Fractal dimensions can lead to spurious interpretations of fault-rock character and slip physics
DOI:
https://doi.org/10.26443/seismica.v5i2.3008Abstract
Cataclasis is defined by a combination of distributed microcracking and frictional sliding. These processes lead to mechanical wear and grain-size reduction along fault surfaces during both seismic and aseismic slip. A preponderance of research has utilized “fractal dimensions” extracted from fault-rock particle size distributions as a vehicle to infer the dynamics of strain accommodation and energy release during fault slip. Little work, however, has been done to quantitatively assess the validity of such metrics. Using a series of simple numerical experiments, we show that the fractal dimension provides an unreliable descriptor of fault-rock microstructures and the cataclastic processes that govern their evolution. Our results demonstrate that the most common approaches to estimating fractal dimensions during microstructural analysis are prone to previously unidentified measurement uncertainties. The magnitude of these uncertainties is large relative to what has been considered mechanically and seismologically meaningful by previous work. We conclude that errors inherent in the use of fractal dimensions have likely led to spurious interpretations of fault-rock character and slip physics over the last several decades.
References
An, L.-J., & Sammis, C. G. (1994). Particle size distribution of cataclastic fault materials from Southern California: A 3-D study. Pure and Applied Geophysics, 143(1–3), 203–227. https://doi.org/10.1007/bf00874329
Ben-zion, Y., & Sammis, C. G. (2003). Characterization of Fault Zones. In Seismic Motion, Lithospheric Structures, Earthquake and Volcanic Sources: The Keiiti Aki Volume (pp. 677–715). Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-8010-7_11
Berger, A., & Herwegh, M. (2022). Grain-size-reducing-and mass-gaining processes in different hydrothermal fault rocks. Geological Magazine, 159(11–12), 2219–2237. https://doi.org/10.1017/s0016756822000218
Blenkinsop, T. G. (1991). Cataclasis and processes of particle size reduction. Pure and Applied Geophysics, 136(1), 59–86. https://doi.org/10.1007/bf00878888
Chester, J. S., Chester, F. M., & Kronenberg, A. K. (2005). Fracture surface energy of the Punchbowl fault, San Andreas system. Nature, 437(7055). https://doi.org/10.1038/nature03942
Clauset, A., Shalizi, C. R., & Newman, M. E. J. (2009). Power-Law Distributions in Empirical Data. SIAM Review, 51(4), 661–703. https://doi.org/10.1137/070710111
Dor, O., Ben-Zion, Y., Rockwell, T. K., & Brune, J. (2006). Pulverized rocks in the Mojave section of the San Andreas Fault Zone. Earth and Planetary Science Letters, 245(3–4), 642–654. https://doi.org/10.1016/j.epsl.2006.03.034
Dyer, H., Amitrano, D., & Boullier, A.-M. (2012). Scaling properties of fault rocks. Journal of Structural Geology, 45, 125–136. https://doi.org/10.1016/j.jsg.2012.06.016
Engelder, J. T. (1974). Cataclasis and the Generation of Fault Gouge. Geological Society of America Bulletin, 85(10), 1515. https://doi.org/10.1130/0016-7606(1974)85<1515:catgof>2.0.co;2
Fagereng, AAke, Remitti, F., & Sibson, R. H. (2011). Incrementally developed slickenfibers—Geological record of repeating low stress-drop seismic events? Tectonophysics, 510(3–4), 381–386. https://doi.org/10.1016/j.tecto.2011.08.015
Hadizadeh, J., & Johnson, W. K. (2003). Estimating local strain due to comminution in experimental cataclastic textures. Journal of Structural Geology, 25(11), 1973–1979. https://doi.org/10.1016/s0191-8141(03)00016-6
Hadizadeh, J., Sehhati, R., & Tullis, T. (2010). Porosity and particle shape changes leading to shear localization in small-displacement faults. Journal of Structural Geology, 32(11), 1712–1720. https://doi.org/10.1016/j.jsg.2010.09.010
Hadizadeh, J., Tullis, T. E., White, J. C., & Konkachbaev, A. I. (2015). Shear localization, velocity weakening behavior, and development of cataclastic foliation in experimental granite gouge. Journal of Structural Geology, 71, 86–99. https://doi.org/10.1016/j.jsg.2014.10.013
Heilbronner, R., & Keulen, N. (2006). Grain size and grain shape analysis of fault rocks. Tectonophysics, 427(1–4), 199–216. https://doi.org/10.1016/j.tecto.2006.05.020
Hirose, T., Mizoguchi, K., & Shimamoto, T. (2012). Wear processes in rocks at slow to high slip rates. Journal of Structural Geology, 38, 102–116. https://doi.org/10.1016/j.jsg.2011.12.007
Johnson, S. E., Song, W. J., Vel, S. S., Song, B. R., & Gerbi, C. C. (2021). Energy Partitioning, Dynamic Fragmentation, and Off‐Fault Damage in the Earthquake Source Volume. Journal of Geophysical Research: Solid Earth, 126(11). https://doi.org/10.1029/2021jb022616
Keulen, N., Heilbronner, R., Stünitz, H., Boullier, A.-M., & Ito, H. (2007). Grain size distributions of fault rocks: A comparison between experimentally and naturally deformed granitoids. Journal of Structural Geology, 29(8), 1282–1300. https://doi.org/10.1016/j.jsg.2007.04.003
Kimura, G., Hamada, Y., Yabe, S., Yamaguchi, A., Fukuchi, R., Kido, Y., Maeda, L., Toczko, S., Okuda, H., Ogawa, N., Morioka, H., Ujiie, K., & Saffer, D. (2022). Deformation Process and Mechanism of the Frontal Megathrust at the Nankai Subduction Zone. Geochemistry, Geophysics, Geosystems, 23(4). https://doi.org/10.1029/2021gc009855
Kohlmayer, N., & Grasemann, B. (2012). Quantitative Characterisation of Cataclasites using a statistical approach (Analysis of Variance). Austrian Journal of Earth Sciences, 105(3), 48–60.
Li, Y., Hu, W., Xu, Q., Huang, R., Chang, C., & McSaveney, M. (2024). Evolution of Power‐Law Particle‐Size Distributions in Dense Grain‐Flow Experiments. Journal of Geophysical Research: Earth Surface, 129(10). https://doi.org/10.1029/2024jf007844
Mancktelow, N. S., Camacho, A., & Pennacchioni, G. (2022). Time‐Lapse Record of an Earthquake in the Dry Felsic Lower Continental Crust Preserved in a Pseudotachylyte‐Bearing Fault. Journal of Geophysical Research: Solid Earth, 127(4). https://doi.org/10.1029/2021jb022878
Marone, C., & Scholz, C. H. (1989). Particle-size distribution and microstructures within simulated fault gouge. Journal of Structural Geology, 11(7), 799–814. https://doi.org/10.1016/0191-8141(89)90099-0
Melosh, B. L., Rowe, C. D., Smit, L., Groenewald, C., Lambert, C. W., & Macey, P. (2014). Snap, Crackle, Pop: Dilational fault breccias record seismic slip below the brittle–plastic transition. Earth and Planetary Science Letters, 403, 432–445. https://doi.org/10.1016/j.epsl.2014.07.002
Morgan, J. K., & Boettcher, M. S. (1999). Numerical simulations of granular shear zones using the distinct element method: 1. Shear zone kinematics and the micromechanics of localization. Journal of Geophysical Research: Solid Earth, 104(B2), 2703–2719. https://doi.org/10.1029/1998jb900056
Muto, J., Nakatani, T., Nishikawa, O., & Nagahama, H. (2015). Fractal particle size distribution of pulverized fault rocks as a function of distance from the fault core. Geophysical Research Letters, 42(10), 3811–3819. https://doi.org/10.1002/2015gl064026
Ord, A., Blenkinsop, T., & Hobbs, B. (2022). Fragment size distributions in brittle deformed rocks. Journal of Structural Geology, 154, 104496. https://doi.org/10.1016/j.jsg.2021.104496
Phillips, N. J., Belzer, B., French, M. E., Rowe, C. D., & Ujiie, K. (2020). Frictional Strengths of Subduction Thrust Rocks in the Region of Shallow Slow Earthquakes. Journal of Geophysical Research: Solid Earth, 125(3). https://doi.org/10.1029/2019jb018888
Phillips, N. J., & Williams, R. T. (2021). To D or not to D? Re-evaluating particle-size distributions in natural and experimental fault rocks. Earth and Planetary Science Letters, 553, 116635. https://doi.org/10.1016/j.epsl.2020.116635
Pizzati, M., Balsamo, F., & Storti, F. (2023). Fingerprints and energy budget of the earthquake cycle in shallow sediments. Journal of Structural Geology, 170, 104858. https://doi.org/10.1016/j.jsg.2023.104858
Rawling, G. C., & Goodwin, L. B. (2003). Cataclasis and particulate flow in faulted, poorly lithified sediments. Journal of Structural Geology, 25(3), 317–331. https://doi.org/10.1016/s0191-8141(02)00041-x
Rockwell, T., Sisk, M., Girty, G., Dor, O., Wechsler, N., & Ben-Zion, Y. (2009). Chemical and physical characteristics of pulverized Tejon Lookout granite adjacent to the San Andreas and Garlock faults: Implications for earthquake physics. In Mechanics, Structure and Evolution of Fault Zones (pp. 1725–1746). Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0138-2_9
Sammis, C. G., & Ben‐Zion, Y. (2008). Mechanics of grain‐size reduction in fault zones. Journal of Geophysical Research: Solid Earth, 113(B2). https://doi.org/10.1029/2006jb004892
Sammis, C. G., & Biegel, R. L. (1989). Fractals, Fault-Gouge, and Friction. In Fractals in Geophysics (pp. 255–271). Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-6389-6_14
Sammis, C. G., Osborne, R. H., Anderson, J. L., Banerdt, M., & White, P. (1986). Self-similar cataclasis in the formation of fault gouge. Pure and Applied Geophysics, 124(1–2), 53–78. https://doi.org/10.1007/bf00875719
Sammis, C., King, G., & Biegel, R. (1987). The kinematics of gouge deformation. Pure and Applied Geophysics, 125(5). https://doi.org/10.1007/bf00878033
Storti, F., Billi, A., & Salvini, F. (2003). Particle size distributions in natural carbonate fault rocks: insights for non-self-similar cataclasis. Earth and Planetary Science Letters, 206(1–2), 173–186. https://doi.org/10.1016/s0012-821x(02)01077-4
White, E. P., Enquist, B. J., & Green, J. L. (2008). ON ESTIMATING THE EXPONENT OF POWER-LAW FREQUENCY DISTRIBUTIONS. Ecology, 89(4), 905–912. https://doi.org/10.1890/07-1288.1
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