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.

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.

scholarly journals Smooth Crustal Velocity Models Cause a Depletion of High-Frequency Ground Motions on Soil in 2D Dynamic Rupture Simulations

2021 ◽  
Author(s):  
Yihe Huang
Keyword(s):  
Shear Wave ◽  
High Frequency ◽  
Ground Motions ◽  
Velocity Model ◽  
Dynamic Rupture ◽  
Ground Acceleration ◽  
Velocity Models ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Crustal Velocity

ABSTRACT A depletion of high-frequency ground motions on soil sites has been observed in recent large earthquakes and is often attributed to a nonlinear soil response. Here, I show that the reduced amplitudes of high-frequency horizontal-to-vertical spectral ratios (HVSRs) on soil can also be caused by a smooth crustal velocity model with low shear-wave velocities underneath soil sites. I calculate near-fault ground motions using both 2D dynamic rupture simulations and point-source models for both rock and soil sites. The 1D velocity models used in the simulations are derived from empirical relationships between seismic wave velocities and depths in northern California. The simulations for soil sites feature lower shear-wave velocities and thus larger Poisson’s ratios at shallow depths than those for rock sites. The lower shear-wave velocities cause slower shallow rupture and smaller shallow slip, but both soil and rock simulations have similar rupture speeds and slip for the rest of the fault. However, the simulated near-fault ground motions on soil and rock sites have distinct features. Compared to ground motions on rock, horizontal ground acceleration on soil is only amplified at low frequencies, whereas vertical ground acceleration is deamplified for the whole frequency range. Thus, the HVSRs on soil exhibit a depletion of high-frequency energy. The comparison between smooth and layered velocity models demonstrates that the smoothness of the velocity model plays a critical role in the contrasting behaviors of HVSRs on soil and rock for different rupture styles and velocity profiles. The results reveal the significant role of shallow crustal velocity structure in the generation of high-frequency ground motions on soil sites.

The high-frequency shape of the source spectrum for earthquakes in eastern and western Canada

1996 ◽  
Vol 86 (1A) ◽  
pp. 106-112 ◽  
Author(s):  
Gail M. Atkinson
Keyword(s):  
High Frequency ◽  
Fourier Spectrum ◽  
Response Spectrum ◽  
Ground Motions ◽  
Source Spectrum ◽  
Western Canada ◽  
Eastern Canada ◽  
Ground Acceleration ◽  
Kappa Effect ◽  
Key Parameter

Abstract The high-frequency shape of the earthquake spectrum strongly influences the amplitude of the peak ground acceleration and of the response spectrum at frequencies of 10 Hz and greater. A key parameter for the description of high-frequency ground motions is “kappa,” which is the decay slope of the Fourier spectrum of acceleration at near-source distances (Anderson and Hough, 1984; note Anderson and Hough originally referred to this parameter as kappa (0)). Kappa may be attributed to site effects (fmax; Hanks, 1982), source processes (Papageorgiou and Aki, 1983), or both. Seismographic data place weak but significant constraints on kappa values. On average, there is no resolved kappa effect on spectra recorded at rock sites in eastern Canada, in the frequency range f ≦ 30 Hz. Four firm-soil sites in southwestern Ontario also show no kappa effect. An implied upper bound for kappa is 0.004 (or lower bound of 30 Hz for fmax). By contrast, source spectra from earthquakes in the Cascadia region, recorded on hard-rock sites in southwestern British Columbia (B.C.), appear to be well described by a kappa of 0.011 ± 0.002. The B.C. spectra are thus intermediate to the eastern case, with zero apparent kappa, and the typical California case, for which kappa is about 0.04.

Seismic radiation from circular cracks growing at variable rupture velocity

1994 ◽  
Vol 84 (4) ◽  
pp. 1199-1215
Author(s):  
Tamao Sato
Keyword(s):  
Radiation Pattern ◽  
High Frequency ◽  
Pulse Width ◽  
Present Method ◽  
Body Waves ◽  
Rupture Velocity ◽  
Continuous Change ◽  
Velocity Change ◽  
Acceleration Pulse ◽  
Frequency Radiation

Abstract We have investigated the far-field body waves emitted by a circular fault growing at variable rupture velocity. The slip motion on the fault is constructed by assuming that the self-similar slip distribution holds at every successive instant of rupture formation for a circular crack. The present method permits us to evaluate not only the high-frequency but also the low-frequency radiation. It is also possible to handle both abrupt and continuous change in rupture velocity. The resultant expression for the radiation does not involve an integral. It is expressed in a closed form that contains information about the isochrone properties of the two extreme points having the minimum and maximum distances from the observer. Because of its simplicity and high computational speed, the present method provides us with a basic tool for simulating the radiation from seismic sources with a multitude of irregular rupture growth. The property of acceleration pulse radiated by continuous change in rupture velocity has been investigated. The time duration of the velocity change is assumed to be short but to take a finite time. The shape of the rupture front that is effective in radiating the high-frequency radiation is presumed to be semicircular. The acceleration pulse demonstrates a directivity with respect to both the pulse width and amplitude. The pulse width is, on average, given by the duration of the velocity change, and it is modulated by the directivity factor, which depends on the rupture velocity averaged over the change in rupture velocity. The pulse width radiated toward the growth direction of the semi-circular rupture front is shorter than that radiated toward the opposite side. The spectral amplitude of the acceleration pulse depends linearly on the strain, the radius of the rupture front at which the rupture velocity starts to change, the magnitude of the change in rupture velocity, and the generalized radiation pattern coefficient. The directivity of the radiation pattern coefficient is stronger than that for the case of an abrupt change in rupture velocity. In the case where the rupture stops completely, the radiation pattern coefficient is simply controlled by the magnitude of the change in rupture velocity. If we deal with a partial drop of the rupture velocity, however, we must consider the average rupture velocity as well to fully describe the radiation pattern. A procedure is presented for retrieving the model parameters from acceleration pulse data. The present results with regard to the acceleration pulse do not require the coherent movement of the rupture front over the entire circle. The results are applicable to more general cases where the rupture front moves coherently over a certain restricted segment, though the range of the segment has to become wider as the duration of the change in rupture velocity increases.

3D simulation of near-field strong ground motion based on dynamic modeling

1998 ◽  
Vol 88 (6) ◽  
pp. 1445-1456
Author(s):  
Tomohiro Inoue ◽  
Takashi Miyatake
Keyword(s):  
Ground Motion ◽  
Stress Drop ◽  
Strong Ground Motion ◽  
Source Parameters ◽  
Peak Ground Velocity ◽  
Crack Model ◽  
Rupture Velocity ◽  
Ground Acceleration ◽  
Fault Trace ◽  
Strong Ground

Abstract We simulate the strong ground motion generated from the earthquake rupture process on a shallow strike-slip fault using a 3D finite-difference method. The faulting process is modeled using a crack model with fixed rupture velocity. The variability of peak ground velocity patterns, correlated with fault location and source parameters such as stress drop or rupture velocity, is investigated. Our findings suggest that these patterns are strongly affected by rupture directivity and the uppermost depth of the fault or that of the asperity. When a fault breaks the ground surface, the peak ground velocity and the peak ground acceleration show a narrow region of strong motion. When a fault is buried under the ground, the high peak ground velocity zone of the fault-parallel component is apart from the fault trace by a distance comparable to the fault depth. On the other hand, the fault-normal peak ground velocity is a maximum along the fault trace. The fault length (or asperity length) is not so effective for peak ground velocities. The effect of heterogeneity in stress drop and rupture velocity on strong ground motion is also investigated. When stress drop is not uniform but increases linearly with depth from zero at the uppermost depth, the peak ground velocity is reduced. These results help better predict the strong ground motion generated from a potential fault.

Radiation and Generation of Short- and Long-Period Ground Motions from the 2011 Off Tohoku, Japan,Mw9.0 Earthquake

2014 ◽  
Vol 9 (3) ◽  
pp. 281-293 ◽  
Author(s):  
Takashi Furumura ◽  
◽  
Keyword(s):  
Ground Motion ◽  
High Frequency ◽  
Ground Motions ◽  
Tohoku Earthquake ◽  
Sedimentary Basins ◽  
Low Velocity ◽  
Ground Acceleration ◽  
Wooden Frame ◽  
Long Period ◽  
Long Period Ground Motion

Ground motion from theMw9.0 March 11, 2011, Off-Tohoku earthquake recorded by dense seismic networks in Japan, K-NET and KiK-net, clearly demonstrated the high-frequency seismic wavefield radiating from the earthquake source and developing longperiod ground motion in sedimentary basins. The photographic sequence of the visualized wavefield demonstrated the process in which the high-frequency seismic waves radiated from large slips at the top of the subducting Pacific Plate at relatively deeper depth of 25-50 km, which caused multiple large shocks of large (>1000-2000 cm/s2) ground acceleration and several minutes lasting ground motions over a wide area along the Pacific Ocean side of northern Japan. An efficient seismic wave propagation along the subducting Pacific slab and ground motion amplification in a superficial thin low-velocity layer overlying rigid bedrock also enhanced high-frequency (>5 Hz) ground motions very drastically. However, the dominant frequency of the strong ground motion recorded in nearfield station was too high such as to cause serious damage to wooden-frame residences having relatively longer-period resonance period (T= 1-2 s); The velocity response in this frequency band was only about one third to one half of those observed in severely damaged area during the destructiveMw6.9 1995 Kobe earthquake. The 2011 Off-Tohoku earthquake also produced long-period ground motion in sedimentary basins such those at Tokyo’s population center but observation of the long-period ground motion withinT=6-8 s was rather weak and of a level comparable to that of anM7.9 Tonankai earthquake occurring along the Nankai Trough in 1944. This was because the surface wave in this period band was not generated efficiently by the relatively deeper slip over the source fault of the Off-Tohoku earthquake.

A high-frequency magnitude scale

1995 ◽  
Vol 85 (3) ◽  
pp. 825-833
Author(s):  
Gail M. Atkinson ◽  
Thomas C. Hanks
Keyword(s):  
North America ◽  
Ground Motion ◽  
Stress Drop ◽  
High Frequency ◽  
Ground Motions ◽  
Amplitude Spectrum ◽  
Average Stress ◽  
Magnitude Scale ◽  
Eastern North America ◽  
Frequency Magnitude

Abstract A high-frequency magnitude scale (m) is proposed: m=2log⁡a˜hf+3, where ãhf is the high-frequency level of the Fourier amplitude spectrum of acceleration in cm/sec (average or random horizontal component), at a hypocentral or closest fault distance of 10 km. m can be determined from either instrumental data or the felt area of an earthquake. The definition of m has been arranged such that m = M (moment magnitude) for events of “average” stress drop, in both eastern North America (ENA) and California. m provides a measure of the stress drop if M is also known. The observed relationship between m and M indicates that the average stress drop is about 150 bars for ENA earthquakes, and about 70 bars for California earthquakes. The variability of stress drop is much larger in ENA than in California. The chief justification for the m scale is its utility in the interpretation of the large preinstrumental earthquakes that are so important to seismic hazard estimation in eastern North America. For such events, m can be determined more reliably than can M or mN (Nuttli magnitude), and forms a much better basis for estimating high-frequency ground motions. When used as a pair, m and M provide a good index of ground motion over the entire engineering frequency band. If both of these magnitudes can be defined for an earthquake then a ground-motion model, such as the stochastic model, can be used to obtain reliable estimates of response spectra and peak ground motions.

Effects of Nonlinear Soil Behavior on Kappa (κ): Observations from the KiK-Net Database

2021 ◽  
Author(s):  
Chunyang Ji ◽  
Ashly Cabas ◽  
Luis Fabian Bonilla ◽  
Céline Gelis
Keyword(s):  
High Frequency ◽  
Ground Motions ◽  
Damping Ratio ◽  
Nonlinear Behavior ◽  
Soil Behavior ◽  
Ground Acceleration ◽  
Ground Shaking ◽  
Soil Nonlinearity ◽  
Nonlinear Soil Behavior ◽  
Shear Strains

ABSTRACT Soil nonlinear behavior is often triggered in soft sedimentary deposits subjected to strong ground shaking and has led to catastrophic damage to civil infrastructure in many past earthquakes. Nonlinear behavior in soils is associated with large shear strains, increased material damping ratio, and reduced stiffness. However, most investigations of the high-frequency spectral decay parameter κ, which captures attenuation, have focused on low-intensity ground motions inducing only small shear strains. Because studies of the applicability of the κ model when larger deformations are induced are limited, this article investigates the behavior of κ (both κr per record and site-specific κ0 estimates) beyond the linear-elastic regime. About 20 stations from the Kiban–Kyoshin network database, with time-average shear-wave velocities in the upper 30 m between 213 and 626  m/s, are used in this study. We find that the classification scheme used to identify ground motions that trigger soil nonlinear behavior biases estimates of κ0 in the linear and nonlinear regimes. A hybrid method to overcome such bias is proposed considering proxies for in situ deformation (via the shear-strain index) and ground shaking intensity (via peak ground acceleration). Our findings show that soil nonlinearity affects κr and κ0 estimates, but this influence is station dependent. Most κ0 at our sites had a 5%–20% increase at the onset of soil nonlinear behavior. Velocity gradients and impedance contrasts influence the degree of soil nonlinearity and its effects on κr and κ0. Moreover, we observe that other complexities in the wave propagation phenomenon (e.g., scattering and amplifications in the high-frequency range) impose challenges to the application of the κ0 model, including the estimation of negative values of κr.

Site effects of the Denis-Perron dam (SM-3): A case study in Eastern North America

2021 ◽  
pp. 875529302110194
Author(s):  
Daniel Verret ◽  
Denis LeBœuf ◽  
Éric Péloquin
Keyword(s):  
North America ◽  
Ground Motion ◽  
Site Effects ◽  
Transfer Functions ◽  
Ground Motions ◽  
Published Data ◽  
Eastern North America ◽  
Ground Acceleration ◽  
Large Dams ◽  
Moderate Seismicity

Eastern North America (ENA) is part of a region with low-to-moderate seismicity; nonetheless, some significant seismic events have occurred in the last few decades. Recent events have reemphasized the need to review ENA seismicity and ground motion models, along with continually reevaluating and updating procedures related to the seismic safety assessment of hydroelectric infrastructures, particularly large dams in Québec. Furthermore, recent researchers have shown that site-specific characteristics, topography, and valley shapes may significantly aggravate the severity of ground motions. To the best of our knowledge, very few instrumental data from actual earthquakes have been published for examining the site effects of hydroelectric dam structures located in eastern Canada. This article presents an analysis of three small earthquakes that occurred in 1999 and 2002 at the Denis-Perron (SM-3) dam. This dam, the highest in Québec, is a rockfill embankment structure with a height of 171 m and a length of 378 m; it is located in a narrow valley. The ground motion datasets of these earthquakes include the bedrock and dam crest three-component accelerometer recordings. Ground motions are analyzed both in the time and frequency domains. The spectral ratios and transfer functions obtained from these small earthquakes provide new insights into the directionality of resonant frequencies, vibration modes, and site effects for the Denis-Perron dam. The crest amplifications observed for this dam are also compared with previously published data for large dams. New statistical relationships are proposed to establish dam crest amplification on the basis of the peak ground acceleration (PGA) at the foundation.

scholarly journals Broadband Strong-Motion Prediction for Future Nankai-Trough Earthquakes Using Statistical Green’s Function Method and Subsequent Building Damage Evaluation

2021 ◽  
Vol 11 (15) ◽  
pp. 7041
Author(s):  
Baoyintu Baoyintu ◽  
Naren Mandula ◽  
Hiroshi Kawase
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Nankai Trough ◽  
Ground Motions ◽  
Building Damage ◽  
Steel Buildings ◽  
Ground Acceleration ◽  
Attenuation Relations ◽  
Strong Ground Motions ◽  
Strong Ground

We used the Green’s function summation method together with the randomly perturbed asperity sources to sum up broadband statistical Green’s functions of a moderate-size source and predict strong ground motions due to the expected M8.1 to 8.7 Nankai-Trough earthquakes along the southern coast of western Japan. We successfully simulated seismic intensity distributions similar to the past earthquakes and strong ground motions similar to the empirical attenuation relations of peak ground acceleration and velocity. Using these results, we predicted building damage by non-linear response analyses and find that at the regions close to the source, as well as regions with relatively thick, soft sediments such as the shoreline and alluvium valleys along the rivers, there is a possibility of severe damage regardless of the types of buildings. Moreover, the predicted damage ratios for buildings built before 1981 are much higher than those built after because of the significant code modifications in 1981. We also find that the damage ratio is highest for steel buildings, followed by wooden houses, and then reinforced concrete buildings.

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