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On the Causes of Frequency-Dependent Apparent Seismological Q

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Abstract

Variability of the Earth’s structure makes a first-order impact on attenuation measurements which often does not receive adequate attention. Geometrical spreading (GS) can be used as a simple measure of the effects of such structure. The traditional simplified GS compensation is insufficiently accurate for attenuation measurements, and the residual GS appears as biases in both Q 0 and η parameters in the frequency-dependent attenuation law Q(f) = Q 0 f η. A new interpretation approach bypassing Q(f) and using the attenuation coefficient χ(f) = γ + πf/Q e(f) resolves this problem by directly measuring the residual GS, denoted γ, and effective attenuation, Q e. The approach is illustrated by re-interpreting several published datasets, including nuclear-explosion and local-earthquake codas, Pn, and synthetic 50–300-s surface waves. Some of these examples were key to establishing the Q(f) concept. In all examples considered, χ(f) shows a linear dependence on the frequency, γ ≠ 0, and Q e can be considered frequency-independent. Short-period crustal body waves are characterized by positive γ SP values of (0.6–2.0) × 10−2 s−1 interpreted as related to the downward upper-crustal reflectivity. Long-period surface waves show negative γ LP ≈ −1.9 × 10−5 s−1, which could be caused by insufficient modeling accuracy at long periods. The above γ values also provide a simple explanation for the absorption band observed within the Earth. The band is interpreted as apparent and formed by levels of Q e ≈ 1,100 within the crust decreasing to Q e ≈ 120 within the uppermost mantle, with frequencies of its flanks corresponding to γ LP and γ SP. Therefore, the observed absorption band could be purely geometrical in nature, and relaxation or scattering models may not be necessary for explaining the observed apparent Q(f). Linearity of the attenuation coefficient suggests that at all periods, the attenuation of both Rayleigh and Love waves should be principally accumulated at the sub-crustal depths (~38–100 km).

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Notes

  1. A comprehensive list of references would include hundreds of publications and grow every month. I only refer to several key papers that shaped the concept of frequency-dependent attenuation.

  2. Morozov, I. (submitted I). Attenuation coefficient, frequency dependence of t* and Q, and structural variability of the Earth, submitted to Seism. Res. Lett.

  3. Morozov, I. (submitted II). Upper-mantle Love wave attenuation without Q and visco-elasticity, submitted to Bull. Seism. Soc. Am.

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Acknowledgments

Stimulating discussions with Anton Dainty, Robert Nowack, Scott Phillips, and Jack Xie have suggested several data examples and greatly helped in improving the argument. I also thank Bill Walter and Jack Xie for their insightful reviews and many suggestions on the manuscript. This research was supported by Canada NSERC Discovery Grant RGPIN261610-03.

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  1. Department of Geological Sciences, University of Saskatchewan, Saskatoon, SK, S7N 5E2, Canada

    Igor B. Morozov

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Morozov, I.B. On the Causes of Frequency-Dependent Apparent Seismological Q . Pure Appl. Geophys. 167, 1131–1146 (2010). https://doi.org/10.1007/s00024-010-0100-6

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