Fast and Robust Earthquake Source Spectra and Moment Magnitudes from Envelope Inversion

ABSTRACT With the present study, we introduce a fast and robust method to calculate the source displacement spectra of small earthquakes on a local to regional scale. The work is based on the publicly available Qopen method of full envelope inversion, which is further tuned for the given purpose. Important source parameters—seismic moment, moment magnitude, corner frequency, and high-frequency fall off—are determined from the source spectra by fitting a simple earthquake source model. The method is demonstrated by means of a data set comprising the 2018 West Bohemia earthquake swarm. We report moment magnitudes, corner frequencies, and centroid moment tensors inverted from short-period body waves with the Grond package for all earthquakes with a local magnitude larger than 1.8. Moment magnitudes calculated by envelope inversion show a very good agreement to moment magnitudes resulting from the probabilisitc moment tensor inversion. Furthermore, source displacement spectra from envelope inversion show a good agreement with spectra obtained by multiple taper analysis of the direct onsets of body waves but are not affected by the large scatter of the second. The seismic moments obtained with the envelope inversion scale with corner frequencies according to M0∝fc−4.7. Earthquakes of the present data set result in a smaller stress drop for smaller magnitudes. Self-similarity of earthquake rupture is not observed. In addition, we report frequency-dependent site amplification at the used stations.

A Damping Modification Factor for Horizontal Acceleration Spectrum from Subduction Slab Earthquakes in Japan Accounting for Site Conditions

ABSTRACT We present a damping modification factor (DMF) model for the total acceleration spectrum from subduction slab earthquakes. The model can be used for scaling a 5% damped design spectrum not associated with a particular earthquake that occurred in a subduction slab. The DMF model uses site-period-based site classes as the site-effect proxy. DMF models were constructed based on the spectrum for 13 damping ratios and 34 spectral periods; the DMF values can be calculated for any damping ratio between 1% and 30% and at any spectral period between 0.03 and 5.0 s. At moderately long and long spectral periods, the DMF values for acceleration spectrum are similar to or less than those for the displacement spectrum for a damping ratio of less than 5%, whereas the DMF values for the acceleration spectrum are similar to or larger than those for the displacement spectrum when the damping ratio is more than 5%. The standard deviations for acceleration and displacement spectra are similar at short or moderately short spectral periods, but those for the acceleration spectrum are about twice those for the displacement spectrum at long spectral periods. All standard deviations decrease linearly with increasing damping ratios in the logarithm scale when the damping ratio is less than 5% and increase linearly with increasing damping ratios in a logarithm scale for the other damping ratios. A set of simple functions for calculating various standard deviations is presented. The spectra from the Zhao, Jiang, et al. (2016) study for slab events scaled by the DMF values for other damping ratios vary smoothly with spectral period and have a trough at short spectral periods for a large event, a short distance, and high damping ratios. The relatively large between-event and within-site standard deviations are from the source and path effects.

Inelastic Displacement Spectra and Its Utilization of DDB Design for Seismic Isolated Bridges Subjected to Near-Fault Pulse-Like Ground Motions

A variety of research has focused on the inelastic displacement demand of a single degree of freedom (SDOF) system when subjected to near-fault pulse-like ground motions, in which the concerned ductility, μ, is typically lower than ten for normal structures. However, for seismic isolated structures that are more prone to large displacement, the corresponding research is limited. The purpose of this paper is to investigate the inelastic displacement spectra of an SDOF system with μ ranging from 5 to 70 and further proposes a direct displacement-based (DDB) design method for seismic isolated bridges. More concretely, a pool of near-fault pulse-like records is assembled, the mean C μ as a function of T/ T p is developed, and the influences of the ductility, μ, and the post-to-pre-yield ratio, α, on C μ are carefully investigated. Then the corresponding inelastic displacement spectra, S d, are obtained, and a comprehensive piecewise expression is proposed to fit S d. After that, the utilization of the spectra for the DDB design of a three-span seismic isolated continuous bridge is performed, and the principal of simplifying the bridge to an SDOF system is carefully explained and verified.

Inelastic displacement spectra for Chinese highway bridges characterized by single-degree-of-freedom bilinear systems

As for the inelastic displacement demand of a single-degree-of-freedom system, previous studies usually focus on the strength reduction factor, R, or the inelastic displacement ratio, C. Only a little literature reports the direct statistical results of the mean inelastic displacement spectra, Sd. Based on 308 earthquake records selected from three types of site soil, differences between the direct mean Sd and the indirect ones that respectively derived from mean R and mean Cμ are investigated, in which Cμ refers to the constant ductility inelastic displacement ratio. It is found the indirect Sd will introduce errors for using mean R and mean Cμ, while the dispersion of the direct spectra need to be reduced before putting into practice. Two methods, the period normalized method and the spectra-matching method, are employed to address the dispersion problem, and the latter one that modified a record to make its acceleration response spectra compatible with the specified standard, Chinese highway bridge seismic design guidelines in this study, works with more acceptable performance. Finally, a comprehensive equation is proposed to characterize the spectra-matching mean Sd, the practicality and efficiency of the identified parameters in the equation are verified. It is advisable to use the proposed equation to assess the inelastic displacement demand of Chinese highway bridges characterized by single-degree-of-freedom bilinear system, and the procedures to obtain the displacement spectra can also be utilized for other corresponding researches.

Pounding Response Spectra of Bridge Decks

Pounding-induced damage to structures, either buildings or bridges, is systematically observed after significant earthquakes. This has emphasized the necessity of accounting for this phenomenon either in the design of new bridges or the seismic assessment of existing bridges. For this reason, practitioners concerned with bridge structures should be provided with concise computational tools to correctly quantify the effects due to pounding. One such tool is represented by pounding spectra, which were already introduced a couple of decades ago. This work presents a proposal of simplified equations for pounding-related displacement spectra. The first part of this paper presents the computational aspects arising when modeling such complex phenomenon. The second part presents the results of numerical analyses, in terms of displacement spectra. The third part presents a set of simple expressions to allow practitioners easily evaluate pounding-related effects in terms of displacement amplification with respect to the no-pounding condition.