The Earth as a Seismic Absorption Band

Anderson, Don L.; Kanamori, Hiroo; Hart, Robert S.; Liu, Hsi‐Ping

doi:10.1126/science.196.4294.1104

Cited by 64 publications

(36 citation statements)

References 22 publications

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“…While this procedure will not yield the elastic constants of an equivalent ideally elastic body, it does make all the seismic data consistent. Following Liu et al [1] and Anderson et al [ 17], the necessary correction term is:…”

Section: Data and Inversionmentioning

confidence: 99%

Shear velocity and density of an attenuating earth

Hart

Anderson

Kanamori

1976

Earth and Planetary Science Letters

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The dispersion that must accompany absorption is taken into account in many recent body-wave investigations but has been largely ignored in surface-wave and free-oscillation studies. In order to compare body-wave and free-oscillation data a correction must be made to travel times or periods to account for absorption-related physical dispersion. The correction depends on the frequency and Q of the data and can be as high as 1% which is much larger than the uncertainty of the raw data, Corrected toroidal mode data is inverted to obtain shear velocity and density versus depth. The average shear velocity in the upper 600 km is ~2% greater than obtained from the uncorrected data. The resulting shear-wave travel times oscillate about the Jeffreys-Bullen values with an average baseline of only +0.5 second. Thus, the discrepancy between body-wave and free-oscillation studies is eliminated.

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Section: Data and Inversionmentioning

confidence: 99%

Shear velocity and density of an attenuating earth

Hart

Anderson

Kanamori

1976

Earth and Planetary Science Letters

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“…In this paper we apply the absorption band concept [Liu et al, 1976;Kanamori and Anderson, 1977;Anderson et al, 1977;Anderson and Minster, 1980;Minster and Anderson, 1981] to the attenuation of body waves, surface waves, and free oscillations. The basic method is described by Anderson and Hart [1978a, b] except that we replace the frequencyindependent Q assumption with the absorption band assumption.…”

Section: Introductionmentioning

confidence: 99%

Absorption band Q model for the Earth

1982

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Body wave, su~ace wave, and .norm~! mode data are used to place constraints on the frequency depe_n.dence of Q m the mantle. With a simple absorption band model it is possible to satisfy the shear sensitive data over a broad frequency range. The quality factor Qs(w) is proportional to w" in the band and to ~ and w-1 at higher and lower frequencies, respectively, as appropriate for a relaxation mech~msm with a spectrum of relaxation times. The parameters of the band are Q(min) = 80, a= 0.15, and w1dt~, 5 decades. The center of the band varies from 10 1 seconds in the upper mantle, to 1.6 x 10 3 seconds m the lower mantle. The shift of the band with depth is consistent with the expected effects of temper~ture, pressure and stress. High Qs regions of the mantle are attributed to a shift of the absorptiOn band to longer periods. To satisfy the gravest fundamental spheroidal modes and the ScS data, the absorption band must shift back into the short-period seismic band at the base of the mantle This may be .due to a ~ig~ te.mp~rature gradient or high shear stresses. A preliminary attempt is als~ made to s~ec1fy bulk dissipation m the mantle and core. Specific features of the absorption band model are lo": Q m the body wave ~mnd at both the top and the base of the mantle, low Q for long-period body wave~ m the outer core, an mner.core ~s that increases with period, and low QP/Qs at short periods in the middle mantle. The short-penod Qs mcreases rapidly at 400 km and is relatively constant from this depth to 2400 km. The deformational Q of the earth at a period of 14 months is predicted to be 463.

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“…However, the earth's Q filtering effect inevitably induces the energy dissipation of high-frequency wave components, and distorts the seismic wavelets, simultaneously (Futterman 1962, Anderson et al 1977, Kjartansson 1979, Wang and Guo 2004. Inverse Q filtering and deconvolution are two common methods for seismic resolution enhancement.…”

Section: Introductionmentioning

confidence: 99%

High-resolution seismic processing by Gabor deconvolution

Chen

Wang

Chen

et al. 2013

Journal of Geophysics and Engineering

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Since viscoelastic attenuation effects are ubiquitous in subsurface media, the seismic source wavelet rapidly evolves as the wave travels through the subsurface. Eliminating the source wavelet and compensating the attenuation effect together may improve seismic resolution. Gabor deconvolution can achieve these two processes simultaneously, by removing the propagating wavelet which is the combination of the source wavelet and the attenuation effect. The Gabor deconvolution operator is determined based on the Gabor spectrum of a nonstationary seismic trace. By assuming white reflectivity, the Gabor amplitude spectrum can be smoothed to produce the required amplitude spectrum of the propagating wavelet. In this paper, smoothing is set as a least-squares inverse problem, and is referred to as regularized smoothing. By assuming that the source wavelet and the attenuation process are both minimum phased, the phase spectrum of the propagating wavelet can be defined by the Hilbert transform of the natural logarithm of the smoothed amplitude spectrum. The inverse of the complex spectrum of the propagating wavelet is the Gabor deconvolution operator. Applying it to the original time-frequency spectrum of the nonstationary trace produces an estimated time-frequency spectrum of reflectivity series. The final time-domain highresolution trace, obtained by an inverse Gabor transform, is close to a band-pass filtered version of the reflectivity series.

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The Earth as a Seismic Absorption Band

Cited by 64 publications

References 22 publications

Shear velocity and density of an attenuating earth

Shear velocity and density of an attenuating earth

Absorption band Q model for the Earth

High-resolution seismic processing by Gabor deconvolution

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