scholarly journals Comparing EGF Methods for Estimating Corner Frequency and Stress Drop From P Wave Spectra

2019 ◽  
Vol 124 (4) ◽  
pp. 3966-3986 ◽  
Author(s):  
Peter M. Shearer ◽  
Rachel E. Abercrombie ◽  
Daniel T. Trugman ◽  
Wei Wang
Keyword(s):  
Stress Drop ◽  
P Wave ◽  
Corner Frequency ◽  
Wave Spectra

P-wave spectra for ML 5 foreshocks, aftershocks, and isolated earthquakes near Parkfield, California

1981 ◽  
Vol 71 (2) ◽  
pp. 423-436
Author(s):  
Willian H. Bakun ◽  
Thomas V. McEvilly
Keyword(s):  
Stress Drop ◽  
High Stress ◽  
P Wave ◽  
Wave Radiation ◽  
Focal Region ◽  
Wave Spectra ◽  
Rupture Length ◽  
Main Shocks ◽  
Relative Stress ◽  
Fault Trace

abstract Wood-Anderson seismograms recorded at Mount Hamilton (MHC, 185 km, 327°), Santa Barbara (SBC, 180 km, 158°), and Tinemaha (TIN, 240 km, 56°) provide data for comparing P-wave spectra for two immediate (17-min) foreshocks, one early (55-hr) foreshock, two aftershocks, and two “isolated” Parkfield earthquakes. All are ML 5.0 shocks with epicenters within 7 km of the common epicenter of the 1934 and 1966 Parkfield main shocks. The set of events is well suited for testing the hypothesis that foreshocks are high-stress-drop sources. Calculated stress drops are controlled by source directivity at azimuths aligned with the fault break (at MHC and SBC). P-wave radiation from the three foreshocks is focused along one fault trace azimuth, suggesting that foreshock sources are characterized by pronounced unilateral rupture expansion. At TIN, broadside to the fault where directivity has minimum effect on calculated relative stress drop, the two immediate foreshocks are higher stress-drop sources. The early foreshock is a low-to-average stress-drop source, indicating the possibility that stress concentration is a rapidly occurring phenomenon in rupture nucleation. Alternatively, the stress field is highly variable on the scale of 2 to 3 km in the focal region of an impending earthquake with a rupture length of 20 to 30 km.

Ground Motion From A Magnitude 3.5 Earthquake Near Massena, New York: Evidence For Poor Resolution of Corner Frequency For Small Events

1989 ◽  
Vol 60 (3) ◽  
pp. 95-100 ◽  
Author(s):  
S.E. Hough ◽  
K. Jacob ◽  
R. Busby ◽  
P.A. Friberg
Keyword(s):  
Earthquake Engineering ◽  
Epicentral Distance ◽  
Wave Spectrum ◽  
P Wave ◽  
Corner Frequency ◽  
Source Spectrum ◽  
Wave Spectra ◽  
S Wave ◽  
High Quality ◽  
Wide Range

Abstract We present analysis of a magnitude 3.5 event which occurred at 9 km epicentral distance from a digital strong motion instrument operated by the National Center for Earthquake Engineering Research. Although the size of this isolated event is such that it can scarcely be considered to be a significant earthquake, a careful analysis of this high quality recording does yield several interesting results: 1) the S-wave spectra can be interpreted in terms of a simple omega-squared source spectrum and frequency-independent attenuation, 2) there is the suggestion of a poorly-resolved resonance in the P-wave spectrum, and perhaps most importantly, 3) the apparently simple S-wave spectra can be fit almost equally well with a surprisingly wide range of seismic corner frequencies, from roughly 5 to 25 Hz. This uncertainty in corner frequency translates into uncertainties in inferred Q values of almost an order of magnitude, and into uncertainties in stress drop of two orders of magnitude. Given the high quality of the data and the short epicentral distance to the station, we consider it likely that resolution of spectral decay and corner frequency will be at least as poor for any other recording of earthquakes with comparable or smaller magnitudes.

Simultaneous inversion for Q and source parameters of microearthquakes accompanying hydraulic fracturing in granitic rock

1991 ◽  
Vol 81 (2) ◽  
pp. 553-575 ◽  
Author(s):  
Michael Fehler ◽  
W. Scott Phillips
Keyword(s):  
Hydraulic Fracturing ◽  
Stress Drop ◽  
Source Parameters ◽  
Low Frequency ◽  
Seismic Energy ◽  
P Wave ◽  
Corner Frequency ◽  
Spectral Amplitude ◽  
Seismic Zone ◽  
Stress Drops

Abstract An inversion that fits spectra of earthquake waveforms and gives robust estimates of corner frequency and low-frequency spectral amplitude has been used to determine source parameters of 223 microearthquakes induced by hydraulic fracturing in granodiorite. Assuming a ω−2 source model, the inversion fits the P-wave spectra of microearthquake waveforms to determine individual values of corner frequency and low-frequency spectral amplitude for each event and one average frequency-independent Q for all source-receiver paths. We also implemented a constraint that stress drops of all microearthquakes be similar but not equal and found that this constraint did not significantly degrade the quality of the fits to the spectra. The waveforms analyzed were recorded by a borehole seismometer. The P-wave Q was found to be 1070. For Q values as low as 600 and as high as 3000, the misfit between model and spectra increased by less than 5 per cent and the average corner frequency changed by less than 15 per cent from those obtained with a Q of 1070. Average stress drop was 3.7 bars. Seismic moments obtained from spectra ranged from 1013 to 1018 dyne-cm. The low stress drops are interpreted to result from underestimation of the actual stress drops because of a nonuniform distribution of stress drop and slip along the fault planes. Spatially varying stress drops and slips result from the strong rock heterogeneity due to the injection of fluid into the rock. Stress drops were found to be larger near the edges of the seismic zone, in regions that had not been seismically active during previous injections. The seismic moments determined from spectra were used to obtain a coda length-to-moment relation. Then, moments were estimated for 1149 events from measurements of coda lengths from events whose moments could not be measured from spectra because of saturation or a low signal-to-noise ratio. The constant of proportionality between cumulative number of events and seismic moment is higher than that found for tectonic regions. The slope is so high that the seismic energy release is dominated by the large number of small events. In the absence of information about the number of events smaller than we studied, we cannot estimate the total seismic energy released by the hydraulic injection.

P-wave spectra of nevada test site events at near and very near distances: Implications for a near-regional body wave-surface wave discriminant

1976 ◽  
Vol 66 (3) ◽  
pp. 803-825
Author(s):  
William A. Peppin
Keyword(s):  
Scaling Laws ◽  
Body Wave ◽  
Test Site ◽  
P Wave ◽  
Spectral Amplitude ◽  
Source Spectrum ◽  
Wave Spectra ◽  
Nevada Test Site ◽  
Field Source ◽  
Source Spectra

abstract Some 140 P-wave spectra of explosions, earthquakes, and explosion-induced aftershocks, all within the Nevada Test Site, have been computed from wide-band seismic data at close-in (< 30 km) and near-regional (200 to 300 km) distances. Observed near-regional corner frequencies indicate that source corner frequencies of explosions differ little from those of earthquakes of similar magnitude for 3 < ML < 5. Plots of 0.8 to 1.0 Hz Pg spectral amplitude versus 12-sec Rayleigh-wave amplitude show a linear trend with unit slope over three orders of magnitude for explosions; earthquakes fail to be distinguished from explosions on such a plot. These spectra also indicate similar source spectra for explosions in different media (tuff, alluvium, rhyolite) which corroborates Cherry et al. (1973). Close-in spectra of three large explosions indicate that: (1) source corner frequencies of explosions scale with yield in a way significantly different from previously published scaling laws; (2) explosion source spectra in tuff are flat from 0.2 to 1.0 Hz (no overshoot); (3) the far-field source spectrum decays at least as fast as frequency cubed. Taken together, these data indicate that the following factors are not responsible for Peppin and McEvilly's (1974) near-regional discriminant: (a) source dimension, (b) source rise time, or (c) shape of the source spectrum.

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.

The relations between the corner frequency, seismic moment and source dynamic parameters derived from the spontaneous rupture of a circular fault

2021 ◽  
Vol 228 (1) ◽  
pp. 134-146
Author(s):  
Jian Wen ◽  
Jiankuan Xu ◽  
Xiaofei Chen
Keyword(s):  
Stress Drop ◽  
Seismic Moment ◽  
Dynamic Models ◽  
Scaling Law ◽  
Boundary Integral ◽  
Corner Frequency ◽  
Dynamic Parameters ◽  
Zone Size ◽  
Dynamic Rupture ◽  
Scaling Relationships

SUMMARY The stress drop is an important dynamic source parameter for understanding the physics of source processes. The estimation of stress drops for moderate and small earthquakes is based on measurements of the corner frequency ${f_c}$, the seismic moment ${M_0}$ and a specific theoretical model of rupture behaviour. To date, several theoretical rupture models have been used. However, different models cause considerable differences in the estimated stress drop, even in an idealized scenario of circular earthquake rupture. Moreover, most of these models are either kinematic or quasi-dynamic models. Compared with previous models, we use the boundary integral equation method to simulate spontaneous dynamic rupture in a homogeneous elastic full space and then investigate the relations between the corner frequency, seismic moment and source dynamic parameters. Spontaneous ruptures include two states: runaway ruptures, in which the rupture does not stop without a barrier, and self-arresting ruptures, in which the rupture can stop itself after nucleation. The scaling relationships between ${f_c}$, ${M_0}$ and the dynamic parameters for runaway ruptures are different from those for self-arresting ruptures. There are obvious boundaries in those scaling relations that distinguish runaway ruptures from self-arresting ruptures. Because the stress drop varies during the rupture and the rupture shape is not circular, Eshelby's analytical solution may be inaccurate for spontaneous dynamic ruptures. For runaway ruptures, the relations between the corner frequency and dynamic parameters coincide with those in the previous kinematic or quasi-dynamic models. For self-arresting ruptures, the scaling relationships are opposite to those for runaway ruptures. Moreover, the relation between ${f_c}$ and ${M_0}$ for a spontaneous dynamic rupture depends on three factors: the dynamic rupture state, the background stress and the nucleation zone size. The scaling between ${f_c}$ and ${M_0}$ is ${f_c} \propto {M_0^{ - n}}$, where n is larger than 0. Earthquakes with the same dimensionless dynamic parameters but different nucleation zone sizes are self-similar and follow a ${f_c} \propto {M_0^{ - 1/3}}$ scaling law. However, if the nucleation zone size does not change, the relation between ${f_c}$ and ${M_0}$ shows a clear departure from self-similarity due to the rupture state or background stress.

A Source Physics Interpretation of Nonself-Similar Double-Corner-Frequency Source Spectral Model JA19_2S

2022 ◽  
Author(s):  
Chen Ji ◽  
Ralph J. Archuleta
Keyword(s):  
Stress Drop ◽  
Wave Speed ◽  
Dynamic Stress ◽  
Corner Frequency ◽  
Rupture Velocity ◽  
Scaling Relation ◽  
Shear Wave Speed ◽  
Dynamic Stress Drop ◽  
Static Stress Drop ◽  
Frequency Source

Abstract We investigate the relation between the kinematic double-corner-frequency source spectral model JA19_2S (Ji and Archuleta, 2020) and static fault geometry scaling relations proposed by Leonard (2010). We find that the nonself-similar low-corner-frequency scaling relation of JA19_2S model can be explained using the fault length scaling relation of Leonard’s model combined with an average rupture velocity ∼70% of shear-wave speed for earthquakes 5.3 < M< 6.9. Earthquakes consistent with both models have magnitude-independent average static stress drop and average dynamic stress drop around 3 MPa. Their scaled energy e˜ is not a constant. The decrease of e˜ with magnitude can be fully explained by the magnitude dependence of the fault aspect ratio. The high-frequency source radiation is generally controlled by seismic moment, static stress drop, and dynamic stress drop but is further modulated by the fault aspect ratio and the relative location of the hypocenter. Based on these two models, the commonly quoted average rupture velocity of 70%–80% of shear-wave speed implies predominantly unilateral rupture.

scholarly journals The comparative analysis of 2018 Alaska earthquakes from surface wave records

2020 ◽  
Vol 2 (1) ◽  
pp. 76-84
Author(s):  
Anastasiya Fomochkina ◽  
Boris Bukchin
Keyword(s):  
Surface Wave ◽  
Focal Mechanism ◽  
Seismic Moment ◽  
Optimal Solution ◽  
Seismic Source ◽  
P Wave ◽  
Wave Spectra ◽  
Earthquake Intensity ◽  
Second Moments ◽  
First Arrival

We consider the source of an earthquake in an approximation of instant point shift dislocation. Such a source is given by its depth, the focal mechanism determined by three angles (strike, dip, and slip), and the seismic moment characterizing the earthquake intensity. We determine the source depth and focal mechanism by a systematic exploration of 4D parametric space, and seismic moment - by solving the problem of minimization of the misfit between observed and calculated surface wave spectra for every combination of all other parameters. As is well known, the focal mechanism cannot be uniquely determined from the surface wave’s amplitude spectra only. We used P-wave first arrival polarities to select the optimal solution. Ana-lyzing the surface wave spectra at shorter periods, we describe the source in an approximation of the stress glut second moments. Using these moments we determine integral estimates of the geometry, the duration of the seismic source, and rupture propagation. The results of the application of this technique for two Alaska earthquakes that occurred in 2018 (with Mw7.9 in January and with Mw7.1 in November) are presented. The possibility of the fault plane identification, which based on the obtained estimates of the focal mechanisms and second mo-ments, is analyzed for both events. Bilateral model of the source is constructed.

scholarly journals Analysis of strong-motion data of the 1990 Eastern Sicily earthquake

1995 ◽  
Vol 38 (2) ◽  
Author(s):  
M. Di Bona ◽  
M. Cocco ◽  
A. Rovelli ◽  
R. Berardi ◽  
E. Boschi
Keyword(s):  
Frequency Band ◽  
Stress Drop ◽  
Seismic Moment ◽  
Ground Motions ◽  
Broad Band ◽  
Strong Motion ◽  
Moment Magnitude ◽  
Corner Frequency ◽  
Local Magnitude ◽  
The Moment

The strong motion accelerograms recorded during the 1990 Eastern Sicily earthquake have been analyzed to investigate source and attenuation parameters. Peak ground motions (peak acceleration, velocity and displacement) overestimate the values predicted by the empirical scaling law proposed for other Italian earthquakes, suggesting that local site response and propagation path effects play an important role in interpreting the observed time histories. The local magnitude, computed from the strong motion accelerograms by synthesizing the Wood-Anderson response, is ML = 5.9, that is sensibly larger than the local magnitude estimated at regional distances from broad-band seismograms (ML = 5.4). The standard omega-square source spectral model seems to be inadequate to describe the observed spectra over the entire frequency band from 0.2 to 20 Hz. The seismic moment estimated from the strong motion accelerogram recorded at the closest rock site (Sortino) is Mo = 0.8 x 1024 dyne.cm, that is roughly 4.5 times lower than the value estimated at regional distances (Mo = 3.7 x 1024 dyne.cm) from broad-band seismograms. The corner frequency estimated from the accelera- tion spectra i.5 J; = 1.3 Hz, that is close to the inverse of the dUl.ation of displacement pulses at the two closest recording sites. This value of corner tì.equency and the two values of seismic moment yield a Brune stress drop larger than 500 bars. However, a corner frequency value off; = 0.6 Hz and the seismic moment resulting from regional data allows the acceleration spectra to be reproduced on the entire available frequency band yielding to a Brune stress drop of 210 bars. The ambiguity on the corner frequency value associated to this earthquake is due to the limited frequency bandwidth available on the strong motion recordil1gs. Assuming the seismic moment estimated at regional distances from broad-band data, the moment magnitude for this earthquake is 5.7. The higher local magnitude (5.9) compared with the moment magnitude (5.7) is due to the weak regional attenuation. Beside this, site amplifications due to surface geology have produced the highest peak ground motions among those observed at the strong motion sites.

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