Model order reduction for seismic waveform modelling: inspiration from normal modes

The computational cost of full waveform simulation in seismological contexts is known to be expensive and generally requires large clusters of computers working in parallel. Although there have been many methods proposed over recent years to reduce this burden, in this work, we focus on a particular method called model order reduction (MOR) whereby a full waveform system of equations is projected onto a lower dimensional space to reduce computational and memory requirements at the cost of introducing approximation errors. In this paper, inspired by normal mode (NM) theory, we use the eigenmodes of the seismic wave equation to span this lower dimensional space. From this we argue that NM theory can be seen as an early form of MOR. Using this as inspiration, we demonstrate how free body oscillations and a form of Petrov–Galerkin projection can be applied in regional scale problems utilizing recent advanced eigensolvers to create a MOR scheme. We also demonstrate how this can be applied to inverse problems. We further conjecture that MOR will have an important role to play in future full waveform applications, particularly those of a time-critical nature such as seismic hazard monitoring.