A dynamic model for far-field acceleration

1982 ◽  
Vol 72 (4) ◽  
pp. 1049-1068
Author(s):  
John Boatwright
Keyword(s):  
Stress Drop ◽  
High Frequency ◽  
Dynamic Stress ◽  
The Body ◽  
Body Waves ◽  
Far Field ◽  
Rupture Velocity ◽  
Frequency Level ◽  
Average Change ◽  
Dynamic Stress Drop

abstract A model for the far-field acceleration radiated by an incoherent rupture is constructed by combining Madariaga's (1977) theory for the high-frequency radiation from crack models of faulting with a simple statistical source model. By extending Madariaga's results to acceleration pulses with finite durations, the peak acceleration of a pulse radiated by a single stop or start of a crack tip is shown to depend on the dynamic stress drop of the subevent, the total change in rupture velocity, and the ratio of the subevent radius to the acceleration pulse width. An incoherent rupture is approximated by a sample from a self-similar distribution of coherent subevents. Assuming the subevents fit together without overlapping, the high-frequency level of the acceleration spectra depends linearly on the rms dynamic stress drop, the average change in rupture velocity, and the square root of the overall rupture area. The high-frequency level is independent, to first order, of the rupture complexity. Following Hanks (1979), simple approximations are derived for the relation between the rms dynamic stress drop and the rms acceleration, averaged over the pulse duration. This relation necessarily depends on the shape of the body-wave spectra. The body waves radiated by 10 small earthquakes near Monticello Dam, South Carolina, are analyzed to test these results. The average change of rupture velocity of Δv = 0.8β associated with the radiation of the acceleration pulses is estimated by comparing the rms acceleration contained in the P waves to that in the S waves. The rms dynamic stress drops of the 10 events, estimated from the rms accelerations, range from 0.4 to 1.9 bars and are strongly correlated with estimates of the apparent 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.

Source physics interpretation of non-self-similar double-corner frequency source spectral model JA19_2S

2021 ◽  
Author(s):  
Chen Ji ◽  
Ralph Archuleta
Keyword(s):  
Aspect Ratio ◽  
Stress Drop ◽  
Dynamic Stress ◽  
Static Stress ◽  
Corner Frequency ◽  
Rupture Velocity ◽  
Dynamic Stress Drop ◽  
Self Similar ◽  
Static Stress Drop ◽  
Frequency Source

<p>Source spectral models developed for strong ground motion simulations are phenomenological models that represent the average effect that the source processes have on near fault ground motion. Their parameters are directly regressed from the observations and often do not have clear meaning for the physics of the source process. We investigate the relation between the kinematic double-corner frequency (DCF) source spectral model JA19_2S (Ji and Archuleta, BSSA, 2020) and static fault geometry scaling relations proposed by Leonard (2010). We derive scaling relations for the low and high corner frequency in terms of static stress drop, dynamic stress drop, fault rupture velocity, fault aspect ratio, and relative hypocenter location. We find that the non-self-similar low corner frequency  scaling relation of JA19_2S model for 5.3<<strong>M</strong><6.9 earthquakes is well explained using the fault length scaling relation of Leonard’s model combined with a constant rupture velocity. Earthquakes following both models have constant average static stress drop and constant average dynamic stress drop. The high frequency source radiation is controlled by seismic moment, static stress drop and dynamic stress drop but strongly modulated by the fault aspect ratio and the hypocenter’s relative location. The mean, scaled energy  (or apparent stress) decreases with magnitude due to the magnitude dependence of the fault aspect ratio. Based on these two models, the commonly quoted average rupture velocity of 70-80% of shear wave speed implies predominantly unilateral rupture.</p>

Use of ray theory to calculate high-frequency radiation from earthquake sources having spatially variable rupture velocity and stress drop

1984 ◽  
Vol 74 (6) ◽  
pp. 2061-2082
Author(s):  
Paul Spudich ◽  
L. Neil Frazer
Keyword(s):  
Stress Drop ◽  
High Frequency ◽  
Slip Velocity ◽  
Green’S Functions ◽  
Ground Motions ◽  
Spatial Variations ◽  
Body Waves ◽  
Ray Theory ◽  
Rupture Velocity ◽  
Ground Acceleration

Abstract We analyze the problem of calculating high-frequency ground motions (>1 Hz) caused by earthquakes having arbitrary spatial variations of rupture velocity and slip velocity (or stress drop) over the fault. We approximate the elastic wave Green's functions by far-field body waves, which we calculate using geometric ray theory. However, we do not make the traditional Fraunhofer approximation, so our method may be used close to large faults. The method is confined to high frequencies (greater than about 1 Hz) due to the omisson of near-field terms, and must be used at source-observer distances less than a few source depths, due to the omission of surface waves. It is easily used in laterally varying velocity structures. Assuming a simple parameterization of the slip function, the computational problem collapses to the evaluation of a series of line integrals over the fault, with one line integral per each time ti in the observer seismogram. The path of integration corresponding to observation time ti consists of only those points on the fault which radiate body waves arriving at the observer at exactly time ti. This path is an isochron of the arrival time function. An isochron velocity may be defined that depends on rupture velocity and resembles the usual directivity function. Observed ground motions are directly dependent upon this isochron velocity. Ground velocity is proportional to isochron velocity and ground acceleration is proportional to isochron acceleration in dislocation models of rupture. Ground acceleration may also be related to spatial variations of slip velocity on the fault, using the square of isochron velocity as a constant of proportionality. We show two rupture models, one with variable slip velocity and the other with variable rupture velocity, that cause the same ground acceleration at a single observer. The computational method is shown to produce reasonably accurate synthetic seismograms, compared to a method using complete Green's functions, and requires about 0.5 per cent of the computer time. It may be very effective in calculating ground motions in the frequency band 1 to 10 Hz at observers within a few source depths of large earthquakes, where most of the high-frequency motions may be caused by direct P and S waves. We suggest a possible method for inverting ground motions for both slip velocity and rupture velocity over the fault.

Broadband analysis of the extended foreshock sequence of the Miyagi-Oki earthquake of 12 June 1978

1982 ◽  
Vol 72 (6A) ◽  
pp. 2017-2036
Author(s):  
George L. Choy ◽  
John Boatwright
Keyword(s):  
Stress Drop ◽  
Dynamic Stress ◽  
Main Shock ◽  
Body Waves ◽  
The Third ◽  
Radiated Energy ◽  
Dynamic Stress Drop ◽  
Static Stress Drop ◽  
Stress Drops ◽  
Seismograph Network

abstract The Miyagi-Oki earthquake of 12 June 1978, a large (Ms 7.8) interplate thrust event, occurred in a region which had not experienced earthquakes of magnitude greater than 7 since 1938. A sequence of four moderate-sized (5.4 < mb < 6.1) earthquakes encircled the rupture zone of the Miyagi-Oki earthquake over a period of 2 yr before the main shock. Broadband displacement and velocity records of body waves recorded digitally by stations of the Global Digital Seismograph Network are analyzed to determine the static and dynamic characteristics of the sequence. These characteristics include moment, radiated energy, dynamic and static stress drop, and apparent stress. Inversions of duration measurements made on the velocity waveforms permit quantifying the complexity of an event as well as constraining its rupture geometry. Intervals of 7 to 8 months separated the first three events; the main shock occurred 4 months after the third event. The rupture process of the third event was relatively complex; the event also had a substantially higher dynamic stress drop (175 bars) than did the stress drops of the first two events (9 and 10 bars, respectively). These observations suggest that the third event was an interme-diate-term precursor to the main shock. The fourth event, a short-term precursor to the main shock, occurred about 8 min before the main shock. Its dynamic stress drop (20 bars) was lower than that of the third event but higher than that of the first two events.

Numerical computation of individual far‐field arrivals excited by an acoustic source in a borehole

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 852-866 ◽  
Author(s):  
Andrew L. Kurkjian
Keyword(s):  
Numerical Computation ◽  
The Body ◽  
Body Waves ◽  
Head Wave ◽  
Far Field ◽  
Trapped Mode ◽  
Full Waveform ◽  
Full Wave ◽  
Head Waves ◽  
Strong Shear

In this paper, I model the acoustic logging problem and numerically compute individual arrivals at far‐field receivers. The ability to compute individual arrivals is useful for examining the sensitivities of each arrival to various factors of interest, as opposed to examining the full waveform as a whole. While the numerical computation of the mode arrivals (Peterson, 1974) and the numerical computation of the first head waves (Tsang and Rader, 1979) have been previously reported, the numerical computation of the entire set of head‐wave arrivals is new and is the major contribution of this paper. Following Roever et al. (1974) and others, the full wave field is represented as a sum of contributions from both poles and branchcuts in the complex wavenumber plane. The pole contributions correspond to mode arrivals while the branch cuts are associated with the body waves (i.e., head waves). Both the pole and branch cut contributions are computed numerically and results are presented for the cases of a slow and a fast formation. The shear event in the slow formation is found to be relatively small, consistent with observations in measured data. Contrary to existing knowledge, the shear event in the fast formation is also relatively small. The apparent strong shear arrival in the full waveforms is due primarily to the trapped mode pole in the vicinity of cutoff.

Far-field pulse shapes from circular sources with variable rupture velocities

1997 ◽  
Vol 87 (5) ◽  
pp. 1288-1296
Author(s):  
Nicholas Deichmann
Keyword(s):  
Stress Drop ◽  
Seismic Moment ◽  
Total Duration ◽  
Source Model ◽  
P Wave ◽  
Far Field ◽  
Rupture Velocity ◽  
P Waves ◽  
S Waves ◽  
Rate Functions

Abstract Recently, Sato (1994) developed a simple earthquake source model of a circular rupture expanding outward from the center of a fault with constant stress drop. In contrast to previous models, the rupture velocity is allowed to vary over the duration of faulting. This model is used to synthesize apparent moment-rate functions for a three-stage source process: first, the rupture starts out with a gradually increasing velocity, then, it continues to expand uniformly until, finally, it slows to a gradual stop. Synthetic velocity seismograms are obtained from a convolution of the apparent moment-rate functions with a causal Q-operator and an appropriate instrument response. Comparisons with an example of an earthquake signal show that, in the context of the proposed model, the observed emergent P-wave onset, which is not compatible with a constant rupture velocity, can be explained by a gradually accelerating rupture front. Systematic departures from the generally expected scaling relationship between seismic moment and rupture duration are often interpreted as evidence for a dependence of stress drop on seismic moment. However, the trade-off between stress drop and rupture velocity inherent in all kinematic source models implies that such deviations can just as well be attributed to systematic variations of rupture velocity. Whereas, in general, the total duration of the far-field displacement pulse is shorter for P waves than for S waves, the model predicts that the rise time, τ1/2, of the displacement pulse should be longer for P waves than for S waves. This feature could constitute a critical test of the model and also provide a constraint on the rupture velocity.

scholarly journals The source mechanism of the August 7, 1966 El Golfo earthquake

1978 ◽  
Vol 68 (5) ◽  
pp. 1281-1292
Author(s):  
John E. Ebel ◽  
L. J. Burdick ◽  
Gordon S. Stewart
Keyword(s):  
Surface Wave ◽  
Stress Drop ◽  
Gulf Of California ◽  
Body Wave ◽  
Source Parameters ◽  
High Stress ◽  
Plate Boundary ◽  
The Body ◽  
Body Waves ◽  
Wave Radiation

abstract The El Golfo earthquake of August 7, 1966 (mb = 6.3, MS = 6.3) occurred near the mouth of the Colorado River at the northern end of the Gulf of California. Synthetic seismograms for this event were computed for both the body waves and the surface waves to determine the source parameters of the earthquake. The body-wave model indicated the source was a right lateral, strike-slip source with a depth of 10 km and a far-field time function 4 sec in duration. The body-wave moment was computed to be 5.0 × 1025 dyne-cm. The surface-wave radiation pattern was found to be consistent with that of the body waves with a surface-wave moment of 6.5 × 1025 dyne-cm. The agreement of the two different moments indicates that the earthquake had a simple source about 4 sec long. A comparison of this earthquake source with the Borrego Mountain and Truckee events demonstrates that all three of these earthquakes behaved as high stress-drop events. El Golfo was shown to be different from the low stress-drop, plate-boundary events which were located on the Gibbs fracture zone in 1967 and 1974.

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