Upscaling acoustic wave equation using renormalization group theory

Abstract

Seismic waves interact with a broad range of heterogeneities as they propagate through the earth. Simulating this full range of scales for wave propagation requires capturing heterogeneities of all scales, which can be computationally unaffordable. In such cases, we have relied on macroscopic representations of media obtained through an upscaling process that preserves the effects of small-scale heterogeneities (in comparison with the wavelengths of interest). Here, we discuss the application of the renormalization group (RG) theory-based upscaling to the 2D acoustic wave equation. RG-based upscaling requires constructing a special Fourier operator and is implemented using a domain decomposition in conjunction with an “expansion and truncation” method to mitigate edge effects. We test this upscaling method on several benchmark models and in the context of reverse time migration. The upscaled models obtained using this method indicate a good consistency for generated waveforms, whereas the runtime for simulations is reduced by at least an order of magnitude.