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

Handle URI:
http://hdl.handle.net/10754/556701
Title:
A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory
Authors:
Gao, Kai; Chung, Eric T.; Gibson, Richard L.; Fu, Shubin; Efendiev, Yalchin R. ( 0000-0001-9626-303X )
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.
KAUST Department:
Numerical Porous Media SRI Center (NumPor)
Citation:
A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory 2015, 80 (4):D385 GEOPHYSICS
Journal:
GEOPHYSICS
Issue Date:
5-Jun-2015
DOI:
10.1190/geo2014-0363.1
Type:
Article
ISSN:
0016-8033; 1942-2156
Additional Links:
http://library.seg.org/doi/abs/10.1190/geo2014-0363.1
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorGao, Kaien
dc.contributor.authorChung, Eric T.en
dc.contributor.authorGibson, Richard L.en
dc.contributor.authorFu, Shubinen
dc.contributor.authorEfendiev, Yalchin R.en
dc.date.accessioned2015-06-10T18:55:20Zen
dc.date.available2015-06-10T18:55:20Zen
dc.date.issued2015-06-05en
dc.identifier.citationA numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory 2015, 80 (4):D385 GEOPHYSICSen
dc.identifier.issn0016-8033en
dc.identifier.issn1942-2156en
dc.identifier.doi10.1190/geo2014-0363.1en
dc.identifier.urihttp://hdl.handle.net/10754/556701en
dc.description.abstractThe 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.en
dc.relation.urlhttp://library.seg.org/doi/abs/10.1190/geo2014-0363.1en
dc.rightsArchived with thanks to GEOPHYSICSen
dc.subjectwave propagationen
dc.subjectanisotropyen
dc.subjectrock physicsen
dc.titleA numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theoryen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalGEOPHYSICSen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionTexas A&M University, Department of Geology and Geophysics, College Station, Texas, USAen
dc.contributor.institutionGeophysics Group, Los Alamos National Laboratory, Los Alamos, New Mexico, USAen
dc.contributor.institutionThe Chinese University of Hong Kong (CUHK), Department of Mathematics, Shatin, Hong Kongen
dc.contributor.institutionTexas A&M University, Department of Mathematics, College Station, Texas, USAen
kaust.authorEfendiev, Yalchin R.en
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