Non-periodic homogenization has proved to be an accurate asymptotic method for
computing long-wavelength equivalent media for the seismic wave equation, turning
small-scale heterogeneities and geometric complexity into smooth elastic properties.
Using homogenized media allows i) decreasing the computation cost of wave propagation
simulation and ii) studying the apparent, small-scale-induced anisotropy. After illustrating
these two aspects briefly, we propose to analyze in great detail the accuracy of body waves
simulated in homogenized 3D models of the subsurface. First, the behaviour of head-,
reflected and refracted waves with respect to source-receiver o\set, maximum frequency
and velocity contrast across a planar interface, is investigated. Then, we consider the SEGEAGE overthrust model to exemplify how the accuracy of simulated body waves anticorrelates with the distance to seismic source and the amount of apparent anisotropy. In
high apparent anisotropy regions, we show that the first-order correction provided by the
homogenization theory significantly improves the computed wavefield. The overall results
of this analysis better frame the use of homogenized media in seismic wave simulation.@en

The Earth interior contains heterogeneities at all scales, ranging from pores and mineral grains to major global units. On the contrary, seismic recordings only contain variations larger than the minimum wavelength λmin. The heterogeneities smaller than λmin are naturally smoothed by the wavefield, leading to effective media when inverting seismic recordings to image the Earth. In particular, oriented small-scale structures lead to apparent anisotropy. In the present work, we apply the non-periodic homogenization method to the SEG-EAGE overthrust model to get the effective properties of a typical subsurface medium and to estimate the magnitude and the symmetry of the apparent anisotropy. We show that such anisotropy can reach 18%, most of it being explained by locally-tilted transverse isotropy. We also show that using the effective properties within an anisotropic wave simulator considerably decreases the computation requirement with respect to a wave simulation in the original model.@en

Within the last decade, non-periodic homogenization proved to be an accurate upscaling method for computing smooth equivalent media of elastic models of the earth interior. Doing so, it reveals the seismic anisotropy induced by small-scale structures and it eases the numerical simulation of wave propagation in complex geological settings by preventing from the use of fine and complex meshes or grids, provided that wave simulators can take anisotropy into account. In the present work, we investigate the small-scale-induced anisotropy of a typical subsurface model, namely the SEG-EAGE overthrust, for a fmax = 10Hz wavefield. We find that the amount of anisotropy can reach 20% locally and that orthorhombic anisotropy can be a poor approximation in some areas, suggesting that the analysis of datasets in terms of orthorhomby may be not relevant. However, while low-symmetry classes of anisotropy are naturally handled by the spectral-element method (SEM), they challenge the finite-difference method (FDM) in terms of implementation and computation cost. To estimate the benefit of using homogenized media in either SEM or FDM codes, we perform numerical simulations in both the initial overthrust model and its smooth version, using either regular SEM meshes or FDM grids of different resolution. We compare the obtained waveforms with a reference solution, which allows us to study the accuracy of the simulations as a function of the computation cost for both the SEM and the FDM.@en