Seismic magnitude calculation based on rate- and state-dependent friction law

Abstract

In the engineering related to seismic activities, such as shale gas extraction and EGS system, numerical simulation is a common research method. In current numerical simulations, the critical value of a variable (e.g., sliding velocity) is often set artificially to determine whether the element is destabilized, on which the seismic magnitude is calculated. This practice is highly subjective and arbitrary, which leads to inaccurate calculation results. In this paper, we propose a new method for calculating seismic magnitude based on the rate-state dependent friction law. Firstly, the sliding history of each element on the sliding surface is divided into stages, and then all elements in the coseismic stage are clustered in time and space. Finally, the seismic moment of an event is obtained by calculating the sum of the corresponding areas of the “cumulative slip-fault location” plot according to the clustering labels, which in turn gives the seismic magnitude.

Keywords

numerical simulation / seismic magnitude / stage division / clustering / critical criterion

References

[1] ChenY, LiuR. Earthquake magnitude [J]. Seismological and Geomagnetic Observation and Research, 2004, 25(6): 1-12

[2] ChenY, LiuR. Moment magnitude and its calculation [J]. Earthquake Research in China, 2018, 32(4): 447-455

[3] ShrivastavaM N, GonzálezG, MorenoM, et al. . Earthquake segmentation in northern Chile correlates with curved plate geometry [J]. Scientific Reports, 2019, 9: 4403

[4] AtkinsonG M, EatonD W, IgoninN. Developments in understanding seismicity triggered by hydraulic fracturing [J]. Nature Reviews Earth & Environment, 2020, 1(5): 264-277

[5] LeeK K, EllsworthW L, GiardiniD, et al. . Managing injection-induced seismic risks [J]. Science, 2019, 364(6442): 730-732

[6] KangJ, ZhuJ, ZhaoJ. A review of mechanisms of induced earthquakes: From a view of rock mechanics [J]. Geomechanics and Geophysics for Geo-Energy and Geo-Resources, 2019, 5(2): 171-196

[7] AkiK, RichardsP GQuantitative seismology: Theory and methods [M], 19862nd ed.California, University Science Books

[8] ChengQ, WangX, GhassemiA. Numerical simulation of reservoir stimulation with reference to the Newberry EGS [J]. Geothermics, 2019, 77327-343

[9] ChongZ, YaoQ, LiX, et al. . Investigations of seismicity induced by hydraulic fracturing in naturally fractured reservoirs based on moment tensors [J]. Journal of Natural Gas Science and Engineering, 2020, 81: 103448

[10] YinZ, HuangH, ZhangF, et al. . Three-dimensional distinct element modeling of fault reactivation and induced seismicity due to hydraulic fracturing injection and backflow [J]. Journal of Rock Mechanics and Geotechnical Engineering, 2020, 12(4): 752-767

[11] ZhangF, YinZ, ChenZ, et al. . Fault reactivation and induced seismicity during multistage hydraulic fracturing: Microseismic analysis and geomechanical modeling [J]. SPE Journal, 2020, 25(2): 692-711

[12] McclureM W, HorneR N. Investigation of injection-induced seismicity using a coupled fluid flow and rate/state friction model [J]. Geophysics, 2011, 76(6): WC181-WC198

[13] LuJ, GhassemiA. Coupled thermo-hydro-mechanical-seismic modeling of EGS collab experiment 1 [J]. Energies, 2021, 14(2): 446

[14] DieterichJ H. Applications of rate- and state-dependent friction to models of fault slip and earthquake occurrence [M]. Treatise on Geophysics, 2007, Amsterdam, Elsevier: 107-129

[15] MaroneC. Laboratory-derived friction laws and their application to seismic faulting [J]. Annual Review of Earth and Planetary Sciences, 1998, 26643-696

[16] RuinaA. Slip instability and state variable friction laws [J]. Journal of Geophysical Research: Solid Earth, 1983, 88(B12): 10359-10370

[17] KatoN, TullisT E. A composite rate- and state-dependent law for rock friction [J]. Geophysical Research Letters, 2001, 28(6): 1103-1106

[18] BeelerN M, TullisT E, WeeksJ D. The roles of time and displacement in the evolution effect in rock friction [J]. Geophysical Research Letters, 1994, 21(18): 1987-1990

[19] LinkerM F, DieterichJ H. Effects of variable normal stress on rock friction: Observations and constitutive equations [J]. Journal of Geophysical Research: Solid Earth, 1992, 97(B4): 4923-4940

[20] AlghannamM, JuanesR. Understanding rate effects in injection-induced earthquakes [J]. Nature Communications, 2020, 11: 3053

[21] ChesterF M. A rheologic model for wet crust applied to strike-slip faults [J]. Journal of Geophysical Research: Solid Earth, 1995, 100(B7): 13033-13044

[22] RiceJ R. Constitutive relations for fault slip and earthquake instabilities [J]. Pure and Applied Geophysics, 1983, 121(3): 443-475

[23] GuJ, RiceJ R, RuinaA L, et al. . Slip motion and stability of a single degree of freedom elastic system with rate and state dependent friction [J]. Journal of the Mechanics and Physics of Solids, 1984, 32(3): 167-196

[24] XiD, XuSFoundations of rock physics [M], 2012, Hefei, Anhui, University of Science and Technology of China Press

[25] ImK, MaroneC, ElsworthD. The transition from steady frictional sliding to inertia-dominated instability with rate and state friction [J]. Journal of the Mechanics and Physics of Solids, 2019, 122116-125

[26] RubinA M, AmpueroJ P. Earthquake nucleation on (aging) rate and state faults [J]. Journal of Geophysical Research: Solid Earth, 2005, 110(B11): B11312

[27] MclaskeyG C, YamashitaF. Slow and fast ruptures on a laboratory fault controlled by loading characteristics [J]. Journal of Geophysical Research: Solid Earth, 2017, 12253719-3738

[28] NodaH, NakataniM, HoriT. Large nucleation before large earthquakes is sometimes skipped due to cascade-up—Implications from a rate and state simulation of faults with hierarchical asperities [J]. Journal of Geophysical Research: Solid Earth, 2013, 118(6): 2924-2952

[29] MclaskeyG C. Earthquake initiation from laboratory observations and implications for foreshocks [J]. Journal of Geophysical Research: Solid Earth, 2019, 124(12): 12882-12904

[30] FangZ, DieterichJ H, XuG. Effect of initial conditions and loading path on earthquake nucleation [J]. Journal of Geophysical Research: Solid Earth, 2010, 115(B6): B06313

[31] LatourS, SchubnelA, NielsenS, et al. . Characterization of nucleation during laboratory earthquakes [J]. Geophysical Research Letters, 2013, 40195064-5069

[32] KanekoY, NielsenS B, CarpenterB M. The onset of laboratory earthquakes explained by nucleating rupture on a rate-and-state fault [J]. Journal of Geophysical Research: Solid Earth, 2016, 121(8): 6071-6091

[33] XieM, ShiB. The periodic and aperiodic slip during earthquake faulting and aseismic faulting slip: 1D fault model analysis. [J]. Acta Seismologica Sinica, 2016, 38(4): 590-608

[34] LapustaN, RiceJ R. Nucleation and early seismic propagation of small and large events in a crustal earthquake model [J]. Journal of Geophysical Research: Solid Earth, 2003, 108(B4): 2205

[35] CebryS B L, MclaskeyG C. Seismic swarms produced by rapid fluid injection into a low permeability laboratory fault [J]. Earth and Planetary Science Letters, 2021, 557116726

[36] RiceJ R. Spatio-temporal complexity of slip on a fault [J]. Journal of Geophysical Research: Solid Earth, 1993, 98B69885-9907

[37] ChinneryM A. The stress changes that accompany strike-slip faulting [J]. Bulletin of the Seismological Society of America, 1963, 53(5): 921-932

[38] PEDREGOSA F, VAROQUAUX G, GRAMFORT A, et al. Scikit-learn: Machine learning in python [EB/OL]. 2012. arXiv: 1201.0490. https://arxiv.org/abs/1201.0490.

[39] NanjoK Z, HirataN, ObaraK, et al. . Decade-scale decrease inb value prior to the M9-class 2011 Tohoku and 2004 Sumatra quakes [J]. Geophysical Research Letters, 2012, 39(20): L20304

[40] ShiH, MengL, ZhangX. Decrease in b value prior to the Wenchuan earthquake (Ms 8.0) [J]. Chinese Journal of Geophysics, 2018, 6151874-1882