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

Full waveform modelling and inversion are essential tools commonly used in seismic imaging. Due to the restrictions from instruments and computing resources, the seismic data are usually frequency-band limited. Thus, the resulting imaging result is a smooth version of the true Earth with the lack of scales smaller than the minimum propagating wavelength. The non-periodic homogenization technique allows for building a long-wave equivalent medium to account for wave interactions with small geological structures and producing similar waveforms as for the original medium at a controlled accuracy. The current non-periodic homogenization implementation is memory and time consuming even with parallel computing techniques. To boost its applicability on large-scale 3D problems, we propose a fully scalable non-periodic homogenization implementation. As the core of the homogenization process, the solution of elastostatic equations and the low-pass filtering operations are formulated as the linear system solution with a matrix-free conjugate-gradient algorithm to exploit highly optimized matrix-vector-product routines developed in our elastic wave modelling and inversion parallel code SEM46. For the algorithm consistency, an approximated Gaussian low-pass filtering is introduced by a cascade of PDE-defined Bessel filters without sacrificing the effectiveness. All these improvements enhance the efficiency, scalability and robustness of the non-periodic homogenization process.