SUMMARY
A geometrical attenuation model is proposed as an alternative to the conventional frequency‐dependent attenuation law Q(f) =Q0(f/f0)η. The new model provides a straightforward differentiation between the geometrical and effective attenuation (Qe) which incorporates the intrinsic attenuation and small‐scale scattering. Unlike the (Q0, η) description, the inversion procedure uses only the spectral amplitude data and does not rely on elaborate theoretical models or restrictive assumptions. Data from over 40 reported studies were transformed to the new parametrization. The levels of geometrical attenuation strongly correlate with crustal tectonic types and decrease with tectonic age. The corrected values of Qe are frequency‐independent and generally significantly higher than Q0 and show no significant correlation with tectonic age. Several case studies were revisited in detail, with significant changes in the interpretations.
The absorption‐band and the ‘10‐Hz transition’ are not found in the corrected Qe data, and therefore, these phenomena are interpreted as related to geometrical attenuation. The absorption band could correspond to changes in the dominant mode content of the wavefield as the frequency changes from about 0.1 to 100 Hz. Alternatively, it could also be a pure artefact related to the power‐law Q(f) paradigm above.
The explicit separation of the geometrical and intrinsic attenuation achieves three goals: (1) it provides an unambiguous, assumption‐ and model‐free description of attenuation, (2) it allows relating the observations to the basic physics and geology and (3) it simplifies the interpretation because of reduced emphasis on the apparent Q(f) dependence. The model also agrees remarkably well with the initial attempts for finite‐difference short‐period coda waveform modelling. Because of its consistency and direct link to the observations, the approach should also help in building robust and transportable coda magnitudes and in seismic regionalization.
We introduce a systematic definition of instantaneous attributes for an arbitrary multicomponent seismic signal. The definition is a natural generalization of known complex trace attributes of a one‐component signal. Instantaneous amplitude and all polarization parameters are defined as invariants of “instantaneous phase rotation.” The principal feature of our approach is the unique definition of the instantaneous phase for a signal with any number of components. Plots of subtle polarization parameters of multicomponent seismic data are easily obtained using conventional seismic plotting routines. We illustrate our approach on a synthetic example and apply it to real 3‐component, wide‐angle crustal data. Plots of polarization attributes provide evidence for shear‐wave splitting in an [Formula: see text] arrival. Having determined the instantaneous polarization vector, we design a new type of time‐domain spatial directional filter. The filter enhances linearly polarized events with specified instantaneous polarization. The filter can work with any number of components in the data, has no user‐specified parameters, and is controlled only by the signal. We conclude that rigorously defined instantaneous phase, amplitude, and polarization attributes provide new effective means for the visualization, analysis, and processing of multicomponent signal.
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