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The purpose of this paper is to give an upscaling tool valid for the wave equation in general elastic media. This paper is focused on P–SV wave propagation in 2-D, but the methodology can be extended without any theoretical difficulty to the general 3-D case. No assumption on the heterogeneity spectrum is made and the medium can show rapid variations of its elastic properties in all spatial directions. The method used is based on the two-scale homogenization expansion, but extended to the non-periodic case. The scale separation is made using a spatial low-pass filter. The ratio of the filter wavelength cut-off and the minimum wavelength of the propagating wavefield defines a parameter ɛ₀ with which the wavefield propagating in the homogenized medium converges to the reference wavefield. In the general case, this non-periodic extension of the homogenization technique is only valid up to the leading …