Intrinsic non-uniqueness of the acoustic full waveform inverse problem

In the context of seismic imaging, full waveform inversion (FWI) is increasingly popular. Because of its lower numerical cost, the acoustic approximation is often used, especially at the exploration geophysics scale, both for tests and for real data. Moreover, some research domains such as helioseismology face true acoustic media for which FWI can be useful. In this work, an argument that combines particle relabelling and homogenization is used to show that the general acoustic inverse problem based on hand-limited data is intrinsically non-unique. It follows that the results of such inversions should be interpreted with caution. To illustrate these ideas, we consider 2-D numerical FWI examples based on a Gauss-Newton iterative inversion scheme and demonstrate effects of this non-uniqueness in the local optimization context.

Automated summary

In the field of seismic imaging, full waveform inversion (FWI) is popular due to its lower numerical cost, but the acoustic approximation may lead to non-uniqueness issues. Therefore, results of acoustic inversions based on hand-limited data should be interpreted with caution.