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

TL;DR

This study uses wavelet analysis to refine pulse period-moment magnitude relations for near-source earthquakes, improving estimates of structural displacements by identifying acceleration pulses with engineering significance.

Contribution

It introduces a wavelet-based method to extract acceleration pulses and proposes new $T_p$--$M_W$ relations that differ from previous velocity-based models, especially for larger earthquakes.

Findings

Wavelet analysis effectively identifies shorter-duration acceleration pulses.

Distinct $T_p$--$M_W$ relations are established for reverse faults versus strike-slip and normal faults.

New relations predict lower pulse periods for large earthquakes, aiding structural displacement estimation.

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 $a_pT_p^{\text{2}}$.