Studies on the effect of shear on compressional wave attenuation.

Published reviews indicate that attenuation coefficients of compressional waves in noncohesive, water‐saturated sediments vary linearly with frequency. Biot’s theory, which accounts for attenuation in terms of the viscous interaction between the solid particles and pore fluid, predicts in its presently published form variation proportional to [Formula: see text] at low frequencies and [Formula: see text] at high frequencies. A modification of Biot’s theory which incorporates a distribution of pore sizes is presented and shown to give excellent agreement with new and published attenuation data in the frequency range 10 kHz to 2.25 MHz. In particular, a linear variation of attenuation with frequency is predicted in that range.

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P-wave attenuation measurements from laboratory resonance and sonic waveform data

Geophysics ◽

10.1190/1.1442579 ◽

1989 ◽

Vol 54 (1) ◽

pp. 76-81 ◽

Cited By ~ 12

Author(s):

D. Goldberg ◽

B. Zinszner

Keyword(s):

Wave Attenuation ◽

Compressional Wave ◽

P Wave ◽

Laboratory Measurements ◽

Frequency Range ◽

Waveform Data ◽

Sonic Log ◽

In Situ Conditions ◽

The Mean

We computed compressional‐wave velocity [Formula: see text] and attenuation [Formula: see text] from sonic log waveforms recorded in a cored, 30 m thick, dolostone reservoir; using cores from the same reservoir, laboratory measurements of [Formula: see text] and [Formula: see text] were also obtained. We used a resonant bar technique to measure extensional and shear‐wave velocities and attenuations in the laboratory, so that the same frequency range as used in sonic logging (5–25 kHz) was studied. Having the same frequency range avoids frequency‐dependent differences between the laboratory and in‐situ measurements. Compressional‐wave attenuations at 0 MPa confining pressure, calculated on 30 samples, gave average [Formula: see text] values of 17. Experimental and geometrical errors were estimated to be about 5 percent. Measurements at elevated effective pressures up to 30 MPa on selected dolostone samples in a homogeneous interval showed mean [Formula: see text] and [Formula: see text] to be approximately equal and consistently greater than 125. At effective stress of 20 MPa and at room temperature, the mean [Formula: see text] over the dolostone interval was 87, a minimum estimate for the approximate in‐situ conditions. We computed compressional‐wave attenuation from sonic log waveforms in the 12.5–25 kHz frequency band using the slope of the spectral ratio of waveforms recorded 0.914 m and 1.524 m from the source. Average [Formula: see text] over the interval was 13.5, and the mean error between this value and the 95 percent confidence interval of the slope was 15.9 percent. The laboratory measurements of [Formula: see text] under elevated pressure conditions were more than five times greater than the mean in‐situ values. This comparison shows that additional extrinsic losses in the log‐derived measurement of [Formula: see text], such as scattering from fine layers and vugs or mode conversion to shear energy dissipating radially from the borehole, dominate the apparent attenuation.

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Plastic yielding as a frequency and amplitude independent mechanism of seismic wave attenuation

Geophysics ◽

10.1190/1.3420734 ◽

2010 ◽

Vol 75 (3) ◽

pp. N51-N63 ◽

Cited By ~ 12

Author(s):

Victoria M. Yarushina ◽

Yuri Y. Podladchikov

Keyword(s):

Wave Attenuation ◽

Mathematical Formulation ◽

Compressional Wave ◽

Solid Matrix ◽

Large Strains ◽

Plastic Yielding ◽

Seismic Wave Attenuation ◽

Local Stresses ◽

Frequency Independent ◽

Volume Energy

We have developed a mathematical formulation of two mechanisms of compressional wave attenuation, which can occur within the solid rock frame prestressed up to its yield stress in part of its volume. Energy losses are attributed to two distinct processes: irreversible plastic yielding and formation of radial microfractures around microscopic cavities. Small-amplitude waves propagating through the rocks prestressed at their yield point would cause nonelastic strain to avoid building local stresses above the yield limit and attenuate some fraction of their energy per every loading cycle. New mechanisms of microscale yielding and microfracturing give rise to frequency-independent attenuation due to rate-independence of plasticity formulation. Quality factor [Formula: see text] predicted by the model is independent of strain amplitude for small strains and decreases with increasing amplitude for large strains. We found that attenuation can be high even for small seismic strains [Formula: see text]. Thus, [Formula: see text] is achieved at effective pressures greater than twice the yield strength of the solid matrix for the plastic yielding mechanism and at overpressures exceeding half tensile strength for microfracturing.

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Sonic to ultrasonic Q of sandstones and limestones: Laboratory measurements at in situ pressures

Geophysics ◽

10.1190/1.3052112 ◽

2009 ◽

Vol 74 (2) ◽

pp. WA93-WA101 ◽

Cited By ~ 22

Author(s):

Clive McCann ◽

Jeremy Sothcott

Keyword(s):

Wave Attenuation ◽

Shear Waves ◽

Compressional Wave ◽

Ultrasonic Frequency ◽

Laboratory Measurements ◽

Compressional Waves ◽

Wave Velocities ◽

Poisson's Ratios ◽

Poisson’S Ratios

Laboratory measurements of the attenuation and velocity dispersion of compressional and shear waves at appropriate frequencies, pressures, and temperatures can aid interpretation of seismic and well-log surveys as well as indicate absorption mechanisms in rocks. Construction and calibration of resonant-bar equipment was used to measure velocities and attenuations of standing shear and extensional waves in copper-jacketed right cylinders of rocks ([Formula: see text] in length, [Formula: see text] in diameter) in the sonic frequency range and at differential pressures up to [Formula: see text]. We also measured ultrasonic velocities and attenuations of compressional and shear waves in [Formula: see text]-diameter samples of the rocks at identical pressures. Extensional-mode velocities determined from the resonant bar are systematically too low, yielding unreliable Poisson’s ratios. Poisson’s ratios determined from the ultrasonic data are frequency corrected and used to calculate thesonic-frequency compressional-wave velocities and attenuations from the shear- and extensional-mode data. We calculate the bulk-modulus loss. The accuracies of attenuation data (expressed as [Formula: see text], where [Formula: see text] is the quality factor) are [Formula: see text] for compressional and shear waves at ultrasonic frequency, [Formula: see text] for shear waves, and [Formula: see text] for compressional waves at sonic frequency. Example sonic-frequency data show that the energy absorption in a limestone is small ([Formula: see text] greater than 200 and stress independent) and is primarily due to poroelasticity, whereas that in the two sandstones is variable in magnitude ([Formula: see text] ranges from less than 50 to greater than 300, at reservoir pressures) and arises from a combination of poroelasticity and viscoelasticity. A graph of compressional-wave attenuation versus compressional-wave velocity at reservoir pressures differentiates high-permeability ([Formula: see text], [Formula: see text]) brine-saturated sandstones from low-permeability ([Formula: see text], [Formula: see text]) sandstones and shales.

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