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