Abstract
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 ( Q c o d a ) 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 Q c o d a 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 Q c o d a 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.
Highlights
Seismic attenuation imaging performed using coda waves provides novel information about tectonic structures and fluid content at crustal [1,2], regional [3], and local [4] scales
S [8,10] and to invert for attenuation in the subsurface at different scales and depths [2,11,12]. These sensitivity kernels define the source parameters observed at a station as a space-weighted average of attenuation characteristics of the sampled medium, where the weights are defined via integral equations [10,12]
The weighting function remains symmetrical around the axis connecting the source to the receiver, in analogy with simulations using radiative transfer theory [10] and spectral elements methods [12]. This symmetry allows one to evaluate the 3D Space weighting functions (SWF) analytically for source and receiver both placed at the surface
Summary
Seismic attenuation imaging performed using coda waves provides novel information about tectonic structures and fluid content at crustal [1,2], regional [3], and local [4] scales. The average of all the observed values weighted by the SWFs provides the value of the attenuation at the point These SWFs have been expressively designed to map scattering attenuation and absorption in volcanoes using a diffusion model and active sources [4,15,16]. Del Pezzo et al [17] obtained that, in the case of a uniform half space and for diffusive propagation, the following function well approximates the numerically calculated SWF for both absorption and scattering attenuation: 2D. The sensitivity is maximum at the source and receiver stations, remains high across the area contouring the seismic ray, decreases at a distance controlled by the extinction length This similarity in shape goes even further, as the spatial pattern of the function is identical to the depth-dependent diffusive sensitivity kernels in 3D defined by Obermann et al [12]. Test images are compared with previous tomography results obtained in the same areas using different seismic attributes, and show consistent features
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