On the Causes of Frequency-Dependent Apparent Seismological Q

Morozov, Igor B.

doi:10.1007/s00024-010-0100-6

Cited by 34 publications

(58 citation statements)

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“…The attenuation-coefficient view on seismic attenuation (Morozov, 2008(Morozov, , 2010a starts from a generalization of the classic scattering-theory approximation (Chernov, 1960;Sato, 1978) and further extends into a critique of the concept of Q and the theory of viscoelasticity (Morozov, 2009c(Morozov, , 2010c. Currently, this approach is undergoing some debate (Morozov, 2009a, b;Xie and Fehler, 2009;Mitchell, 2010;Xie, 2010).…”

Section: Attenuation Coefficient and Qmentioning

confidence: 99%

“…In today's observations (Morozov, 2008(Morozov, , 2009a(Morozov, , 2010a, only a frequencyindependent Q e can typically be measured, and therefore we only have two observable parameters ( and Q e ) to constrain the three physical factors associated with attenuation (which are the GS, scattering, and anelastic attenuation). Consequently, one of these factors remains inherently unconstrained, and as argued by Morozov (2008Morozov ( , 2009aMorozov ( and 2010a, this factor is the scattering. Note that "scattering" as a part of wave propagation through a structure can only be identified subjectively, by the observer's treatment of a part of this structure as "random" or as a "perturbation" of some selected background 1 .…”

Section: Attenuation Coefficient and Qmentioning

confidence: 99%

“…In all data cases considered so far (Morozov, 2008(Morozov, , 2009a(Morozov, , 2010a, the use of  simplified the interpretation and revealed data relationships that would be hard to notice in the form of Q. A general observation from these studies is that  often shows a linear dependence on f with a non-zero limit  = | f = 0 , which suggests its presentation in 5 the general form…”

Section: Introductionmentioning

confidence: 97%

“…The (f) parameterization of the seismic-amplitude data is stable in respect to the selection of background models, and the trade-off with GS assumptions is only introduced after its transformation to the quality factor as Q = f/. Note that this transformation also leads to Q often increasing with frequency (up to Q  f) when the zero-frequency limit | f  0 is non-zero and positive (Morozov, 2008(Morozov, , 2009a(Morozov, , 2010a. Such increases in local-coda Q(f) were reported in many studies.…”

Section: Introductionmentioning

confidence: 99%

“…Without these models, even the definition of scattering Q becomes uncertain, and its frequency dependence changes dramatically when different models are considered (Morozov, 2008(Morozov, , 2009a(Morozov, , 2010a. Although giving a convenient framework for comparing the observations by reducing them to some in situ Q i and Q s , scattering models are based on so strongly simplified assumptions that they should lead to a fairly distorted physical picture of coda attenuation.…”

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confidence: 99%

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Temporal variations of coda Q: An attenuation-coefficient view

Morozov

2011

Physics of the Earth and Planetary Interiors

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Spatial and temporal variations of coda wave attenuation were identified in many studies, and particularly in relation to major earthquakes and volcanic eruptions. Both the coda quality factor, Q c , and its frequency dependence often change following such events, which is often attributed to variations in the properties of large volumes of the subsurface. However, Q c is also strongly sensitive to the assumed theoretical models, which are usually insufficiently accurate for constraining the actual relationships between the geometrical spreading, anelastic dissipation, and scattering. This inaccuracy often leads to significant exaggeration of attenuation effects and complicates the interpretation of temporal variations. To resolve this problem, this study uses a phenomenological approach based on the temporal attenuation coefficient  instead of Q c . The attenuation coefficient often linearly depends on frequency f, with intercept  = (0) related to the geometrical spreading and slope giving the "effective quality" factor Q e as d/df = Q e and Q e changed from 400 before the eruption to 750 after it. The observed temporal variations are explained by the near-surface changes caused by seasonal variations in the non-volcanic case and gas-, magma-, and geothermal-system related in the volcanic case.Scattering attenuation does not appear to be a significant factor in these areas, or otherwise it may be indistinguishable due to its fundamental trade-off with the background structure and anelastic attenuation in the data.

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Section: Attenuation Coefficient and Qmentioning

confidence: 99%

Section: Attenuation Coefficient and Qmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Temporal variations of coda Q: An attenuation-coefficient view

Morozov

2011

Physics of the Earth and Planetary Interiors

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

Xie

2010

Pure Appl. Geophys.

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Abstract-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 -ct Ác 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 highfrequency 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.

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Strongly Frequency-Dependent Intrinsic and Scattering Q for the Western Margin of the Sichuan Basin, China, as Revealed by a Phenomenological Model

2010

Pure Appl. Geophys.

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Through applying the energy-flux model to teleseismic P-wave data, seismological scattering Q and intrinsic Q for the western margin of the Sichuan basin in southwestern China are estimated separately. The results exemplify the frequency-dependent Q values in the seismic frequency band. The scattering Q is heavily frequency-dependent and reaches a minimum at *1.5 Hz. The intrinsic Q is nearly invariant for frequencies above 2 Hz and rapidly increases at lower frequencies. A major advantage of the energy-flux model is that it is a phenomenological model based on the conservation of energy and requires no geometrical spreading correction. The results are good counterexamples against the claim of a frequency-independent seismological Q.Recently, MOROZOV (2010) argued that the frequencydependent Q predicted by theoretical studies and observed in numerical modeling and laboratory experiments could not be considered as rigorous proof for the presence of frequency-dependent seismological Q. He also argued that traditional methods for attenuation estimates based on the concept of wavefronts or rays generally presumed simple but ''insufficiently accurate'' geometrical spreading and thus the observed frequency dependence of seismological Q resulted from inaccurate compensation for geometrical spreading. Morozov preferred phenomenological models to traditional methods, because ''phenomenological models do not require detailed descriptions of the mechanisms of the wave processes but may be based on some general principles, such as the conservation of energy and time/spatial continuity.'' Here we present a counterexample with strong frequency-dependent Q using a phenomenological model called the energy-flux model. This model, first proposed by FRANKEL and WENNERBERG (1987) and further developed by LANGSTON (1989) andKORN (1990), is based on the conservation of energy. The model predicts that the scattering Q can be determined by the coda level relative to the direct arrival and the coda Q by the decay rate.The teleseismic P wavefields used in our analysis were recorded by an array consisting of 17 threecomponent stations deployed in the western margin of the Sichuan basin. The data selection and processing strategies are similar to those of HOCK and KORN (2000). The values of scattering Q and intrinsic Q at different frequencies are plotted in Fig.

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On the Causes of Frequency-Dependent Apparent Seismological Q

Cited by 34 publications

References 38 publications

Temporal variations of coda Q: An attenuation-coefficient view

Temporal variations of coda Q: An attenuation-coefficient view

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

Strongly Frequency-Dependent Intrinsic and Scattering Q for the Western Margin of the Sichuan Basin, China, as Revealed by a Phenomenological Model

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