Repeatability-dependent detection thresholds for time-lapse seismic CO₂ monitoring

We quantify the smallest CO₂ layer that a time-lapse seismic survey pair can detect as a function of repeatability, measured by the normalized root-mean-square (NRMS) difference, in a controlled, Sleipner-like synthetic study. Gassmann fluid substitution under four fluid-mixing treatments feeds one-dimensional layer models, checked against two-dimensional finite-difference gathers, and calibrated nonrepeatability sets NRMS from 10% to 60%. Detection is a hypothesis test at a false-alarm probability of 0.05, with 1200 null realizations for each frequency and noise level and 40 held-out signal realizations in each of 1728 cells, for four detectors: windowed energy, a clean-template matched filter, a generic-template filter, and a small convolutional neural network (CNN). At 30 Hz, a CO₂ saturation of 0.8, and uniform (Reuss) mixing, the energy detector's minimum detectable thickness rises from the 1-m grid floor at NRMS 10% to 4.5 m at NRMS 60%, and Voigt mixing roughly doubles the latter. The energy detector's minimum detectable free-phase mass per area rises over the same NRMS range from 25 (a censored grid corner) to 253 kg/m², both at the lowest saturation tested. At 30 and 45 Hz and NRMS of 40% and above, the energy detector and the CNN increasingly exceed the matched filter's area under the receiver operating characteristic curve, consistent with nonrepeatability misaligning the signal; at 15 Hz the matched filter keeps its advantage. At fixed NRMS, in-window reflectivity and host stiffness also move the 30-Hz energy-detector threshold, and a consolidated host suppresses detection. Predictions agree with 11 published Sleipner observables within a factor of 1.41, a consistency check rather than validation. Published Sleipner NRMS of 45%–53% lies near the 50% grid level, where energy-detector, matched-filter, and CNN thresholds span 1.8–3.0 m. A credible detection claim therefore states the repeatability, the false-alarm probability, and the detector together.