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![]() As might be expected, the final portion of the sequence is the most important, while uncertainty on the start of the sequence is less important. We find that for heterogeneous systems, there is a critical proportion of the sequence that needs to have occurred before a forecast time converges on relatively low errors. We then analyse the effect of having an incomplete data sequence, as might be the case for real-time forecasting scenarios. We demonstrate that the heterogeneity of a system is crucial to making accurate forecasts on the sample scale, such that homogeneous systems are inherently unpredictable. We explore the success of these tools in the laboratory by briefly reviewing datasets that have been presented previously and comparing the range of errors on forecast times with the range of errors associated with attempts to retrospectively forecast eruptions. In both cases, empirical relationships between the acceleration and the time of the singular final event have offered tantalizing possibilities for forecast of eruptions and material failure. At the volcano scale, eruption is often preceded by accelerating seismicity, while at the laboratory scales, sample failure appears to be preceded by similarly accelerating Acoustic Emission (AE). Magmas fracture under high shear stresses, producing radiating elastic waves. The presented method will contribute to our ability of unraveling the physical processes at the base of catastrophic rock failure, including the nucleation of earthquakes, landslides, and volcanic eruptions. We detected the abrupt change in the fracture pattern from distributed tensile microcracks to localized shear failure in a fracture network produced by triaxial deformation of a sandstone core plug. For the first time, we used an image analysis tool developed to investigate orientation changes at different scales in images of fracture patterns in faulted materials, based on a two-dimensional continuous wavelet analysis. However, considerable uncertainty exists regarding both the length scale at which this transition occurs and the underlying causes that prompt this shift from a distributed to a localized assemblage of cracks or fractures. The mechanics of brittle failure is a well-described multiscale process that involves a rapid transition from distributed microcracks to localization along a single macroscopic rupture plane. Finally, we provide a quantitative and pragmatic correction for the systematic error in the forecast failure time, valid for structurally isotropic porous materials, which could be tested against larger-scale natural failure events, with suitable scaling for the relevant inter-flaw distances. When this is not the case, the predicted failure time is much less accurate and failure is preceded by an exponential AE rate trend. A smooth inverse power-law acceleration of AE rate to failure, and an accurate forecast, occurs when the cracks are sufficiently long to bridge pore spaces. ![]() The style of acceleration of AE rate prior to failure, and the accuracy of forecast failure time, both depend on whether the cracks can span the inter-flaw length or not. We use new experimental datasets for the deformation of porous materials to infer the critical crack length at failure from a static damage mechanics model. Here we test the hypothesis that the accuracy of the forecast failure time depends on the inter-flaw distance in the starting material. Until now, the length scale associated with precursory events has not been well quantified, resulting in forecasting tools that are often unreliable. A key unsolved research question is how to accurately forecast the time of system-sized catastrophic failure, based on observations of precursory events such as acoustic emissions (AE) in laboratory samples, or, on a larger scale, small earthquakes. Multi-scale failure of porous materials is an important phenomenon in nature and in material physics – from controlled laboratory tests to rockbursts, landslides, volcanic eruptions and earthquakes. ![]()
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