Pseudo Relative Velocity Spectra Research Articles

Seismic microzoning of the Delhi metropolitan area, India—II: Hazard computation and zoning maps

AbstractWe present seismic microzonation maps of New Delhi, India, using the probabilistic seismic hazard analysis (PSHA) method with input seismic activity parameters estimated in Part‐I of this two‐part paper. Our calculations required three different attenuation equations for amplitude scaling of strong ground motion from three principal contributing sources: the National Capital Region (NCR), Northwestern Himalaya (NWH), and the Hindu Kush subduction (HKS). We show that uniform hazard spectral (UHS) amplitudes are dominated only by the local seismicity in the NCR at high frequencies beyond about 2 Hz. For intermediate and long periods, UHS amplitudes are dominated by contributions from the NWH and HKS earthquakes. Our results show that specifying strong motion amplitudes for use in engineering design by means of peak ground acceleration can lead to serious errors for buildings higher than four to five stories and hence should not be used. Our results also show that the shape of design spectra must depend on the nature of contributing earthquake sources, their relative activity, potential to create large magnitudes, and geographical placement relative to the site of interest, and thus a standard design‐spectrum shape cannot satisfy all these requirements. We use local geological site condition parameters directly in all calculations and present hazard maps for three different soil site conditions (“rock,” stiff soil sites, and deep soil sites). Thus, the user can extract the UHS amplitudes of pseudo relative velocity spectra at any site in the National Capital Territory by experimentally determining the local soil site conditions and then applying the corresponding maps shown in this paper.

Attenuation of fourier amplitude and pseudo relative velocity spectra due to local earthquakes in the national capital region of India

In this paper we present attenuation of spectral amplitudes of strong earthquake ground motion in the National Capital Region (NCR) of India that surrounds and includes the National Capital Territory (NCT) of Delhi. In this region, because of the small volume of seismogenic zone in the shallow crust and the coincidence of this volume with a network of recording strong-motion stations, it is possible to determine the amplitude attenuation and scaling equations along the wave paths in this well-defined shallow geological environment. Similar to the Northeastern region of India, the basement in the NCR zone also comprises the Precambrian metamorphic rocks of the peninsular shield. The frequency-dependent attenuation function for the NCR is therefore obtained by assuming the applicability of the dependence on magnitude and site-condition parameters for the local earthquakes in Northeast India. The validity of the empirical scaling equations thus developed has been established by comparing the estimates of seismic moment and peak ground displacement from long-period extensions and the estimates of seismic wave energy and peak ground acceleration from short-period extensions of the empirical spectra with the expected theoretical trend or recorded values of the same parameters. The presented scaling relations for Fourier (FS) and pseudo relative velocity (PSV) spectra can be considered to provide a sound basis for macro- and micro-zoning specific to the highly risk-prone Delhi region.

Attenuation of strong earthquake ground motion – II: Dependence on geology along the wave paths from the Burmese subduction zone to northeastern India

This paper presents another example of event-specific, region-specific attenuation equations for strong earthquake ground motion through essentially the same geological region defined by geometrically constrained ray paths. The current study describes strong motion wave attenuation from deep earthquakes in the Burmese subduction zone, as recorded by strong motion accelerographs in northeastern India. The accompanying empirical scaling equations to determine the Fourier and pseudo-relative velocity (PSV) spectra for the same events are also presented. To demonstrate the validity of the long-period extension of the above spectra, independent estimates of peak ground displacement from recorded accelerograms and estimates of the seismic moment from distant recordings of earthquakes are shown to be in good agreement with the extended spectral amplitudes. The validity of a short-period extension has been tested by comparing the values of pseudo acceleration spectral amplitudes at short periods with the recorded peak ground accelerations. Presented Fourier and PSV spectra can thus be considered to provide a sound basis for macro- and micro-zoning specific to the highly seismic regions of northeastern India.

Empirical scaling relations for pseudo relative velocity spectra in western Himalaya and northeastern India

In this paper, frequency-dependent empirical scaling equations are developed for pseudo relative velocity (PSV) spectrum amplitudes of strong earthquake ground accelerations in western Himalaya and northeastern India for five ratios of critical damping ζ = 0.00, 0.02, 0.05, 0.10, and 0.20. These are based on the frequency-dependent attenuation functions developed in our recent work (Gupta and Trifunac [38]) for these two regions. The proposed scaling relations are shown to have physically realistic dependence on earthquake magnitude, source-to-site distance, and local site geological and soil conditions. The extension of the empirical PSV amplitudes to short and long periods, beyond the empirical period range, is also illustrated using available techniques (Trifunac [89,90]). To demonstrate the validity of a long-period extension, independent estimates of peak ground displacement from recorded accelerograms and estimates of the seismic moment from distant recordings of earthquakes are shown to be in good agreement with the extended spectral amplitudes. The validity of a short-period extension has been also tested by comparing the values of pseudo acceleration spectral amplitudes at short periods with the recorded peak ground accelerations. The realistic nature of short- and long-period extensions provides additional tests for the accuracy of the present scaling relationships. Such relationships can thus be considered to provide a sound basis for macro- and micro-zoning specific to the highly seismic regions of western Himalaya and northeastern India.

Preliminary empirical scaling of pseudo relative velocity spectra in Serbia from the Vrancea earthquakes

First frequency-dependent empirical scaling equations of pseudo-relative velocity spectral amplitudes (PSV) of strong earthquake ground motions in the former Yugoslavia were introduced in the mid-1990s by Lee and Trifunac (1990) [15]. This followed the development of the Fourier spectral amplitudes (FS) scaling equations by Lee and Trifunac (1993) [17] in terms of earthquake source parameters, and the region-specific frequency dependent attenuation function given by Lee and Trifunac (1992) [16]. More recently, a new frequency-dependent attenuation function was developed for central and eastern Serbia for earthquakes of intermediate and large magnitudes and for large epicentral distances—exceeding 300km—suggested by Lee et al. (2016) [19] that occur in the Vrancea source region in Romania. In this paper we use this frequency-dependent attenuation function to develop empirical scaling equations for PSV spectral amplitudes in Serbia. These scaling equations will form a basis for macro- and micro-zoning earthquake hazard studies in Serbia.

A preliminary empirical model for frequency-dependent attenuation of Fourier amplitude spectra In Serbia from the Vrancea earthquakes

We present the frequency-dependent attenuation model for Fourier amplitude spectra of strong earthquake ground motion in Serbia from intermediate depth earthquakes in the Vrancea source zone in Romania. The development of this type of scaling is the essential first step toward developing the corresponding attenuation and scaling equations for pseudo relative velocity spectra (PSV), which are necessary for seismic macro- and microzoning in the territory of Serbia. Such scaling is necessary because the Vrancea source zone produces large earthquakes with shaking that attenuates differently from the local earthquakes in Serbia. Development of such a scaling model is associated with several difficulties, the principal one being the lack of recorded strong motion accelerograms at epicentral distances exceeding 300km. To reduce uncertainties with such scaling, we require our preliminary scaling equations to be consistent with independent estimates of seismic moment, stress drop, and radiated wave energy. In the future, when the recorded strong motion data from Vrancea earthquakes increases several-fold of what it is today, it will become possible to perform this analysis again, thus leading to more reliable and permanent scaling estimates.

Pseudo relative velocity spectra of earthquake ground motion at long periods : M. D. Trifunac, Soil Dyanmics & Earthquake Engineering, 4(5), 1995, pp 331–346

Pseudo relative velocity spectra of earthquake ground motion at long periods : M. D. Trifunac, Soil Dyanmics & Earthquake Engineering, 4(5), 1995, pp 331–346

Pseudo relative velocity spectra of earthquake ground motion at high frequencies : M. D. Trifunac, Earthquake Engineering & Structural Dynamics, 24(8), 1995, pp 1113–1130

Pseudo relative velocity spectra of earthquake ground motion at high frequencies : M. D. Trifunac, Earthquake Engineering & Structural Dynamics, 24(8), 1995, pp 1113–1130

Pseudo relative velocity spectra of earthquake ground motion at high frequencies

SUMMARY The currently available empirical scaling laws for estimation of spectral amplitudes are limited to periods longer than 0.04 s. However, for design of equipment and stiff structures on multiple and distant supports, exposed to strong shaking near faults where peak accelerations can exceed 1g, specification of design ground motions at higher frequencies is required. This paper presents a method for extrapolation of pseudo-relative velocity spectral amplitudes of strong earthquake shaking to short periods (0.01 < T < 0.04 sec). The extrapolated spectra can be used as a physical basis for defining design spectral amplitudes in this higher-frequency range. The analysis in this paper implies that for typical strong motion accelerations, particularly on sedimentary sites in California, the peak ground accelerations are projected to be unaffected by frequencies higher than those recorded. Consequently, in California, the high-frequency pseudo-acceleration spectra can be approximated from the recorded absolute peak accelerations.

Pseudo relative velocity spectra of earthquake ground motion at long periods

This paper analyses the processes which govern structural response, and uses observations of strong earthquake ground motion to propose quantitative extrapolation of pseudo relative velocity spectral amplitudes to long (100 > T > 1 s) periods. This will eliminate the current difficulties with rough estimation of long period spectral amplitudes and will open new possibilities by enabling the strong motion hazard calculations to be extended to the same long period band. So far, the scaling equations of response spectrum amplitudes have been valid only up to periods less than several seconds. The design of long structures and of structures on multiple distant supports requires knowledge and specification of design ground motions well beyond 1–10 s periods. With the results presented in this paper it will be possible to compute site-specific uniform hazard spectra and associated synthetic accelograms for essentially all long period response problems.

Correlation of pseudo relative velocity spectra with site intensity, local soil classification and depth of sediments : Soil Dynam Earthq Engng V10, N3, April 1991, P141–151

Correlation of pseudo relative velocity spectra with site intensity, local soil classification and depth of sediments : Soil Dynam Earthq Engng V10, N3, April 1991, P141–151

Correlation of pseudo relative velocity spectra with site intensity, local soil classification and depth of sediments

Empirical regression equations are presented for scaling Pseudo Relative Velocity Spectra, PSV(T), in terms of the Modified Mercalli Intensity M.M.I., local soil classification at the recording site (‘rock’, stiff or deep soil), and local geological condition (depth of sediments). It is shown that both the local soil classification and the local geological depth of sediments should be used simultaneously in the evaluation of site specific response spectra.

Empirical models for scaling pseudo relative velocity spectra of strong earthquake accelerations in terms of magnitude, distance, site intensity and recording site conditions

Our previous empirical scaling model for Pseudo Relative Velocity (PSV) spectrum amplitudes has been refined here by introducing the frequency dependent attenuation of amplitudes with distance 9 . The new model also considers the depth of earthquake focus and the approximate characterization of the source size to compute the ‘representative’ source to station distances in addition to all other scaling parameters used previously 4 . The form of the probability distribution function of spectral amplitudes proposed by Trifunac and Anderson 4 to describe the distribution of the residuals about the chosen regression model has been confirmed by this analysis.