Novel Approach to Uncertainty Study of Microseismic Hypocentres Using Bootstrap and Monte Carlo Methods in the Patuha Geothermal Field

Abstract Due to data acquisition and processing limitations, uncertainty is an inherent part of geophysics, which hinders the ability to capture Earth’s complex and variable nature. Geophysicists rely on assumptions, simplifications, homogeneity, and linearity to approximate and understand these natural phenomena, including modeling. Additionally, statistical methods are employed to assess the geophysicist’s probability of understanding these natural phenomena. The statistical method in this study is used to refine human-induced uncertainty derived from seismogram analysis software using Bootstrap and Monte Carlo. The Bootstrap method, a technique involving random sampling, is employed to estimate a new deterministic arrival time and its standard deviation. Subsequently, a Monte Carlo simulation is conducted, generating numerous samples of the latest synthetic dataset based on a Gaussian distribution. A sensitivity analysis is then performed using the hypocentre locating software. This study showcases an innovative approach that uses the uncertainty of a single standard deviation to provide lower X- and Y-axis (distant) errors compared to other uncertainty time windows. Bootstrap and Monte Carlo methods provide standard deviation values after manual picking using seismogram analysis software. Statistically, after the software runs, the uncertainty value is no more sensitive for an error distance lower than or equal to 100 meters. Within this error distance, the difference in the hypocentre location of different uncertainty values is less than 25 meters. Therefore, an error distance lower than or equal to 100 meters has a high confidence level.