Abstract
It has been argued that power-law time-to-failure fits for cumulative Benioff strain and an evolution in size-frequency statistics in the lead-up to large earthquakes are evidence that the crust behaves as a Critical Point (CP) system. If so, intermediate-term earthquake prediction is possible. However, this hypothesis has not been proven. If the crust does behave as a CP system, stress correlation lengths should grow in the lead-up to large events through the action of small to moderate ruptures and drop sharply once a large event occurs. However this evolution in stress correlation lengths cannot be observed directly. Here we show, using the lattice solid model to describe discontinuous elasto-dynamic systems subjected to shear and compression, that it is for possible correlation lengths to exhibit CP-type evolution. In the case of a granular system subjected to shear, this evolution occurs in the lead-up to the largest event and is accompanied by an increasing rate of moderate-sized events and power-law acceleration of Benioff strain release. In the case of an intact sample system subjected to compression, the evolution occurs only after a mature fracture system has developed. The results support the existence of a physical mechanism for intermediate-term earthquake forecasting and suggest this mechanism is fault-system dependent. This offers an explanation of why accelerating Benioff strain release is not observed prior to all large earthquakes. The results prove the existence of an underlying evolution in discontinuous elasto-dynamic systems which is capable of providing a basis for forecasting catastrophic failure and earthquakes.
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References
Abe, S., Mora, P., and Place, D. (2000), Extension of the Lattice Solid Model to Incorporate Temperature Related Effects, Pure Appl. Geophys. 157, 1867-1887.
Aki, K. (2000), Scale Dependence in Earthquake Processes and Seismogenic Structures, Pure Appl. Geophys., 157, 2249-2258.
Bowman, D. D., Ouillon, G., Sammis, C. G., Sornette, A., and Sornette, D. (1998), An Observational Test of the Critical Earthquake Hypothesis, J. Geophys. Res. 103, 24,359-24,372.
Bufe, C. G., and Varnes, D. J. (1993), Predictive Modeling of the Seismic Cycle in the Greater San Francisco Bay region, J. Geophys. Res. 98, 9,871-9,833.
Cundall, P. A. and Strack, O. D. L. (1979), A Discrete Numerical Model for Granular Assemblies, Géotectonique, 29, 47-65.
Geller, R. J., Jackson, D. D., Kagan, Y. Y., and Mulargia, F. (1997), Earthquakes Cannot be Predicted, Science 275, 1,616.
Jaumé, S. C. (2000), Changes in earthquake size frequency distributions underlying accelerating seismic momentlenergy release prior to large and great earthquakes. In GeoComplexity and the Physics of Earthquakes (Geophysical Monograph series; no. 120) (eds Rundle, J.B., Turcotte, D.L. and Klein, W.) pp 199-210 (Am. Geophys. Union, Washington, DC 2000).
Jaumé, S. C., Weatherley, D., and Mora, P. (2000), Accelerating Seismic Energy Release and Evolution of Event Time and Size Statistics: Results from two Heterogeneous Cellular Automaton Models, Pure appl. Geophys. 157, 2209-2226.
Jaumé, S. C. and Sykes, L. (1999), Evolving Towards a Critical Point: a Review of Accelerating Seismic Momentl Energy Release Prior to Large and Great Earthquakes, Pure appl. Geophys 155, 279-305.
Knopoff, L. (2000), The Magnitude Distribution of Declustered Earthquakes in Southern California, Proc. Nat. Acad. Sci. 97, 11,880-11,884.
Mora, P. (1992), A Lattice Solid Model for Rock Rheology and Tectonics, The Seismic Simulation Project Tech. Rep. 4, 3-28 (Institut de Physique du Globe, Paris).
Mora, P. and Place, D. (1993), A Lattice Solid Model for the Nonlinear Dynamics of Earthquakes, Int. J. Mod. Phys. C 4, 1059-1074.
Mora, P. and Place, D. (1994), Simulation of the Frictional Stick-slip Instability Pure Appl. Geophys. 143, 61-87.
Mora, P. and Place, D. (1998), Numerical Simulation of Earthquake Faults with Gouge: Towards a Comprehensive Explanation of the Heat Flow Paradox, J. Geophys. Res. I03/B9, 21,067-21,089.
Mora, P. and Place, D. (1999), The Weakness of Earthquake Faults, Geophys. Res. Lett. 26, 123-126.
Mora, P., Place, D., Abe, S., and Jaumé, S. (2000), Lattice solid simulation of the physics of earthquakes: The model, results and directions. In GeoComplexity and the Physics of Earthquakes (Geophysical Monograph series; no. 120) (eds. Rundle, J.B., Turcotte, D.L. and Klein, W.) pp 105-125 (American Geophys. Union, Washington, DC 2000).
Mora, P., Wang, Y. C., Yin, C., Place, D., and Yin, X. C. (2002), Simulation of the Load-unload Response Ratio and Critical Sensitivity in the Lattice Solid Model, Pure Appl. Geophys. 159, 2525-2536.
Place, D. and Mora, P. (1999), A Lattice Solid Model to Simulate the Physics of Rocks and Earthquakes: Incorporation of Friction, J. Comp. Phys. 150, 1-41.
Place, D. and Mora, P. (2000), Numerical Simulation of Localisation Phenomena in a Fault Zone, Pure Appl. Geophys. 157, 1821-1845.
Place, D. and Mora, P. (2001), A random lattice solid model for simulation of fault zone dynamics and fracture processes. In Bifurcation and Localisation Theory for Soils and Rocks’99 (eds Miihlhaus H-B., Dyskin A.V. and Pasternak, E.) (AA Balkema, Rotterdam/Brookfield 2001).
Place, D., Lombard, F., Mora, P., and Abe, S. (2002), Simulation of the Micro-physics of Rocks Using LSMearth, Pure Appl. Geophys. 159, 1911-1932.
Rundle, J. B., Klein, W., and Gross, S. (1999), A Physical Basis for Statistical Patterns in Complex Earthquake Populations: Models, Predictions and Tests Pure Appl. Geophys. 155, 575-607.
Sammis, C. G. and Smith, S. W. (1999), Seismic Cycles and the Evolution of Stress Correlations in Cellular Automaton Models of Fault Networks, Pure Appl. Geophys. 155, 307-334.
Sornette, D. and Sammis, C. G. (1995), Complex Critical Exponents from Renormalization Group Theory of Earthquakes: Implications for Earthquake Prediction, J. Phys. I. 5, 607-619.
Weatherley, D., Jaume, S. C., and Mora, P. (2000), Evolution of Stress Deficit and Changing Rates of Seismicity in Cellular Automaton Models of Earthquake Faults, Pure appl. Geophys. 157, 2183-2207.
Weatherley, D., Mora, P., and Xia, M. (2002), Long-range Automaton Models of Earthquakes: Power-law Accelerations, Correlation Evolution, and Mode Switching, Pure Appl. Geophys. 159, 2469-2490.
Wu, Z.L. (2000), Frequency-size Distribution of Global Seismicity seen from Broadband Radiated Energy, Geophys. J. Int. 142, 59-66.
Yin, X-C, Mora, P., Peng, K., Wang, Y., and Weatherley, D. (2002), Load-Unload Response Ratio, Accelerating Momentl Energy Release, Critical Region Scaling, and Earthquake Prediction, Pure Appl. Geophys. 159, 2511-2523.
Zoeller, G., Hatnzl, S., and Kurths, J. (2001), Observation of Growing Correlation Length as an Indicator for Critical Point Behaviour Prior to Large Earthquakes, J. Geophys. Res. 106, 2,167-2,175.
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Mora, P., Place, D. (2002). Stress Correlation Function Evolution in Lattice Solid Elasto-dynamic Models of Shear and Fracture Zones and Earthquake Prediction. In: Matsu’ura, M., Mora, P., Donnellan, A., Yin, Xc. (eds) Earthquake Processes: Physical Modelling, Numerical Simulation and Data Analysis Part II. Pageoph Topical Volumes. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8197-5_13
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DOI: https://doi.org/10.1007/978-3-0348-8197-5_13
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