On: “Dynamic Photoelastic Studies on P and S Wave Propagation in Prestressed Media,” by Ker C. Thomson, T. J. Ahrens, and M. N. Toksöz (GEOPHYSICS, October 1969, p. 696–712)

Geophysics ◽  
1970 ◽  
Vol 35 (4) ◽  
pp. 716-716
Author(s):  
A. Grover
Keyword(s):  
Wave Propagation ◽  
S Wave ◽  
S Waves ◽  
Explosive Source

The authors mention in the section, “P and S waves in a stress‐free plate,” that they could observe propagating in an unstressed plate the P and S waves which were produced by an explosive source. Furthermore, they have related the observed S wave isoclinics (Figure 7) to the theoretical isoclinics.

scholarly journals A new acoustic assumption for orthorhombic media

2020 ◽  
Vol 223 (2) ◽  
pp. 1118-1129
Author(s):  
Mohammad Mahdi Abedi ◽  
Alexey Stovas
Keyword(s):  
Wave Propagation ◽  
Conventional Approach ◽  
P Wave ◽  
Model Parameters ◽  
Governing Equations ◽  
S Wave ◽  
S Waves ◽  
Exploration Seismology ◽  
And Inversion ◽  
Approximate Equations

SUMMARY In exploration seismology, the acquisition, processing and inversion of P-wave data is a routine. However, in orthorhombic anisotropic media, the governing equations that describe the P-wave propagation are coupled with two S waves that are considered as redundant noise. The main approach to free the P-wave signal from the S-wave noise is the acoustic assumption on the wave propagation. The conventional acoustic assumption for orthorhombic media zeros out the S-wave velocities along three orthogonal axes, but leaves significant S-wave artefacts in all other directions. The new acoustic assumption that we propose mitigates the S-wave artefacts by zeroing out their velocities along the three orthogonal symmetry planes of orthorhombic media. Similar to the conventional approach, our method reduces the number of required model parameters from nine to six. As numerical experiments on multiple orthorhombic models show, the accuracy of the new acoustic assumption also compares well to the conventional approach. On the other hand, while the conventional acoustic assumption simplifies the governing equations, the new acoustic assumption further complicates them—an issue that emphasizes the necessity of simple approximate equations. Accordingly, we also propose simpler rational approximate phase-velocity and eikonal equations for the new acoustic orthorhombic media. We show a simple ray tracing example and find out that the proposed approximate equations are still highly accurate.

Application of seismic interferometry to extract P- and S-wave propagation and observation of shear-wave splitting from noise data at Cold Lake, Alberta, Canada

Geophysics ◽  
2008 ◽  
Vol 73 (4) ◽  
pp. D35-D40 ◽  
Author(s):  
Masatoshi Miyazawa ◽  
Roel Snieder ◽  
Anupama Venkataraman
Keyword(s):  
Wave Propagation ◽  
Shear Wave ◽  
Structural Parameters ◽  
Shear Wave Splitting ◽  
Seismic Interferometry ◽  
Stress Axis ◽  
S Wave ◽  
S Waves ◽  
Wave Splitting ◽  
Cold Lake

We extract downward-propagating P- and S-waves from industrial noise generated by human and/or machine activity at the surface propagating down a borehole at Cold Lake, Alberta, Canada, and measure shear-wave splitting from these data. The continuous seismic data are recorded at eight sensors along a downhole well during steam injection into a 420–470-m-deep oil reservoir. We crosscorrelate the waveforms observed at the top sensor and other sensors to extract estimates of the direct P- and S-wave components of the Green’s function that account for wave propagation between sensors. Fast high-frequency and slow low-frequency signals propagating vertically from the surface to the bottom are found for the vertical and horizontal components of the wave motion, which are identified with P- and S-waves, respectively. The fastest S-wave polarized in the east-northeast–west-southwest direction is about 1.9% faster than the slowest S-wave polarized in the northwest-southeast direction. The direction of polarization of the fast S-wave is rotated clockwise by [Formula: see text] from the maximum principal stress axis as estimated from the regional stress field. This study demonstrates the useful application of seismic interferometry to field data to determine structural parameters, which are P- and S-wave velocities and a shear-wave-splitting coefficient, with high accuracy.

Separation and enhancement of split S‐waves on multicomponent shot records from the BIRPS WISPA experiment

Geophysics ◽  
1994 ◽  
Vol 59 (1) ◽  
pp. 131-139 ◽  
Author(s):  
M. Boulfoul ◽  
D. R. Watts
Keyword(s):  
Synthetic Data ◽  
P Wave ◽  
Moving Window ◽  
Wave Analysis ◽  
S Wave ◽  
Near Surface ◽  
S Waves ◽  
Wave Velocities ◽  
Wave Splitting ◽  
Explosive Source

Instantaneous rotations are combined with f-k filtering to extract coherent S‐wave events from multicomponent shot records recorded by British Institutions Reflection Profiling Syndicate (BIRPS) Weardale Integrated S‐wave and P‐wave analysis (WISPA) experiment. This experiment was an attempt to measure the Poisson’s ratio of the lower crest by measuring P‐wave and S‐wave velocities. The multihole explosive source technique did generate S‐waves although not of opposite polarization. Attempts to produce stacks of the S‐wave data are unsuccessful because S‐wave splitting in the near surface produced random polarizations from receiver group to receiver group. The delay between the split wavelets varies but is commonly between 20 to 40 ms for 10 Hz wavelets. Dix hyperbola are produced on shot records after instantaneous rotations are followed by f-k filtering. To extract the instantaneous polarization, the traces are shifted back by the length of a moving window over which the calculation is performed. The instantaneous polarization direction is computed from the shifted data using the maximum eigenvector of the covariance matrix over the computation window. Split S‐waves are separated by the instantaneous rotation of the unshifted traces to the directions of the maximum eigenvectors determined for each position of the moving window. F-K filtering is required because of the presence of mode converted S‐waves and S‐waves produced by the explosive source near the time of detonation. Examples from synthetic data show that the method of instantaneous rotations will completely separate split S‐waves if the length of the moving window over which the calculation is performed is the length of the combined split wavelets. Separation may be achieved on synthetic data for wavelet delays as small as two sample intervals.

scholarly journals DYNAMIC PHOTOELASTIC STUDIES OF P AND S WAVE PROPAGATION IN PRESTRESSED MEDIA

Geophysics ◽  
1969 ◽  
Vol 34 (5) ◽  
pp. 696-712 ◽  
Author(s):  
Ker C. Thomson ◽  
Thomas J. Ahrens ◽  
M. Nafi Toksöz
Keyword(s):  
Wave Propagation ◽  
High Speed ◽  
Seismic Waves ◽  
Theoretical Calculations ◽  
Body Waves ◽  
S Wave ◽  
S Waves ◽  
Model Study ◽  
Experimental Apparatus ◽  
Fringe Patterns

The occasional existence of very pronounced, anomalous, horizontally polarized seismic waves from underground nuclear bomb blasts has been reported by several investigators. In order to further understanding of this phenomenon and the processes of mechanical radiation from explosions, particularly in prestressed media, a model study has been undertaken. Experimental apparatus has been developed which permits the generation and propagation of body waves from explosions in transparent plate models prestressed to various two‐dimensional stress configurations. High‐speed framing camera sequences are presented showing the explosion process and the resulting plate compressional and shear wave propagation in prestressed models. These are compared to theoretical calculations of isochromatic and [Formula: see text] isoclinic fringe patterns associated with the wave propagation in stressfree plates and plates prestressed in tension and shear. The following distinctive optical phenomena were predicted theoretically and observed in the high‐speed photoelastic patterns: a [Formula: see text] discontinuity between P and S wave isoclinics for the unstressed case; a tendency for the isoclinics to broaden and envelope the isochromatics in regions where the P and S waves are superimposed; development of serrations in the dynamic isoclinics in the presence of a prestressing field (yielding a pseudo‐isochromatic appearance to isoclinics when viewed monochromatically); and finally, a general similarity between the dynamic optical effects in media under tensile and shear prestress.

scholarly journals Responses of dipole-source reflected shear waves in acoustically slow formations

2019 ◽  
Author(s):  
Hao Wang ◽  
Ning Li ◽  
Caizhi Wang ◽  
Hongliang Wu ◽  
Peng Liu ◽  
...  
Keyword(s):  
Finite Difference Time Domain ◽  
Dipole Source ◽  
Sh Wave ◽  
S Wave ◽  
High Fracture ◽  
S Waves ◽  
Angle Fracture ◽  
Dip Angle ◽  
Difference Time

Abstract In the process of dipole-source acoustic far-detection logging, the azimuth of the fracture outside the borehole can be determined with the assumption that the SH–SH wave is stronger than the SV–SV wave. However, in slow formations, the considerable borehole modulation highly complicates the dipole-source radiation of SH and SV waves. A 3D finite-difference time-domain method is used to investigate the responses of the dipole-source reflected shear wave (S–S) in slow formations and explain the relationships between the azimuth characteristics of the S–S wave and the source–receiver offset and the dip angle of the fracture outside the borehole. Results indicate that the SH–SH and SV–SV waves cannot be effectively distinguished by amplitude at some offset ranges under low- and high-fracture dip angle conditions, and the offset ranges are related to formation properties and fracture dip angle. In these cases, the fracture azimuth determined by the amplitude of the S–S wave not only has a $180^\circ $ uncertainty but may also have a $90^\circ $ difference from the actual value. Under these situations, the P–P, S–P and S–S waves can be combined to solve the problem of the $90^\circ $ difference in the azimuth determination of fractures outside the borehole, especially for a low-dip-angle fracture.

Estimates of Q in central Asia as a function of frequency and depth using the coda of locally recorded earthquakes

1982 ◽  
Vol 72 (1) ◽  
pp. 129-149
Author(s):  
S. W. Roecker ◽  
B. Tucker ◽  
J. King ◽  
D. Hatzfeld
Keyword(s):  
Frequency Dependence ◽  
Central Asia ◽  
Wide Frequency Range ◽  
S Wave ◽  
Uppermost Mantle ◽  
Regional Heterogeneity ◽  
S Waves ◽  
Tectonic Processes ◽  
Hindu Kush ◽  
Attenuation Mechanism

abstract Digital recordings of microearthquake codas from shallow and intermediate depth earthquakes in the Hindu Kush region of Afghanistan were used to determine the attenuation factors of the S-wave coda (Qc) and primary S waves (Qβ). An anomalously rapid decay of the coda shortly after the S-wave arrival, observed also in a study of coda in central Asia by Rautian and Khalturin (1978), seems to be due primarily to depth-dependent variations in Qc. In particular, we deduce the average Qc in the crust and uppermost mantle (<100-km depth) is approximately four times lower than the deeper mantle (<400-km depth) over a wide frequency range (0.4 to 24 Hz). Further, while Qc generally increases with frequency at any depth, the degree of frequency dependence of Qc depends on depth. Except at the highest frequency studied here (∼48 Hz), the magnitude of Qc at a particular frequency increases with depth while its frequency dependence decreases. For similar depths, determinations of Qβ and Qc agree, suggesting a common wave composition and attenuation mechanism for S waves and codas. Comparison of these determinations of Qc in Afghanistan with those in other parts of the world shows that the degree of frequency dependence of Qc correlates with the expected regional heterogeneity. Such a correlation supports the prejudice that Qc is primarily influenced by scattering and suggests that tectonic processes such as folding and faulting are instrumental in creating scattering environments.

scholarly journals Array data processing techniques applied to long-period shear waves at Fennoscandian seismograph stations

1969 ◽  
Vol 59 (5) ◽  
pp. 1863-1887
Author(s):  
James H. Whitcomb
Keyword(s):  
Data Processing ◽  
Velocity Ratio ◽  
Underground Explosion ◽  
High Signal ◽  
S Wave ◽  
Array Data ◽  
S Waves ◽  
Long Period ◽  
Normal Record ◽  
The Individual

abstract Array data processing is applied to long-period records of S waves at a network of five Fennoscandian seismograph stations (Uppsala, Umeå, Nurmijärvi, Kongsberg, Copenhagen) with a maximum separation of 1300 km. Records of five earthquakes and one underground explosion are included in the study. The S motion is resolved into SH and SV, and after appropriate time shifts the individual traces are summed, both directly and after weighting. In general, high signal correlation exists among the different stations involved resulting in more accurate time readings, especially for records which have amplitudes that are too small to be read normally. S-wave station residuals correlate with the general crustal type under each station. In addition, the Fennoscandian shield may have a higher SH/SV velocity ratio than the adjacent tectonic area to the northwest.SV-to-P conversion at the base of the crust can seriously interfere with picking the onset of Sin normal record reading. The study demonstrates that, for epicentral distances beyond about 30°, existing networks of seismograph stations can be successfully used for array processing of long-period arrivals, especially the S arrivals.

Numerical simulation of azimuthal acoustic logging in a borehole penetrating a rock formation boundary

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. D283-D291 ◽  
Author(s):  
Peng Liu ◽  
Wenxiao Qiao ◽  
Xiaohua Che ◽  
Xiaodong Ju ◽  
Junqiang Lu ◽  
...  
Keyword(s):  
Domain Model ◽  
P Wave ◽  
S Wave ◽  
Angle Variation ◽  
P Waves ◽  
Acoustic Logging ◽  
S Waves ◽  
Rock Formation ◽  
Logging Tool ◽  
Difference Time

We have developed a new 3D acoustic logging tool (3DAC). To examine the azimuthal resolution of 3DAC, we have evaluated a 3D finite-difference time-domain model to simulate a case in which the borehole penetrated a rock formation boundary when the tool worked at the azimuthal-transmitting-azimuthal-receiving mode. The results indicated that there were two types of P-waves with different slowness in waveforms: the P-wave of the harder rock (P1) and the P-wave of the softer rock (P2). The P1-wave can be observed in each azimuthal receiver, but the P2-wave appears only in the azimuthal receivers toward the softer rock. When these two types of rock are both fast formations, two types of S-waves also exist, and they have better azimuthal sensitivity compared with P-waves. The S-wave of the harder rock (S1) appears only in receivers toward the harder rock, and the S-wave of the softer rock (S2) appears only in receivers toward the softer rock. A model was simulated in which the boundary between shale and sand penetrated the borehole but not the borehole axis. The P-wave of shale and the S-wave of sand are azimuthally sensitive to the azimuth angle variation of two formations. In addition, waveforms obtained from 3DAC working at the monopole-transmitting-azimuthal-receiving mode indicate that the corresponding P-waves and S-waves are azimuthally sensitive, too. Finally, we have developed a field example of 3DAC to support our simulation results: The azimuthal variation of the P-wave slowness was observed and can thus be used to reflect the azimuthal heterogeneity of formations.

A computer program for focal mechanism determination combining P and S wave data

1969 ◽  
Vol 59 (2) ◽  
pp. 503-519
Author(s):  
Agustin Udias ◽  
Dieter Baumann
Keyword(s):  
Computer Program ◽  
Focal Mechanism ◽  
Total Error ◽  
Source Model ◽  
Polarization Angle ◽  
S Wave ◽  
Period Range ◽  
S Waves ◽  
Double Couple ◽  
The Relationship

abstract A computer program has been developed to find the orientation of a double couple source model for the mechanism of an earthquake which best satisfies the data from P and S waves. The relationship between the two axes of the solution given by the equations for the polarization angle of S is used in order to rapidly find the orientation of the source model for which a total error value involving the error of S and P data is a minimum. The program gives best results for data from homogeneous instruments of similar period range. Solutions for three earthquakes, selected because of the orientation of the source, are presented and the reliability of their solutions under ideal conditions is discussed.

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