Do Aftershock Forecasts Work After Great Earthquakes? Maximum Likelihood Omori–Utsu Fits, Gutenberg–Richter b-Values and Reasenberg–Jones Probabilities for Gorkha 2015, Kaikoura 2016 and Kahramanmaras 2023

After a large earthquake, agencies forecast aftershocks with the Reasenberg–Jones model: a modified Omori law for the decay of the rate in time combined with the Gutenberg–Richter law for magnitudes. Engineers use these forecasts to decide when damaged buildings can be re-entered and when repairs can begin. I derive the maximum likelihood equations for the Omori–Utsu point process, including the closed-form profile for the productivity K, and fit them to one year of USGS ComCat aftershocks of three magnitude 7.8 earthquakes: Gorkha, Nepal (2015), Kaikoura, New Zealand (2016) and Kahramanmaras, Turkiye (2023). Above the completeness magnitude (4.2 to 4.5), the decay exponent p is 1.135, 1.215 and 1.193, and the b-value 0.984, 1.104 and 1.302. Full-year fits reproduce counts in most time windows, but forecasts made from the first ten days fail badly in two of three cases: for Gorkha the model expected 18 events from day 10 to day 365 and 118 occurred, because an M7.3 aftershock on day 17 started its own sequence; for Kaikoura it expected 57 and 35 occurred. Full-year fits imply 5.5 to 6.9 events of magnitude 5 or more between days 30 and 365, against 3 to 5 observed, and probabilities of 0.29 to 0.51 for at least one magnitude 6, against none observed. Båth's law, that the largest aftershock is about 1.2 units below the mainshock, failed for two sequences (differences 0.5 and 0.3).