Numerically calculated 3d space-weighting functions to image crustal volcanic structures using diffuse coda waves

Seismic coda measurements retrieve parameters linked to the physical characteristics of rock volumes illuminated by high frequency scattered waves. Space weighting functions (SWF) and kernels are different tools that model the spatial sensitivity of coda envelopes to scattering and absorption anomalies in these rock matrices, allowing coda-wave attenuation (Qcoda) imaging. This note clarifies the difference between SWF and sensitivity kernels developed for coda wave imaging. It extends the SWF previously developed in 2D to the third dimension by using radiative transfer and the diffusion equation, based on the assumption that variations of Qcoda depend solely on variations of the extinction length. When applied to active data (Deception Island, Antarctica), 3D SWF images strongly resemble 2D images, making this 3D extension redundant. On the other hand, diffusion does not efficiently model coda waveforms when using earthquake datasets spanning depths between 0 and 20 km, such as at Mount St. Helens volcano. In this setting, scattering attenuation and absorption suffer tradeoffs and cannot be separated by fitting a single seismogram energy envelope for SWF imaging. We propose that an approximate analytical 3D SWF, similar in shape to the common coda kernels used in literature, can still be used in a space weighted back-projection approach. While Qcoda is not a physical parameter of the propagation medium, its spatially-dependent modeling allows improved reconstruction of crustal-scale tectonic and geological features. It is even more efficient as a velocity independent imaging tool for magma and fluid storage when applied to deep volcanism.