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.

Three Kamchatka earthquakes

1960 ◽  
Vol 50 (3) ◽  
pp. 347-388
Author(s):  
William Stauder
Keyword(s):  
Fault Plane ◽  
Focal Depth ◽  
Analytical Techniques ◽  
Aftershock Sequence ◽  
Great Earthquake ◽  
S Wave ◽  
Fault Plane Solutions ◽  
S Waves ◽  
Double Couple ◽  
First Motion

ABSTRACT Three earthquakes, two with previously determined fault-plane solutions, are selected in order to study the relation between the S waves and the source mechanism. The S waves are observed at favorable epicentral distances at stations distributed in all quadrants about the epicenter. The earthquakes are of a focal depth of 40 to 60 kilometers and belong to the aftershock sequence of the great earthquake of November 4, 1952. The direction of first motion and the plane of polarization of S are determined by the construction of particle-motion diagrams. In the case of the two earthquakes for which the fault-plane solutions have been published, no correspondence is found between the observed S wave data and the character of the S motion expected on the basis of the given nodal planes of P, whether the source be considered as a single couple or as a double couple. For the third earthquake it is found that the first motion of P is compressional along all rays leaving the focus downward and that the S waves are strongly SV polarized. No faulting mechanism can explain this distribution of the motion in the initial P and S phases. The motion is explained as corresponding to that generated by a simple force acting almost vertically downward. Graphical and analytical techniques of analysis determine the trend of the force at the source to be N 12° W, with a plunge of 85°. A reconsideration of the other two shocks shows that these, too, are better explained by a simple force source than by a faulting mechanism.

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.

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.

S waves: Alaska and other earthquakes

1960 ◽  
Vol 50 (4) ◽  
pp. 581-597 ◽  
Author(s):  
William Stauder
Keyword(s):  
Focal Mechanism ◽  
Fault Plane ◽  
P Wave ◽  
Wave Analysis ◽  
Point Model ◽  
S Wave ◽  
S Waves ◽  
Wave Solutions ◽  
Single Force

ABSTRACT Techniques of S wave analysis are used to investigate the focal mechanism of four earthquakes. In all cases the results of the S wave analysis agree with previously determined P wave solutions and conform to a dipole with moment or single couple as the point model of the focus. Further, the data from S waves select one of the two nodal planes of P as the fault plane. Small errors in the determination of the angle of polarization of S are shown to result in scatter in the data of a peculiar character which might lead to misinterpretation. The same methods of analysis which in the present instances show excellent agreement with a dipole with moment source are the methods which in a previous paper required a single force type mechanism for a different group of earthquakes.

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.

scholarly journals DETERMINATION OF FAULT PLANE SOLUTIONS USING WAVEFORM AMPLITUDES AND RADIATION PATTERN

2004 ◽  
Vol 36 (3) ◽  
pp. 1529
Author(s):  
D. A. Vamvakaris ◽  
C. B. Papazachos ◽  
E. E. Karagianni ◽  
E. M. Scordilis ◽  
P. M. Chatzidimitriou
Keyword(s):  
Radiation Pattern ◽  
Multiple Solutions ◽  
Fault Plane ◽  
Synthetic Data ◽  
P Wave ◽  
Original Version ◽  
Fault Plane Solutions ◽  
S Waves ◽  
Short Period

In the present work a modified version of the program FPFIT (Reasenberg and Oppenheimer, 1985) is developed, in order to improve the calculation of the fault plane solutions. The method is applied on selected earthquakes from short period waveform data in the Mygdonia basin (N. Greece) as recorded by the permanent network of the Seismological Station of Aristotle University of Thessaloniki during the period 1989-1999. The proposed modification of the FPFIT program was developed in order to minimize the derivation of multiple solutions, as well as the uncertainties in the location of Ρ and Τ axis of the determined fault plane solutions. Compared to the original version of FPFIT the modified approach takes also into account the radiation pattern of SV and SH waves. For each earthquake horizontal and vertical components of each station were used and the first arrivals of Ρ and S waves were picked. Using the maximum peak-to-peak amplitude of Ρ and S waves the ratio Pmax/(S/\/2max+SE2max)1/2 was estimated, where S/Vmax and SEmax are the maximum amplitudes of the two horizontal components (N-S, E-W) for the S waves and Pmax is the maximum amplitude of the vertical one for the P- waves. This ratio for the observed data, as well as the corresponding ratio Prad/iS/Aad+SlAad)1'2 of the synthetic data was used as a weight for the determination of the observed and theoretical P-wave polarities, respectively. The method was tested using synthetic data. A significant improvement of the results was found, compared to the original version of FPFIT. In particular, an improved approximation of the input focal mechanism is found, without multiple solutions and the best-estimated Ρ and Τ axes exhibit much smaller uncertainties. The addition of noise in the synthetic data didn't significantly change the results concerning the fault plane solutions. Finally, we have applied the modified program on a real data set of earthquakes that occurred in the Mygdonia basin.

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).

The effect of an initial hypocentral stress upon the radiation patterns of P and S waves

1972 ◽  
Vol 62 (5) ◽  
pp. 1173-1182 ◽  
Author(s):  
F. A. Dahlen
Keyword(s):  
Radiation Pattern ◽  
Fault Plane ◽  
Deviatoric Stress ◽  
P Wave ◽  
Stress Deviator ◽  
Radiation Patterns ◽  
Fault Plane Solutions ◽  
S Waves ◽  
Quadrupole Component ◽  
Sufficient Magnitude

Abstract The effect of an initial hypocentral deviatoric stress upon the radiation patterns of radiated P and S waves is explicitly described for the case of an infinitesimal, nonpropagating seismic dislocation. A nonzero hypocentral stress deviator produces two small changes in the familiar quadrupole radiation pattern; it gives rise to a small additional explosion-like component, and it acts to skew slightly the quadrupole component relative to the fault plane and auxiliary plane. The latter phenomenon is not of sufficient magnitude to give rise to any serious uncertainties in the interpretation of fault-plane solutions; in fact, both phenomena are so small that they will be exceedingly difficult ever to detect. The recent measurements of P-wave amplitudes on the focal sphere by Randall and Knopoff (1970) cannot be explained by these results.

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