On the Causes of Frequency-Dependent Apparent Seismological Q

Research paper by Igor B. Morozov

Indexed on: 16 Mar '10Published on: 16 Mar '10Published in: Pure and Applied Geophysics


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 Q0 and η parameters in the frequency-dependent attenuation law Q(f) = Q0fη. A new interpretation approach bypassing Q(f) and using the attenuation coefficient χ(f) = γ + πf/Qe(f) resolves this problem by directly measuring the residual GS, denoted γ, and effective attenuation, Qe. 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 Qe can be considered frequency-independent. Short-period crustal body waves are characterized by positive γSP 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 γLP ≈ −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 Qe ≈ 1,100 within the crust decreasing to Qe ≈ 120 within the uppermost mantle, with frequencies of its flanks corresponding to γLP and γSP. 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).