On the Causes of Frequency-Dependent Apparent Seismological Q

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 eta parameters in the frequency-dependent attenuation law Q(f) = Q (0) f (eta) . A new interpretation approach bypassing Q(f) and using the attenuation coefficient chi(f) = gamma + pi f/Q (e)(f) resolves this problem by directly measuring the residual GS, denoted gamma, 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, chi(f) shows a linear dependence on the frequency, gamma not equal 0, and Q (e) can be considered frequency-independent. Short-period crustal body waves are characterized by positive gamma (SP) values of (0.6-2.0) x 10(-2) s(-1) interpreted as related to the downward upper-crustal reflectivity. Long-period surface waves show negative gamma (LP) a parts per thousand -1.9 x 10(-5) s(-1), which could be caused by insufficient modeling accuracy at long periods. The above gamma 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) a parts per thousand 1,100 within the crust decreasing to Q (e) a parts per thousand 120 within the uppermost mantle, with frequencies of its flanks corresponding to gamma (LP) and gamma (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 (similar to 38-100 km).