Graphical and PC-software analysis of volcano eruption precursors according to the Materials Failure Forecast Method (FFM)

doi:10.1016/0377-0273(94)00078-U

Journal of Volcanology and Geothermal Research

Volume 64, Issues 3–4, March 1995, Pages 295-320

https://doi.org/10.1016/0377-0273(94)00078-U Get rights and content

Abstract

The Materials Failure Forecasting Method for volcanic eruptions (FFM) analyses the rate of precursory phenomena. Time of eruption onset is derived from the time of “failure” implied by accelerating rate of deformation. The approach attempts to fit data, Ω, to the differential relationship $\ddot{Ω} = A \dot{Ω}$ , where the dot superscript represents the time derivative, and the data Ω may be any of several parameters describing the accelerating deformation or energy release of the volcanic system. Rate coefficients,A and α, may be derived from appropriate data sets to provide an estimate of time to “failure”. As the method is still an experimental technique, it should be used with appropriate judgment during times of volcanic crisis. Limitations of the approach are identified and discussed.

Several kinds of eruption precursory phenomena, all simulating accelerating creep during the mechanical deformation of the system, can be used with FFM. Among these are tilt data, slope-distance measurements, crater fault movements and seismicity. The use of seismic coda, seismic amplitude-derived energy release and time-integrated amplitudes or coda lengths are examined. Usage of cumulative coda length directly has some practical advantages to more rigorously derived parameters, and RSAM and SSAM technologies appear to be well suited to real-time applications.

One graphical and four numerical techniques of applying FFM are discussed. The graphical technique is based on an inverse representation of rate versus time. For α = 2, the inverse rate plot is linear; it is concave upward for α < 2 and concave downward for α > 2. The eruption time is found by simple extrapolation of the data set toward the time axis. Three numerical techniques are based on linear least-squares fits to linearized data sets. The “linearized least-squares technique” is most robust and is expected to be the most practical numerical technique. This technique is based on an iterative linearization of the given rate-time series. The hindsight technique is disadvantaged by a bias favouring a too early eruption time in foresight applications. The “log rate versus log acceleration technique”, utilizing a logarithmic representation of the fundamental differential equation, is disadvantaged by large data scatter after interpolation of accelerations. One further numerical technique, a nonlinear least-squares fit to rate data, requires special and more complex software.

PC-oriented computer codes were developed for data manipulation, application of the three linearizing numerical methods, and curve fitting. Separate software is required for graphing purposes. All three linearizing techniques facilitate an eruption window based on a data envelope according to the linear least-squares fit, at a specific level of confidence, and an estimated rate at time of failure.

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The Failure Forecast Method (FFM) has been used to forecast the onset of volcanic eruptions with varying degrees of success. The method involves fitting its empirical equation to precursory observables, e.g., seismic data. Current models explaining the empirical equation assume that the seismic observables used (e.g., seismic event-rate, seismic moment-rate or seismic energy-rate) are related to accelerated fracture growth. In these models, such fracture growth results in an apparent increase in seismic activity. In this study, however, we propose an alternative explanation for the increase in seismicity culminating in volcanic eruptions. We suggest that the increase in seismicity, particularly in the seismic amplitudes, can result from ascending seismic sources towards the surface and that the increase can be used for eruption forecasts using the FFM. Our argument is based on the need for magma to migrate towards the surface to produce an eruption.
To test our argument, we used synthetic and field/real data and fitted them with the FFM model. The synthetic data is generated using the body wave attenuation equation, and the real data is from the Piton de la Fournaise eruption on January 2nd, 2010. We used seismic amplitudes and seismic amplitude ratios as the precursory observables and used a combination of Simulated Annealing and Bayesian Inversion algorithms to obtain the best-fit parameters of the FFM model and their posterior distributions. For the synthetic cases, we found that the method gave reasonable estimates of failure or eruption time, suggesting that the seismic amplitudes and the seismic amplitude ratios can be used for forecasting using the FFM. For the field/real cases, the results gave information about the timing of magma chamber failure, magma propagation, and the eruption onset. Our results highlight an example of modelling volcano monitoring data with the FFM that gives reasonable estimates of eruption time even if the data may not fully represent failure processes. We suggest that the result may still be reasonable owing to the empirical and asymptotic nature of the FFM combined with the underlying physics of magma and seismic migrations.
Spatial heterogeneity of precursory accelerating deformation in uniaxially compressed sandstones and prediction of failure time
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The power law acceleration has been validated as an effective method for predicting failure time, however, the precursory acceleration distribution in local monitoring signals is still unclear. In this paper, the spatial distributions of precursory acceleration of strains at different positions and in various size windows are reported based on surface strain fields measured from sandstone. The sandstone specimens are uniaxially compressed and a digital image correlation technique is applied to monitor the evolution of surface strain fields. The precursory acceleration of strains exhibits heterogeneities in amplitudes and durations, which are related to the evolution of strain localization in a higher strain zone. Strain rates at higher strain zones are prone to acceleration. There exists a well-defined size for monitoring and identifying the precursory acceleration of strains. In the vicinity of failure, strain accelerations in different positions and various size windows are described by a power law behavior with a constant exponent. The results show that prediction is stable and agrees well with the actual failure time.
Creep of clayey soil induced by elevated pore-water pressure: Implication for forecasting the time of failure of rainfall-triggered landslides
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Many models have been proposed to forecast the time of failure of landslides, among them the Voight model ( $\ddot{Ω} = A {\dot{Ω}}^{α}$ ) has been widely used. Values for controlling parameters of α and A, defined by accelerating movement, are representative of kinematic behavior prior to material failure. Nevertheless, due to the unknowns in the key parameters (α and A), failure-time forecast using this model remains elusive. To examine the nature of these two parameters and their physical background, we conducted ring-shear tests on clayey soil to reproduce tertiary creep through two different approaches: a pore-water pressure-controlled approach to simulate the initiation process of landslides resulting from elevated pore-water pressure during rainfall, and a shear-stress-controlled approach often used in studies of the creep behavior of clayey soils. By examining the creeping behavior observed in the pore-water pressure-controlled tests, we found a 3-stage log-linear relationship between velocity and acceleration. The sample showed drastic dilation with short shear displacement in the first stage, and the dilation decreased in the subsequent two stages with further progress of shear displacement. The smaller value of α in the first stage increased to another value which was larger in the third stage. This variation might result from changes in the dominant shear mechanisms, i.e., in the first stage the observed creeping displacement results from pervasive grain realignment within a relatively wide shear zone, while in the following two stages, it may arise from more localized grain slip within a narrowing domain of shear zone along the sliding surface. In contrast, no evident variations in α value or sample height were found in the shear-stress-controlled tests. The effects of increasing rate of pore-water pressure or shear stress on the value of α were not pronounced in our tests. These results provide further information for understanding the progressive failure process and the Voight model of failure-time forecast. The failure-time forecast of rainfall-triggered landslides could be fundamentally difficult because of a changeable α value with the intricate volumetric variation and a diverse range of operating shear mechanisms involved.
Method selection in short-term eruption forecasting
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For accurate and timely information on the evolving state of our volcanoes we need reliable short-term forecasts. These forecasts directly impact crisis management from evacuations, exclusion zones, and when it is safe to return. Eruption forecasting should not be viewed as an academic exercise or a theoretical discussion in a back room, nor is now the time for dramatic data interpretations or a set of ‘we-told-you-so’ hindcasting demonstrations. To produce a short-term eruption forecast, a systematic evaluation of options is required with a critical assessment of outstanding issues and assumption validity. We run this lens over a set of existing short-term eruption forecasting methods and provide a straightforward data-driven methodology for forecast selection. Six eruption forecasting methods are discussed here: (1) Expert interpretation, (2) Event trees, (3) Belief networks, (4) Failure forecasting, (5) Process / Source models, and (6) Machine-learning algorithms with a view to forecasting: (1) Eruption occurrence (onset time), (2) Eruptive vent location(s), (3) Eruption size, (4) Initial eruption style/phase, (5) Eruption phase duration, and (6) Eruption specific hazards.
This work constitutes a decision tool that can be directly applied to a volcanic system of interest to determine which eruption forecasting methods are possible, plausible, and with what implementation steps. Accompanying this is an extensive evaluation of assumption validity (and assumption avoidance options) to ensure the accurate and transparent application of any eruption forecasting method. Significant potential is identified in methods that are generally data-hungry (e.g., belief networks and machine-learning algorithms), and/or by the coupling of probabilistic methods to process/source models. However, as most volcanic systems are data-poor, expert interpretation and event trees remain the only currently available forecasting methods that can be readily and widely applied during volcanic crises.
A probabilistic estimation approach for the failure forecast method using Bayesian inference
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Positive-feedback mechanisms such as fatigue induce a self-accelerating behavior, captured by models displaying infinite limit-state asymptotics, collectively known as the failure forecast method (FFM). This paper presents a Bayesian model parameter estimation approach to the fully nonlinear FFM implementation and compares the results to the classic linear regression formulation, including a regression uncertainty model. This process is demonstrated in a cyclic loading fatigue crack propagation application, both on a synthetic data set and on a full fatigue experiment. A novel ”switch point” parameter is included in the Bayesian formulation to account for nonstationary changes in the growth parameter.
Differences of precursory seismic energy release for the 2007 effusive dome-forming and 2014 Plinian eruptions at Kelud volcano, Indonesia
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Citation Excerpt :
Tokarev (1971) calculated the seismic strain before the 1955–1961 Bezymianny eruption, the 1964 Shiveluch eruption, and the 1962 Tokachi eruption, finding that the cumulative increase in seismic strain is described by a hyperbolic function and that the eruption times corresponded approximately to the time at which the hyperbola approaches the vertical asymptote. Voight (1988, 1989), Voight and Cornelius (1991), and Cornelius and Voight (1995) developed a method for calculating the predicted onset time of eruptions based on analysis of the rate of precursory phenomena (the material failure forecast method, or FFM). In this paper, we focus on the VT seismic activity recorded at the Kelud Volcano Observatory (Fig. 1) during the five-week periods immediately preceding the 2007 and 2014 eruptions.
Early warnings of the timing, style, and size of volcanic eruptions, made on the basis of seismic monitoring, are important for mitigation of the hazards associated with volcanic eruptions. We calculated the rates of seismic energy release at Kelud volcano, Indonesia, preceding both the 2007 effusive lava-dome eruption and the 2014 Plinian eruption. For the 2007 eruption, there was first a step-wise increase in the rate of release of seismic energy, followed by a gradual decrease until the eruption. For the 2014 eruption, the rate of energy release was almost constant until 10 days before the eruption, then gradually increased until there was a dramatic acceleration during the last day before the eruption. The total seismic energy released by the 2007 and 2014 eruptions were 3 × 10⁸ J and 2.2 × 10⁹ J, respectively. The relative difference between the ejected volumes of the 2007 and 2014 eruptions is roughly equivalent to that of the total seismic energy released preceding the eruptions. We conducted several trials of the material failure forecast method (FFM), applying it to the square root of the rate of seismic energy released, to assess its usefulness for predicting the timing of eruptions. The predicted onset of the 2007 eruption was one day earlier than the actual eruption and the seismic energy release preceding the actual eruption did not increase dramatically as suggested by the FFM model. Several trials of FFM for the 2014 eruption predicted the onset of the eruption to be three days to two weeks later than the actual eruption. Even as the end time of the FFM time window approaches several hours to 10 min before the actual eruption onset, the predicted eruption onset is still 3 h later than the actual onset. Thus, the results of our FFM modeling did not show the method to be useful for predicting eruption times for Kelud volcano. The differences of the FFM modeling results for the 2007 and 2014 eruptions likely reflect the differences in the rate of energy release immediately before the two eruptions: a deceleration before the 2007 eruption and an acceleration before the 2014 eruption. These differences may reflect differences in precursory processes for effusive lava-dome and Plinian eruptions.

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: This contribution is part of a collection of papers presented in tribute to Dr. Harry Glicken. The contributions appear in issue (64/3/4) and in a Special Issue (Vol. 66) of this journal.

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Research paperGraphical and PC-software analysis of volcano eruption precursors according to the Materials Failure Forecast Method (FFM)

Abstract

J. Volcanol. Geotherm. Res.

J. Volcanol. Geotherm. Res.

J. Volcanol. Geotherm. Res.

Nature

Analysis of the seismic coda of local earthquakes as scattered waves

J. Geophys. Res.

Deep volcanic tremor and magma ascent mechanism under Kilauea, Hawaii

J. Geophys. Res.

Quantitative Scismology

Data Reduction and Error Analysis for Physical Sciences

Feasibility Study for the Materials Science Approach to Volcano Eruption Prediction

A materials failure relation of accelerating creep as empirical description of damage accumulation

Rock Mech. Rock Eng.

Determination of eruption-prediction constants for accelerated creep or seismicity

Geol. Soc. Am., Abstr. Progr.

Feasibility of material failure approach to eruption prediction for Mount St. Helens, 1985 and 1986

EOS Trans. Am. Geophys. Union

Monitoring volcano precursory activity with the materials failure approach, using rates of cumulative seismic coda length

Geol. Soc. Am., Abstr. Progr.

RSAM and SSAM seismic analyses with the Materials Failure Forecast Method (FFM),June 1991 explosive eruption at Pinatubo Volcano, Philippines

U.S. Geol. Surv., Prof. Pap.

Small earthquakes, structure, and tectonics of the Puget Sound region

Bull. Seismol. Soc. Am.

Determination of amplitude and duration magnitudes and site residuals from short-period seismographs in northern California

Bull. Seismol. Soc. Am.

Real-time seismic amplitude measurement (RSAM): a volcano monitoring and prediction tool

Bull. Volcanol.

Locations, magnitudes, and statistics of the March 20–May 18 earthquake sequence

U.S. Geol. Surv., Prof. Pap.

Observations of volcanic tremor at Mount St. Helens volcano

J. Geophys. Res.

A new method for predicting the failure time of a slope

Research paper
Graphical and PC-software analysis of volcano eruption precursors according to the Materials Failure Forecast Method (FFM)