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Pure and Applied Geophysics

, Volume 175, Issue 8, pp 2595–2607 | Cite as

On Strong Positive Frequency Dependencies of Quality Factors in Local-Earthquake Seismic Studies

  • Igor B. Morozov
  • Atul Jhajhria
  • Wubing Deng
Article

Abstract

Many observations of seismic waves from local earthquakes are interpreted in terms of the frequency-dependent quality factor \(Q\left( f \right) = Q_{0} f^{\eta }\), where η is often close to or exceeds one. However, such steep positive frequency dependencies of Q require careful analysis with regard to their physical consistency. In particular, the case of η = 1 corresponds to frequency-independent (elastic) amplitude decays with time and consequently requires no Q-type attenuation mechanisms. For η > 1, several problems with physical meanings of such Q-factors occur. First, contrary to the key premise of seismic attenuation, high-frequency parts of the wavefield are enhanced with increasing propagation times relative to the low-frequency ones. Second, such attenuation cannot be implemented by mechanical models of wave-propagating media. Third, with η > 1, the velocity dispersion associated with such Q(f) occurs over unrealistically short frequency range and has an unexpected oscillatory shape. Cases  η = 1 and  η > 1 are usually attributed to scattering; however, this scattering must exhibit fortuitous tuning into the observation frequency band, which appears unlikely. The reason for the above problems is that the inferred Q values are affected by the conventional single-station measurement procedure. Both parameters Q0 and are apparent, i.e., dependent on the selected parameterization and inversion method, and they should not be directly attributed to the subsurface. For η  ≈ 1, parameter Q0 actually describes the frequency-independent amplitude decay in access of some assumed geometric spreading tα, where α is usually taken equal one. The case η > 1 is not allowed physically and could serve as an indicator of problematic interpretations. Although the case \(0 < \eta < 1\) is possible, its parameters Q0 and may also be biased by the measurement procedure. To avoid such difficulties of Q-based approaches, we recommend measuring and interpreting the amplitude-decay rates (such as parameter α) directly.

Keywords

Direct waves coda waves dispersion seismic attenuation crust mantle 

Notes

Acknowledgements

We thank two anonymous reviewers for suggestions that helped in improving this paper.

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Authors and Affiliations

  1. 1.Department of Geological SciencesUniversity of Saskatchewan, SaskatoonSaskatoonCanada
  2. 2.Kurukshetra UniversityKurukshetraIndia

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