Processing, correlating, and interpreting converted shear waves from borehole data in southern Alberta

Geophysics ◽  
1990 ◽  
Vol 55 (6) ◽  
pp. 660-669 ◽  
Author(s):  
W. T. Geis ◽  
R. R. Stewart ◽  
M. J. Jones ◽  
P. E. Katapodis
Keyword(s):  
P Wave ◽  
Equation Modeling ◽  
S Wave ◽  
Borehole Data ◽  
P Waves ◽  
S Waves ◽  
Sonic Log ◽  
Lake Formation ◽  
Southern Alberta ◽  
The Time Domain

Borehole measurements coupled with phase information from Zoeppritz equation modeling has assisted in accurate correlation between a VSP converted S-wave section and both the surface and VSP P-wave sections from southern Alberta. For the most part, both the character and polarities of the sections agree; however, there are some differences. Some reflections are stronger and more distinct on the S-wave section than on the P-wave section. Spectral analysis of the time‐domain upgoing P-wave and S-wave energy shows that the frequency content of the S-waves is comparable to the P-waves. Thus, the slower velocity S-waves have a shorter wavelenght and provide better vertical resolution of some interfaces. Other upgoing S-wave modes can interfere with the P‐SV mode and contribute to the differences between the P- and S-wave sections. The match between P-wave and S-wave velocities ([Formula: see text] and [Formula: see text]), determined from VSP traveltime inversion and the full‐waveform sonic log, is best in the Paleozoic carbonate section; there is some discrepancy in Cretaceous sandstone intervals. A basal salt unit in the Paleozoic Beaverhill Lake formation has a VSP‐determined [Formula: see text] ratio of 1.97, suggesting that salt can be distinguished from carbonates using both P-wave and S-wave velocity information in this region.

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.

Comparison of P‐ and S‐wave velocities and Q’S from VSP and sonic log data

Geophysics ◽  
1994 ◽  
Vol 59 (10) ◽  
pp. 1512-1529 ◽  
Author(s):  
Gopa S. De ◽  
Donald F. Winterstein ◽  
Mark A. Meadows
Keyword(s):  
Velocity Dispersion ◽  
P Wave ◽  
S Wave ◽  
S Waves ◽  
Wave Velocities ◽  
Sonic Log ◽  
Transit Times ◽  
Wave Slope ◽  
Northern Alberta ◽  
Q Values

We compared P‐ and S‐wave velocities and quality factors (Q’S) from vertical seismic profiling (VSP) and sonic log measurements in five wells, three from the southwest San Joaquin Basin of California, one from near Laredo, Texas, and one from northern Alberta. Our purpose was to investigate the bias between sonic log and VSP velocities and to examine to what degree this bias might be a consequence of dispersion. VSPs and sonic logs were recorded in the same well in every case. Subsurface formations were predominantly clastic. The bias found was that VSP transit times were greater than sonic log times, consistent with normal dispersion. For the San Joaquin wells, differences in S‐wave transit times averaged 1–2 percent, while differences in P‐wave transit times averaged 6–7 percent. For the Alberta well, the situation was reversed, with differences in S‐wave transit times being about 6 percent, while those for P‐waves were 2.5 percent. For the Texas well, the differences averaged about 4 percent for both P‐ and S‐waves. Drift‐curve slopes for S‐waves tended to be low where the P‐wave slopes were high and vice versa. S‐wave drift‐curve slopes in the shallow California wells were 5–10 μs/ft (16–33 μs/m) and the P‐wave slopes were 15–30 μs/ft (49–98 μs/m). The S‐wave slope in sandstones in the northern Alberta well was up to 50 μs/ft (164 μs/m), while the P‐wave slope was about 5 μs/ft (16 μs/m). In the northern Alberta well the slopes for both P‐ and S‐waves flattened in the carbonate. In the Texas well, both P‐ and S‐wave drifts were comparable. We calculated (Q’s) from a velocity dispersion formula and from spectral ratios. When the two Q’s agreed, we concluded that velocity dispersion resulted solely from absorption. These Q estimation methods were reliable only for Q values smaller than 20. We found that, even with data of generally outstanding quality, Q values determined by standard methods can have large uncertainties, and negative Q’s may be common.

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.

A comparison of some S-wave studies of earthquake mechanisms

1961 ◽  
Vol 51 (2) ◽  
pp. 277-292
Author(s):  
William Stauder ◽  
Adams W. M.
Keyword(s):  
Fault Plane ◽  
Analytical Techniques ◽  
P Wave ◽  
Graphical Methods ◽  
S Wave ◽  
Fault Plane Solutions ◽  
P Waves ◽  
S Waves ◽  
Analytical Technique ◽  
Direction Of Polarization

Abstract Graphical and analytical techniques for using S-waves in focal mechanism studies are compared. In previous applications the analytical technique has shown little or no agreement with the results of fault-plane solutions from P-waves, whereas for other groups of earthquakes the graphical methods have shown good agreement between the S-waves and the P-wave solutions. It is shown that the graphical and analytical techniques are identical in principle and that when the graphical methods are applied to the same three earthquakes to which the analytical technique had been applied the identical results are obtained. Closer examination of the graphical presentation of the data, however, shows that the disagreement between the S-waves and the fault plane solutions from P is largely apparent. The discrepancy follows upon the peculiar scatter in the S-wave data and the chance occurrence of observations of S at stations located along closely parallel planes of polarization of S. Once this is understood, it is seen that the direction of polarization of S-waves is in substantial agreement with the methods of analysis of focal mechanisms from P-waves, and that the data are consistent with a simple dipole as the point model of the earthquake focus.

Investigation of multiple reflections and wave conversion by means of a vertical wave test (vertical seismic profiling) in southern Mississippi

Geophysics ◽  
1982 ◽  
Vol 47 (7) ◽  
pp. 977-1000 ◽  
Author(s):  
C. C. Lash
Keyword(s):  
Wave Train ◽  
Low Frequency ◽  
P Wave ◽  
Multiple Reflections ◽  
Low Velocity ◽  
P Waves ◽  
S Waves ◽  
Seismic Profiling ◽  
Vertical Seismic Profiling ◽  
Sonic Log

A vertical wave test employing the vertical seismic profiling (VSP) technique in southern Mississippi confirmed suspicions that apparent multiple reflections might include converted waves as well as multiply reflected compressional waves. Both compressional (P) and shear (S) waves generated near the source were observed to travel to great depths, and P‐to‐S conversions were apparent in deep zones as well as shallow. P‐wave reflections were observed in agreement with predictions from synthetic records based on the sonic log. Up‐traveling P‐waves were reflected a short distance below the surface, at the base of the low‐velocity layer, and were followed as down‐traveling P‐waves to 200 ft depth by means of a vertical spread. Below 2000 ft and following the first P wave train, the predominate energy appeared to be down‐traveling P‐waves which could not be traced back to the reflection of up‐traveling P‐waves. The continuity of wavelets indicated instead that the strong down‐traveling S‐waves generated near the source produced P‐waves by S‐to‐P conversion somewhere in the zone between 800 and 1400 ft. The interference on the recordings made with an individual seismometer, or a small group of seismometers, using dynamite shots as the source was generally of a low‐frequency nature, so that the signal‐to‐noise (S/N) ratio was improved by the use of a high passband filter. The interference was greatly reduced without the need for a filter on recordings in which the source was a distributed charge of 100 ft length. The distributed charge produced much less shear‐wave energy in the P reflection band, demonstrating that the interference encountered when using a concentrated charge source was the consequence of the generation of S‐waves near the source. The distributed charges were previously chosen as a means for effectively eliminating secondary (ghost) reflections, an unwanted form of multiple reflections.

Seismic vertical transversely isotropic parameter inversion from P- and S-wave cross-borehole measurements in an aquifer environment

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. D101-D116
Author(s):  
Julius K. von Ketelhodt ◽  
Musa S. D. Manzi ◽  
Raymond J. Durrheim ◽  
Thomas Fechner
Keyword(s):  
Transversely Isotropic ◽  
P Wave ◽  
Perturbation Equation ◽  
S Wave ◽  
P Waves ◽  
Data Set ◽  
Near Surface ◽  
S Waves ◽  
Wave Measurements ◽  
Wave Splitting

Joint P- and S-wave measurements for tomographic cross-borehole analysis can offer more reliable interpretational insight concerning lithologic and geotechnical parameter variations compared with P-wave measurements on their own. However, anisotropy can have a large influence on S-wave measurements, with the S-wave splitting into two modes. We have developed an inversion for parameters of transversely isotropic with a vertical symmetry axis (VTI) media. Our inversion is based on the traveltime perturbation equation, using cross-gradient constraints to ensure structural similarity for the resulting VTI parameters. We first determine the inversion on a synthetic data set consisting of P-waves and vertically and horizontally polarized S-waves. Subsequently, we evaluate inversion results for a data set comprising jointly measured P-waves and vertically and horizontally polarized S-waves that were acquired in a near-surface ([Formula: see text]) aquifer environment (the Safira research site, Germany). The inverted models indicate that the anisotropy parameters [Formula: see text] and [Formula: see text] are close to zero, with no P-wave anisotropy present. A high [Formula: see text] ratio of up to nine causes considerable SV-wave anisotropy despite the low magnitudes for [Formula: see text] and [Formula: see text]. The SH-wave anisotropy parameter [Formula: see text] is estimated to be between 0.05 and 0.15 in the clay and lignite seams. The S-wave splitting is confirmed by polarization analysis prior to the inversion. The results suggest that S-wave anisotropy may be more severe than P-wave anisotropy in near-surface environments and should be taken into account when interpreting cross-borehole S-wave data.

Theory and modeling of constant-Q P- and S-waves using fractional time derivatives

Geophysics ◽  
2009 ◽  
Vol 74 (1) ◽  
pp. T1-T11 ◽  
Author(s):  
José M. Carcione
Keyword(s):  
Heterogeneous Media ◽  
Fourier Method ◽  
P Wave ◽  
Difference Operators ◽  
S Wave ◽  
Central Difference ◽  
S Waves ◽  
The Time Domain ◽  
Derivatives Of ◽  
Modeling Algorithm

I have developed and solved the constant-[Formula: see text] model for the attenuation of P- and S-waves in the time domain using a new modeling algorithm based on fractional derivatives. The model requires time derivatives of order [Formula: see text] applied to the strain components, where [Formula: see text] and [Formula: see text], with [Formula: see text] the P-wave or S-wave quality factor. The derivatives are computed with the Grünwald-Letnikov and central-difference fractional approximations, which are extensions of the standard finite-difference operators for derivatives of integer order. The modeling uses the Fourier method to compute the spatial derivatives, and therefore can handle complex geometries and general material-property variability. I verified the results by comparison with the 2D analytical solution obtained for wave propagation in homogeneous Pierre Shale. Moreover, the modeling algorithm was used to compute synthetic seismograms in heterogeneous media corresponding to a crosswell seismic experiment.

scholarly journals PHASE SHIFTS AND RESONANCES IN THE DIRAC EQUATION

2004 ◽  
Vol 19 (21) ◽  
pp. 3557-3581 ◽  
Author(s):  
PIERS KENNEDY ◽  
NORMAN DOMBEY ◽  
RICHARD L. HALL
Keyword(s):  
Dirac Equation ◽  
Wave Scattering ◽  
Numerical Procedure ◽  
Phase Shifts ◽  
P Wave ◽  
S Wave ◽  
P Waves ◽  
Gaussian Potential ◽  
S Waves ◽  
Relativistic Scattering

We review the analytic results for the phase shifts δl(k) in nonrelativistic scattering from a spherical well. The conditions for the existence of resonances are established in terms of time-delays. Resonances are shown to exist for p-waves (and higher angular momenta) but not for s-waves. These resonances occur when the potential is not quite strong enough to support a bound p-wave of zero energy. We then examine relativistic scattering by spherical wells and barriers in the Dirac equation. In contrast to the nonrelativistic situation, s-waves are now seen to possess resonances in scattering from both wells and barriers. When s-wave resonances occur for scattering from a well, the potential is not quite strong enough to support a zero momentum s-wave solution at E=m. Resonances resulting from scattering from a barrier can be explained in terms of the "crossing" theorem linking s-wave scattering from barriers to p-wave scattering from wells. A numerical procedure to extract phase shifts for general short range potentials is introduced and illustrated by considering relativistic scattering from a Gaussian potential well and barrier.

A simple method for resolving large converted‐wave (P-SV) statics

Geophysics ◽  
1993 ◽  
Vol 58 (3) ◽  
pp. 429-433 ◽  
Author(s):  
Peter W. Cary ◽  
David W. S. Eaton
Keyword(s):  
P Wave ◽  
S Wave ◽  
Converted Wave ◽  
P Waves ◽  
Simple Method ◽  
Near Surface ◽  
S Waves ◽  
Static Solutions ◽  
Surface Fluctuations

The processing of converted‐wave (P-SV) seismic data requires certain special considerations, such as commonconversion‐point (CCP) binning techniques (Tessmer and Behle, 1988) and a modified normal moveout formula (Slotboom, 1990), that makes it different for processing conventional P-P data. However, from the processor’s perspective, the most problematic step is often the determination of residual S‐wave statics, which are commonly two to ten times greater than the P‐wave statics for the same location (Tatham and McCormack, 1991). Conventional residualstatics algorithms often produce numerous cycle skips when attempting to resolve very large statics. Unlike P‐waves, the velocity of S‐waves is virtually unaffected by near‐surface fluctuations in the water table (Figure 1). Hence, the P‐wave and S‐wave static solutions are largely unrelated to each other, so it is generally not feasible to approximate the S‐wave statics by simply scaling the known P‐wave static values (Anno, 1986).

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