Wave Attenuation and Internal Friction as Functions of Frequency in Rocks

Attewell, P. B.; Ramana, Y. V.

doi:10.1190/1.1439838

Cited by 65 publications

(17 citation statements)

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“…One is related to irreversible processes in a singlephase solid medium. Laboratory experiments on rock specimens as well as field measurements have been interpreted in terms of plane-wave attenuation coefficients for P-and S-waves that are approximately proportional to the frequency over the entire frequency range of interest in seismology and in logging (Attewell and Ramana, 1966;Gardner et al, 1964). The other has been described by Biot (1956) and is based on the conceptual model of a twophase medium consisting of an elastic solid matrix and a viscous pore fluid.…”

Section: Introductionmentioning

confidence: 99%

Synthetic Microseismograms: Logging in Porous Formations

1974

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Biot' s theory of wave propagation in a fluidfilled porous elastic solid takes account of energy dissipation due to relative motion between viscous pore fluid and solid matrix. This theory has been applied to a numerical study of sound pulses propagating along a cylindrical borehole and along a plane interface. It is found that properties such as permeability affect the attenuation of the signal only at high frequencies. For the plane interface, the effect on the P-arrival is small; on the S-arrival it is moderate; and on the Stoneleywave it is large, but only if source and detector are close to the interface and the flow of fluid across the interface is relatively unrestricted. With a wide-band signal, the low-frequency pseudo-Rayleigh wave can partially mask the Sarrival. Similar conclusions hold for the logging tool centered in the borehole, and arrivals other than the first P may be difficult to pick, especially for narrow-band signals. The amplitude of the wave train arriving with approximately the tubewave velocity is particularly sensitive to the fluid-transfer conditions at the borehole wall. The results suggest that acoustic permeability logging tools require high-frequency signals: their performance could depend critically on the acoustic characteristics of mud cake in situ. Narrow-band signals are not suitable for the identification of phases other than the first P-arrival; attenuation measurements probably must be based on the energies observed in gated sections of the pressure response. For signals in the seismic range, inelastic effects predicted by Biot(s theory are too small for the detection of formation properties, especially when thin impermeable beds are also present. INTRODUCTIONThe purpose of this investigation was to establish the feasibility and the required characteristics of an acoustic permeability logging tool. Biot (1956) has derived a theory which relates wavepropagation phenomena to the permeability, porosity, and pore-fluid viscosity of a porous elastic medium. With the aid of this theory, we can numerically investigate the behavior of an acoustic pulse generated in a fluid-filled borehole, which is surrounded by a porous formation. The presence of mud cake can be taken into account by the specification of an acoustic fluid-flow impedance at the borehole wall. The results computed in this report refer to an ideal system, where seismic noise, interbed reflections, borehole irregularities, and inelastic effects in the borehole fluid and in the formation matrix are absent. Formulas have been derived and computations have been carried out both for the plane interface and for the cylindrical geometry with the tool centered in the borehole. From the results, which are summarized in the abstract, we conclude that prospects for a sensitive acoustic logging device to measure low-permeability formations are not favorable, especially if the mud cake seriously inhibits acoustic flow across the borehole wall. Since little is known about the influence of mud cake on the acoustic flow of fluid in...

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Section: Introductionmentioning

confidence: 99%

Synthetic Microseismograms: Logging in Porous Formations

1974

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“…The value of k = 0.015 sec/km determined above appears to be reasonable, although it is lower than most values reported in Ref. 13 for a variety of rock types. This value of attenuation can also be expressed as 1.5 X 10 f dB/cm.…”

Section: Experimental Verification Of Frequencydependent Attenuationmentioning

confidence: 44%

Project Pre-Gondola. Seismic Site Calibration

Kurtz¹,

Redpath²

1968

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Measurements of intermediate range ground motions and of structural response were made during the Pre-Gondola high explosive cratering experiments at Fort Peck, Montana. Liquid nitromethane charges (1000-lb and 20-ton), emplaced at various depths of burst, and a 140-ton row charge were detonated in the Bearpaw shale, which is a weak, wet clay-shale medium. An additional experiment to validate a charge emplacement concept designed to decouple seismic energy proved inconclusive. All seismic measurements were of particle velocity. Using an inverse power law equation to describe the attenuation of seismic amplitudes with distance, it is found that the amplitudes -2 4 from the single charges decayed as approximately R ' , and amplitudes from the row--1 7 charge decayed as R " . A dependence of amplitudes on depth of burst exists, and a yield scaling exponent near 0.8 appears to be appropriate.-A -kfR It is suggested that a variation of particle velocity with distance as R e , where f is the signal frequency, is a more physically realistic description of attenuation than is the inverse power law. The preliminary data from the 140-ton row charge appear to fit this type of attenuation law, and indicate that A = 0.5 and k = 0.015 sec/km. An estimate is made of the near-source variation of peak seismic amplitude with frequency for the row charge, and predictions are made for possible future row-charge cratering experiments at the site.

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“…Constant Q implies that the loss of pulse energy per cycle is equal for all frequencies. Numerous citations of experimental work supporting this relationship are given in review papers by Attewell and Ramana (1966) and Hamilton (1972Hamilton ( , 1976. Results from previous near-surface in-situ attenuation studies by McDonal et al, (1958), Tullos and Reid (1969), and Newman and Worthington (1982) also validate the constant Q model of attenuation.…”

Section: Attenuation Analysismentioning

confidence: 61%

Attenuation Measurements from Vertical Seismic Profile Data: Leg 104, Site 642

Rutledge¹,

Winkler²

1989

Proceedings of the Ocean Drilling Program

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In-situ seismic attenuation was measured through the upper basalt series using vertical seismic profile (VSP) data collected on ODP Leg 104 at the Vdring Plateau, located along the Norwegian continental margin. Assuming a constant Q model, measurements were made using the spectral ratio method over the bandwidth 7.8 to 62.5 Hz. An effective attenuation of 2.7 x 10 _4 dB-s/m ± 0.6 x 10~4 (Q-effective = 25) was measured over a 525-m interval. Apparent attenuation due to intrabed multiple reflections was computed using synthetic VSP data generated from a well log-derived impedance model. The contribution of apparent attenuation can account for all of the observed attenuation in the upper basalt series. Further, the computed apparent attenuation was found to vary with frequency /as/ 09 over the bandwidth 7.8 to 62.5 Hz, indicating that the initial assumption of constant Q was not valid. Q-apparent was computed at two frequencies: at 30 Hz Q-apparent = 55, and at 60 Hz Q-apparent = 29. Within our range of error, intrinsic attenuation in the upper basalt series is less than 0.6 x 10 ~4 dB-s/m (Q-intrinsic > 115).

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Wave Attenuation and Internal Friction as Functions of Frequency in Rocks

Cited by 65 publications

References 0 publications

Synthetic Microseismograms: Logging in Porous Formations

Synthetic Microseismograms: Logging in Porous Formations

Project Pre-Gondola. Seismic Site Calibration

Attenuation Measurements from Vertical Seismic Profile Data: Leg 104, Site 642

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