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.

Scalar reverse‐time depth migration of prestack elastic seismic data

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1519-1527 ◽  
Author(s):  
Robert Sun ◽  
George A. McMechan
Keyword(s):  
Seismic Waves ◽  
Velocity Model ◽  
P Wave ◽  
Common Source ◽  
Reverse Time ◽  
S Wave ◽  
Wave Source ◽  
Reflected Waves ◽  
S Waves ◽  
Elastic Data

Reflected P‐to‐P and P‐to‐S converted seismic waves in a two‐component elastic common‐source gather generated with a P‐wave source in a two‐dimensional model can be imaged by two independent scalar reverse‐time depth migrations. The inputs to migration are pure P‐ and S‐waves that are extracted by divergence and curl calculations during (shallow) extrapolation of the elastic data recorded at the earth’s surface. For both P‐to‐P and P‐to‐S converted reflected waves, the imaging time at each point is the P‐wave traveltime from the source to that point. The extracted P‐wave is reverse‐time extrapolated and imaged with a P‐velocity model, using a finite difference solution of the scalar wave equation. The extracted S‐wave is reverse‐time extrapolated and imaged similarly, but with an S‐velocity model. Converted S‐wave data requires a polarity correction prior to migration to ensure constructive interference between data from adjacent sources. Synthetic examples show that the algorithm gives satisfactory results for laterally inhomogeneous models.

Robust Empirical Time–Frequency Relations for Seismic Spectral Amplitudes, Part 1: Application to Regional S Waves in Southeastern Iran

2020 ◽  
Author(s):  
Maryam Safarshahi ◽  
Igor B. Morozov
Keyword(s):  
Seismic Waves ◽  
Joint Inversion ◽  
Vertical Component ◽  
Transverse Component ◽  
Model Parameters ◽  
S Wave ◽  
Near Surface ◽  
S Waves ◽  
Time Frequency ◽  
Frequency Independent

ABSTRACT Empirical models of geometrical-, Q-, t-star, and kappa-type attenuation of seismic waves and ground-motion prediction equations (GMPEs) are viewed as cases of a common empirical standard model describing variation of wave amplitudes with time and frequency. Compared with existing parametric and nonparametric approaches, several new features are included in this model: (1) flexible empirical parameterization with possible nonmonotonous time or distance dependencies; (2) joint inversion for time or distance and frequency dependencies, source spectra, site responses, kappas, and Q; (3) additional constraints removing spurious correlations of model parameters and data residuals with source–receiver distances and frequencies; (4) possible kappa terms for sources as well as for receivers; (5) orientation-independent horizontal- and three-component amplitudes; and (6) adaptive filtering to reduce noise effects. The approach is applied to local and regional S-wave amplitudes in southeastern Iran. Comparisons with previous studies show that conventional attenuation models often contain method-specific biases caused by limited parameterizations of frequency-independent amplitude decays and assumptions about the models, such as smoothness of amplitude variations. Without such assumptions, the frequency-independent spreading of S waves is much faster than inferred by conventional modeling. For example, transverse-component amplitudes decrease with travel time t as about t−1.8 at distances closer than 90 km and as t−2.5 beyond 115 km. The rapid amplitude decay at larger distances could be caused by scattering within the near surface. From about 90 to 115 km distances, the amplitude increases by a factor of about 3, which could be due to reflections from the Moho and within the crust. With more accurate geometrical-spreading and kappa models, the Q factor for the study area is frequency independent and exceeds 2000. The frequency-independent and Q-type attenuation for vertical-component and multicomponent amplitudes is somewhat weaker than for the horizontal components. These observations appear to be general and likely apply to other areas.

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.

Crustal structures across the young and oblique North-eastern Gulf of Aden margin

2020 ◽  
Author(s):  
Louise Watremez ◽  
Sylvie Leroy ◽  
Elia d'Acremont ◽  
Stéphane Rouzo
Keyword(s):  
Seismic Waves ◽  
Seismic Refraction ◽  
P Wave ◽  
Gulf Of Aden ◽  
S Wave ◽  
Acoustic Basement ◽  
S Waves ◽  
P Wave Velocity ◽  
North Eastern ◽  
Lower Crustal

<p>The Gulf of Aden is a young and active oceanic basin, which separates the south-eastern margin of the Arabian Plate from the Somali Plate. The rifting leading to the formation of the north-eastern Gulf of Aden passive margin started ca. 34 Ma ago when the oceanic spreading in this area initiated at least 17.6 Ma ago. The opening direction (N26°E) is oblique to the mean orientation of the Gulf (N75°E), leading to a strong structural segmentation.</p><p>The Encens cruise (2006) allowed for the acquisition of a large seismic refraction dataset with profiles across (6 lines) and along (3 lines) the margin, between the Alula-Fartak and Socotra-Hadbeen fracture zones, which define a first order segment of the Gulf. P-wave velocity modelling already allowed us to image the crustal thinning and the structures, from continental to oceanic domains, along some of the profiles. A lower crustal intermediate body is observed in the Ashawq-Salalah segment, at the base of the transitional and oceanic crusts. The nature of this intermediate body is most probably mafic, linked to a post-rift thermal anomaly. The thin (1-2 km) sediment layer in the study area allows for a clear conversion of P-waves to S-waves at the top basement. Thus, most seismic refraction records show very clear S-wave arrivals.</p><p>In this study, we use both P-wave and S-wave arrivals to delineate the crustal structures and segmentation along and across the margin and add insight into the nature of the rocks below the acoustic basement. P-wave velocity modelling allows for the delineation of the structure variations across and along the margin. The velocity models are used as a base for the S-wave modelling, through the definition of Poisson’s ratios in the different areas of the models. Picking and modelling of S-wave arrivals allow us to identify two families of converted waves: (1) seismic waves converted at the basement interface on the way up, just before arriving to the OBS and (2) seismic waves converted at the basement on the way down, which travelled into the deep structures as S-waves. The first set of arrivals allows for the estimation the S-wave velocities (Poisson’s ratio) in the sediments, showing that the sediments in this area are unconsolidated and water saturated. The second set of arrivals gives us constraints on the S-wave velocities below the acoustic basement. This allows for an improved mapping of the transitional and oceanic domains and the confirmation of the mafic nature of the lower crustal intermediate body.</p>

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.

A site effect study in Acapulco, Guerrero, Mexico: Comparison of results from strong-motion and microtremor data

1992 ◽  
Vol 82 (2) ◽  
pp. 642-659 ◽  
Author(s):  
Carlos Gutierrez ◽  
Shri Krishna Singh
Keyword(s):  
Seismic Waves ◽  
Site Response ◽  
Nonlinear Behavior ◽  
Strong Motion ◽  
Site Effect ◽  
Seismic Gap ◽  
S Wave ◽  
Data Set ◽  
S Waves ◽  
The City

Abstract The city of Acapulco is located near or above the mature seismic gap of Guerrero along the Mexican subduction zone. With the purpose of studying the character of strong ground motion on soft sites, four digital accelerographs have been installed in the city on such sites. These instruments have been in operation since 1988. Two additional instruments, part of the Guerrero Accelerograph Array, are located on hard sites in the area. One of these, VNTA, has been in operation since 1985 and the other, ACAN, since 1989. These stations have recorded several earthquakes. We use data from eight events (4.2 ≤ M ≤ 6.9) to study spectral amplification of seismic waves at the soft sites with respect to VNTA. The S waves are amplified by a factor of 6 to 25 at the soft sites in a fairly broad range of frequencies; both the amplification and the frequency band over which it occurs depend upon the site. Although the largest earthquake in our data set (M = 6.9) gave rise to a peak horizontal acceleration exceeding 0.3 g at one of the soft sites, no clear evidence of nonlinear behavior of the subsoil is found. Spectral amplifications of S-wave coda are very similar to those of S waves. We also measured microtremors at the strong-motion sites. The microtremor spectra were interpreted, using reasonable assumptions, to test the feasibility of this technique in reproducing the spectral amplifications observed during earthquakes. Our results show that only a rough estimate of site response can be obtained from this technique, at least in Acapulco; caution is warranted in its use elsewhere.

The partition of radiated energy between P and S waves

1984 ◽  
Vol 74 (2) ◽  
pp. 361-376
Author(s):  
John Boatwright ◽  
Jon B. Fletcher
Keyword(s):  
Wave Energy ◽  
Body Wave ◽  
Focal Mechanisms ◽  
The Body ◽  
Body Waves ◽  
P Wave ◽  
Corner Frequency ◽  
S Wave ◽  
S Waves ◽  
Radiated Energy

Abstract Seventy-three digitally recorded body waves from nine multiply recorded small earthquakes in Monticello, South Carolina, are analyzed to estimate the energy radiated in P and S waves. Assuming Qα = Qβ = 300, the body-wave spectra are corrected for attenuation in the frequency domain, and the velocity power spectra are integrated over frequency to estimate the radiated energy flux. Focal mechanisms determined for the events by fitting the observed displacement pulse areas are used to correct for the radiation patterns. Averaging the results from the nine events gives 27.3 ± 3.3 for the ratio of the S-wave energy to the P-wave energy using 0.5 〈Fi〉 as a lower bound for the radiation pattern corrections, and 23.7 ± 3.0 using no correction for the focal mechanisms. The average shift between the P-wave corner frequency and the S-wave corner frequency, 1.24 ± 0.22, gives the ratio 13.7 ± 7.3. The substantially higher values obtained from the integral technique implies that the P waves in this data set are depleted in energy relative to the S waves. Cursory inspection of the body-wave arrivals suggests that this enervation results from an anomalous site response at two of the stations. Using the ratio of the P-wave moments to the S-wave moments to correct the two integral estimates gives 16.7 and 14.4 for the ratio of the S-wave energy to the P-wave energy.

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.

scholarly journals Rayleigh-to-shear wave conversion at the tunnel face — From 3D-FD modeling to ahead-of-drill exploration

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. T67-T79 ◽  
Author(s):  
Thomas Bohlen ◽  
Ulrich Lorang ◽  
Wolfgang Rabbel ◽  
Christof Müller ◽  
Rüdiger Giese ◽  
...  
Keyword(s):  
Rayleigh Waves ◽  
Damage Zone ◽  
Tunnel Boring Machine ◽  
High Amplitude ◽  
Body Waves ◽  
Front Face ◽  
S Wave ◽  
Tunnel Face ◽  
S Waves ◽  
Cutter Head

For safe tunnel excavation, it is important to predict lithologic and structural heterogeneities ahead of construction. Conventional tunnel seismic prediction systems utilize body waves (P- and S-waves) that are directly generated at the tunnel walls or near the cutter head of the tunnel boring machine (TBM). We propose a new prediction strategy that has been discovered by 3D elastic finite-difference (FD) modeling: Rayleigh waves arriving at the front face of the tunnel are converted into high-amplitude S-waves propagating further ahead. Reflected or backscattered S-waves are converted back into Rayleigh waves which can be recorded along the sidewalls. We name these waves RSSR waves. In our approach, the front face acts as an S-wave transceiver. One technical advantage is that both the sources and the receivers may be placed behind the cutter head of the TBM. The modeling reveals that the RSSR waves exhibit significantly higher amplitudes than the directly reflected body waves. The excavation damage zone causes dispersion of the RSSR wave leading to multimodal reflection response. For the detection of geologic interfaces ahead, RSSR waves recorded along the sidewalls are corrected for dispersion and stacked. From the arrival times, the distance to the S-S reflection point can be estimated. A recurrent application, while the tunnel approaches the interface, allows one to quantify the orientation of the reflecting interfaces as well. Our approach has been verified successfully in a field experiment at the Piora adit of the Gotthard base tunnel. The distance to the Piora fault zone estimated from stacked RSSR events agrees well with the information obtained by geologic surveying and exploratory drilling.

scholarly journals Seismic Response for Wave Propagation across Joints with Equally and Unequally Close-Open Behaviours

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Qi Zhang ◽  
Zhengliang Li ◽  
Tao Yu
Keyword(s):  
Wave Propagation ◽  
Seismic Response ◽  
Seismic Waves ◽  
Incident Angle ◽  
In Situ Stress ◽  
Rock Joints ◽  
Stress Wave Propagation ◽  
S Wave ◽  
Maximum Deformation

The interaction between rock joints and seismic waves is critical in rock engineering when rock mass is suffered from human-induced or natural earthquakes. Stress wave propagation across rock joints is usually dependent on the seismic response of the joints. Wave propagation may cause joints close or open under the in situ stress. In this paper, the seismic response for wave propagation with an arbitrary incident angle impinging on joints is studied. Both reflection and transmission usually occurring at the two interfaces of the joint are considered, respectively. Wave propagation equations with equally and unequally close-open behaviours are deduced firstly, which can be applied for the general cases of arbitrary incident P- or S-wave. Then, wave propagation across joints with normal and oblique incident P- and S-waves is analyzed by considering the equally and unequally close-open behaviours and verified by comparing with the existing methods. Finally, several parametric studies are conducted to evaluate the effect of in situ stress on transmitted waves, the effect of the incident frequency on the maximum deformation of joints, and the effect of the incident angle on the maximum deformation of joints. The wave propagation equations derived in the study are more feasible and can well analyze the seismic response of wave propagation for the most general cases of different incident waveforms.

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