A theory of compressional wave attenuation in noncohesive sediments

Geophysics ◽  
1985 ◽  
Vol 50 (8) ◽  
pp. 1311-1317 ◽  
Author(s):  
C. McCann ◽  
D. M. McCann
Keyword(s):  
Wave Attenuation ◽  
Compressional Wave ◽  
Solid Particles ◽  
Biot’S Theory ◽  
Attenuation Coefficients ◽  
Low Frequencies ◽  
Biot's Theory ◽  
Compressional Waves ◽  
High Frequencies ◽  
Water Saturated

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.

Relationships among compressional wave attenuation, porosity, clay content, and permeability in sandstones

Geophysics ◽  
1990 ◽  
Vol 55 (8) ◽  
pp. 998-1014 ◽  
Author(s):  
T. Klimentos ◽  
C. McCann
Keyword(s):  
Seismic Data ◽  
Wave Attenuation ◽  
Clay Content ◽  
Spectral Ratio ◽  
Confining Pressure ◽  
Compressional Wave ◽  
Biot Theory ◽  
Attenuation Coefficients ◽  
Compressional Waves ◽  
High Attenuation

Anelastic attenuation is the process by which rocks convert compressional waves into heat and thereby modify the amplitude and phase of the waves. Understanding the causes of compressional wave attenuation is important in the acquisition, processing, and interpretation of high‐resolution seismic data, and in deducing the physical properties of rocks from seismic data. We have measured the attenuation coefficients of compressional waves in 42 sandstones at a confining pressure of 40 MPa (equivalent to a depth of burial of about 1.5 km) in a frequency range from 0.5 to 1.5 MHz. The compressional wave measurements were made using a pulse‐echo method in which the sample (5 cm diameter, 1.8 cm to 3.5 cm long) was sandwiched between perspex (lucite) buffer rods inside the high‐pressure rig. The attenuation of the sample was estimated from the logarithmic spectral ratio of the signals (corrected for beam spreading) reflected from the top and base of the sample. The results show that for these samples, compressional wave attenuation (α, dB/cm) at 1 MHz and 40 MPa is related to clay content (C, percent) and porosity (ϕ, percent) by α=0.0315ϕ+0.241C−0.132 with a correlation coefficient of 0.88. The relationship between attenuation and permeability is less well defined: Those samples with permeabilities less than 50 md have high attenuation coefficients (generally greater than 1 dB/cm) while those with permeabilities greater than 50 md have low attenuation coefficients (generally less than 1 dB/cm) at 1 MHz at 40 MPa. These experimental data can be accounted for by modifications of the Biot theory and by consideration of the Sewell/Urick theory of compressional wave attenuation in porous, fluid‐saturated media.

STUDIES OF ELASTIC WAVE ATTENUATION IN POROUS MEDIA

Geophysics ◽  
1962 ◽  
Vol 27 (5) ◽  
pp. 569-589 ◽  
Author(s):  
M. R. J. Wyllie ◽  
G. H. F. Gardner ◽  
A. R. Gregory
Keyword(s):  
Porous Media ◽  
Elastic Wave ◽  
Wave Attenuation ◽  
Fluid Motion ◽  
Fluid Viscosity ◽  
Biot’S Theory ◽  
Biot's Theory ◽  
High Frequencies ◽  
Very High Frequencies

Elastic wave attenuation in porous media is due in part to the relative motion of the liquid and the solid. Biot’s theory expresses this component in terms of permeability, fluid viscosity, frequency, and the elastic constants of the material. Experiments were performed to measure attenuation in the frequency range f <20,000 cps by a resonant bar method; attempts to measure attenuation at very high frequencies gave more equivocal results. Alundum bars were used to test the validity of the theory, for with these the loss not due to fluid motion is relatively small. Experiments were also made with natural specimens of rock. These showed that when not subjected to compacting pressure both the velocities and decrements of specimens were affected chemically and physically by the presence of liquid pore saturants. It is concluded that Biot’s theory seems generally applicable to the determination of the fluid‐solid or “sloshing” losses in resonated porous media. There is still some doubt about the applicability of the theory in the case of measurements made by pulse techniques. The use of attenuation measurements as a logging technique, possibly to estimate permeability, is also discussed.

Evaluation of Thermal Degradation of 2.25Cr-1Mo Steel by High Frequency Ultrasonic Attenuation Measurement

2005 ◽  
Vol 475-479 ◽  
pp. 257-260 ◽  
Author(s):  
Jai Won Byeon ◽  
C.S. Kim ◽  
S.I. Kwun ◽  
S.J. Hong
Keyword(s):  
Attenuation Coefficient ◽  
High Frequency ◽  
Ultrasonic Attenuation ◽  
Attenuation Coefficients ◽  
Low Frequencies ◽  
High Frequencies ◽  
Noticeable Increase ◽  
Mean Size ◽  
Longitudinal Ultrasonic Wave ◽  
Degradation Time

It was attempted to assess nondestructively the degree of isothermal degradation of 2.25Cr-1Mo steel by using high frequency longitudinal ultrasonic wave. Microstructural parameter (mean size of carbides), mechanical property (Vickers hardness) and ultrasonic attenuation coefficient were measured for the 2.25Cr-1Mo steel isothermally degraded at 630°C for up to 4800 hours in order to find the correlation among these parameters. The ultrasonic attenuation coefficients at high frequencies (over 35MHz) were observed to increase rapidly in the initial 1000 hours of degradation time and then slowly thereafter, while the ones at low frequencies showed no noticeable increase. Ultrasonic attenuation at high frequencies increased as a function of mean size of carbides. Ultrasonic attenuation coefficient was found to have a linear correlation with the hardness, and suggested accordingly as a potential nondestructive evaluation parameter for assessing the mechanical strength reduction of the isothermally degraded 2.25Cr-1Mo steel.

Experimental measurements of seismic attenuation In microfractured sedimentary rock

Geophysics ◽  
1994 ◽  
Vol 59 (9) ◽  
pp. 1342-1351 ◽  
Author(s):  
Sheila Peacock ◽  
Clive McCann ◽  
Jeremy Sothcott ◽  
Timothy R. Astin
Keyword(s):  
Sedimentary Rock ◽  
Wave Attenuation ◽  
Crack Density ◽  
Seismic Attenuation ◽  
Experimental Measurements ◽  
Effective Pressure ◽  
Carrara Marble ◽  
Compressional Waves ◽  
Linear Relationships ◽  
Water Saturated

Ultrasonic compressional‐ and shear‐wave attenuation in water‐saturated Carrara Marble increase with increasing crack density and decreasing effective pressure. Between 0.4 and 1.0 MHz, empirical linear relationships between 1/Q and crack density CD were found to be: CD = 1.96 ± 0.63 × 1/Q, for compressional waves and CD = 6.7 ± 1.5 × 1/Q, for shear waves.

Attenuation of seismic waves in dry and saturated rocks: I. Laboratory measurements

Geophysics ◽  
1979 ◽  
Vol 44 (4) ◽  
pp. 681-690 ◽  
Author(s):  
M. N. Toksöz ◽  
D. H. Johnston ◽  
A. Timur
Keyword(s):  
Seismic Waves ◽  
Reference Sample ◽  
Spectral Ratios ◽  
Attenuation Coefficients ◽  
Compressional Waves ◽  
S Waves ◽  
Pulse Transmission ◽  
Water Saturated ◽  
Quality Factor Q ◽  
Q Values

The attenuation of compressional (P) and shear (S) waves in dry, saturated, and frozen rocks is measured in the laboratory at ultrasonic frequencies. A pulse transmission technique and spectral ratios are used to determine attenuation coefficients and quality factor (Q) values relative to a reference sample with very low attenuation. In the frequency range of about 0.1–1.0 MHz, the attenuation coefficient is linearly proportional to frequency (constant Q) both for P‐ and S‐waves. In dry rocks, [Formula: see text] of compressional waves is slightly smaller than [Formula: see text] of shear waves. In brine and water‐saturated rocks, [Formula: see text] is larger than [Formula: see text]. Attenuation decreases substantially (Q values increase) with increasing differential pressure for both P‐ and S‐waves.

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

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. WA93-WA101 ◽  
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.

scholarly journals Laboratory measurements of low- and high-frequency elastic moduli in Fontainebleau sandstone

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. D369-D379 ◽  
Author(s):  
Emmanuel C. David ◽  
Jérome Fortin ◽  
Alexandre Schubnel ◽  
Yves Guéguen ◽  
Robert W. Zimmerman
Keyword(s):  
Bulk Modulus ◽  
Elastic Moduli ◽  
High Pressures ◽  
Low Frequency ◽  
Frequency Dispersion ◽  
Low Frequencies ◽  
High Frequencies ◽  
Fontainebleau Sandstone ◽  
Wave Velocities ◽  
Water Saturated

The presence of pores and cracks in rocks causes the fluid-saturated wave velocities in rocks to be dependent on frequency. New measurements of the bulk modulus at low frequencies (0.02–0.1 Hz) were obtained in the laboratory using oscillation tests carried out on two hydrostatically stressed Fontainebleau sandstone samples, in conjunction with ultrasonic velocities and static measurements, under a range of differential pressures (10–95 MPa), and with three different pore fluids (argon, glycerin, and water). For the 13% and 4% porosity samples, under glycerin- and water-saturated conditions, the low-frequency bulk modulus at 0.02 Hz matched well the low-frequency and ultrasonic dry bulk modulus. The glycerin- and water-saturated samples were much more compliant at low frequencies than at high frequencies. The measured bulk moduli of the tested rocks at low frequencies (0.02–0.1 Hz) were much lower than the values predicted by the Gassmann equation. The frequency dispersion of the P and S velocities was much higher at low differential pressures than at high pressures, due to the presence of open cracks at low differential pressures.

Scattering of Compressional Waves by a Rigid Spheroidal Inclusion

1973 ◽  
Vol 40 (4) ◽  
pp. 1073-1077 ◽  
Author(s):  
Michael A. Oien ◽  
Yih-Hsing Pao
Keyword(s):  
Dynamic Stress ◽  
Translational Motion ◽  
Expansion Method ◽  
Compressional Wave ◽  
Low Frequencies ◽  
Compressional Waves ◽  
Spheroidal Inclusion ◽  
Eigenfunction Expansion Method ◽  
Concentration Factors ◽  
Stress Concentration Factors

The scattering of an axial plane harmonic compressional wave by a mobile rigid spheroidal inclusion in an elastic medium is investigated. A solution valid for low frequencies is obtained using the eigenfunction expansion method. Numerical results are presented for the excited translational motion of the spheroid and for dynamic stress-concentration factors.

COMPRESSIONAL‐WAVE ATTENUATION IN MARINE SEDIMENTS

Geophysics ◽  
1972 ◽  
Vol 37 (4) ◽  
pp. 620-646 ◽  
Author(s):  
Edwin L. Hamilton
Keyword(s):  
Marine Sediments ◽  
Wave Attenuation ◽  
Unit Length ◽  
Viscoelastic Model ◽  
Compressional Wave ◽  
Coarse Sand ◽  
Sediment Types ◽  
Viscous Losses ◽  
Clayey Silt ◽  
Water Saturated

In‐situ measurements of compressional (sound) velocity and attenuation were made in the sea floor off San Diego in water depths between 4 and 1100 m; frequencies were between 3.5 and 100 khz. Sediment types ranged from coarse sand to clayey silt. These measurements, and others from the literature, allowed analyses of the relationships between attenuation and frequency and other physical properties. This permitted the study of appropriate viscoelastic models which can be applied to saturated sediments. Some conclusions are: (1) attenuation in db/unit length is approximately dependent on the first power of frequency, (2) velocity dispersion is negligible, or absent, in water‐saturated sediments, (3) intergrain friction appears to be, by far, the dominant cause of wave‐energy damping in marine sediments; viscous losses due to relative movement of pore water and mineral structure are probably negligible, (4) a particular viscoelastic model (and concomitant equations) is recommended; the model appears to apply to both water‐saturated rocks and sediments, and (5) a method is derived which allows prediction of compressional‐wave attenuation, given sediment‐mean‐grain size or porosity.

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