Source characteristics of small to moderate earthquakes in the Kanto region, Japan: application of a new definition of the S-wave time window length

1996 ◽  
Vol 86 (5) ◽  
pp. 1284-1291
Author(s):  
Kazutoshi Watanabe ◽  
Haruo Sato ◽  
Shigeo Kinoshita ◽  
Masakazu Ohtake
Keyword(s):  
Wave Energy ◽  
Seismic Moment ◽  
Time Window ◽  
P Wave ◽  
Corner Frequency ◽  
Window Length ◽  
S Wave ◽  
S Waves ◽  
Source Characteristics ◽  
Kanto Region

Abstract The S wave from a local earthquake generally consists of several pulses, in contrast to a simple pulse of P wave. This results in a large uncertainty in the estimation of seismic moment and wave energy when the window length for S-wave analysis is not chosen properly. In this study, we propose a new method to define objectively an appropriate time window length of the S wave for estimation of source characteristics based on the S-wave to P-wave energy ratio for a point shear dislocation source. Analyzing waveform data of 97 local earthquakes in the Kanto region, Japan, whose magnitudes M range from 3.3 to 6.0, we obtained simple equations for predicting the time window length of the S-wave TS as a function of earthquake magnitude or pulse width of P-wave TP; we got TS ≈ 1.8 TP for the relation between TP and TS. Applying the S-wave window thus defined, we estimated seismic energy E, seismic moment M0, and corner frequency fc for both P and S waves. Regression analysis of those parameters revealed (1) our method to define TS is confirmed by the fact that the seismic moment determined from P and S waves are consistent; (2) in the range of 1014 < M0 < 1018 (N·m), M0 is almost proportional to f−3c both for P and S waves; (3) the value of E/M0 is 2.7 ∼ 4.0 × 10−5; and (4) breakdown of the scaling relation is seen at M ≦ 4.

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.

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.

Analysis of conventional and converted mode reflections at Putah sink, California using three‐component data

Geophysics ◽  
1990 ◽  
Vol 55 (6) ◽  
pp. 646-659 ◽  
Author(s):  
C. Frasier ◽  
D. Winterstein
Keyword(s):  
Time Window ◽  
Structural Features ◽  
Low Noise ◽  
P Wave ◽  
Bright Spot ◽  
High Signal ◽  
Converted Wave ◽  
Gas Field ◽  
Seismic Line ◽  
S Waves

In 1980 Chevron recorded a three‐component seismic line using vertical (V) and transverse (T) motion vibrators over the Putah sink gas field near Davis, California. The purpose was to record the total vector motion of the various reflection types excited by the two sources, with emphasis on converted P‐S reflections. Analysis of the conventional reflection data agreed with results from the Conoco Shear Wave Group Shoot of 1977–1978. For example, the P‐P wave section had gas‐sand bright spots which were absent in the S‐S wave section. Shot profiles from the V vibrators showed strong P‐S converted wave events on the horizontal radial component (R) as expected. To our surprise, shot records from the T vibrators showed S‐P converted wave events on the V component, with low amplitudes but high signal‐to‐noise (S/N) ratios. These S‐P events were likely products of split S‐waves generated in anisotropic subsurface media. Components of these downgoing waves in the plane of incidence were converted to P‐waves on reflection and arrived at receivers in a low‐noise time window ahead of the S‐S waves. The two types of converted waves (P‐S and S‐P) were first stacked by common midpoint (CMP). The unexpected S‐P section was lower in true amplitude but much higher in S/N ratio than the P‐S section. The Winters gas‐sand bright spot was missing on the converted wave sections, mimicking the S‐S reflectivity as expected. CRP gathers were formed by rebinning data by a simple ray‐tracing formula based on the asymmetry of raypaths. CRP stacking improved P‐S and S‐P event resolution relative to CMP stacking and laterally aligned structural features with their counterparts on P and S sections. Thus, the unexpected S‐P data provided us with an extra check for our converted wave data processing.

Retrieval of source-extent parameters and the interpretation of corner frequency

1983 ◽  
Vol 73 (6A) ◽  
pp. 1499-1511
Author(s):  
Paul Silver
Keyword(s):  
Body Wave ◽  
Amplitude Spectrum ◽  
Low Frequency ◽  
P Wave ◽  
Corner Frequency ◽  
S Wave ◽  
Dislocation Source ◽  
Statistical Measures ◽  
Dislocation Models ◽  
Planar Dislocation

Abstract A method is proposed for retrieving source-extent parameters from far-field body-wave data. At low frequency, the normalized P- or S-wave displacement amplitude spectrum can be approximated by |Ω^(r^,ω)| = 1 − τ2(r^)ω2/2 where r^ specifies a point on the focal sphere. For planar dislocation sources, τ2(r^) is linearly related to statistical measures of source dimension, source duration, and directivity. τ2(r^) can be measured as the curvature of |Ω^(r^,ω)| at ω = 0 or the variance of the pulse Ω^(r^,t). The quantity ωc=2τ−1(r^) is contrasted with the traditional corner frequency ω0, defined as the frequency at the intersection of the low- and high-frequency trends of |Ω^(r^,ω)|. For dislocation models without directivity, ωc(P) ≧ ωc(S) for any r^. A mean corner frequency defined by averaging τ2(r^) over the focal sphere, ω¯c=2<τ2(r^)>−1/2, satisfies ωc(P) > ωc(S) for any dislocation source. This behavior is not shared by ω0. It is shown that ω0 is most sensitive to critical times in the rupture history of the source, whereas ωc is determined by the basic parameters of source extent. Evidence is presented that ωc is the corner frequency measured on actual seismograms. Thus, the commonly observed corner frequency shift (P-wave corner greater than the S-wave corner), now viewed as a shift in ωc is simply a result of spatial finiteness and is expected to be a property of any dislocation source. As a result, the shift cannot be used as a criterion for rejecting particular dislocation models.

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.

On the ratio of P-wave to S-wave corner frequencies for shallow earthquake sources

1974 ◽  
Vol 64 (4) ◽  
pp. 1159-1180 ◽  
Author(s):  
F. A. Dahlen
Keyword(s):  
Single Point ◽  
Three Dimensional ◽  
P Wave ◽  
Corner Frequency ◽  
S Wave ◽  
Earthquake Sources ◽  
Kinematical Model ◽  
Self Similar ◽  
Smooth Deceleration ◽  
Shallow Focus

abstract We construct a theoretical three-dimensional kinematical model of shallow-focus earthquake faulting in order to investigate the ratio of the P- and S-wave corner frequencies of the far-field elastic radiation. We attempt to incorporate in this model all of the important gross kinematical features which would arise if ordinary mechanical friction should be the dominant traction resisting fault motion. These features include a self-similar nucleation at a single point, a subsonic spreading of rupture away from that point, and a termination of faulting by smooth deceleration. We show that the ratio of the P-wave corner frequency to the S-wave corner frequency for any model which has these features will be less than unity at all points on the focal sphere.

Spatial distribution of high-frequency energy radiation on the fault of the 1995 Hyogo-Ken Nanbu, Japan, earthquake (MW 6.9) on the basis of the seismogram envelope inversion

1999 ◽  
Vol 89 (1) ◽  
pp. 22-35 ◽  
Author(s):  
Hisashi Nakahara ◽  
Haruo Sato ◽  
Masakazu Ohtake ◽  
Takeshi Nishimura
Keyword(s):  
Spatial Distribution ◽  
Wave Energy ◽  
High Frequency ◽  
Fault Plane ◽  
Time Window ◽  
Source Region ◽  
Inversion Method ◽  
S Wave ◽  
Energy Radiation ◽  
Initial Rupture

Abstract We studied the generation and propagation of high-frequency (above 1 Hz) S-wave energy from the 1995 Hyogo-Ken Nanbu (Kobe), Japan, earthquake (MW 6.9) by analyzing seismogram envelopes of the mainshock and aftershocks. We first investigated the propagation characteristics of high-frequency S-wave energy in the heterogeneous lithosphere around the source region. By applying the multiple lapse time window analysis method to aftershock records, we estimated two parameters that quantitatively characterize the heterogeneity of the medium: the total scattering coefficient and the intrinsic absorption of the medium for S waves. Observed envelopes of aftershocks were well reproduced by the envelope Green functions synthesized based on the radiative transfer theory with the obtained parameters. Next, we applied the envelope inversion method to 13 strong-motion records of the mainshock. We divided the mainshock fault plane of 49 × 21 km into 21 subfaults of 7 × 7 km square and estimated the spatial distribution of the high-frequency energy radiation on that plane. The average constant rupture velocity and the duration of energy radiation for each subfault were determined by grid searching to be 3.0 km/sec and 5.0 sec, respectively. Energy radiated from the whole fault plane was estimated as 4.9 × 1014 J for 1 to 2 Hz, 3.3 × 1014 J for 2 to 4 Hz, 1.5 × 1014 J for 4 to 8 Hz, 8.9 × 1012 J for 8 to 16 Hz, and 9.8 × 1014 J in all four frequency bands. We found that strong energy was mainly radiated from three regions on the mainshock fault plane: around the initial rupture point, near the surface at Awaji Island, and a shallow portion beneath Kobe. We interpret that energetic portions were associated with rupture acceleration, a fault surface break, and rupture termination, respectively.

Green's function of the Lord–Shulman thermo-poroelasticity theory

2020 ◽  
Vol 221 (3) ◽  
pp. 1765-1776 ◽  
Author(s):  
Jia Wei ◽  
Li-Yun Fu ◽  
Zhi-Wei Wang ◽  
Jing Ba ◽  
José M Carcione
Keyword(s):  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Heterogeneous Media ◽  
Numerical Algorithms ◽  
Heat Diffusion ◽  
P Wave ◽  
Wave Analysis ◽  
S Wave ◽  
S Waves

SUMMARY The Lord–Shulman thermoelasticity theory combined with Biot equations of poroelasticity, describes wave dissipation due to fluid and heat flow. This theory avoids an unphysical behaviour of the thermoelastic waves present in the classical theory based on a parabolic heat equation, that is infinite velocity. A plane-wave analysis predicts four propagation modes: the classical P and S waves and two slow waves, namely, the Biot and thermal modes. We obtain the frequency-domain Green's function in homogeneous media as the displacements-temperature solution of the thermo-poroelasticity equations. The numerical examples validate the presence of the wave modes predicted by the plane-wave analysis. The S wave is not affected by heat diffusion, whereas the P wave shows an anelastic behaviour, and the slow modes present a diffusive behaviour depending on the viscosity, frequency and thermoelasticity properties. In heterogeneous media, the P wave undergoes mesoscopic attenuation through energy conversion to the slow modes. The Green's function is useful to study the physics in thermoelastic media and test numerical algorithms.

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.

scholarly journals Time–frequency windowing in multiparameter elastic FWI of shallow seismic wavefield

2020 ◽  
Vol 222 (2) ◽  
pp. 1164-1177
Author(s):  
Nikolaos Athanasopoulos ◽  
Edgar Manukyan ◽  
Thomas Bohlen ◽  
Hansruedi Maurer
Keyword(s):  
Wave Velocity ◽  
Time Window ◽  
Mass Density ◽  
Waveform Inversion ◽  
P Wave ◽  
S Wave ◽  
Time Frequency ◽  
Full Waveform ◽  
Shallow Seismic ◽  
P Wave Velocity

SUMMARY Full-waveform inversion of shallow seismic wavefields is a promising method to infer multiparameter models of elastic material properties (S-wave velocity, P-wave velocity and mass density) of the shallow subsurface with high resolution. Previous studies used either the refracted Pwaves to reconstructed models of P-wave velocity or the high-amplitude Rayleigh waves to infer the S-wave velocity structure. In this work, we propose a combination of both wavefields using continuous time–frequency windowing. We start with the contribution of refracted P waves and gradually increase the time window to account for scattered body waves, higher mode Rayleigh waves and finally the fundamental Rayleigh wave mode. The opening of the time window is combined with opening the frequency bandwidth of input signals to avoid cycle skipping. Synthetic reconstruction tests revealed that the reconstruction of P-wave velocity model and mass density can be improved. The S-wave velocity reconstruction is still accurate and robust and is slightly benefitted by time–frequency windowing. In a field data application, we observed that time–frequency windowing improves the consistency of multiparameter models. The inferred models are in good agreement with independent geophysical information obtained from ground-penetrating radar and full-waveform inversion of SH waves.

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