006) P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

Acoustic Attenuation in Self-Affine Porous Structures

Pride

Masson²

2006

Phys. Rev. Lett.

View full text Add to dashboard Cite

Section: Prl 97 184301 (2006) P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

Acoustic Attenuation in Self-Affine Porous Structures

Pride

Masson²

2006

Phys. Rev. Lett.

View full text Add to dashboard Cite

“…The random velocity perturbation is calculated in wavenumber space based on the statistical characteristics of the random medium (Klimeš 2002;Sato et al 2012). Utility programs to calculate these random velocity fluctuations in 2D and 3D are provided in OpenSWPC.…”

Section: Model Inputmentioning

confidence: 99%

OpenSWPC: an open-source integrated parallel simulation code for modeling seismic wave propagation in 3D heterogeneous viscoelastic media

Maeda

Takemura

Furumura

2017

Earth Planets Space

100

View full text Add to dashboard Cite

We have developed an open-source software package, Open-source Seismic Wave Propagation Code (OpenSWPC), for parallel numerical simulations of seismic wave propagation in 3D and 2D (P-SV and SH) viscoelastic media based on the finite difference method in local-to-regional scales. This code is equipped with a frequency-independent attenuation model based on the generalized Zener body and an efficient perfectly matched layer for absorbing boundary condition. A hybrid-style programming using OpenMP and the Message Passing Interface (MPI) is adopted for efficient parallel computation. OpenSWPC has wide applicability for seismological studies and great portability to allowing excellent performance from PC clusters to supercomputers. Without modifying the code, users can conduct seismic wave propagation simulations using their own velocity structure models and the necessary source representations by specifying them in an input parameter file. The code has various modes for different types of velocity structure model input and different source representations such as single force, moment tensor and plane-wave incidence, which can easily be selected via the input parameters. Widely used binary data formats, the Network Common Data Form (NetCDF) and the Seismic Analysis Code (SAC) are adopted for the input of the heterogeneous structure model and the outputs of the simulation results, so users can easily handle the input/output datasets. All codes are written in Fortran 2003 and are available with detailed documents in a public repository.

show abstract

“…This makes the ratio of computation time for the fine-grid homogenized medium simulations to be approximately ð93303 sÞ∕ð9.13 sÞ, i.e., 10 4 , for the same total wave propagation time (0.5 s). The second model is a random medium generated with the von Kármán correlation function (Goff and Jordan, 1988;Klimeš, 2002) …”

Section: Arbitrarily Heterogeneous Mediamentioning

confidence: 99%

A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

et al. 2015

View full text Add to dashboard Cite

The development of reliable methods for upscaling finescale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. Therefore, we have proposed a numerical homogenization algorithm based on multiscale finite-element methods for simulating elastic wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that was similar to the rotated staggered-grid finite-difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity in which the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.

show abstract

Correlation Functions of Random Media

Cited by 93 publications

References 26 publications

Acoustic Attenuation in Self-Affine Porous Structures

Acoustic Attenuation in Self-Affine Porous Structures

OpenSWPC: an open-source integrated parallel simulation code for modeling seismic wave propagation in 3D heterogeneous viscoelastic media

A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

Contact Info

Product

Resources

About