Characterizing occurrence of ultrasound contrast agent (UCA) microbubble destruction is important for development of functional and therapeutic applications. Previously , it was demonstrated that post-excitation acoustic emissions detected with passive cavitation detection (PCD) result from inertial cavitation (IC) of UCA after shell rupture. That work relied on time-consuming visual inspection of PCD data to identify IC signals and characterized only minimum rarefactional pressure thresholds for rupture of a single Optison™ microbubble in the sampled population. This work introduces an algorithm for automatic detection of IC signals. The algorithm was applied to the 71424 waveforms in the PCD data set. At each incident frequency (0.9, 2.8 or 4.6 MHz) and pulse duration (3, 5 or 7 cycles) combination, ruptured microbubble occurrence with incident peak rarefactional pressure (PRP) was well described by a logistic regression curve with an inflection point near 50% occurrence and a plateau at 100%. With a 5-cycle pulse duration at 0.9, 2.8 and 4.6 MHz the incident PRPs leading to 5% microbubble rupture were 0.66, 0.83 and 1.1 MPa; and 1.1, 1.6 and 2.5 MPa for 50%. This automatic algorithm combined with the PCD approach provides a practical tool for the characterization of UCA destruction occurrence across a significant range of incident PRPs.