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

Journal Article · Fri Jun 05 00:00:00 EDT 2015 · Geophysics

DOI:https://doi.org/10.1190/geo2014-0363.1· OSTI ID:1221549

Gao, Kai ^[1]; Chung, Eric T. ^[2]; Gibson, Richard L. ^[3]; Fu, Shubin ^[3]; Efendiev, Yalchin ^[4]

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1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2. Chinese Univ. of Hong Kong, Shatin (Hong Kong)
3. Texas A & M Univ., College Station, TX (United States)
4. Texas A & M Univ., College Station, TX (United States); King Abdullah Univ. of Science and Technology, Thuwal (Saudi Arabia)

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. We therefore propose 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 is 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 where 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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1221549
• Report Number(s): LA-UR-15-22499
• Journal Information: Geophysics, Vol. 80, Issue 4; ISSN 0016-8033
• Publisher: Society of Exploration Geophysicists
• Country of Publication: United States
• Language: English

Related Subjects

58 GEOSCIENCES
multiscale
homogenization
anisotropy