Chu-Chuan Peter Tsai

A New Method for Estimation of the Attenuation Relationship with Variance Components

A new approach to estimation of strong-motion attenuation relations with multiple variance components is proposed. In the terminology of Abrahamson and Youngs (1992), the attenuation relationship considered is a “mixed” model, where the regression coefficients are treated as the “fixed effects” and the components of deviations are treated as the “random effects.” Following Dempster et al. (1981), an MLR procedure is adopted, which performs the maximum likelihood (ML) estimation of mixed models where the fixed effects are treated as random (R) effects with infinite variance. Both the fixed and random effects are estimated in a unified framework via an expectation-maximization (EM) algorithm. A modification of the MLR procedure is performed to accommodate nonlinear attenuation models. Compared with other methods, our proposal requires no additional regression or searching procedures and hence is neat and simple. Explicit formulae are provided for the variance estimates of the estimated model parameters. Two types of the strong-motion prediction are discussed: the unconditional prediction without accounting for the site-specific deviation, and the conditional prediction that further incorporates that deviation. A simulation study shows that the proposed procedure yields estimates with smallest biases and least computation time, compared with the EM procedure in Brillinger and Preisler (1985) and with the two-stage method in Joyner and Boore (1993). The new method is applied to a dataset of Taiwans ground motions for illustration. This application reveals that the site-to-site variability in this dataset is remarkable; hence, the ergodic assumption ignoring “the spatial variability of ground motions” (Anderson and Brune, 1999) may not be suitable for probabilistic seismic hazard analyses in Taiwan. Also, in this application the conditional prediction is shown to be much more accurate than the unconditional prediction. Manuscript received 23 July 2001.

A Model for the High-Cut Process of Strong-Motion Accelerations in Terms of Distance, Magnitude, and Site Condition: An Example from the SMART 1 Array, Lotung, Taiwan

Parameters controlling the high-cut process of strong-motion accelerations are analyzed using the recordings collected from the SMART 1 array in Lotung, Taiwan. A regression model in terms of distance, earthquake magnitude, and site condition is generally found to be suitable to describe the parameters under investigation. Results show that the high-cut process is controlled by both the site and source effects, which might bring resolution to the long-standing controversy over the origin of the cutoff frequency. In this note, it becomes almost certain that distance is the least significant parameter controlling the high-cut process.

An Observation of Rupture Pulses of the 20 September 1999 Chi-Chi, Taiwan, Earthquake from Near-Field Seismograms

The ground-velocity recordings of the 20 September 1999, Chi-Chi, Taiwan earthquake recorded at stations near the ruptured fault trace show a simple, large-amplitude, and long-period pulse following the S wave, which is closely associated with the surface faulting and the rupture process of thrust faulting. The conspicuous pulse on the ground-velocity seismogram following the S -wave arrival, called the S 1 phase, is interpreted as the superposition of the rupture pulses that nucleate at an asperity near and underneath the station and propagate up-dip and laterally along the fault plane toward the surface stations. The arrival times of the S 1 phase and the onsets of the permanent displacement at stations near and along the ruptured fault trace increase with hypocentral distance, suggesting that the rupture of the Chi-Chi earthquake might have initiated at the hypocenter of the mainshock and propagated both upward and laterally from south to north. On the basis of the travel-time differences between the S 1 phase and the direct S wave at the stations near and along the ruptured fault trace, the rupture velocities varied from 2.28 to 2.69 km/sec, with an average rupture velocity of about 2.49 km/sec. The rupture velocities decreased from south to north.

Estimates of Stress Drop of the Chi-Chi, Taiwan, Earthquake of 20 September 1999 from Near-Field Seismograms

The apparent stress and stress drop of the Chi-Chi, Taiwan, earthquake are estimated from near-field seismograms. The estimated apparent stress and stress drop for the southern part of the fault are about 100 bars lower than those for the northern part. The estimated ratio E s/ M also suggests that there is a higher dynamic stress drop in the northern part than in the southern one. This indicates the transformation of a higher percentage of strain energy into the seismic-wave energy in the northern part than in the southern part. Based on a parameter proposed by Ramon Zuniga (1993), we propose that the stress model of frictional overshoot can interpret the rupture of the Chelungpu fault, on which the Chi-Chi, Taiwan, earthquake occurred. Manuscript received 31 July 2000.

Estimates of source parameters for the 1999 Chi-Chi, Taiwan, earthquake based on Brune's source model

The general features of the rupture of the 1999 Chi-Chi, Taiwan, earthquake ( M s 7.6) can be explained by the displacement waveforms derived from the accelerograms recorded at short distances from the fault traces. Applying Brunes model, we have determined important source parameters, such as rise time, stress drop, offset, and particle velocity. Generally, the earthquake is characterized as having had two distinct fault segments. The southern segment, dominated by thrust motion, started from the focus on a fault plane raking at 78° and extended about 30 km to the north. The northern segment, dominated by thrust with significant strike-slip motion, began next to the end of the southern segment on a fault plane raking at 53° and extended northward for 25 km. Slips in the southern segment were followed by a small dislocation (∼1 m), while those in the northern segment were followed by a much larger dislocation (∼9 m). The average slip velocity was distributed at 34-49 cm/sec, along the southern segment, and an unusual slip velocity exceeding 2 m/sec was observed along the northern segment. Furthermore, the southern segment experienced a rise time of 1.8 sec and a stress drop of 65 bars, in contrast to a rise time longer than 4 sec and a stress drop larger than 300 bars registered to the north. Our results also indicate that, along the southern segment, the rupture propagated northward at an average velocity of 2.84 km/sec, but along the northern segment, the rate declined to less than 2 km/sec. The difference in the source parameters between these two segments suggests that the rupturing associated with the Chi-Chi earthquake may have encountered a resistive patch and changed course in the middle part of the fault. After crushing that resistance, the long rise time and high stress drop probably caused substantially slower motion and larger slip along the northern segment. Manuscript received 10 November 2000.

Characteristics of strong ground motion across a thrust fault tip from the September 21, 1999, Chi‐Chi, Taiwan earthquake

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.

Probabilistic Seismic Hazard Analysis Considering Nonlinear Site Effect

A modified method is proposed for the probabilistic seismic hazard analysis considering nonlinear site effect. A case study is presented to show the hazard curves that consider the nonlinearity of the soil layers at Gilroy #2. Source parameters and an earthquake occurrence model are assigned to the Caleveras fault, which is assumed the dominant seismic source to the site. A relationship between ground surface and bedrock accelerations at the site is established by recordings from three earthquake events using the program NONLI3, which calculates the nonlinear responses of the soil layers to strong motions. Various values of standard errors of the estimated surface PGA, given the bedrock motions, are assumed to perform a sensitivity analysis. An alternative nonlinear relation is included in the case study. In addition to the nonlinear models, a linear-response model is also performed using the same soil profile at Gilroy #2. The results demonstrate that the hazard curves are sensitive to the standard error of the estimated surface PGA values at the site. The hazard curve may be severely distorted if the soil condition of a nonlinear site is treated inadequately. The alternative nonlinear model obtained empirically from regression analysis and the linear response model are both unsuitable for the hazard assessment considering nonlinear site effect.

The Path Effect in Ground-Motion Variability: An Application of the Variance-Components Technique

Chen and Tsai (2002) proposed a variance-components technique to decompose the prediction error of ground motions into three components: the earthquake-to-earthquake, the site-to-site, and the residual errors, with three corresponding variance components. From a data set of over seven thousand records with various site conditions, Tsai and Chen (2003) found that the relative percentages of the three components of variances are dependent upon the numbers of earthquake events and stations providing the sampled records, and the variances of the earthquake and the site components are in general smaller than that of the residual. Noting that the residual encompasses the path-to-path error in ground motions, in this work we show that if the variability of the path effect can be sensibly specified a priori, the path- to-path component of error can be further differentiated from the residual errors. The prediction error can be reduced dramatically after ground-motion estimates have been corrected for the site as well as the path effects of variability in ground motion. Although the path component of error, unlike the site component, cannot be directly eliminated from the ground-motion estimates for future earthquake events, we propose to account for the path effect by turning it into useful information such as the three-dimensional (3D) velocity structural model obtained by the inversion technique. If a 3D model describing the path effect for each source-to-site pair can be constructed, the ground-motion prediction with both the site and path effects accounted for may be feasibly practical.

Ground Motion Modeling for Seismic Hazard Analysis in the Near-source Regime: An Asperity Model

Abstract—A new, yet simple, method using the asperity model to estimate ground motion in the near-source regime for probabilistic seismic hazard analyses is proposed in this study. This near-source model differs from conventional empirical attenuation equations. It correlates peak ground motions with the local contributing source in terms of the static stress drop released non-uniformly on the causative fault plane rather than with the whole seismic source in terms of magnitude. Here the model is simplified such that ground motions at a rock or firm soil site near extended vertical strike-slip faults are dominated by direct shear waves. The proposed model is tested by comparing its predictions with strong ground motion observations from the 1979 Imperial Valley and the 1984 Morgan Hill earthquakes. The results have revealed that ground motions in the near-source region can be adequately predicted using the asperity model with appropriate calibration factors. The directivity effect of ground motion in the near-source region is negligible for high-frequency accelerations. The cut-off frequency (ƒmax ) at a site is an important parameter in the near-source region. Higher values of ƒmax yield higher estimates of peak ground accelerations. For high-frequency structures, ƒmax should be carefully estimated. In the near- source region both non-uniform and uniform source models can produce non-stationary high-frequency ground motions. Peak motions may not be caused by the nearest sections of the fault (even if the uniform source model is considered).