A new spatio-temporal misfit function for waveform inversion of DAS data

The novel technology of Distributed Acoustic Sensing (DAS) has gained widespread adoption over the last decade and is increasingly applied across various seismic applications. However, its use in Full-Waveform Inversion (FWI) remains limited. A key challenge in utilizing surface DAS data for FWI lies in the heightened sensitivity of DAS-measured strain data to the often highly heterogeneous near-surface compared to traditional inertial measurements. This sensitivity complicates the recovery of the velocity model in deeper regions, which are typically of primary interest.

To address this issue, we propose a new misfit function defined in a time-frequency-location-wavenumber domain, extending the concepts of time-frequency misfits into the spatial domain. By interpreting DAS data as a discrete sampling of a two-dimensional time-space wavefield, rather than a collection of seismograms, we uncover a symmetry between time and space. This symmetry allows us to process the DAS data in both its original domain and the transformed domain in a consistent manner across both domains. The transformation into the time-frequency-location-wavenumber domain is achieved via a two-dimensional Gabor transform, where phase and envelope misfits are defined analogously to their counterparts in the time-frequency domain.

By comparing the sensitivity kernels derived from misfit functions in the time-frequency-location-wavenumber domain with those from the time-frequency domain, we observe a threefold improvement in sensitivity to deeper velocity anomalies relative to near-surface anomalies. This enhancement significantly accelerates, and in high-noise environments enables, the effective use of DAS data in the context of FWI.