A fully scalable homogenization method to upscale 3-D elastic media

Modelling seismic wavefields in complex 3-D elastic media is the key in many fields of Earth Science: seismology, seismic imaging, seismic hazard assessment and earthquake source mechanism reconstruction. This modelling operation can incur significant computational cost, and its accuracy depends on the ability to take into account the scales of the subsurface heterogeneities varying. The theory of homogenization describes how the small-scale heterogeneities interact with the seismic waves and allows to upscale elastic media consistently with the wave equation. In this study, an efficient and scalable numerical homogenization tool is developed, relying on the similarity between the equations describing the propagation of elastic waves and the homogenization process. By exploiting the optimized implementation of an elastic modelling kernel based on a spectral-element discretization and domain decomposition, a fully scalable homogenization process, working directly on the spectral-element mesh, is presented. Numerical experiments on the entire SEAM II foothill model and a 3-D version of the Marmousi II model illustrate the efficiency and flexibility of this approach. A reduction of two orders of magnitude in terms of absolute computational cost is observed on the elastic wave modelling of the entire SEAM II model at a controlled accuracy.