Gamma rays at rest frame energies as high as 90 GeV have been reported from gamma-ray bursts (GRBs) by the Fermi Large Area Telescope (LAT). There is considerable hope that a confirmed GRB detection will be possible with the upcoming Cherenkov Telescope Array (CTA), which will have a larger effective area and better low-energy sensitivity than current-generation imaging atmospheric Cherenkov telescopes (IACTs). To estimate the likelihood of such a detection, we have developed a phenomenological model for GRB emission between 1 GeV and 1 TeV that is motivated by the high-energy GRB detections of Fermi-LAT, and allows us to extrapolate the statistics of GRBs seen by lower energy instruments such as the Swift-BAT and BATSE on the Compton Gamma-ray Observatory. We show a number of statistics for detected GRBs, and describe how the detectability of GRBs with CTA could vary based on a number of parameters, such as the typical observation delay between the burst onset and the start of ground observations. We also consider the possibility of using GBM on Fermi as a finder of GRBs for rapid ground follow-up. While the uncertainty of GBM localization is problematic, the small field-of-view for IACTs can potentially be overcome by scanning over the GBM error region. Overall, our results indicate that CTA should be able to detect one GRB every 20 to 30 months with our baseline instrument model, assuming consistently rapid pursuit of GRB alerts, and provided that spectral breaks below 100 GeV are not a common feature of the bright GRB population. With a more optimistic instrument model, the detection rate can be as high as 1 to 2 GRBs per year.
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