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


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.


Direct waves coda waves dispersion seismic attenuation crust mantle 



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


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

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

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