Estimation of Jayapura 2023 Aftershock Decay Time Using Python-Based Secant Algorithm - Rayhan Irfan Hielmy; Sandy Tri Gustono (Journal of Computation Physics and Earth Science (JoCPES), 2025)
Accurately determining the termination time of aftershocks is crucial for disaster mitigation and establishing safe periods for community recovery. This study aimed to estimate the decay time of the January 2023 Jayapura aftershock sequence (M 5.4) using a numerical computational approach. The Mogi II decay model was selected due to its high compatibility with local seismicity. To resolve its complex non-linear exponential equations without analytical derivatives, the Secant Method was implemented using Python. The algorithm was initialized with starting guess values of x0=0 and x1=1, and an error tolerance of 0.0001. To validate algorithmic robustness and efficiency, a sensitivity test was conducted, and the method was benchmarked against the Bisection method. Results demonstrated that the Secant algorithm achieved superior computational efficiency, converging in exactly 10 iterations (~0.000115 seconds) compared to Bisection's 18 iterations, while remaining highly stable under arbitrary extreme initial guesses. The numerical solution predicted the decay termination at day 12.765, subsequently rounded to 13 days following the mainshock. This finding showed exact agreement with manual observational data, successfully extrapolating the decay trajectory beyond the 10-day BMKG recording window. The study concluded that the Python-based Secant algorithm is effective, rapid, robust, and precise in solving the Mogi II equation, demonstrating significant potential as an automated analytical tool to enhance disaster mitigation decision-making.