Natural Hazards Research Summit 2024: Pulse-period–moment-magnitude relations derived with wavelet analysis and their relevance to estimate structural deformations

Motivated from the quadratic dependence of peak structural displacements to the pulse period, 𝑇𝑝, of pulse-like ground motions, this paper revisits the pulse-period – moment-magnitude (𝑇𝑝–𝑀w) relations of ground motions generated from recorded near-source ground motions with epicentral distances, 𝐷 ≤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, 𝑇𝑝, amplitude, 𝑎𝑝, phase, 𝜙 and number of half-cycles, 𝛾. 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 and they are not necessarily of random character. Our wavelet analysis identified 109 pulse-like records from normal faults, 188 pulse-like records from reverse faults and 125 pulse-like records from strike-slip faults, all with epicentral distances 𝐷 ≤ 20 km. Regression analysis on the extracted data concluded that the same 𝑇𝑝–𝑀w relation can be used for pulse-like ground motions generated either from strike-slip faults or from dip-slip normal faults; whereas, a different 𝑇𝑝–𝑀w relation is proposed for dip-slip reverse faults. The study concludes that for the same moment magnitude, 𝑀w, the pulse periods of ground motions generated from strike-slip faults are on average larger than these from reverse faults—a result that is in agreement with findings from past investigations. Most importantly, our wavelet analysis on acceleration records produces 𝑇𝑝–𝑀w relations with a slope that is lower than the slopes of the 𝑇𝑝–𝑀w relations presented by past investigators after merely fitting velocity pulses. As a result, our proposed 𝑇𝑝–𝑀w relations yield lower 𝑇𝑝 values for larger-magnitude earthquakes (say 𝑀w > 6), allowing for the estimation of dependable peak structural displacements that scale invariably with 𝑎𝑝𝑇𝑝^2.