Pulse-Period--Moment-Magnitude Relations Derived with Wavelet Analysis and their Relevance to Estimate Structural Deformations

Abstract

Motivated from the quadratic dependence of peak structural displacements to the pulse period, $T_p$, of pulse-like ground motions, this paper revisits the $T_p$--$M_\text{W}$ relations of ground motions generated from near-source earthquakes with epicentral distances, $D\leq$ 20 km. A total of 1260 ground motions are interrogated with wavelet analysis to identify energetic acceleration pulses (not velocity pulses) and extract their optimal period, $T_p$, amplitude, $a_p$, phase, $\phi$ and number of half-cycles, $\gamma$. The interrogation of acceleration records with wavelet analysis is capable of extracting shorter-duration distinguishable pulses with engineering significance, which override the longer near-source pulses. Our wavelet analysis identified 109 pulse-like records from normal faults, 188 records from reverse faults and 125 records from strike-slip faults, all with epicentral distances $D\leq$ 20 km. Regression analysis on the extracted data concluded that the same $T_p$--$M_\text{W}$ relation can be used for pulse-like ground motions generated either from strike-slip faults or from normal faults; whereas, a different $T_p$--$M_{\text{W}}$ relation is proposed for reverse faults. The study concludes that for the same moment magnitude, $M_{\text{W}}$, the pulse periods of ground motions generated from strike-slip faults are on average larger than these from reverse faults. Most importantly, our wavelet analysis on acceleration records produces $T_p$--$M_{\text{W}}$ relations with a lower slope than the slopes of the $T_p$--$M_{\text{W}}$ relations presented by past investigators after merely fitting velocity pulses. As a result, our proposed $T_p$--$M_{\text{W}}$ relations yield lower $T_p$ values for larger-magnitude earthquakes (say $M_{\text{W}}>$ 6), allowing for the estimation of dependable peak structural displacements that scale invariably with $a_pT_p^{\text{2}}$.