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Estimates of Source Parameters of Two Large Aftershocks of the 1999 Chi-Chi, Taiwan, Earthquake in the Chia-Yi Area
Abstract
Two large aftershocks of the 1999 Chi-Chi earthquake (ML=6.4 and 6) occurred to the south of the Chelungpu fault and in the Chia-Yi in Taiwan. Near-field seismograms estimated some source parameters of the two events. The near-field displacement spectra can be described by Brune's ω-square model. The estimated values of stress drop (Δσ), apparent stress (σa), and scaled energy (Es/Mo), of these two events varied from station to station with mean values of: Δσ=991 bars, σa=402 bars, and Es/Mo=1.3×10-3 for the ML6.4 event; and Δσ=831 bars, σa=337 bars, and Es/Mo=1.0×10-3 for the ML6.0 one. This shows a high dynamic stress drop between these two events. The larger values calculated from the ML6.4 event indicated a higher percentage transformation of strain energy into seismic-wave energy comparing to the ML6.0 event.
... There exists a good azimuthal covering distribution of the stations in far field used in this study, with regard to the epicenter of the examined event, displayed in Figure 1. The focal mechanism of this event is related thrust fault and the fault plane solution is (strike, dip, rake)=( 46 , 52, 125) by Harvard CMT shown in Figure 2. Since 1991, the Central Weather Bureau (CWB) in Taiwan has constructed an island-wide network composed of more 1218 The Kinematic Source Process of the MW 5.9, 1999 Chia-Yi Taiwan Earthquake from Teleseismic Data Using the Hybrid Blind Deconvolution Method than 700 free-field strong-motion stations [2]. Several stations in the vicinity of the epicenter well recorded and generated seismograms of the event. ...
The kinematics rupture process of the Chia-Yi earthquake occurred on October 22, 1999 (Mw 5.9) in Taiwan is investigated. The hybrid blind deconvolution technique is applied to the teleseismic waves to invert source parameters, including slip amplitudes, rise times and rupture velocities on the fault. From the directivity effect of the fault, the actual fault plane is determined as east dipping. According to the derived ASFT, the total duration of the rupture process is 6.5 sec. A good correlation notices that the larger slip amplitude corresponds to the longer rise time of the subfault. By using the inverted source parameters and combining the stochastic method for finite fault, the strong ground motions of 12 stations at epicentral distances ranging from 3.28 to 29 km are simulated. The results show that the agreements between simulated and recorded spectra are quite satisfying. It means that the inverted source parameters are reliable and the stations where located at near source distance are dominated by source effects. The inhomogeneous distribution of slip and the variable corner frequency could play important roles in the simulation process. Although the source effects are dominant, there are some significant discrepancies existing at stations, implying the site effects are influential.
... Moreover, readings of the low-frequency flat levels and corner frequencies from displacement spectra are usually done by eye, making results subjective and, consequently, strongly affecting the estimation for stress drop (Moya et al. 2000). Recently, Huang et al. (2002) also suggested high dynamic stress drop proportional to the magnitude of the aftershocks of 1999 Chi-Chi earthquake. Their estimates are ∆σ = 991 bars for M L = 6.4 aftershock and ∆σ = 831 bars for M L = 6.0 one, respectively, by calculating the integrals of squared velocities and squared displacements. ...
Empirical regional attenuation relationships for the amplitude of S and Lg waves were achieved by performing regressions over a large number of accelerograms, collected from TSMIP stations in southwestern Taiwan over a ∼7-year period. From estimations of effective ground-motion duration, utilized to characterize the source term and path effects, a piecewise continuous duration function relating to hypocentral distance was derived. For simplicity, Brune's ω-square model was used in this article. Assuming a high-frequency approximated decay parameter of κ 0 = 0.03 sec and static stress drop Δσ = 100 bars for the averaging characteristics of the source spectra, the attenuation curves of peak horizontal accelerations that relate to the hypocentral distance for the given moment magnitudes were effectively obtained using random vibration theory. However, the current model cannot be arbitrarily generalized for the prediction by individual specific earthquake and does not include extended faults based on the source assumption applied. Due to sensitive variation of peak ground motion predictions (strongly associated with the stress drop and attenuation factors), it is suggested that the source parameters and the sites chosen should be localized into several subsets (as far as this is possible) through analyses of historic earthquakes and strong-motion records. In practice, this work should be valid in predicting peak ground motions well when simulating a characterized event.
... Kanamori and Heaton 2000;Kanamori and Rivera 2004). The measured values of ê range from 10 -6 to 10 -3 (Kanamori 1977;Vassiliou and Kanamori 1982;Kikuchi and Fukao 1988;Choy and Boatwright 1995;Brodsky and Kanamori 2001;Hwang et al. 2001;Huang et al. 2002Huang et al. , 2009Kinoshita and Ohike 2002). A large range of ê might be due to the uncertainty of measuring E s , because the signals are often affected by several factors, including finite frequency bandwidth limitation as the major one (cf. ...
The correlation of the scaled energy, ê = E
s/M
0, versus earthquake magnitude, M
s, is studied based on two models: (1) Model 1 based on the use of the time function of the average displacements, with a ω
−2 source spectrum, across a fault plane; and (2) Model 2 based on the use of the time function of the average displacements, with a ω
−3 source spectrum, across a fault plane. For the second model, there are two cases: (a) As τ ≒ T, where τ is the rise time and T the rupture time, lg(ê) ~ −M
s; and (b) As τ ≪ T, lg(ê) ~ −(1/2)M
s. The second model leads to a negative value of ê. This means that Model 2 cannot work for studying the present problem. The results obtained from Model 1 suggest that the source model is a factor, yet not a unique one, in controlling the correlation of ê versus M
s.
... An average stress drop of 30 bar was specified as an input parameter in the predictive model. As indicated from previous investigations (Ou and Tsai, 1993;Huang et al., 1996;Huang and Yeh, 1999;Wu, 2000;Huang et al., 2002), the variation in the estimation of the stress drop for earthquakes in different regions of Taiwan might be large enough to result in a significant bias in the ground motion prediction. These potential sources of error will be unavoidable when using a general source model with fixed parameters. ...
A stochastic method called the random vibration theory (Boore, 1983) has been used to estimate the peak ground motions caused by shallow moderate-to-large earthquakes in the Taiwan area. Adopting Brune’s ω-square source spectrum, attenuation models for PGA and PGV were derived from path-dependent parameters which were empirically modeled from about one thousand accelerograms recorded at reference sites mostly located in a mountain area and which have been recognized as rock sites without soil amplification. Consequently, the predicted horizontal peak ground motions at the reference sites, are generally comparable to these observed. A total number of 11,915 accelerograms recorded from 735 free-field stations of the Taiwan Strong Motion Network (TSMN) were used to estimate the site factors by taking the motions from the predictive models as references. Results from soil sites reveal site amplification factors of approximately 2.0 ~ 3.5 for PGA and about 1.3 ~ 2.6 for PGV. Finally, as a result of amplitude corrections with those empirical site factors, about 75% of analyzed earthquakes are well constrained in ground motion predictions, having average misfits ranging from 0.30 to 0.50. In addition, two simple indices, R
0.57 and R
0.38, are proposed in this study to evaluate the validity of intensity map prediction for public information reports. The average percentages of qualified stations for peak acceleration residuals less than R
0.57 and R
0.38 can reach 75% and 54%, respectively, for most earthquakes. Such a performance would be good enough to produce a faithful intensity map for a moderate scenario event in the Taiwan region.
In this work, we reviewed the studies of aftershocks in Taiwan for the following topics: The spatial-Temporal distributions and focal-plane solutions of aftershocks of thirty larger earthquakes with magnitudes>5; the correlations between mainshock and the largest aftershock based on dependence of the differences in magnitudes (ΔM), occurrence times (ΔT), epicenters (ΔH), and focal depths (ΔD) upon the mainshock magnitude, Mm; magnitude-dependence of p value of the Omori's law of aftershocks; the correlation between the b-value of the Gutenberg-Richter's frequency-magnitude law and the p value; the application of the epidemic-Type aftershock sequences (ETAS) model to describe the aftershock sequence; the mechanisms of triggering aftershocks; and dynamical modeling of aftershocks. The main results are: (1) The spatial distribution of aftershocks for some earthquakes is consistent with the recognized fault; (2) Unlike Båth's law, ΔM slightly increases with Mm; (3) ΔT does not correlate with Mm; (4) ΔD does not correlate with Mm; (5) ΔT somewhat increases with ΔD; (6) The p value slightly increases with Mm; (7) There is a negative correlation between the b and p values. (8) There was seismic quiescence over a broader region of Taiwan before the 1999 Chi-Chi earthquake; (9) Both the static and dynamic stress changes trigger aftershocks; and (10) Dynamical modeling shows that a decrease in elastic modulus is a significant factor in triggering aftershocks. © 2016 Terrestrial, Atmospheric and Oceanic Sciences (TAO). All rights reserved.
This paper reviews studies on earthquake energies, seismic efficiency, radiation efficiency, scaled energy and energy- magnitude law conducted by Taiwan seismologists and foreigners who used seismic data from Taiwan to study these problems. Sufficient seismic and geodetic data permits energy measurements from the 20 September 1999 Ms 7.6 Chi-Chi earthquake and its larger-sized aftershocks. The results provide significant information on earthquake physics. The issues in this review paper include measures of these physical quantities and related theoretical or analytical studies of these physical quantities made by both Taiwan's seismologists and foreigners who used seismic data of Taiwan to study related problems.
The scaling law of seismic radiation energy, E
s
, versus surface-wave magnitude, M
s
, proposed by Gutenberg and Richter (1956) was originally based on earthquakes with M
s
> 5.5. In this review study, we examine if this law is valid for 0
Radiated energies from shallow earthquakes with magnitudes >=5.8 that occurred between 1986 and 1991 are used to examine global patterns of energy release and apparent stress. In contrast to traditional methods which have relied upon empirical formulas, these energies are computed through direct spectral analysis of broadband seismic waveforms. Velocity-squared spectra of body waves are integrated after they have been corrected for effects arising from depth phases, frequency-dependent attenuation, and focal mechanism. The least squares regression fit of energy ES to surface wave magnitude MS for a global set of 397 earthquakes yields log ES=4.4+1.5MS, which implies that the Gutenberg-Richter relationship overestimates the energies of earthquakes. The least squares fit between ES and seismic moment M0 is given by the relationship ES=1.6×10-5M0, which yields 0.47 MPa as the average global value of apparent stress. However, the regression lines of both ES-MS and ES-M0 yield poor empirical predictors for the actual energy radiated by any given earthquake; the scatter of data is more than an order of magnitude about each of the regression lines.On the other hand, global variations between ES and M0, while large, are not random. When subsets of ES-M0 are plotted as function of seismic region and faulting type, the scatter in data is substantially reduced. The ES-M0 fits for many seismic regions and tectonic environments are very distinctive, and a characteristic apparent stress tauc can be derived. The lowest apparent stresses (3.0 MPa) are associated with strike-slip earthquakes that occur at oceanic ridge-ridge transforms and in intraplate environments seaward of island arcs. Intermediate values of apparent stress (1.5
Recently, a renewed interest in an old controversy has revived surrounding the idea that
shear stress on a fault after an earthquake rupture may reach a value that differs from the
one corresponding to dynamic friction (Smith et al., 1991; Brune et al., 1986). The case in
which final stress is equal to the dynamic frictional stress is the well-known Orowan's
hypothesis (Orowan, 1960). Two other outcomes are also possible, a) final stress (eg
averaged over the fault surface) is greater than frictional stress, a case known as partial ...
Near fault tip strong motion records from the northern part of the major earthquake (Mw=7.6), namely the Chi-Chi earthquake on September 21, 1999 in central Taiwan demonstrated systematic differences on the hanging wall and footwall, and simulated by the finite element method. The extraordinary ground motion differences on either side of the northern fault tip can be explained by a 2-dimension kinematic source model with fault rupture breaking to surface. In this study, the earthquake faulting was considered as bilateral from the center of a low angle thrust fault which is 30 km in length with a dip angle of 31°. Based on waveform modeling, the source rupture velocity, rise-time and dislocation of 2.0 km/sec, 5 sec and 6 meters, respectively are suggested. The results of this study show that on the northern part of the Chi-Chi earthquake fault there was lower rupture velocity and longer rise-time of the fault slip than that previously reported. Furthermore, the effects of surface breaking from the fault movement contributed large ground deformations near the fault tip and, consequently, induced extensive damage.
The source mechanism of earthquakes in the California-Nevada region was studied using surface wave analyses, surface displacement observations in the source region, magnitude determinations, and accurate epicenter locations. Fourier analyses of surface waves from thirteen earthquakes in the Parkfield region have yielded the following relationship between seismic moment, Mo and Richter magnitude, M,: log Mo -- 1.4 M, n u 17.0, where 3 < M, < 6. The following relation between the surface wave envelope parameter AR and seismic moment was obtained: log Mo -- log ARsoo n u 20.1. This relation was used to estimate the seismic moment of 259 additional earthquakes in the western United States. The combined data yield the following relationship between moment and local magnitude: log Mo -- 1.7 M, n u 15.1, where 3 < M, < 6. These data together with the Gutenberg-Richter energy-magnitude formula suggest that the average stress multiplied by the seismic efficiency is about 7 bars for small earthquakes at Parkfield and in the Imperial Valley, about 30 bars for small earthquakes near Wheeler Ridge on the White Wolf fault, and over 100 bars for small earthq.uakes in the Arizona-Nevada and Laguna Salada (Bain California) regions. Field observations of displacement associated with eight Parkfield shocks, along with estimates of fault area, indicate that fault dimensions similar to the values found earlier for the Imperial earthquake are the rule rather than the exception for small earthquakes along the San Andreas fault. Stress drops appear to be about 10% of the average stress multiplied by the seismic efficiency. The revised curve for the moment versus magnitude further emphasizes that small earthquakes are not important in strain release and indicate that the zone of shear may be about 6 km in vertical extent for the Imperial Valley and even less for oceanic transform faults.
In the early morning (01:47 local time) of September 21, 1999, the
largest earthquake of the century in Taiwan (Mw=7.6, ML=7.3) struck the
central island near the small town of Chi-Chi. The hypocenter was
located by the Central Weather Bureau Seismological Center at
23.87°N, 120.75°E, with a depth of about 7 km.There were
extensive surface ruptures for about 85 km along the Chelungpu fault
with vertical thrust and left lateral strike-slip offsets. The maximum
displacement of about 9.8 meters is among the largest fault movements
ever measured for modern earthquakes. There was severe destruction in
the towns of Chungliao, Nantou,Taichung, FengYuan, and Tungshi, with
over 2300 fatalities and 8700 injuries.
There remains much uncertainty on the absolute elastic wave energy released by fault rupture. Few direct estimates of the partition of seismic wave energy in ground shaking have been made. In this work, ground particle velocities from integrated accelerograms are used to compute the kinetic energy crossing unit area per unit time. Simplified theory for the near-field strong-motion case would appear to give a valid lower energy bound; the wave attenuation does not present a major problem. The partition of energy in predominantly P, S, and surface wave portions, for given frequency windows, is tabulated using strong-motion accelerograms recorded at different azimuths to the fault-sources of six California earthquakes (5.5M
LM
L and momentM
0 correlations indicate significantly higher overall wave energy outputs than expected, but further calibration is needed.The study demonstrates that stable estimates of frequency-dependent seismic wave energies in the nearfield can be obtained from strong-motion records. Hence, energy flux may have a wider application to risk mapping than previously thought. In particular, a shift from peak acceleration scaling to (kinetic) energy inputs for engineering design appears to involve only routine processing.
We have integrated velocity squared spectra in order to determine the seismic energy radiated during fault rupture. The high frequency spectral fall-off and the shape of the spectrum at the corner frequency are critical to the energy calculation. High frequency spectral fall-offs of ω−2 beyond the corner frequency, in a Brune (1970) source model, return radiated energies approximately equal to that of an Orowan (1960) type fault failure, where the final stress level is equal to the dynamic frictional stress. Any spectra with an extended intermediate slope of ω−1 would therefore result in higher radiated energies. Savage and Wood (1971) proposed a model in which the final stress level was less than the dynamic stress level and that this was the result of “overshoot”. They based their model on the observation that the ratio of twice the apparent stress to the stress drop was typically around 0.3. We show that for such a ratio to exist high frequency spectral fall-offs of ≈ ω−3 would be required. Composite spectra have been constructed for several moderate to large earthquakes, these spectra have been compared to that predicted by the Haskell (1966) model and velocity squared spectra have been integrated to determine the radiated energy. In all cases this ratio, twice the apparent stress to the stress drop, is greater than or equal to one, violating the Savage and Wood (1971) inequality, and provides evidence against “overshoot” as a source model.
An earthquake model is derived by considering the effective stress available to accelerate the sides of the fault. The model describes near- and far-field displacement-time functions and spectra and includes the effect of fractional stress drop. It successfully explains the near- and far-field spectra observed for earthquakes and indicates that effective stresses are of the order of 100 bars. For this stress, the estimated upper limit of near-fault particle velocity is 100 cm/sec, and the estimated upper limit for accelerations is approximately 2g at 10 Hz and proportionally lower for lower frequencies. The near field displacement u is approximately given by u(t) = (sigma/mu) beta r (1 - exp(-t/r)) where sigma is the effective stress, mu is the rigidity, beta is the shear wave velocity, and tau is of the order of the dimension of the fault divided by the shear-wave velocity. The corresponding spectrum is Omega(omega) = (sigma beta)/mu 1/(omega(omega^2 + tau^-2)^(1/2)). The rms average far-field spectru