Bayesian spatiotemporal stochastic partial differential equation for high-resolution earthquake magnitude mapping: Application to Sumatra Island, Indonesia.

Indonesia's location at the convergence of the Eurasian, Indo-Australian, and Pacific plates makes it highly susceptible to earthquakes, particularly along the megathrust zone in Sumatra. Given the potential for severe damage and loss of life, spatiotemporal modeling of earthquake risk is crucial, especially in areas without recorded seismic events. One of the key preventive strategies is the development of an Early Warning System, which can help predict potential earthquakes based on seismic activity in specific locations. However, not all areas have recorded earthquake events, making it necessary to estimate seismic activity in unmeasured regions using spatial interpolation technique. This study applies the Stochastic Partial Differential Equation (SPDE) approach to estimate earthquake magnitude potential in unmeasured regions. The SPDE method transforms a continuous Gaussian Field (GF) into a computationally efficient Gaussian Markov Random Field (GMRF) by discretizing the spatial domain using triangulation. This approach overcomes the computational burden of the 'big n problem' in traditional GF models. By applying SPDE with a 10 km spatial range and 0.1 standard deviation, we produce high-resolution maps that support the development of early warning systems and inform seismic risk mitigation strategies.