Role of critical stress in quantifying the magnitude of fluid-injection triggered earthquakes

Abstract

Here we define and report the relationship between the maximum seismic magnitude (M) and injection volume (ΔV) through fluid-injection fault-reactivation experiments and analysis. This relationship incorporates the in situ shear modulus (G) and fault pre-stress as a fraction of the strength drop (c), expressed as M = c/(1-c) GΔV. Injection response defines a sigmoidal relation in M−ΔV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M-\\Delta {V}$$\\end{document} space with unit gradient limbs linked by an intermediate up-step. Both laboratory observations and analysis for a rigid fault with slip limited to the zone of pressurization show trajectories of cumulative M−ΔV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M-\\Delta {V}$$\\end{document} that evolve at a gradient of unity, are offset in order of increasing pre-stress and are capable of step changes in moment with shear reactivation at elevated critical-stresses – key features apparent in field observations. The model and confirmatory laboratory observations explain the occurrence of some triggered earthquakes at EGS sites significantly larger than expected relative to injection volumes and based on previous models.