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

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    Type
    Article
    Authors
    Gao, Kai
    Chung, Eric T.
    Gibson, Richard L.
    Fu, Shubin
    Efendiev, Yalchin R. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Numerical Porous Media SRI Center (NumPor)
    Date
    2015-05-29
    Online Publication Date
    2015-05-29
    Print Publication Date
    2015-07
    Permanent link to this record
    http://hdl.handle.net/10754/556701
    
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    Abstract
    The development of reliable methods for upscaling fine-scale 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.
    Citation
    A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory 2015, 80 (4):D385 GEOPHYSICS
    Publisher
    Society of Exploration Geophysicists
    Journal
    GEOPHYSICS
    DOI
    10.1190/geo2014-0363.1
    Additional Links
    http://library.seg.org/doi/abs/10.1190/geo2014-0363.1
    ae974a485f413a2113503eed53cd6c53
    10.1190/geo2014-0363.1
    Scopus Count
    Collections
    Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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