Incorporating spatial gradient observations into seismic noise interferometry

With an increasing availability of next-generation instruments in seismology such as Distributed Acoustic Sensing (DAS) interrogators and rotation sensors, as well as public datasets from these instruments, there is a demand for incorporating these new gradient observables into the workflows of seismic interferometry and noise source inversion.

Dropping the common assumption of Green’s function retrieval, we derive a generalized formulation for seismic interferometry that can utilize not only displacement measurements but also spatial and temporal gradients thereof – including velocity, strain and rotation.

Based on this formulation, we are able to simulate interferometric wavefields of displacement and gradient observations or arbitrary combinations of these observables, for heterogeneous visco-elastic media, and for arbitrary noise source distributions.

We demonstrate how to derive adjoint-based expressions for finite-frequency sensitivity kernels of the interferometric wavefields with respect to subsurface structure and noise source distributions, for a wide range of observed quantitates and combinations thereof. We provide numerical examples of such sensitivity kernels.

Especially in environments where the common assumption of a homogeneous noise source distribution is violated, our formulation enables correlation-wavefield based inversions, combining different seismic observables.

The discussed theoretical and numerical developments bring us one step closer to multi-observational full waveform ambient noise inversion, underlining the potential and possible impact of recent developments in seismic instrumentation to seismology across all scales.