Homogenization and Very High Degree Spectral Elements for Elastic and Acoustic Waves Propagation in Multi-Scale Geological Media

Date: 4/25/2019

Time: 09:30 AM

Room: Elliott Bay

Non-periodic homogenization is a tool designed to upscale complex deterministic elastic and acoustic multi-scale media with no specific scale separation. For a given signal frequency band, it makes possible to compute an effective version of a true model. Waveforms computed in a true model and its effective version are the same up to the desired accuracy, including for backscattered, refracted or surface waves. In the forward modeling, context homogenization can be used as a preprocessing tool relaxing the meshing constraint and leading to a low numerical cost to solve the wave equations. In the full waveform inversion context, it can be used to constrain the solution space. Effective media are always anisotropic, even for isotropic true media. In the acoustic case, an interesting aspect is that homogenization leads to an anisotropic density.

In this work, we focus on three aspects: the homogenization of elastic media with fluid inclusions, source heterogeneity iterations and the option to use very high degree spectral elements. Even if fluid inclusions in an elastic matrix are theoretically prohibited in the non-periodic homogenization framework, we show that effective media of true media with fluid inclusions give very good results for a specific range of inclusion sizes. We will discuss how the interaction of the source with the small fluid heterogeneities strongly affects the source apparent moment tensors. And finally, we will discuss how homogenization open the door to the use of very high degree spectral element (up to degree 40) leading to an as low as 2.5 points per wavelength spatial sampling without degrading computing time performances despite the time marching stability criteria.

Presenting Author: Yann Capdeville

Authors