Upscaling Acoustic Wave Equation using Renormalization Group Theory

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 rely on macroscopic representations of media obtained through an upscaling process that preserves the effects of small-scale heterogeneities (in comparison to the wavelengths of interest). Here we discuss the application of the renormalization-group (RG) theory-based upscaling to the two-dimensional 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 show a good consistency for generated waveforms, while the runtime for simulations is reduced by at least an order of magnitude.