Elastic velocity anisotropy in the presence of an anisotropic initial stress

1972 ◽  
Vol 62 (5) ◽  
pp. 1183-1193 ◽  
Author(s):  
F. A. Dahlen
Keyword(s):  
Initial Stress ◽  
Elastic Anisotropy ◽  
Body Wave ◽  
Homogeneous Medium ◽  
Body Waves ◽  
P Waves ◽  
S Waves ◽  
Velocity Anisotropy ◽  
First Order ◽  
Wave Velocities

Abstract The effect of a homogeneous anisotropic initial stress on the propagation of infinitesimal amplitude elastic body waves in a perfectly elastic, homogeneous medium is investigated. If the medium is inherently isotropic in the reference configuration and if the magnitude τ0 of the deviatoric part of the initial static stress is small compared to the rigidity μ of the medium, then the apparent body-wave velocities of P waves are unaffected by the initial stress to first order in τ0/μ. The apparent body-wave velocities of S waves are rendered anisotropic to first order, and this effect is described explicitly. It is concluded that the direct effect of an anisotropic initial stress cannot contribute appreciably to the observed velocity anisotropy of horizontally propagating P waves in the oceanic upper mantle. Those observations require an inherent elastic anisotropy of the oceanic uppermantle material.

Velocity anisotropy in shale determined from crosshole seismic and vertical seismic profile data

Geophysics ◽  
1990 ◽  
Vol 55 (4) ◽  
pp. 470-479 ◽  
Author(s):  
D. F. Winterstein ◽  
B. N. P. Paulsson
Keyword(s):  
Seismic Profile ◽  
P Wave ◽  
Isotropic Model ◽  
S Wave ◽  
Vertical Seismic Profile ◽  
Near Surface ◽  
S Waves ◽  
Velocity Anisotropy ◽  
Wave Velocities ◽  
Late Tertiary

Crosshole and vertical seismic profile (VST) data made possible accurate characterization of the elastic properties, including noticeable velocity anisotropy, of a near‐surface late Tertiary shale formation. Shear‐wave splitting was obvious in both crosshole and VSP data. In crosshole data, two orthologonally polarrized shear (S) waves arrived 19 ms in the uppermost 246 ft (75 m). Vertically traveling S waves of the VSP separated about 10 ms in the uppermost 300 ft (90 m) but remained at nearly constant separation below that level. A transversely isotropic model, which incorporates a rapid increase in S-wave velocities with depth but slow increase in P-wave velocities, closely fits the data over most of the measured interval. Elastic constants of the transvesely isotropic model show spherical P- and [Formula: see text]wave velocity surfaces but an ellipsoidal [Formula: see text]wave surface with a ratio of major to minor axes of 1.15. The magnitude of this S-wave anisotropy is consistent with and lends credence to S-wave anisotropy magnitudes deduced less directly from data of many sedimentary basins.

scholarly journals Elastic anisotropy estimation from laboratory measurements of velocity and polarization of quasi-P-waves using laser interferometry

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. WA83-WA89 ◽  
Author(s):  
Maxim Lebedev ◽  
Andrej Bóna ◽  
Roman Pevzner ◽  
Boris Gurevich
Keyword(s):  
Particle Velocity ◽  
Elastic Anisotropy ◽  
Laser Interferometry ◽  
Elasticity Tensor ◽  
Ultrasonic Waves ◽  
Body Waves ◽  
P Wave ◽  
Surface Element ◽  
Laboratory Measurements ◽  
P Waves

A new method for conducting laboratory measurements of the velocities and polarizations of compressional and shear waves in rock samples uses a laser Doppler interferometer (LDI). LDI can measure the particle velocity of a small (0.03 mm2) element of the surface of the sample along the direction of the laser beam. By measuring the particle velocity of the same surface element in three linearly independent directions and then transforming those velocities to Cartesian coordinates, three orthogonal components of the particle-velocity vector are obtained. Thus, LDI can be used as a localized three-component (3C) receiver of ultrasonic waves, and, together with a piezoelectric transducer as a source, it can simulate a 3C seismic experiment in the laboratory. Performing such 3C measurements at various locations on the surface of the sample produces a 3C seismogram, which can be used to separate the P-wave and two S-waves and to find the polarizations and traveltimes of those waves. Then, the elasticity tensor of the medium can be obtained by minimizing the misfit between measured and predicted polarizations and traveltimes. Computation of the polarizations and traveltimes of body waves inside a sample with a given elasticity tensor is based on the Christoffel equation. The predicted polarizations on the surface then are obtained using the anisotropic Zoeppritz equations. The type of velocity measured (phase or group velocity) depends on the acquisition geometry and the material properties. This is taken into account in the inversion procedure. A “walkaway” laboratory experiment demonstrates the high accuracy of this method.

Surface waves in structures with locally irregular boundaries

1980 ◽  
Vol 70 (3) ◽  
pp. 791-808
Author(s):  
Anne Suteau ◽  
Louis Martel
Keyword(s):  
Surface Waves ◽  
Body Wave ◽  
Complex Structure ◽  
Additional Term ◽  
The Body ◽  
Body Waves ◽  
First Order ◽  
Irregular Region ◽  
Regular Medium ◽  
General Method

abstract The transmitted field due to surface waves incident on a local irregularity of a plane-layered medium has been studied. A perturbation method to the first order and the Born approximation can be used if the variations in the thickness of the layers are sufficiently smooth and the wavelengths are long when compared to the size of the irregularities. The spectrum of the perturbed part of the displacement field at the surface is a sum over the surface-wave modes for the regular medium, with an additional term involving the scattered body waves. Numerical computations have been performed for structures composed of a layer overlying a half-space. The contribution of the various modes to the transmitted Love or Rayleigh fields has been studied for several structures. A general method has been obtained to analyze the effect of a complex structure as the superposition of the fields due to simpler ones. When the layer thickness is kept unchanged, the incident mode is not perturbed to the first order. Synthetic seismograms, computed at stations sufficiently close to the irregular region, show how the perturbation of the signal depends on distance. A comparison has been made for Love waves with a finite element method. Both methods give very similar results when the stations are not too close to the irregularities so that the body-wave contribution is negligible. The local phase velocity shows departures from the curves for a regular model.

Crustal structure in the Gangetic Plains of the Indian sub-continent from body waves

1974 ◽  
Vol 64 (3-1) ◽  
pp. 571-579
Author(s):  
R. K. Dube ◽  
J. C. Bhayana
Keyword(s):  
Crustal Structure ◽  
Body Wave ◽  
Bottom Layer ◽  
Body Waves ◽  
P Wave ◽  
Gangetic Plains ◽  
S Waves ◽  
Shear Wave Velocities ◽  
P Wave Velocity ◽  
Peninsular Shield

abstract Crustal structure in the Gangetic Plains of India has been investigated using body-wave data of earthquakes. A three-layered crust has been interpreted, consisting of a top layer of 2.7-km/sec P-wave velocity and 3.7-km thickness, an intermediate layer of 5.64-km/sec velocity and 15.2-km thickness and a bottom layer of 6.49-km/sec velocity and 21.4-km thickness. The average depth of the M discontinuity obtained is 40.3 km. The shear-wave velocities for the Sg, S*, Sn phases are 3.45, 3.85 and 4.61 km/sec, respectively. The velocities of both P and S waves are lower than those obtained for the Peninsular Shield of India.

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.

Multichannel Alignment of S Waves

2021 ◽  
Author(s):  
Michael Bostock ◽  
Alexandre Plourde ◽  
Doriane Drolet ◽  
Geena Littel
Keyword(s):  
Effective Means ◽  
Principal Component ◽  
Singular Value ◽  
Body Waves ◽  
Common Source ◽  
Multiple Sources ◽  
P Waves ◽  
Moment Tensors ◽  
Additional Degree ◽  
S Waves

ABSTRACT High-resolution earthquake locations and structural inversions using body waves rely on precise delay-time measurements. Subsample accuracy can be realized for P waves using multichannel cross correlation (MCCC), as developed by VanDecar and Crosson (1990), which exploits redundancy in pairwise cross correlations to determine delays between similar waveforms in studies of mantle structure using teleseismic sources (common source and multiple stations) and regional studies of structure and seismicity (multiple sources and common station). For regional S waves, alignment is complicated by the additional degree of freedom in waveform polarity that is expressed for sources with different moment tensors. Here, we recast MCCC within a principal component framework and demonstrate the equivalence between maximizing waveform correlation and minimization of various singular value–based objective functions for P waves. The singular-value framework is more general and leads naturally to an MCCC linear system for S waves that possesses an order of magnitude greater redundancy than that for P waves. Robust L1 solution of the system provides an effective means of mitigating outliers at the expense of subsample precision. Residual time shifts associated with higher-order singular vectors are employed in an iterative adaptive alignment that achieves subsample resolution. We demonstrate application of the approach on a seismicity cluster within the northern Cascadia crustal fore-arc.

scholarly journals Experimental study of acoustic anisotropy and birefringence in dry and saturated Fontainebleau sandstone

Geophysics ◽  
1990 ◽  
Vol 55 (11) ◽  
pp. 1455-1465 ◽  
Author(s):  
M. Zamora ◽  
J. P. Poirier
Keyword(s):  
Crack Density ◽  
Uniaxial Stress ◽  
P Waves ◽  
Thermally Induced ◽  
S Waves ◽  
Velocity Anisotropy ◽  
Fontainebleau Sandstone ◽  
Plane Normal ◽  
Acoustic Anisotropy ◽  
Scanning Electron

The velocities of ultrasonic P, SH, and SV waves have been measured in two perpendicular directions, in samples of Fontainebleau sandstone as received or thermally cracked, dry, or saturated, under uniaxial stress. We have investigated the effect of cracking, saturation, and uniaxial stress on the velocity of P and S waves in two orthogonal directions (anisotropy) and the velocity of S waves with two orthogonal polarizations in each direction of propagation (birefringence). The effect of cracking, saturation, and uniaxial stress on Poisson’s ratio has also been investigated. The velocity anisotropy is larger for S waves than for P waves and practically disappears in saturated samples. Birefringence is attenuated in saturated samples. Inversion of the results using Crampin’s model gives values of the crack densities in three directions, in qualitative agreement with the state of cracking observed by scanning electron microscopy. In particular, the crack density is found to be near zero in sandstones with rounded pores only. After thermally induced cracking the crack density is found to be ≈20 percent; uniaxial stress closes the cracks in the plane normal to the stress. Also, in naturally cracked samples the crack density is found to be quite high. Uniaxial stress causes the density of cracks to decrease, mostly in the plane normal to the stress.

scholarly journals Comparison of recent S-wave indicating methods

2018 ◽  
Vol 29 ◽  
pp. 00019
Author(s):  
Katarzyna Hubicka ◽  
Jakub Sokolowski
Keyword(s):  
Real Data ◽  
The Body ◽  
Body Waves ◽  
Identification Accuracy ◽  
P Wave ◽  
S Wave ◽  
P Waves ◽  
S Waves ◽  
Mode Decomposition ◽  
Wave Arrival

Seismic event consists of surface waves and body waves. Due to the fact that the body waves are faster (P-waves) and more energetic (S-waves) in literature the problem of their analysis is taken more often. The most universal information that is received from the recorded wave is its moment of arrival. When this information is obtained from at least four seismometers in different locations, the epicentre of the particular event can be estimated [1]. Since the recorded body waves may overlap in signal, the problem of wave onset moment is considered more often for faster P-wave than S-wave. This however does not mean that the issue of S-wave arrival time is not taken at all. As the process of manual picking is time-consuming, methods of automatic detection are recommended (these however may be less accurate). In this paper four recently developed methods estimating S-wave arrival are compared: the method operating on empirical mode decomposition and Teager-Kaiser operator [2], the modification of STA/LTA algorithm [3], the method using a nearest neighbour-based approach [4] and the algorithm operating on characteristic of signals’ second moments. The methods will be also compared to wellknown algorithm based on the autoregressive model [5]. The algorithms will be tested in terms of their S-wave arrival identification accuracy on real data originating from International Research Institutions for Seismology (IRIS) database.

Relation between P- and S-wave corner frequencies in the seismic spectrum

1974 ◽  
Vol 64 (6) ◽  
pp. 1621-1627 ◽  
Author(s):  
J. C. Savage
Keyword(s):  
High Frequency ◽  
Body Wave ◽  
Fault Model ◽  
P Wave ◽  
Corner Frequency ◽  
Rupture Propagation ◽  
S Wave ◽  
P Waves ◽  
Fault Surface ◽  
S Waves

abstract A comprehensive set of body-wave spectra has been calculated for the Haskell fault model generalized to a circular fault surface. These spectra are used to show that in practice the P-wave corner frequency (ƒp) may exceed the S-wave corner frequency (ƒs) when near-sonic or transonic rupture propagation obtains. The explanation appears to be that in such cases ƒs is so large that it is not identified within the recorded band, but rather a secondary corner is mistaken for ƒs. As a consequence of failing to detect the true asymptotic trend, the high-frequency falloff of the spectrum with frequency is substantially less for S waves than for P waves. This explanation appears to be consistent with the demonstration by Molnar, Tucker, and Brune (1973) that ƒp may exceed ƒs.

SYNTHETIC SEISMOGRAMS OF P WAVES PROPAGATING IN SOLID WEDGES WITH FREE BOUNDARIES

Geophysics ◽  
1966 ◽  
Vol 31 (3) ◽  
pp. 524-535 ◽  
Author(s):  
Karl Fuchs
Keyword(s):  
Transition Zone ◽  
Body Wave ◽  
Body Waves ◽  
Interference Signal ◽  
Free Boundaries ◽  
Multiple Reflections ◽  
P Waves ◽  
Model Studies ◽  
Diffracted Waves ◽  
The Time Domain

A numerical method for the synthesis of seismograms for body wave propagation in solid wedges is presented. The method is based on the superposition of multiple reflections arising from the entrance of a plane primary wave. Therefore the method is restricted to that part of the time domain where no diffracted waves from the wedge axis occur. In spite of this restriction, dispersion of body waves in wedges can well be studied by this method. Seismograms have been synthesized which show the dispersion of a primary p‐signal propagating in a solid 10‐degree and a 5‐degree wedge with free boundaries. For wedge angles less than 10 degrees the signal front (to be distinguished from the wavefront) suddenly decreases its velocity from that in the infinite medium to about that of the plate wave as the signal approaches the wedge axis. Simultaneously in this transition zone a decrease of the dominant period of the interference signal occurs. These observations are concordant with previous model studies. Particle motion diagrams disclose elliptical polarization of the interference signal in the neighborhood of the wedge axis; the polarization changes its sense from prograde to retrograde on passing through the transition zone.

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