  The round trip time of the light pulse limits the maximum detectable
vibration frequency response range of phase-sensitive optical time domain
reflectometry ({\phi}-OTDR). Unlike the uniform laser pulse interval in
conventional {\phi}-OTDR, we randomly modulate the pulse interval, so that an
equivalent sub-Nyquist additive random sampling (sNARS) is realized for every
sensing point of the long interrogation fiber. For an {\phi}-OTDR system with
10 km sensing length, the sNARS method is optimized by theoretical analysis and
Monte Carlo simulation, and the experimental results verify that a wide-band
spars signal can be identified and reconstructed. Such a method can broaden the
vibration frequency response range of {\phi}-OTDR, which is of great
significance in sparse-wideband-frequency vibration signal detection, such as
rail track monitoring and metal defect detection.
