Numerically Calculated 3-D Space-Weighting Functions to Image Crustal Volcanic Structures Using Diffuse Coda Waves

Seismic coda measurements retrieve parameters linked to the physical characteristics of the rock volumes illuminated by high-frequency scattered waves. Space Weighting Functions (SWF) and kernels are different tools, which model the spatial sensitivity of coda envelopes to scattering and absorption anomalies in these rock matrices, allowing coda-wave attenuation (Qcoda 4 ) imaging. This note clarifies the difference between SWF and sensitivity kernels developed for coda wave imaging. It extends to the third dimension the SWF previously developed in 2D using radiative transfer and diffusion equation, based on the assumption of Qcoda variations dependent 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, as at Mount St. Helens volcano. In this setting, scattering attenuation and absorption suffer trade-off 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 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 modelling 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, once applied to deep volcanism.