Forecasting volcanic eruptions and other material failure phenomena: An evaluation of the failure forecast method

Abstract

Power‐law accelerations in the mean rate of strain, earthquakes and other precursors have been widely reported prior to material failure phenomena, including volcanic eruptions, landslides and laboratory deformation experiments, as predicted by several theoretical models. The Failure Forecast Method (FFM), which linearizes the power‐law trend, has been routinely used to forecast the failure time in retrospective analyses; however, its performance has never been formally evaluated. Here we use synthetic and real data, recorded in laboratory brittle creep experiments and at volcanoes, to show that the assumptions of the FFM are inconsistent with the error structure of the data, leading to biased and imprecise forecasts. We show that a Generalized Linear Model method provides higher‐quality forecasts that converge more accurately to the eventual failure time, accounting for the appropriate error distributions. This approach should be employed in place of the FFM to provide reliable quantitative forecasts and estimate their associated uncertainties.

An accelerating precursor to predict “time-to-failure” in creep and volcanic eruptions

“…For both the classical FFM (Voight, 1988(Voight, , 1989Kilburn and Voight, 1998;De la Cruz-Reyna and Reyes-Davila, 2001;Kilburn and Petley, 2003;Sparks, 2003;Smith et al, 2007;Lengliné et al, 2008;Lavallée et al, 2008;Bell et al, 2011aBell et al, , 2011bBell et al, , 2013Bell and Kilburn, 2012;Kilburn, 2012;Boué et al, 2015;Salvage and Neuberg, 2016) and the present method, the signal has to be differentiated with respect to time and inverted, hence large fluctuations introduced by these operations pose an important limitation in terms of real-time operational usage. In the relation of Eq.…”

“…Such acceleration precursors have been confirmed in the laboratory (Cornelius and Scott, 1993;Lavallée et al, 2008;Heap et al, 2009;Smith et al, 2009;Kilburn, 2012;Hao et al, 2014;Bell et al, 2011aBell et al, , 2011bVasseur et al, 2015). To provide insights into the accelerating behavior near the failure point, damage models have been developed to explain accelerating seismicity or deformation rates prior to rock failure (Main, 1999), volcanic eruptions (Kilburn and Petley, 2003), and landslides (Helmstetter et al, 2004).…”

Volcano Seismology: Detecting Unrest in Wiggly Lines

“…Although assuming that a ¼ 2 is the simplest method to estimate the timing of an eruption through a linear regression and therefore the most common application of the FFM in hindsight analysis, some authors have suggested that it may not be an appropriate assumption for use with the FFM (e.g. Bell et al 2011). Additionally, some authors have argued that a may evolve with time as precursory sequences develop, which is not detailed in the FFM (Kilburn 2003).…”

“…Greenhough and Main (2008) have suggested that since earthquake occurrence is a point process, the rate uncertainties are best described by a Poisson distribution. In this instance, a generalised linear model (GLM) where a ¼ 1, rather than a least squares regression model a ¼ 2 ð Þ may be more appropriate, since it can allow for a distribution of data that is non-Gaussian (Bell et al 2011). At Soufrière Hills volcano, however, the use a GLM to forecast the timing of eruptive events in 1997 and 2003 failed to generate an appropriate forecast (Salvage and Neuberg 2016).…”

“…Additionally, some authors have argued that a may evolve with time as precursory sequences develop, which is not detailed in the FFM (Kilburn 2003). As the FFM follows a least squares regression analysis when a is equal to 2, the residual error between the observed event rate and the mean event rate of seismicity should follow a typical Gaussian distribution (Bell et al 2011). Greenhough and Main (2008) have suggested that since earthquake occurrence is a point process, the rate uncertainties are best described by a Poisson distribution.…”