Physics-informed deep learning to forecast $${\widehat{{\varvec{M}}}}_{{\varvec{m}}{\varvec{a}}{\varvec{x}}}$$ during hydraulic fracturing

Abstract

Short-term forecasting of estimated maximum magnitude ($${\widehat{M}}_{max}$$ M ^ max ) is crucial to mitigate risks of induced seismicity during fluid stimulation. Most previous methods require real-time injection data, which are not always available. This study proposes two deep learning (DL) approaches, along with two data-partitioning methods, that rely solely on preceding patterns of seismicity. The first approach forecasts $${\widehat{M}}_{max}$$ M ^ max directly using DL; the second incorporates physical constraints by using DL to forecast seismicity rate, which is then used to estimate $${\widehat{M}}_{max}$$ M ^ max . These approaches are tested using a hydraulic-fracture monitoring dataset from western Canada. We find that direct DL learns from previous seismicity patterns to provide an accurate forecast, albeit with a time lag that limits its practical utility. The physics-informed approach accurately forecasts changes in seismicity rate, but sometimes under- (or over-) estimates $${\widehat{M}}_{max}$$ M ^ max . We propose that significant exceedance of $${\widehat{M}}_{max}$$ M ^ max may herald the onset of runaway fault rupture.