Acoustic pulse transmission in half‐spaces and finite‐length cylindrical rods

Geophysics ◽  
1985 ◽  
Vol 50 (11) ◽  
pp. 1676-1683 ◽  
Author(s):  
D. P. Blair
Keyword(s):  
Finite Length ◽  
Pulse Shape ◽  
Pulse Propagation ◽  
Acoustic Pulse ◽  
Analytical Techniques ◽  
P Wave ◽  
Shape Distortion ◽  
P Wave Velocity ◽  
Independent Form ◽  
Good Agreement

A combination of both dynamic finite‐element modeling (DFEM) and analytical techniques is used to evaluate the geometric attenuation of acoustic pulses propagated in elastic half‐spaces and finite‐length elastic cylindrical rods. Solutions for the half‐space are presented in a scale‐independent form and are relevant to the study of pulse propagation in large rock masses. For example, it is shown that if a surface‐mounted source has most of its spectral output below approximately 20 kHz, then the transmitted acoustic pulse within 1 m of the source exhibits a pulse‐shape distortion due to geometric attenuation that may dominate the distortion due to material attenuation. The results for the cylindrical rod are relevant to the study of pulse propagation in rock cores, and for this case the geometric effect yields a large increase in pulse‐shape distortion as a function of the distance from the source. For an aluminum cylindrical rod 1.0 m long, 0.05 m in diameter, and having a P‐wave velocity of 6 175 m/s, the geometric attenuation of acoustic pulses having rise times of approximately five microseconds is over 20 times larger than the material attenuation obtained for silica dolomite. In all studies, good agreement was found between the DFEM solution and the appropriate analytical solution. Furthermore, good agreement was also found between a DFEM solution and experimental results for acoustic pulse propagation along the cylindrical aluminum bar.

Experimental study of fracture size effect on elastic-wave velocity dispersion and anisotropy

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. C49-C59 ◽  
Author(s):  
Da Shuai ◽  
Jianxin Wei ◽  
Bangrang Di ◽  
Sanyi Yuan ◽  
Jianyong Xie ◽  
...  
Keyword(s):  
Wave Velocity ◽  
Seismic Velocity ◽  
Effective Medium Theory ◽  
Transversely Isotropic ◽  
Elastic Wave Velocity ◽  
P Wave ◽  
S Wave ◽  
P Wave Velocity ◽  
Fracture Size ◽  
Good Agreement

We have designed transversely isotropic models containing penny-shaped rubber inclusions, with the crack diameters ranging from 2.5 to 6.2 mm to study the influence of fracture size on seismic velocity under controlled conditions. Three pairs of transducers with different frequencies (0.5, 0.25, and 0.1 MHz) are used for P- and S-wave ultrasonic sounding, respectively. The P-wave measurements indicate that the scattering effect is dominant when the waves propagate perpendicular to the fractures. Our experimental results demonstrate that when the wavelength-to-crack-diameter ratio ([Formula: see text]) is larger than 14, the P-wave velocity can be described predominantly by the effective medium theory. Although the ratio is larger than four, the S-wave velocity is close to the equivalent medium results. When [Formula: see text] < 14 or [Formula: see text] is < 4, the elastic velocity is dominated by scattering. The magnitudes of the Thomsen anisotropic parameters [Formula: see text] and [Formula: see text] are scale and frequency dependent on the assumption that the transversely isotropic models are vertical transversely isotropic medium. Furthermore, we compare the experimental velocities with the Hudson theory. The results illustrate that there is a good agreement between the observed P-wave velocity and the Hudson theory when [Formula: see text] > 7 in the directions parallel and perpendicular to the fractures. For small fracture diameters, however, the P-wave velocity perpendicular to the fractures predicted from the Hudson theory is not accurate. When [Formula: see text] < 4, there is good agreement between the experimental fast S-wave velocity and the Hudson theory, whereas the experimental slow S-wave velocity diverges with the Hudson theory. When [Formula: see text] > 4, the deviation of fast and slow S-wave velocities with the Hudson prediction is stable.

0π PULSE SHAPE IN THE SHARP LINE LIMIT CASE

1996 ◽  
Vol 05 (03) ◽  
pp. 579-589
Author(s):  
M. MATUSOVSKY ◽  
B. VAYNBERG ◽  
M. ROSENBLUH
Keyword(s):  
Resonance Frequency ◽  
Pulse Shape ◽  
Pulse Propagation ◽  
Resonant Excitation ◽  
Limit Case ◽  
Pulse Spectrum ◽  
Sharp Line ◽  
Low Intensity ◽  
Theoretical Predictions ◽  
Good Agreement

We observe the propagation and the reshaping of low intensity (zero area) 60 fs pulses through high density atomic Cs vapor. The breakup of the pulses is measured for both resonant excitation of the Cs atoms and for laser detunings such that the atomic resonance frequency is in the wings of the pulse spectrum. The theory of 0π pulse propagation, in the extreme sharp-line limit, is extended to include both resonant and off resonant excitation. Good agreement is demonstrated between the observations and the theoretical predictions.

scholarly journals Geophysical and analytical determination of overstressed zones in exploited coal seam: a case study

2021 ◽  
Author(s):  
Dariusz Chlebowski ◽  
Zbigniew Burtan
Keyword(s):  
Coal Seam ◽  
Wave Velocity ◽  
Seismic Tomography ◽  
Analytical Modeling ◽  
Coal Mines ◽  
Vertical Stress ◽  
P Wave ◽  
Rockburst Hazard ◽  
State Of Stress ◽  
P Wave Velocity

AbstractA variety of geophysical methods and analytical modeling are applied to determine the rockburst hazard in Polish coal mines. In particularly unfavorable local conditions, seismic profiling, active/passive seismic tomography, as well as analytical state of stress calculating methods are recommended. They are helpful in verifying the reliability of rockburst hazard forecasts. In the article, the combined analysis of the state of stress determined by active seismic tomography and analytical modeling was conducted taking into account the relationship between the location of stress concentration zones and the level of rockburst hazard. A longwall panel in the coal seam 501 at a depth of ca.700 m in one of the hard coal mines operating in the Upper Silesian Coal Basin was a subject of the analysis. The seismic tomography was applied for the reconstruction of P-wave velocity fields. The analytical modeling was used to calculate the vertical stress states basing on classical solutions offered by rock mechanics. The variability of the P-wave velocity field and location of seismic anomaly in the coal seam in relation to the calculated vertical stress field arising in the mined coal seam served to assess of rockburst hazard. The applied methods partially proved their adequacy in practical applications, providing valuable information on the design and performance of mining operations.

scholarly journals No mafic layer in 80 km thick Tibetan crust

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Gaochun Wang ◽  
Hans Thybo ◽  
Irina M. Artemieva
Keyword(s):  
Seismic Data ◽  
P Wave ◽  
Indian Plate ◽  
Low Velocity ◽  
Crustal Earthquakes ◽  
Tectonic Processes ◽  
P Wave Velocity ◽  
Juvenile Crust ◽  
Mafic Lower Crust ◽  
Thick Crust

AbstractAll models of the magmatic and plate tectonic processes that create continental crust predict the presence of a mafic lower crust. Earlier proposed crustal doubling in Tibet and the Himalayas by underthrusting of the Indian plate requires the presence of a mafic layer with high seismic P-wave velocity (Vp > 7.0 km/s) above the Moho. Our new seismic data demonstrates that some of the thickest crust on Earth in the middle Lhasa Terrane has exceptionally low velocity (Vp < 6.7 km/s) throughout the whole 80 km thick crust. Observed deep crustal earthquakes throughout the crustal column and thick lithosphere from seismic tomography imply low temperature crust. Therefore, the whole crust must consist of felsic rocks as any mafic layer would have high velocity unless the temperature of the crust were high. Our results form basis for alternative models for the formation of extremely thick juvenile crust with predominantly felsic composition in continental collision zones.

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