Frequency dependence of Q for seismic body waves in the Earth's mantle

Main Article Content

A. Ulug
H. Berckhemer


In this paper an attempt is made to determine the frequency dependence of Q in the Earth's mantle in the frequency range 0.03–1.5 Hz from the spectral ratio of teleseismic S- and P-waves. Digital broad-band data of 17 earthquakes at 40° < < 90° recorded at the Central Seismological Observatory of the Federal Republic of Germany at Erlangen were analysed. The method implies the following assumptions: frequency independence of the crustal transfer function, proportionality of Qp (f) and Qs (f), and proportionality of P- and S-source spectra. This last and most critical assumption was carefully investigated by kinematic and dynamic source models. The calculated Q-spectra for the individual events vary considerably but all have in common a general increasing trend with frequency which can best be represented by a power law Q ≈ f α with 0.25 < α < 0.6. A further increase in slope near 1 Hz suggests an absorption band corner with an upper cut-off relaxation time τm = 0.33 ± 0.18 s. The significance of the Q-spectra and their variability is estimated by manipulating semi-synthetic seismograms with different error-producing processes such as length and shape of the time window, superposition of noise, digital filter process and source spectra. It is concluded that none of these processes is able to destroy or to imitate the observed increasing trend of Q with frequency. The results are compared with those from other seismological investigations and from laboratory experiments on mantle rocks at high temperature and in the seismic frequency band.

Google Scholar           ARK:



Article Details

How to Cite
Ulug, A., & Berckhemer, H. (1984). Frequency dependence of Q for seismic body waves in the Earth’s mantle. Journal of Geophysics, 56(1), 9-19. Retrieved from


Abramovici, F. (1973) Numerical application of a technique for recovering the spectrum of a time function. Geophys. J. R. Astron. Soc. 32:65-78

Aki, K. (1980) Attenuation of shear waves in the lithosphere for frequencies from 0.05 to 25 Hz. Phys. Earth Planet. Inter. 21:50-60

Anderson, D.L., Given, J.W. (1982) Absorption band Q model for the Earth. J. Geophys. Res. 87:3893-3904

Anderson, D.L., Hart, R.S. (1978) Attenuation models of the Earth. Phys. Earth Planet. Inter. 16:289-306

Anderson, D.L., Minster, J.B. (1979) The frequency dependence of Q in the Earth and implications for mantle rheology and chandler wobble. Geophys. J. R. Astron. Soc. 58:431-440

Berckhemer, H., Auer, F., Drisler, J. (1979) High-temperature anelasticity and elasticity of mantle peridotite. Phys. Earth Planet. Inter. 20:48-59

Berckhemer, H., Kampfmann, W., Aulbach, E., Schmeling, H. (1982) Shear modulus and Q of forsterite and dunite near partial melting from forced-oscillation experiments. Phys. Earth Planet. Inter. 29:30-41

Burdick, L.J. (1978) t* for S waves with a continental raypath. Bull. Seismol. Soc. Am. 68:1013-1030

Clements, J. (1982) Intrinsic Q and its frequency dependence. Phys. Earth Planet. Inter. 27:286-299

Der, Z.A., McEifresh, T.W., O'Donnell, A. (1982) An investigation of the regional variations and frequency dependence of anelastic attenuation in the mantle under the Umted States in the 0.5-4 Hz band. Geophys. J. R. Astron. Soc. 69:67-99

Frasier, C.W., Chowdhury, D.K. (1974) Effect of scattering on PcP/P amplitude ratios at Lasa from 40° to 84° distance. J. Geophys. Res. 79:5469-5477

Futterman, W.I. (1962) Dispersive body waves. J. Geophys. Res. 67:5279-5291

Hanks, T.C. (1981) The corner frequency shift, earthquake source models, and Q. Bull. Seismol. Soc. Am. 71:597-612

Ito, K., Kennedy, G.C. (1967) Melting and phase relations in a natural peridotite to 40 kilobars. Am. J. Sci. 265:519-538

Kanamori, H. (1967) Spectrum of short-period core phases in relation to the attenuation in the mantle. J. Geophys. Res. 72:2181-2186

Kanamori, H., Anderson, D.L. (1977) Importance of physical dispersion in surface wave and free oscillation problems: Review. Rev. Geophys. Space Phys. 15:105-112

Kara to, S. (1981) Comment on the effect of pressure on the rate of dislocation recovery in olivine, by D. L. Kohlstedt et al. J. Geophys. Res. 86:9319

Karato, S., Ogawa, M. (1982) High pressure recovery of olivine: Implications for creep mechanism and creep activation volume. Phys. Earth Planet. Inter. 28:102-117

Kohlstedt, D.L., Nichols, H.P.K., Hornack, P. (1980) The effect of pressure on the rate of dislocation recovery in olivine. J. Geophys. Res. 85:3122-3130

Kurita, T. (1969) Spectral analysis of seismic waves, Part 1. Data windows for the analysis of transient waves. Spec. Contnb. Geophys. Inst. Kyoto Univ. 9:97-122

Leblanc, G.S.J. (1967) Truncated crustal transfer functions and fine crustal structure determination. Bull. Seismol. Soc. Am. 57:719-733

Liu, H.-P., Anderson, D.L., Kanamori, H. (1976) Velocity dispersion due to anelasticity; implications for seismology and mantle composition. Geophys. J. R. Astron. Soc. 47:41-58

Lundquist, G.M., Cormier, V.F. (1980) Constraints on the absorption band model of Q. J. Geophys. Res. 85:5244-5256

Madariaga, R. (1976) Dynamics of an expanding circular fault. Bull. Seismol. Soc. Am. 66:639-666

Mitchell, B.J. (1980) Frequency dependence of shear wave internal friction in the continental crust of eastern North Amenca. J. Geophys. Res. 85:5212-5218

Mitchell, B.J., Helmberger, D.V. (1973) Shear velocities at the base of the mantle from observations of S and ScS. J. Geophys. Res. 78:6009-6020

Okada, H., Suzuki, S., Asano, S. (1970) Anomalous underground structure in the Matsushiro earthquake swarm area as derived from a fan shooting technique. Bull. Earthquake Res. Inst. 48:811-833

Roecker, S.W., Tucker, B., King, J., Hatzfeld, D. (1982) Estimates of Q in Central Asia as a function of frequency and depth using the coda of locally recorded earthquakes. Bull. Se1smol. Soc. Am. 72:129-150

Ross, J.V., Ave'Lallemant, H.C., Carter, N.L. (1979) Activation volume for creep in the upper mantle. Science 203:261-263

Sacks, I.S. (1989) Qs of the lower mantle-A body wave determination. Carnegie Institution, Ann. Rep. Dir. Department of Terrestrial Magnetism, Year Book 79:508-512

Shimsoni, M., Ben-Menahem, A. (1970) Computation of the divergence coefficient for seismic phases. Geophys. J. R. Astron. Soc. 21:285-294

Singh, K., Fried, J., Aspel, R., Brune, J. (1982) Spectral attenuation of SH-wave along the Imperial Fault and a prehmmary model of Q in the region. Bull. Seismol. Soc. Am. 72:2003-2016

Sipkin, S.A., Jordan, T.H. (1979) Frequency dependence of Q ScS. Bull. Seismol. Soc. Am. 69:1055-1079

Touvenot, F. (1983) Frequency dependence of the quality factor in the upper crust: A deep seismic sounding approach. Geophys. J. R. Astron. Soc. 73:427-447

Tsujiura, M. (1966) Frequency analysts of seismic waves (1). Bull. Earthquake Res. Inst. 44:873-891

Ulug, A. (1983) Frequenzabhangigkeit von Q seismischer Raumwellen im Erdmantel. Ber. Inst. Meteorol. u. Geophys. Umv. Frankfurt, 49

Wielandt, E., Streckeisen, G. (1982) The leaf-spring seismometer: design and performance. Bull. Seismol. Soc. Am. 72:2349-2367