Can We Improve Estimates of Seismological Q Using a New “Geometrical Spreading” Model?

摘要

Precise measurements of seismological Q are difficult because we lack detailed knowledge on how the Earth’s fine velocity structure affects the amplitude data. In a number of recent papers, Morozov (Geophys J Int 175:239–252, 2008; Seism Res Lett 80:5–7, 2009; Pure Appl Geophys, this volume, 2010) proposes a new procedure intended to improve Q determinations. The procedure relies on quantifying the structural effects using a new form of geometrical spreading (GS) model that has an exponentially decaying component with time, e −γt·γ is a free parameter and is measured together with Q. Morozov has refit many previously published sets of amplitude attenuation data. In general, the new Q estimates are much higher than previous estimates, and all of the previously estimated frequency-dependence values for Q disappear in the new estimates. In this paper I show that (1) the traditional modeling of seismic amplitudes is physically based, whereas the new model lacks a physical basis; (2) the method of measuring Q using the new model is effectively just a curve fitting procedure using a first-order Taylor series expansion; (3) previous high-frequency data that were fit by a power-law frequency dependence for Q are expected to be also fit by the first-order expansion in the limited frequency bands involved, because of the long tails of power-law functions; (4) recent laboratory measurements of intrinsic Q of mantle materials at seismic frequencies provide independent evidence that intrinsic Q is often frequency-dependent, which should lead to frequency-dependent total Q; (5) published long-period surface wave data that were used to derive several recent Q models inherently contradict the new GS model; and (6) previous modeling has already included a special case that is mathematically identical to the new GS model, but with physical assumptions and measured Q values that differ from those with the new GS model. Therefore, while individually the previous Q measurements have limited precision, they cannot be improved by using the new GS model. The large number of Q measurements by seismologists are sufficient to show that Q values in the Earth are highly laterally variable and are often frequency dependent.