Ground Motion Displacement Research Articles

A Simplified Displacement Spectrum Model Based on Recent Digital Strong-Motion Data

ABSTRACT Displacement spectrum is an essential aspect in displacement-based seismic design (DBSD) philosophy that, comparing to force-based, describes in a more explicit way the structural response and the damage. To better apply DBSD, the displacement spectrum model in period ranging up to 15 s is rephrased using recent high-quality digital strong motion data worldwide, particularly from China territory. After systematical analysis conducted of the influence factors as magnitude, distance, and site conditions on displacement spectrum, it is found that magnitude played a more predominant role in characterizing displacement spectrum that is normalized by peak ground-motion displacement than site conditions and distance. A simplified magnitude-scaled model consisting of four straight line segments constrained by three corner periods and their corresponding amplitudes is proposed to model the normalized displacement spectrum. Comparison with seismic data and the published models verifies the applicability of the proposed model especially for strong earthquakes. Residual analysis indicates the simplified model satisfactorily matches the records with respect to magnitude and distance but the variability of model prediction slightly tends to grow as magnitude and distance increase.

Baseline correction of near-fault ground motion records based on the hilbert spectral analysis

A new automatic baseline correction method based on the Hilbert spectral analysis (HSA) is proposed to recover a relatively reasonable time history of baseline offset, permanent displacement, and stable peak ground motion displacement (PGD) from a raw near-fault ground motion record. This method can get rid of the selection of the start time of strong motion (corresponding to t1 in traditional methods) by an adaptive extraction procedure, then a stable PGD as well as an accurate permanent displacement can be obtained. For baseline offsets, there is no two-stage-segment assumption in this procedure, and the extracted time histories of these offsets include complex frequency changes, which is more consistent with the explanations of causes for baseline offsets. All causes of baseline offsets are treated as contaminants that exist in all frequency ranges in a record. Uncontaminated components can be extracted from the original record by the HSA, then information about strong motions can be retained as much as possible. The residual part is regarded as a heavily contaminated component of which the energy of the noise rivals that of the real ground motion. It is corrected based on only one time point. Finally, the corrected record is contributed by both of the uncontaminated and adjusted contaminated components. The HSA method, which depends on the energy distribution of original record in different frequency component, can obtain the baseline offset, PGD, and permanent displacement reasonably, stably, and automatically.

Modified Multi-Support Response Spectrum Analysis of Structures with Multiple Supports under Incoherent Ground Excitation

This study develops a modified multi-support response spectrum (MSRS) method, in order to efficiently and accurately calculate the response of multi-support structures under incoherent ground motions. The modified MSRS method adopts three ancillary processes, constructing structural displacement vectors or constructing infinite stiffness members or increasing the degrees of freedom at structural supports. Then, the modified MSRS method is verified in a comparison with the existing MSRS method through a model of a five-span reinforced concrete continuous rigid frame bridge. Finally, the collective structural response spectrum, the structural power spectrum, and the simplified structural power spectrum are deduced from the equation of the motion taking ground motion displacements as the input, and validated through the same bridge model.

PROPOSITION OF A SPECTRAL AMPLIFICATION MODEL FOR NEAR FAULT DIRECTIVITY EFFECT WITH UTILIZING PROBABILISTIC EARTHQUAKE SCENARIOS

Near fault ground motions with directivity effect show larger spectral demands due to their specific waveform features. Directivity effect occur due to S-wave polarization when the fault rupture propagation and waveform travel direction coincide on each other. In this situation, a pulse arises in the beginning of ground motion displacement and velocity waveforms which is mostly seen in the fault normal direction. The pulse period (Tp) is directly proportional to the earthquake magnitude (moment magnitude, Mw) and its amplitude is inversely proportional to the rupture distance (Rrup) from the site. The other characteristic of the near fault ground motions due to S-wave polarization is known as “Fling Step” in which a residual displacement is seen in the fault parallel displacement waveform. This study summarizes the observations from the effect of near fault ground motions on design spectrum. The results of these observations are used to develop simplified equations for incorporation of near fault effect in design spectrum. Probabilistic seismic hazard scenarios are utilized in this study in order to investigate the effect of fault seismicity, fault length (characteristic magnitude of the fault), pulse period and source-to-site geometry on the level of spectral amplification due to directivity effect. The near fault effect is modelled with assembling two narrow-band directivity models (Shahi and Baker 2011; Chiou and Spudich 2013) on the probabilistic seismic hazard scenarios respectively. In the last part of this study the significance of seismological and geometrical parameters on the level of spectral amplification due to directivity will be shown and discussed. The results are used to propose relationships for the incorporation of near fault directivity effect for different geometrical distributions of the sites around the fault.

A new baseline correction method for near-fault strong-motion records based on the target final displacement

Most current baseline correction methods for near-fault ground motion records focus on eliminating and minimizing baseline errors and obtaining true ground motion records that are in accordance with GPS-measured coseismic displacements. Though these methods can recover true ground motions, the single value of ground permanent displacement cannot meet the requirement of seismic response analysis of fault-crossing bridge with the consideration of various levels of relative static displacements. Besides, the corrected final displacements are often too large which will cause an extremely large pseudo-static response and a relatively small dynamic response in bridge structures. To provide across-fault seismic excitations with a reasonable series of final displacements, a new baseline correction scheme based on the target final displacement is proposed in this study, in which an additional offset displacement is introduced based on the Iwan correction scheme. The new baseline correction scheme aims at modifying the pseudo-static displacement of ground motion records to facilitate the agreement between the achieved final displacement and the target final displacement. The correction scheme is then examined in three aspects including time histories, response spectra and bridge responses. The analysis results indicate that sets of the corrected time history records with a large range of final displacements can be well achieved with a minor influence on spectral characteristics. The seismic response analysis of a cable-stayed bridge crossing a dip-slip fault-rupture zone shows that the pseudo-static response can be controlled, meanwhile, the dynamic response remains almost intact by using the new baseline correction scheme. This work can be used as a reference for input excitations of bridge crossing fault-rupture zones.

The determination of interseismic, coseismic and postseismic deformations caused by the Gökçeada-Samothraki earthquake (2014, Mw: 6.9) based on GNSS data

Since the 1990s, seismic deformations have been commonly determined using the Global Navigation Satellite System (GNSS). Recently, the GNSS systems have become even more powerful with the use of new technologies in innovative studies. In this study, the GNSS data was used to investigate interseismic, coseismic and postseismic deformation and velocity of the Gökçeada-Samothraki earthquake (Mw = 6.9) that occurred on May 24, 2014. The data was obtained at 30 s (0.033 Hz) and 1 s (1 Hz) intervals from the GNSS receivers in the network of Continuously Operating Reference Stations, Turkey (CORS-TR). For the interseismic period, the daily coordinate time series of 12 stations located within 90–250 km of the earthquake epicenter was evaluated for the displacement of stations over a period of approximately 2000 days prior to the day of the earthquakes, from October 1, 2008 to May 23, 2014. In order to analyze the ground motion displacement during the Gökçeada-Samothraki earthquake, 1 Hz data from 8 continuous GNSS stations was processed using precise point positioning (PPP) and relative positioning methods to estimate the epoch-by-epoch positions of the stations. During the earthquake, coseismic displacements of approximately 7 and 30 mm were detected in the NW direction at the YENC and CANA stations, respectively. However, at the IPSA station, a coseismic deformation of 20 mm was observed in the NE direction. There were no significant changes at the other stations during the earthquake. For the postseismic period, the daily coordinate time series of the 12 stations were evaluated for station displacements for 570 days after the day of the earthquakes, from May 24, 2014 to January 1, 2016. The results demonstrated that no significant postseismic deformation with the exception of the EDIR station. An abnormal deformation caused by local factors was determined at the EDIR station. In this study, the PPP and the relative solution were also compared in terms of capturing the earthquake wave motion. The results demonstrated that the PPP-based solutions showed good agreement with those of relative positioning in terms of the ability to capture coseismic displacement.

A strong-motion hot spot of the 2016 Meinong, Taiwan, earthquake (Mw = 6.4)

Despite a moderate magnitude, M_w = 6.4, the 5 February 2016 Meinong, Taiwan, earthquake caused significant damage in Tainan City and the surrounding areas. Several seismograms display an impulsive S-wave velocity pulse with an amplitude of about 1 m s-1, which is similar to large S-wave pulses recorded for the past several larger damaging earthquakes, such as the 1995 Kobe, Japan, earthquake (M_w = 6.9) and the 1994 Northridge, California, earthquake (M_w = 6.7). The observed PGV in the Tainan area is about 10 times larger than the median PGV of M_w = 6.4 crustal earthquakes in Taiwan. We investigate the cause of the localized strong ground motions. The peak-to-peak ground-motion displacement at the basin sites near Tainan is about 35 times larger than that at a mountain site with a similar epicentral distance. At some frequency bands (0.9 - 1.1 Hz), the amplitude ratio is as large as 200. Using the focal mechanism of this earthquake, typical “soft” and “hard” crustal structures, and directivity inferred from the observed waveforms and the slip distribution, we show that the combined effect yields an amplitude ratio of 17 to 34. The larger amplitude ratios at higher frequency bands can be probably due to the effects of complex 3-D basin structures. The result indicates that even from a moderate event, if these effects simultaneously work together toward amplifying ground motions, the extremely large ground motions as observed in Tainan can occur. Such occurrences should be taken into consideration in hazard mitigation measures in the place with frequent moderate earthquakes.

Real time monitoring ground motion using GPS with real time corrections

The high rate GPS velocity determination technology which is based on the broadcast ephemeris and epoch differenced model can retrieve displacement of ground motion with the precision of a few centimetres to decimetres in real time. Moreover, the precision of the recovered displacement can be improved if the un-modelled errors such as broadcast ephemeris residuals, atmospheric residuals, multipath effects and high frequency noise are tackled more accurately. In this paper, we propose a method to improve the precision of the recovered displacement by appropriately making use of reference station corrections. For the reference stations, the coordinates are highly constrained to extract the error corrections that are to be broadcast via a communication link to the rover. After correcting the rover’s observations, some errors such as ephemeris residuals and atmospheric residuals are effectively eliminated or at least reduced. This improves the accuracy of the observations and thus enhances the reliability of the velocity estimation. The displacement can be recovered by integrating the estimated velocity after de-trending using a linear trend that is caused by the un-corrected residuals. The series of validation results in the experiment have shown that the displacement of the simulated motion can be real time recovered with a precision of 1–2 cm, and is thus applicable for real time monitoring of the ground motion.

Rupture process of the Lorca (southeast Spain) 11 May 2011 (M w = 5.1) earthquake

On 11 May 2011, a M w = 5.1 earthquake shook the town of Lorca (SE Spain) causing a disproportionately large damage for its magnitude. In order to contribute to knowledge of the behavior of the active faults present in the region and define the parameters which control their motion, we made a detailed study of the rupture process of this earthquake from inversion of body waves at regional and teleseismic distances. Ground motion displacements obtained in this way are in agreement with near-field strong motion data and GPS observations recorded in Lorca. We have obtained a partly bilateral rupture propagating to WSW (238°, 54°, 59°) with 27 cm of maximum slip and shallow focus (4 km). The fault plane orientation corresponds to that of the Cejo de los Enamorados Fault located NE of the Lorca town and parallel to the Alhama de Murcia Fault. The distribution of slip on the fault plane can explain the lack of any observed surface rupture as we found that the rupture started at 4-km depth along a plane dipping at 54°, with motion propagating upward to stop at 1.5 km below the surface. The strong motion and GPS data recorded near the epicenter are in agreement with the maximum slip on the fault. Directivity effects and the extreme shallowness of the rupture could explain the considerable damage that the earthquake caused in the town of Lorca.

Research on Seismic Response Estimation of Reinforced Concrete Pier under Pulse-Type Near-Fault Ground Motion

For estimating seismic response of pier-structure under near-fault ground motion, The typical pulse-type near-fault ground motion records were chosen to establish a record base, and three pier models with different natural period were established; The non-elastic response spectral displacement of ground motion was used to estimate the nonlinear response; The yield displacement of the nonlinear oscillator was defined based on the static pushover analysis result, and its influence on response estimation was studied. The study result is important for structural seismic response estimation by using the non-elastic response spectral displacement and the probability-based seismic performance evaluation.

Long-Period Displacement Spectra of Near-Fault Strong-Motion from Tremendous Earthquakes

The characteristics of near-fault ground motion displacements, with the obvious directivity, were analyzed. Along moving direction of the fault, displacements take on the feature of fling-step, and the large pulse is the main characteristic of displacements in the vertical moving direction of the fault. The models of near-fault ground motion with different detailed scales can be obtained by median filtering with different window length on the velocity series. Displacement spectra of the models were compared with observations from tremendous earthquakes. The results show that the highly simplified model can predict the response spectrum in very long periods, but there are distinct errors in the period range in which engineering is interested (Tp 5 sec). The refined model is necessary for very large magnitude earthquakes which include multiple rupture, and should be established according to characteristics of velocity.

Baseline Correction of Digital Strong-Motion Data-Examples from the 2008 Wenchuan, China, Earthquake

This paper analyzes key noises within digital strong-motion acceleration recording that can result in baseline offset, and according to their specific position provide a baseline correction scheme for preserving the long-period ground motion. This correction method is then applied to the digital acceleration records from the 2008 Wenchuan earthquake, and also, when compared with GPS data (including some high frequency of 1Hz GPS data), it is shown that this method can well restore displacement of ground motion, including permanent displacement which is the main concern of seismologists. Furthermore, compared with other methods that aim to restore the ground displacement, it has much greater stability.

Empirical equations for the prediction of displacement spectrum intensity and its correlation with other intensity measures

Displacement spectrum intensity ( DSI), defined as the integral of a ground motion's displacement response spectrum from 2.0 to 5.0 s, is proposed as an indicator of the severity of the long period content of a ground motion. It is demonstrated how the distribution of DSI can be predicted using existing ground motion prediction equations for (pseudo) spectral accelerations, which is necessary for it to be a useful intensity measure (IM) in either probabilistic or deterministic seismic hazard analysis. Empirical correlation equations between DSI and other common ground motion IMs are developed for active shallow crustal earthquakes using a dataset of ground motions from active shallow crustal earthquakes. The ability of DSI to account for near-source ground motions exhibiting forward directivity, potentially damaging far-source long-period ground motion, and its use with other spectrum intensity parameters to characterise short, medium, and long period severity of ground motions is discussed. The developed ground motion prediction and correlation equations enable DSI to be utilised in rigorous ground motion selection frameworks such as the generalised conditional intensity measure (GCIM) approach.

Seismic vulnerability assessment to slight damage based on experimental modal parameters

AbstractThe aim of this paper is to adjust behaviour models for each class of structure for vulnerability assessment by using ambient vibration. A simple model based on frequencies, mode shapes and damping, taken from ambient vibrations, allows computation of the response of the structures and comparison of inter‐storey drifts with the limits found in the literature for the slight damage grade, considered here as the limit of elastic behaviour. Two complete methodologies for building fragility curves are proposed: (1) using a multi‐degree of freedom system including higher modes and full seismic ground‐motion and (2) using a single‐degree of freedom model considering the fundamental mode f0 of the structure and ground‐motion displacement response spectra SD(f0). These two methods were applied to the city of Grenoble, where 60 buildings were studied. Fragility curves for slight damage were derived for the various masonry and reinforced concrete classes of buildings. A site‐specific earthquake scenario, taking into account local site conditions, was considered, corresponding to an ML = 5.5 earthquake at a distance of 15 km. The results show the benefits of using experimental models to reduce variability of the slight damage fragility curve. Moreover, by introducing the experimental modal model of the buildings, it is possible to improve seismic risk assessment at an overall scale (the city) or a local scale (the building) for the first damage grade (slight damage). This level of damage, of great interest for moderate seismic‐prone regions, may contribute to the seismic loss assessment. Copyright © 2011 John Wiley & Sons, Ltd.

Rapid Assessment of Damage Potential of Earthquakes in Taiwan from the Beginning of P Waves

To rapidly assess the potential for damage of an earthquake for purposes of earthquake early warning in Taiwan, we used the peak displacement and velocity amplitudes of the first 3 sec of the P wave. The vertical-component records, high-pass filtered at 0.075 Hz, are used. We found that the peak initial-displacement amplitude (Pd) correlates well with the peak ground-motion displacement (PGD) and the peak ground-motion velocity (PGV) at the same site. When Pd > 0.5 cm, the event is most likely damaging. If Pd is combined with the period parameter τ_c, determined in an earlier study, then τ_c × Pd provides an even more robust parameter for assessing the potential for damage.

Forced vibration testing of buildings using the linear shaker seismic simulation (LSSS) testing method

AbstractThis paper describes the development and numerical verification of a test method to realistically simulate the seismic structural response of full‐scale buildings. The result is a new field testing procedure referred to as the linear shaker seismic simulation (LSSS) testing method. This test method uses a linear shaker system in which a mass mounted on the structure is commanded a specified acceleration time history, which in turn induces inertial forces in the structure. The inertia force of the moving mass is transferred as dynamic force excitation to the structure. The key issues associated with the LSSS method are (1) determining for a given ground motion displacement, xg, a linear shaker motion which induces a structural response that matches as closely as possible the response of the building if it had been excited at its base by xg (i.e. the motion transformation problem) and (2) correcting the linear shaker motion from Step (1) to compensate for control–structure interaction effects associated with the fact that linear shaker systems cannot impart perfectly to the structure the specified forcing functions (i.e. the CSI problem). The motion transformation problem is solved using filters that modify xg both in the frequency domain using building transfer functions and in the time domain using a least squares approximation. The CSI problem, which is most important near the modal frequencies of the structural system, is solved for the example of a linear shaker system that is part of the NEES@UCLA equipment site. Copyright © 2005 John Wiley & Sons, Ltd.

Magnitude scales for very local earthquakes. Application for Deception Island Volcano (Antarctica)

Different magnitude scales are calculated for a set of volcano-tectonic earthquakes recorded in Deception Island Volcano (Antarctica). The data set includes earthquakes recorded during an intense seismic series that occurred in January–February 1999, with hypocentral distances that range between 0.5 and 15 km. This data set is enlarged to include some regional earthquakes with hypocentral distances up to 200 km. The local magnitude scale, M L, fixed at a hypocentral distance of 17 km, is used as the reference for the other magnitude scales studied in the present work. M L is determined on a standard Wood–Anderson simulated trace assuming a gain of 2080. Maximum peak-to-peak amplitudes are measured on the vertical components of a short-period sensor. The M w scale is calculated, in the vertical component, both for P and S waves. The attenuation correction of the ground motion displacement spectra is introduced using data from coda waves studied in the area. The comparison between M L values and M w estimations indicates severe discrepancies between both values. A magnitude–duration scale is calibrated from the comparison between coda durations of the recorded events and their assigned local magnitude scales. In order to investigate the causes of the discrepancy between the M L and M w values we analyze two possible error sources: a wrong coda Q value, or the effects of the near-surface attenuation that initially are not taken into account in the correction of the ground displacement spectra. The analysis reveals that the main cause of this discrepancy is the effect of the near-surface attenuation. The near-surface attenuation is also the cause of the determination of an anomalous spectral decay slope, after the corner frequency, and the determination of this corner frequency value. This near-surface attenuation, represented by κ, is estimated over the data set, obtaining an average value of 0.025. With this κ value, the M w scale is recalculated using an automatic algorithm. The new M w values are more consistent with the M L values, obtaining a relationship of M w=0.78 M L−0.02.

Time‐Frequency Signal Analysis of Earthquake Records Using Mexican Hat Wavelets

Abstract: A method is presented for time‐frequency signal analysis of earthquake records using Mexican hat wavelets. Ground motions in earthquakes are postulated as a sequence of simple penny‐shaped ruptures at different locations along a fault line and occurring at different times. The single point source displacement of ground motion is idealized by a Gaussian function. For the purpose of signal analysis of accelerograms, the ground motion record generated by a simple penny‐shaped rupture is used to form the basis wavelet function. After a careful study of the characteristics of various wavelet functions, the Mexican hat wavelet was found to be the most appropriate wavelet basis function to represent the acceleration of a single point source rupture. The result of the signal processing of an accelerogram is presented in the form of a scalogram using the coefficients of the continuous Mexican hat wavelet transform to describe the signal energy in the time‐scale domain. The proposed signal processing methodology can be used to investigate the characteristics of accelerograms recorded on various types of sites and their effects on different types of structures.

Creation of a Digital Database for XXth Century Historical Earthquakes Occurred in the Iberian Area

—The problems of recovering the seismic information contained in the old seismograms through their digitization and processing by computer methods are discussed. We present the main principles of a simple manual technique for digitization of early seismic records of the Wiechert seismograph. Detrending of the zero-line slope, circular arc removal, smoothing and interpolation treatment of the digital data are made. The accuracy of the digitizing process is assessed and its reliability is tested by a comparison with automatically obtained digital data and their spectral amplitudes. The deconvolution of the seismograph response has allowed us to obtain the time variation of ground motion which is then contrasted with direct measurements of ground motion displacement amplitudes given in the old-time bulletins. We have created a digital database for historical earthquakes which occurred in the Iberian area during the period 1912–1940 and recorded by the Wiechert seismograph at the Geophysical Observatory of Toledo, Spain. It contains the following output data the digitized original records; the geometrically corrected and interpolated data; the time variation of ground motion; maximum amplitudes and corresponding periods; total duration of the seismic oscillations and amplitude spectra. We carry out magnitude estimates and give formulae for magnitude classification based on the signal duration and on the maximum ground displacement amplitude. We also perform seismic moment determinations by spectral analysis of waveforms and propose a new seismic moment-magnitude relation.

Slip, Stress Drop and Ground Motion of Earthquakes: A View from the Perspective of Fractional Brownian Motion

—The characteristics of slip and stress drop distributions accompanying earthquakes are explored from the perspective of fractional Brownian motion (fBm). Slip and stress drop distributions are assumed to be processes of fBm.The Hurst exponent (H), which reveals the roughness of a random process of fBm, is first estimated from ten inferred slip maps for six crustal earthquakes occurring in California. The relationships between the Hurst exponents with respect to static slip (H u ),stress (H τ ), static stress drop (H δσ ) and slip velocity (H u ) are then established following Andrews (1980). They are found to be H δσ = H τ = H u -1 = H u -0.5. Empirically, H u is recognized as being about 1 which, according to the theory of fBm, implies that the static slip distribution of an earthquake is just on the margin between being and not being self-similar, depending on the individual case. Cases where H u is less than 1 (i.e., self-similar) suggest that H δσ < 0(i.e., the distribution of static stress drop diverges), which is, in light of fBm, invalid. One possible explanation for this paradox is that H u is less than 1 in crustal earthquake phenomena only over a certain specific bandwidth of wavenumbers, or it could be that the relation H δσ = H u -1 is not valid, which implies that static stress drop in the wavenumber domain is not the product of stiffness and slip as described in Andrews (1980). It could be that some different physics apply over this particular bandwidth. In such cases, multi-fractals may be a better way to explore the characteristics of the Hurst exponents of slip. In general, static stress drop and stress distributions are more likely to be self-similar than static slip distribution. H u ≌ 1 and H δσ ≌ 0 are good first approxima tions for the slip and stress drop distributions. The spectrum of ground motion displacement falls off as ω -(Hδσ + 2) with H δσ ≌ 0, consistent with an ω-2 model of the earthquake source.