Applicability of time-to-failure analysis to accelerated strain before earthquakes and volcanic eruptions

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Abstract / Description of output

We examine quantitatively the ranges of applicability of the equation Ω=A+B[1−t/tf ]m for predicting ‘system-sized’ failure times tf in the Earth. In applications Ω is a proxy measure for strain or crack length, and A, B and the index m are model parameters determined by curve fitting. We consider constitutive rules derived from (a) Charles’ law for subcritical crack growth; (b) Voight’s equation; and (c) a simple percolation model, and show in each case that this equation holds only when m < 0. When m > 0, the general solution takes the form Ω = A + B[1 + t/T ]m, where T is a positive time constant, and no failure time can be defined. Reported values for volcanic precursors based on rate data are found to be within the range of applicability of time-to-failure analysis (m < 0). The same applies to seismic moment release before earthquakes, at the expense of poor retrospective predictability of the time of the a posteriori-defined main shock. In contrast, reported values based on increasing cumulative Benioff strain occur in the region where a system-sized failure time cannot be defined (m > 0; commonly m ≈ 0.3). We conclude on physical grounds that cumulative seismic moment is preferred as the most direct measure of seismic strain. If cumulative Benioff strain is to be retained on empirical grounds, then it is important that these data either be re-examined with the independent constraint m < 0, or that for the case 0 < m + 1 < 1, a specific correction for the time-integration of cumulative data be applied, of the form ΣΩ = At + B′{1 − [1 − t/tf ]m+1 }.
Original languageEnglish
Pages (from-to)F1-F6
Number of pages6
JournalGeophysical Journal International
Issue number3
Publication statusPublished - 1 Dec 1999


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