| 參考文獻 |
[1] W. T. Coffey, Y. P. Kalmykov, and J. T. Waldron, The Langevin Equation: With
Applications In Physics, Chemistry And Electrical Engineering. World Scientific,
Jul. 1996, vol. 10, isbn: 978-981-4502-40-5.
[2] H. Kanamori and D. L. Anderson, “Theoretical basis of some empirical relations
in seismology,” Bulletin of the Seismological Society of America, vol. 65, no. 5,
pp. 1073–1095, Oct. 1975, issn: 0037-1106.
[3] C. H. Scholz, “Scaling laws for large earthquakes: Consequences for physical models,”
Bulletin of the Seismological Society of America, vol. 72, no. 1, pp. 1–14, Feb.
1982, issn: 0037-1106.
[4] G. A. Pavliotis, Stochastic Processes and Applications: Diffusion Processes, the
Fokker-Planck and Langevin Equations (Texts in Applied Mathematics). New
York: Springer-Verlag, 2014, isbn: 978-1-4939-1322-0. doi: 10 . 1007 / 978 - 1 -
4939-1323-7.
[5] R. M. Gray, “Ergodic theorems,” in Probability, Random Processes, and Ergodic
Properties, R. M. Gray, Ed., Boston, MA: Springer US, 2009, pp. 239–262, isbn:
978-1-4419-1090-5. doi: 10.1007/978-1-4419-1090-5_8.
[6] 吳宗羲, “地震破裂的隨機動力模型,” 國立中央大學, 桃園縣, 2018, 92 pp. [Online].
Available: https://hdl.handle.net/11296/29k28a.
[7] A. Sornette and D. Sornette, “Self-organized criticality and earthquakes,” Europhysics
Letters, vol. 9, no. 3, p. 197, Jun. 1989, issn: 0295-5075. doi: 10.1209/
0295-5075/9/3/002. [Online]. Available: https://dx.doi.org/10.1209/0295-
5075/9/3/002 (visited on 02/15/2024).
[8] D. Sornette, “Self-organized criticality in plate tectonics,” in Spontaneous Formation
of Space-Time Structures and Criticality, T. Riste and D. Sherrington, Eds.,
Dordrecht: Springer Netherlands, 1991, pp. 57–106, isbn: 978-94-011-3508-5. doi:
10.1007/978- 94- 011- 3508- 5_6. [Online]. Available: https://doi.org/10.
1007/978-94-011-3508-5_6.
[9] G. Albertini, S. Karrer, M. D. Grigoriu, and D. S. Kammer, “Stochastic properties
of static friction,” Journal of the Mechanics and Physics of Solids, p. 104 242, Nov.
2020, issn: 0022-5096. doi: 10.1016/j.jmps.2020.104242.
[10] W. F. Brace and J. D. Byerlee, “Stick-slip as a mechanism for earthquakes,”
Science, vol. 153, no. 3739, pp. 990–992, Aug. 1966, issn: 0036-8075, 1095-9203.
doi: 10.1126/science.153.3739.990.
[11] C. H. Scholz, The Mechanics of Earthquakes and Faulting. Cambridge University
Press, 1990, isbn: 0-521-40760-5.
[12] D. A. Haessig and B. Friedland, “On the modeling and simulation of friction,”
Journal of Dynamic Systems, Measurement, and Control, vol. 113, no. 3, pp. 354–
362, Sep. 1991, issn: 0022-0434, 1528-9028. doi: 10.1115/1.2896418.
[13] B. M. Kaproth and C. Marone, “Slow earthquakes, preseismic velocity changes,
and the origin of slow frictional stick-slip,” Science, vol. 341, no. 6151, pp. 1229–
1232, Sep. 2013, issn: 0036-8075, 1095-9203. doi: 10.1126/science.1239577.
[14] A. Ruina, “Slip instability and state variable friction laws,” Journal of Geophysical
Research: Solid Earth, vol. 88, no. B12, pp. 10 359–10 370, Dec. 1983, issn: 0148-
0227. doi: 10.1029/JB088iB12p10359.
[15] P. G. Okubo and J. H. Dieterich, “Effects of physical fault properties on frictional
instabilities produced on simulated faults,” Journal of Geophysical Research: Solid
Earth, vol. 89, no. B7, pp. 5817–5827, 1984, issn: 2156-2202. doi: 10 . 1029 /
JB089iB07p05817.
[16] F. Adjemian and P. Evesque, “Experimental study of stick-slip behaviour,” International
Journal for Numerical and Analytical Methods in Geomechanics, vol. 28,
no. 6, pp. 501–530, 2004, issn: 1096-9853. doi: 10.1002/nag.350.
[17] C. A. Vargas, E. Basurto, L. Guzmán-Vargas, and F. Angulo-Brown, “Sliding size
distribution in a simple spring-block system with asperities,” Physica A: Statistical
Mechanics and its Applications, vol. 387, no. 13, pp. 3137–3144, May 2008, issn:
0378-4371. doi: 10.1016/j.physa.2008.01.108.
[18] M. Ohnaka, Y. Kuwahara, K. Yamamoto, and T. Hirasawa, “Dynamic breakdown
processes and the generating mechanism for high-frequency elastic radiation
during stick-slip instabilities,” in Earthquake Source Mechanics, American Geophysical
Union (AGU), 1986, pp. 13–24, isbn: 978-1-118-66486-5. doi: 10.1029/
GM037p0013.
[19] L. R. Moreno-Torres, A. Gomez-Vieyra, M. Lovallo, A. Ramírez-Rojas, and L.
Telesca, “Investigating the interaction between rough surfaces by using the Fisher–
Shannon method: Implications on interaction between tectonic plates,” Physica A:
Statistical Mechanics and its Applications, vol. 506, pp. 560–565, Sep. 2018, issn:
0378-4371. doi: 10.1016/j.physa.2018.04.023.
[20] J. Wojewoda, A. Stefański, M. Wiercigroch, and T. Kapitaniak, “Hysteretic effects
of dry friction: Modelling and experimental studies,” Philosophical Transactions
of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 366,
no. 1866, pp. 747–765, Mar. 2008. doi: 10.1098/rsta.2007.2125.
[21] L. Pei, S. Hyun, J. F. Molinari, and M. O. Robbins, “Finite element modeling
of elasto-plastic contact between rough surfaces,” Journal of the Mechanics and
Physics of Solids, vol. 53, no. 11, pp. 2385–2409, Nov. 2005, issn: 0022-5096. doi:
10.1016/j.jmps.2005.06.008.
[22] D. Monelli and P. M. Mai, “Bayesian inference of kinematic earthquake rupture
parameters through fitting of strong motion data,” Geophys. J. Int., vol. 173,
no. 1, pp. 220–232, Apr. 2008, issn: 0956-540X. doi: 10.1111/j.1365- 246X.
2008.03733.x. [Online]. Available: https://onlinelibrary.wiley.com/doi/
full/10.1111/j.1365-246X.2008.03733.x (visited on 08/05/2019).
[23] A. H. Olson and R. J. Apsel, “Finite faults and inverse theory with applications
to the 1979 Imperial Valley earthquake,” Bull. Seismol. Soc. Am., vol. 72, no. 6A,
pp. 1969–2001, Dec. 1982, issn: 0037-1106. [Online]. Available: https://pubs.
geoscienceworld . org / ssa / bssa / article / 72 / 6A / 1969 / 337982 / finite -
faults-and-inverse-theory-with-applications (visited on 07/17/2019).
[24] N. A. Haskell, “Elastic displacements in the near-field of a propagating fault,”
Bull. Seismol. Soc. Am., vol. 59, no. 2, pp. 865–908, Apr. 1969, issn: 0037-1106.
[Online]. Available: https://pubs.geoscienceworld.org/ssa/bssa/article/
59/2/865/116741/elastic-displacements-in-the-near-field-of-a (visited
on 07/17/2019).
[25] A. Ozgun Konca, Y. Kaneko, N. Lapusta, and J.-P. Avouac, “Kinematic inversion
of physically plausible earthquake source models obtained from dynamic rupture
simulations,” Bull. Seismol. Soc. Am., vol. 103, no. 5, pp. 2621–2644, Oct. 2013,
issn: 0037-1106. doi: 10.1785/0120120358. [Online]. Available: https://pubs.
geoscienceworld.org/bssa/article/103/5/2621- 2644/349786 (visited on
07/17/2019).
[26] S. Peyrat and K. B. Olsen, “Nonlinear dynamic rupture inversion of the 2000
Western Tottori, Japan, earthquake,” Geophys. Res. Lett., vol. 31, no. 5, Mar.
2004, issn: 0094-8276. doi: 10.1029/2003GL019058. [Online]. Available: https:
/ / agupubs . onlinelibrary . wiley . com / doi / full / 10 . 1029 / 2003GL019058
(visited on 08/01/2019).
[27] S. H. Hartzell and T. H. Heaton, “Inversion of strong ground motion and teleseismic
waveform data for the fault rupture history of the 1979 Imperial Valley, California,
earthquake,” Bull. Seismol. Soc. Am., vol. 73, no. 6A, pp. 1553–1583, Dec.
1983, issn: 0037-1106. [Online]. Available: https : / / pubs . geoscienceworld .
org/ssa/bssa/article/73/6A/1553/118510/inversion-of-strong-groundmotion-
and-teleseismic (visited on 07/29/2019).
[28] R. Madariaga, “Seismic source theory,” in Treatise on Geophysics, Elsevier, 2007,
pp. 59–82, isbn: 978-0-444-52748-6. doi: 10.1016/B978-044452748-6.00061-
4. [Online]. Available: https : / / linkinghub . elsevier . com / retrieve / pii /
B9780444527486000614 (visited on 08/05/2019).
[29] R. Madariaga and K. B. Olsen, “Earthquake dynamics,” International Geophysics
Series, vol. 81, no. A, pp. 175–194, 2002, issn: 0074-6142.
[30] D. J. Wald, D. V. Helmberger, and T. H. Heaton, “Rupture model of the 1989
Loma Prieta earthquake from the inversion of strong-motion and broadband teleseismic
data,” Bull. Seismol. Soc. Am., vol. 81, no. 5, pp. 1540–1572, Oct. 1991,
issn: 0037-1106. [Online]. Available: https://pubs.geoscienceworld.org/ssa/
bssa / article / 81 / 5 / 1540 / 119510 / rupture - model - of - the - 1989 - loma -
prieta-earthquake (visited on 07/29/2019).
[31] S. Ide, “4.09-slip inversion,” Treatise on geophysics, 2nd edn. Elsevier, Oxford,
pp. 215–241, 2015.
[32] Y.-Y. Wen, D. D. Oglesby, B. Duan, and K.-F. Ma, “Dynamic rupture simulation
of the 2008 Mw 7.9 Wenchuan earthquake with heterogeneous initial stress,” Bull.
Seismol. Soc. Am., vol. 102, no. 4, pp. 1892–1898, Aug. 2012, issn: 0037-1106. doi:
10.1785/0120110153. [Online]. Available: https://pubs.geoscienceworld.
org/bssa/article/102/4/1892-1898/325530 (visited on 08/05/2019).
[33] T. Mikumo, K. B. Olsen, E. Fukuyama, and Y. Yagi, “Stress-breakdown time and
slip-weakening distance inferred from slip-velocity functions on earthquake faults,”
Bull. Seismol. Soc. Am., vol. 93, no. 1, pp. 264–282, 2003, issn: 1943-3573.
[34] K. B. Olsen, R. Madariaga, and R. J. Archuleta, “Three-dimensional dynamic
simulation of the 1992 Landers earthquake,” Science, vol. 278, no. 5339, pp. 834–
838, Oct. 1997, issn: 0036-8075, 1095-9203. doi: 10.1126/science.278.5339.
834. [Online]. Available: https : / / science . sciencemag . org / content / 278 /
5339/834 (visited on 08/05/2019).
[35] P. Bormann, “From earthquake prediction research to time-variable seismic hazard
assessment applications,” Pure and Applied Geophysics, vol. 168, no. 1, pp. 329–
366, Jan. 1, 2011, issn: 1420-9136. doi: 10.1007/s00024- 010- 0114- 0. [Online].
Available: https://doi.org/10.1007/s00024- 010- 0114- 0 (visited on
02/02/2024).
[36] D. E. Smith and J. H. Dieterich, “Aftershock sequences modeled with 3-D stress
heterogeneity and rate-state seismicity equations: Implications for crustal stress
estimation,” Pure and Applied Geophysics, vol. 167, no. 8, pp. 1067–1085, Aug. 1,
2010, issn: 1420-9136. doi: 10.1007/s00024-010-0093-1. [Online]. Available:
https://doi.org/10.1007/s00024-010-0093-1 (visited on 02/02/2024).
[37] A. Helmstetter and B. E. Shaw, “Relation between stress heterogeneity and aftershock
rate in the rate-and-state model,” Journal of Geophysical Research: Solid
Earth, vol. 111, no. B7, 2006, issn: 2156-2202. doi: 10 . 1029 / 2005JB004077.
[Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1029/
2005JB004077 (visited on 02/02/2024).
[38] L. Rivera and H. Kanamori, “Spatial heterogeneity of tectonic stress and friction
in the crust,” Geophysical Research Letters, vol. 29, no. 6, pp. 12-1-12–4, 2002,
issn: 1944-8007. doi: 10.1029/2001GL013803.
[39] M. Ohnaka, M. Akatsu, H. Mochizuki, A. Odedra, F. Tagashira, and Y. Yamamoto,
“A constitutive law for the shear failure of rock under lithospheric conditions,”
Tectonophysics, Earthquake Generation Processes: Environmental Aspects
and Physical Modelling, vol. 277, no. 1, pp. 1–27, Aug. 1997, issn: 0040-1951. doi:
10.1016/S0040-1951(97)00075-9.
[40] J. B. Rundle, D. L. Turcotte, R. Shcherbakov, W. Klein, and C. Sammis, “Statistical
physics approach to understanding the multiscale dynamics of earthquake
fault systems,” Reviews of Geophysics, vol. 41, no. 4, p. 1019, Dec. 2003, issn:
1944-9208. doi: 10.1029/2003RG000135.
[41] C. H. Scholz and C. A. Aviles, “The fractal geometry of faults and faulting,”
in Earthquake Source Mechanics, American Geophysical Union (AGU), 1986,
pp. 147–155, isbn: 978-1-118-66486-5. doi: 10.1029/GM037p0147.
[42] A. Carpinteri and M. Paggi, “A fractal interpretation of size-scale effects on
strength, friction and fracture energy of faults,” Chaos, Solitons and Fractals,
vol. 39, no. 2, pp. 540–546, Jan. 2009, issn: 0960-0779.
[43] T. H. W. Goebel, C. G. Sammis, T. W. Becker, G. Dresen, and D. Schorlemmer,
“A comparison of seismicity characteristics and fault structure between stick–slip
experiments and nature,” Pure and Applied Geophysics, vol. 172, no. 8, pp. 2247–
2264, Aug. 2015, issn: 1420-9136. doi: 10.1007/s00024-013-0713-7.
[44] R. J. Geller, “Scaling relations for earthquake source parameters and magnitudes,”
Bulletin of the Seismological Society of America, vol. 66, no. 5, pp. 1501–1523, Oct.
1976, issn: 0037-1106.
[45] D. Legrand, “Fractal dimensions of small, intermediate, and large earthquakes,”
Bulletin of the Seismological Society of America, vol. 92, no. 8, pp. 3318–3320,
Dec. 2002, issn: 0037-1106. doi: 10.1785/0120020025.
[46] J.-H. Wang, “A review on scaling of earthquake source spectra,” Surveys in Geophysics,
vol. 40, no. 2, pp. 133–166, Mar. 2019, issn: 1573-0956. doi: 10.1007/
s10712-019-09512-4.
[47] S. R. Brown and C. H. Scholz, “Closure of random elastic surfaces in contact,”
Journal of Geophysical Research: Solid Earth, vol. 90, no. B7, pp. 5531–5545, 1985,
issn: 2156-2202. doi: 10.1029/JB090iB07p05531.
[48] S. R. Brown and C. H. Scholz, “Broad bandwidth study of the topography of natural
rock surfaces,” Journal of Geophysical Research: Solid Earth, vol. 90, no. B14,
pp. 12 575–12 582, 1985, issn: 2156-2202. doi: 10.1029/JB090iB14p12575.
[49] F. Renard and T. Candela, “Scaling of fault roughness and implications for earthquake
mechanics,” in Fault Zone Dynamic Processes, American Geophysical Union
(AGU), 2017, ch. 10, pp. 195–215, isbn: 978-1-119-15689-5. doi: 10.1002/9781119156895.
ch10.
[50] Y. Y. Kagan, “Are earthquakes predictable?” Geophysical Journal International,
vol. 131, no. 3, pp. 505–525, Dec. 1997, issn: 0956-540X. doi: 10.1111/j.1365-
246X.1997.tb06595.x.
[51] C. A. Aviles, C. H. Scholz, and J. Boatwright, “Fractal analysis applied to characteristic
segments of the San Andreas Fault,” Journal of Geophysical Research:
Solid Earth, vol. 92, no. B1, pp. 331–344, 1987, issn: 2156-2202. doi: 10.1029/
JB092iB01p00331.
[52] B. Velde, J. Dubois, D. Moore, and G. Touchard, “Fractal patterns of fractures
in granites,” Earth and Planetary Science Letters, vol. 104, no. 1, pp. 25–35, May
1991, issn: 0012-821X. doi: 10.1016/0012-821X(91)90234-9.
[53] K. Aki, “Magnitude-frequency relation for small earthquakes: A clue to the origin
of ƒmax of large earthquakes,” Journal of Geophysical Research: Solid Earth,
vol. 92, no. B2, pp. 1349–1355, 1987, issn: 2156-2202. doi: 10.1029/JB092iB02p01349.
[54] T. Hirata, “Fractal dimension of fault systems in Japan: Fractal structure in rock
fracture geometry at various scales,” Pure Appl Geophys, vol. 131, no. 1, pp. 157–
170, Mar. 1989, issn: 1420-9136. doi: 10.1007/BF00874485. [Online]. Available:
https://doi.org/10.1007/BF00874485 (visited on 10/29/2018).
[55] L. A. Sunmonu and V. P. Dimri, “Fractal geometry of faults and seismicity
of Koyna-Warna region west india using LANDSAT images,” Pure Appl Geophys,
vol. 157, no. 9, pp. 1393–1405, Sep. 2000, issn: 1420-9136. doi: 10.1007/
PL00001125. [Online]. Available: https://doi.org/10.1007/PL00001125 (visited
on 10/29/2018).
[56] T. Babadagli and K. Develi, “Fractal characteristics of rocks fractured under tension,”
Theor Appl Fract Mech, vol. 39, no. 1, pp. 73–88, 2003, issn: 0167-8442.
[57] X. L. Xu and Z. Z. Zhang, “Fractal characteristics of rock fracture surface under
triaxial compression after high temperature,” Adv Mater Sci Eng, vol. 2016, pp. 1–
10, 2016, issn: 1687-8434, 1687-8442. doi: 10 . 1155 / 2016 / 2181438. [Online].
Available: https://www.hindawi.com/journals/amse/2016/2181438/ (visited
on 10/29/2018).
[58] P. Bak and M. Creutz, “Fractals and self-organized criticality,” in Fractals in Science,
A. Bunde and S. Havlin, Eds., Berlin, Heidelberg: Springer Berlin Heidelberg,
1994, pp. 27–48, isbn: 978-3-662-11779-8 978-3-662-11777-4. doi: 10.1007/978-
3-662-11777-4_2. [Online]. Available: http://link.springer.com/10.1007/
978-3-662-11777-4_2 (visited on 02/15/2024).
[59] C. Hooge, S. Lovejoy, D. Schertzer, S. Pecknold, J.-F. Malouin, and F. Schmitt,
“Mulifractal phase transitions: The origin of self-organized criticality in earthquakes,”
Nonlinear Processes in Geophysics, vol. 1, no. 2/3, pp. 191–197, Sep. 30,
1994, issn: 1607-7946. doi: 10 . 5194 / npg - 1 - 191 - 1994. [Online]. Available:
https://npg.copernicus.org/articles/1/191/1994/ (visited on 02/15/2024).
[60] C. H. Scholz, “Earthquakes and faulting: Self-organized critical phenomena with a
characteristic dimension,” in Spontaneous Formation of Space-Time Structures and
Criticality, T. Riste and D. Sherrington, Eds., Dordrecht: Springer Netherlands,
1991, pp. 41–56, isbn: 978-94-011-3508-5. doi: 10.1007/978-94-011-3508-5_5.
[Online]. Available: https://doi.org/10.1007/978-94-011-3508-5_5.
[61] C. W. Gardiner, “Handbook of stochastic processes,” Springer-Verlag, Berlin,
1985.
[62] W. T. Coffey and Y. P. Kalmykov, The Langevin Equation: With Applications to
Stochastic Problems in Physics, Chemistry and Electrical Engineering. World Scientific,
Jul. 31, 2012, 850 pp., isbn: 978-981-4483-80-3. Google Books: pi27CgAAQBAJ.
[63] P. M. Mai and G. C. Beroza, “A spatial random field model to characterize
complexity in earthquake slip,” Journal of Geophysical Research: Solid Earth,
vol. 107, no. B11, ESE 10-1-ESE 10–21, 2002, issn: 2156-2202. doi: 10.1029/
2001JB000588.
[64] D. Lavallée, P. Liu, and R. J. Archuleta, “Stochastic model of heterogeneity in
earthquake slip spatial distributions,” Geophysical Journal International, vol. 165,
no. 2, pp. 622–640, May 2006, issn: 0956-540X. doi: 10.1111/j.1365- 246X.
2006.02943.x.
[65] J. Sun, Y. Yu, and Y. Li, “Stochastic finite-fault simulation of the 2017 Jiuzhaigou
earthquake in China,” Earth, Planets and Space, vol. 70, no. 1, p. 128, Aug. 2018,
issn: 1880-5981. doi: 10.1186/s40623-018-0897-2.
[66] S. Murphy and A. Herrero, “Surface rupture in stochastic slip models,” Geophysical
Journal International, vol. 221, no. 2, pp. 1081–1089, May 2020, issn: 0956-540X.
doi: 10.1093/gji/ggaa055.
[67] V. C. Tsai and G. Hirth, “Elastic impact consequences for high-frequency earthquake
ground motion,” Geophysical Research Letters, vol. 47, no. 5, e2019GL086302,
2020, issn: 1944-8007. doi: 10.1029/2019GL086302.
[68] M. Otsuka, “A chain-reaction-type source model as a tool to interpret the magnitudefrequency
relation of earthquakes,” Journal of Physics of the Earth, vol. 20, no. 1,
pp. 35–45, 1972, issn: 0022-3743.
[69] D. Vere-Jones, “A branching model for crack propagation,” Pure Appl Geophys,
vol. 114, no. 4, pp. 711–725, 1976, issn: 0033-4553, 1420-9136. doi: 10.1007/
BF00875663. [Online]. Available: http://link.springer.com/10.1007/BF00875663
(visited on 07/23/2018).
[70] K. Watanabe, “Stochastic evaluation of the two dimensional continuity of fractures
in a rock mass,” International Journal of Rock Mechanics and Mining Sciences
& Geomechanics Abstracts, vol. 23, no. 6, pp. 431–437, Dec. 1986, issn: 0148-
9062. doi: 10 . 1016 / 0148 - 9062(86 ) 92308 - 9. [Online]. Available: http : / /
www.sciencedirect.com/science/article/pii/0148906286923089 (visited on
02/11/2019).
[71] Y. Y. Kagan, “Stochastic model of earthquake fault geometry,” Geophys J R
Astron Soc, vol. 71, no. 3, pp. 659–691, Dec. 1982, issn: 1365-246X. doi: 10.1111/
j.1365-246X.1982.tb02791.x. [Online]. Available: https://onlinelibrary.
wiley . com / doi / abs / 10 . 1111 / j . 1365 - 246X . 1982 . tb02791 . x (visited on
10/28/2018).
[72] J. Zhuang and S. Touati, “Stochastic simulation of earthquake catalogs,” Community
Online Resource for Statistical Seismicity Analysis, 2015. doi: 10.5078/
corssa-43806322.
[73] A. M. Selvam, “Universal quantification for deterministic chaos in dynamical systems,”
arXiv:physics/0008010, Aug. 2000, arXiv: physics/0008010. [Online]. Available:
http://arxiv.org/abs/physics/0008010 (visited on 01/31/2019).
[74] M. Cattani, I. L. Caldas, S. L. d. Souza, et al., “Deterministic chaos theory:
Basic concepts,” Revista Brasileira de Ensino de Física, vol. 39, no. 1, 2017, issn:
1806-1117. doi: 10 . 1590 / 1806 - 9126 - rbef - 2016 - 0185. [Online]. Available:
http : / / www . scielo . br / scielo . php ? script = sci _ abstract & pid = S1806 -
11172017000100409&lng=en&nrm=iso&tlng=en (visited on 01/31/2019).
[75] F. Cecconi, M. Cencini, M. Falcioni, and A. Vulpiani, “Brownian motion and diffusion:
From stochastic processes to chaos and beyond,” Chaos: An Interdisciplinary
Journal of Nonlinear Science, vol. 15, no. 2, p. 026 102, Jun. 2005, issn: 1054-1500.
doi: 10.1063/1.1832773. [Online]. Available: https://aip.scitation.org/
doi/abs/10.1063/1.1832773 (visited on 03/26/2018).
[76] J. .-. Eckmann, “Roads to turbulence in dissipative dynamical systems,” Rev Mod
Phys, vol. 53, no. 4, pp. 643–654, Oct. 1981. doi: 10.1103/RevModPhys.53.643.
[Online]. Available: https://link.aps.org/doi/10.1103/RevModPhys.53.643
(visited on 03/26/2018).
[77] J. B. Rundle, D. L. Turcotte, R. Shcherbakov, W. Klein, and C. Sammis, “Statistical
physics approach to understanding the multiscale dynamics of earthquake fault
systems,” Rev Geophys, vol. 41, no. 4, p. 1019, Dec. 2003, issn: 1944-9208. doi:
10.1029/2003RG000135. [Online]. Available: http://onlinelibrary.wiley.
com/doi/10.1029/2003RG000135/abstract (visited on 09/11/2017).
[78] A. Einstein, Investigation on the Theory of the Brownian Movement, R. Fürth,
Ed., trans. by A. D. Cowper. Mineola: Dover, 2003, isbn: 978-0-486-60304-9.
[79] J. Renn, “Einstein’s invention of Brownian motion,” Annalen der Physik, vol. 14,
no. S1, pp. 23–37, 2005, issn: 1521-3889. doi: 10.1002/andp.200410131.
[80] P. Hänggi and F. Marchesoni, “Introduction: 100 years of Brownian motion,”
Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 15, no. 2, p. 026 101,
Jun. 2005, issn: 1054-1500. doi: 10.1063/1.1895505.
[81] W. T. Coffey and Y. P. Kalmykov, The Langevin Equation: With Applications
to Stochastic Problems in Physics, Chemistry and Electrical Engineering. World
Scientific, Jul. 2012, Google-Books-ID: pi27CgAAQBAJ, isbn: 978-981-4483-80-3.
[82] K. Itō, On Stochastic Differential Equations. American Mathematical Society,
1951, isbn: 978-0-8218-9983-0.
[83] N. G. van Kampen, Stochastic Processes in Physics and Chemistry. North-Holland,
1981, isbn: 978-0-444-86200-6.
[84] D. S. Lemons and A. Gythiel, “Paul Langevin’s 1908 paper “On the Theory of
Brownian Motion” [“Sur la théorie du mouvement brownien,” C. R. Acad. Sci.
(Paris) 146, 530–533 (1908)],” American Journal of Physics, vol. 65, no. 11,
pp. 1079–1081, Nov. 1997, issn: 0002-9505. doi: 10.1119/1.18725.
[85] J. Renn, “Einstein’s invention of Brownian motion,” Ann Phys, vol. 14, no. S1,
pp. 23–37, 2005, issn: 1521-3889. doi: 10.1002/andp.200410131.
[86] R. Yulmetyev, R. Khusnutdinoff, T. Tezel, Y. Iravul, B. Tuzel, and P. Hänggi,
“The study of dynamic singularities of seismic signals by the generalized Langevin
equation,” Physica A, vol. 388, no. 17, pp. 3629–3635, Sep. 2009, issn: 0378-
4371. doi: 10.1016/j.physa.2009.05.010. [Online]. Available: http://www.
sciencedirect . com / science / article / pii / S0378437109003744 (visited on
12/14/2018).
[87] H. Eslamizadeh and H. Razazzadeh, “Statistical and dynamical modeling of heavyion
fusion–fission reactions,” Phys Lett B, vol. 777, pp. 265–269, Feb. 2018, issn:
0370-2693. doi: 10.1016/j.physletb.2017.12.029. [Online]. Available: http://
www.sciencedirect.com/science/article/pii/S0370269317310067 (visited
on 05/18/2018).
[88] J. B. Rundle, W. Klein, and S. Gross, “Dynamics of a traveling density wave model
for earthquakes,” Phys Rev Lett, vol. 76, no. 22, pp. 4285–4288, May 1996, issn:
1079-7114. doi: 10.1103/PhysRevLett.76.4285.
[89] S. Nakamula, M. Takeo, Y. Okabe, and M. Matsuura, “Automatic seismic wave
arrival detection and picking with stationary analysis: Application of the KM2o-
Langevin equations,” Earth Planets Space, vol. 59, no. 6, pp. 567–577, Jun. 2007,
issn: 1880-5981. doi: 10.1186/BF03352719. [Online]. Available: http://earthplanets-
space.springeropen.com/articles/10.1186/BF03352719 (visited on
10/28/2018).
[90] S. Boutareaud, D.-G. Calugaru, R. Han, et al., “Clay-clast aggregates: A new
textural evidence for seismic fault sliding?” Geophysical Research Letters, vol. 35,
no. 5, 2008, issn: 1944-8007. doi: 10.1029/2007GL032554. [Online]. Available:
https://onlinelibrary.wiley.com/doi/abs/10.1029/2007GL032554 (visited
on 07/28/2023).
[91] N. Brantut, A. Schubnel, J.-N. Rouzaud, F. Brunet, and T. Shimamoto, “Highvelocity
frictional properties of a clay-bearing fault gouge and implications for
earthquake mechanics,” Journal of Geophysical Research: Solid Earth, vol. 113,
no. B10, 2008, issn: 2156-2202. doi: 10.1029/2007JB005551. [Online]. Available:
https://onlinelibrary.wiley.com/doi/abs/10.1029/2007JB005551 (visited
on 07/28/2023).
[92] X. Chen, A. S. Elwood Madden, and Z. Reches, “Friction evolution of granitic
faults: Heating controlled transition from powder lubrication to frictional melt,”
Journal of Geophysical Research: Solid Earth, vol. 122, no. 11, pp. 9275–9289,
2017, issn: 2169-9356. doi: 10.1002/2017JB014462. [Online]. Available: https:
/ / onlinelibrary . wiley . com / doi / abs / 10 . 1002 / 2017JB014462 (visited on
01/21/2024).
[93] X. Chen, A. S. E. Madden, and Z. Reches, “Powder rolling as a mechanism of
dynamic fault weakening,” in Fault Zone Dynamic Processes, American Geophysical
Union (AGU), 2017, pp. 133–150, isbn: 978-1-119-15689-5. doi: 10.1002/
9781119156895.ch7. [Online]. Available: https://onlinelibrary.wiley.com/
doi/abs/10.1002/9781119156895.ch7 (visited on 07/28/2023).
[94] C.-C. Hung, L.-W. Kuo, E. Spagnuolo, et al., “Grain fragmentation and frictional
melting during initial experimental deformation and implications for seismic slip
at shallow depths,” Journal of Geophysical Research: Solid Earth, vol. 124, no. 11,
pp. 11 150–11 169, 2019, issn: 2169-9356. doi: 10.1029/2019JB017905. [Online].
Available: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/
2019JB017905 (visited on 11/05/2020).
[95] C. E. Shannon, “A mathematical theory of communication,” The Bell System
Technical Journal, vol. 27, no. 3, pp. 379–423, Jul. 1948, issn: 0005-8580. doi:
10.1002/j.1538-7305.1948.tb01338.x.
[96] M. Martin, F. Pennini, and A. Plastino, “Fisher’s information and the analysis of
complex signals,” Phys Lett A, vol. 256, no. 2-3, pp. 173–180, 1999, issn: 0375-
9601.
[97] M. T. Martin, J. Perez, and A. Plastino, “Fisher information and nonlinear dynamics,”
Physica A, vol. 291, no. 1, pp. 523–532, 2001. [Online]. Available: https:
//ideas.repec.org/a/eee/phsmap/v291y2001i1p523- 532.html (visited on
12/18/2018).
[98] M. Lovallo and L. Telesca, “Complexity measures and information planes of xray
astrophysical sources,” J Stat Mech: Theory Exp, vol. 2011, no. 03, P03029,
2011, issn: 1742-5468. doi: 10 . 1088 / 1742 - 5468 / 2011 / 03 / P03029. [Online].
Available: http://stacks.iop.org/1742-5468/2011/i=03/a=P03029 (visited
on 12/18/2018).
[99] L. Telesca and M. Lovallo, “Analysis of the time dynamics in wind records by
means of multifractal detrended fluctuation analysis and the Fisher–Shannon
information plane,” J Stat Mech: Theory Exp, vol. 2011, no. 07, P07001, 2011, issn:
1742-5468. doi: 10.1088/1742-5468/2011/07/P07001. [Online]. Available: http:
//stacks.iop.org/1742-5468/2011/i=07/a=P07001 (visited on 12/18/2018).
[100] L. Telesca, M. Lovallo, H.-L. Hsu, and C.-C. Chen, “Analysis of dynamics in
magnetotelluric data by using the Fisher–Shannon method,” Physica A, vol. 390,
no. 7, pp. 1350–1355, 2011, issn: 0378-4371.
[101] L. Telesca, M. Lovallo, and R. Carniel, “Time-dependent Fisher Information Measure
of volcanic tremor before the 5 April 2003 paroxysm at Stromboli volcano,
Italy,” J Volcanol Geotherm Res, vol. 195, no. 1, pp. 78–82, 2010, issn: 0377-0273.
[102] L. Telesca, M. Lovallo, A. Ramirez-Rojas, and F. Angulo-Brown, “A nonlinear
strategy to reveal seismic precursory signatures in earthquake-related self-potential
signals,” Physica A, vol. 388, no. 10, pp. 2036–2040, 2009, issn: 0378-4371.
[103] M. Nosonovsky, “Entropy in tribology: In the search for applications,” Entropy,
vol. 12, no. 6, pp. 1345–1390, Jun. 2010. doi: 10.3390/e12061345. [Online]. Available:
https://www.mdpi.com/1099-4300/12/6/1345 (visited on 12/18/2018).
[104] P. Fleurquin, H. Fort, M. Kornbluth, R. Sandler, M. Segall, and F. Zypman,
“Negentropy generation and fractality in the dry friction of polished surfaces,”
Entropy, vol. 12, no. 3, pp. 480–489, Mar. 11, 2010, issn: 1099-4300. doi: 10.3390/
e12030480. [Online]. Available: http://www.mdpi.com/1099- 4300/12/3/480
(visited on 02/15/2024).
[105] L. Ruff and H. Kanamori, “Seismic coupling and uncoupling at subduction zones,”
Tectonophysics, vol. 99, no. 2-4, pp. 99–117, Dec. 1983, issn: 00401951. doi:
10.1016/0040- 1951(83)90097- 5. [Online]. Available: https://linkinghub.
elsevier.com/retrieve/pii/0040195183900975 (visited on 02/15/2024).
[106] J. B. Rundle, W. Klein, and S. Gross, “Dynamics of a traveling density wave
model for earthquakes,” Physical Review Letters, vol. 76, no. 22, pp. 4285–4288,
May 1996, issn: 1079-7114. doi: 10.1103/PhysRevLett.76.4285.
[107] M. Ohnaka, “A constitutive scaling law and a unified comprehension for frictional
slip failure, shear fracture of intact rock, and earthquake rupture,” Journal of
Geophysical Research: Solid Earth, vol. 108, no. B2, 2003, issn: 2156-2202. doi:
10.1029/2000JB000123.
[108] K. Aki, “Characterization of barriers on an earthquake fault,” Journal of Geophysical
Research: Solid Earth, vol. 84, no. B11, pp. 6140–6148, Oct. 1979, issn:
2156-2202. doi: 10.1029/JB084iB11p06140.
[109] A. S. Papageorgiou and K. Aki, “A specific barrier model for the quantitative description
of inhomogeneous faulting and the prediction of strong ground motion. I.
Description of the model,” Bulletin of the Seismological Society of America, vol. 73,
no. 3, pp. 693–722, Jun. 1983, issn: 0037-1106. doi: 10.1785/BSSA0730030693.
[110] K. Aki, “Asperities, barriers, characteristic earthquakes and strong motion prediction,”
Journal of Geophysical Research: Solid Earth, 1984. doi: 10 . 1029 /
JB089IB07P05867.
[111] H. Kanamori and G. S. Stewart, “Seismological aspects of the Guatemala Earthquake
of February 4, 1976,” Journal of Geophysical Research: Solid Earth, vol. 83,
no. B7, pp. 3427–3434, 1978, issn: 2156-2202. doi: 10.1029/JB083iB07p03427.
[112] J. D. Byerlee, “Frictional characteristics of granite under high confining pressure,”
Journal of Geophysical Research (1896-1977), vol. 72, no. 14, pp. 3639–3648, 1967,
issn: 2156-2202. doi: 10.1029/JZ072i014p03639.
[113] R. Costamagna, J. Renner, and O. T. Bruhns, “Relationship between fracture and
friction for brittle rocks,” Mechanics of Materials, vol. 39, no. 4, pp. 291–301, Apr.
2007, issn: 0167-6636. doi: 10.1016/j.mechmat.2006.06.001.
[114] R. Burridge and L. Knopoff, “Model and theoretical seismicity,” Bulletin of the
Seismological Society of America, vol. 57, no. 3, pp. 341–371, Jun. 1967, issn:
0037-1106.
[115] S. J. Gross, “Traveling wave and rough fault earthquake models: Illuminating the
relationship between slip deficit and event frequency statistics,” in Geocomplexity
and the Physics of Earthquakes, J. B. Rundle, D. L. Turcotte, and W. Klein,
Eds., American Geophysical Union, 2000, pp. 73–82, isbn: 978-1-118-66837-5. doi:
10.1029/GM120p0073.
[116] C. C. de Wit, H. Olsson, K. J. Astrom, and P. Lischinsky, “A new model for control
of systems with friction,” IEEE Transactions on Automatic Control, vol. 40, no. 3,
pp. 419–425, Mar. 1995, issn: 0018-9286. doi: 10.1109/9.376053.
[117] J. Liang, S. Fillmore, and O. Ma, “An extended bristle friction force model with
experimental validation,” Mechanism and Machine Theory, vol. 56, pp. 123–137,
Oct. 2012, issn: 0094-114X. doi: 10.1016/j.mechmachtheory.2012.06.002.
[118] S. Saltiel, B. P. Bonner, T. Mittal, B. Delbridge, and J. B. Ajo-Franklin, “Experimental
evidence for dynamic friction on rock fractures from frequency-dependent
nonlinear hysteresis and harmonic generation,” Journal of Geophysical Research:
Solid Earth, vol. 122, no. 7, pp. 4982–4999, Jul. 2017, issn: 2169-9313. doi: 10.
1002/2017JB014219.
[119] J. F. Labuz and A. Zang, “Mohr–Coulomb failure criterion,” Rock Mechanics and
Rock Engineering, vol. 45, no. 6, pp. 975–979, Nov. 2012, issn: 1434-453X. doi:
10.1007/s00603-012-0281-7.
[120] A. Zang and O. Stephansson, “Rock fracture criteria,” in Stress Field of the Earth’s
Crust, A. Zang and O. Stephansson, Eds., Dordrecht: Springer Netherlands, 2010,
pp. 37–62, isbn: 978-1-4020-8444-7. doi: 10.1007/978-1-4020-8444-7_3.
[121] M. Marder and J. Fineberg, “How things break,” Physics Today, vol. 49, no. 9,
pp. 24–29, Sep. 1, 1996, issn: 0031-9228. doi: 10 . 1063 / 1 . 881515. [Online].
Available: https://physicstoday.scitation.org/doi/10.1063/1.881515
(visited on 08/17/2021).
[122] J. .-. Eckmann, “Roads to turbulence in dissipative dynamical systems,” Reviews
of Modern Physics, vol. 53, no. 4, pp. 643–654, Oct. 1981. doi: 10.1103/
RevModPhys.53.643.
[123] J. Nussbaum and A. Ruina, “A two degree-of-freedom earthquake model with
static/dynamic friction,” pure and applied geophysics, vol. 125, no. 4, pp. 629–
656, Jul. 1, 1987, issn: 1420-9136. doi: 10.1007/BF00879576. [Online]. Available:
https://doi.org/10.1007/BF00879576 (visited on 02/27/2024).
[124] J. Huang and D. L. Turcotte, “Chaotic seismic faulting with a mass-spring model
and velocity-weakening friction,” pure and applied geophysics, vol. 138, no. 4,
pp. 569–589, Dec. 1992, issn: 1420-9136. doi: 10.1007/BF00876339.
[125] J. Huang and D. L. Turcotte, “Are earthquakes an example of deterministic
chaos?” Geophysical Research Letters, vol. 17, no. 3, pp. 223–226, Mar. 1990,
issn: 0094-8276. doi: 10.1029/GL017i003p00223.
[126] N. G. Van Kampen, Stochastic processes in physics and chemistry. Elsevier, 1992,
vol. 1, isbn: 0-08-057138-7.
[127] R. Kubo, “The fluctuation-dissipation theorem,” Reports on Progress in Physics,
vol. 29, pp. 255–284, Jan. 1966, issn: 0034-4885. doi: 10.1088/0034-4885/29/
1/306.
[128] A. H. Jazwinski, Stochastic Processes and Filtering Theory. Academic Press, Jan.
1970, isbn: 978-0-08-096090-6.
[129] H. Risken, The Fokker-Planck equation: methods of solution and applications
(Springer series in synergetics v. 18), 2nd ed. Berlin ; New York: Springer-Verlag,
1989, isbn: 978-0-387-50498-8.
[130] K. Jacobs, Stochastic processes for physicists: understanding noisy systems. Cambridge
University Press, 2010, isbn: 1-139-48679-9.
[131] S. Cyganowski, P. Kloeden, and J. Ombach, From Elementary Probability to
Stochastic Differential Equations with MAPLE®. Springer Science & Business
Media, 2001, isbn: 3-540-42666-3.
[132] J. Byerlee, “Friction of rocks,” Pure Appl Geophys, vol. 116, no. 4, pp. 615–626,
Jul. 1978, issn: 1420-9136. doi: 10.1007/BF00876528. [Online]. Available: https:
//doi.org/10.1007/BF00876528 (visited on 10/28/2018).
[133] B. Armstrong-Hélouvry, Control of Machines with Friction (The Springer International
Series in Engineering and Computer Science). Springer US, 1991,
isbn: 978-0-7923-9133-3. [Online]. Available: //www.springer.com/la/book/
9780792391333 (visited on 11/27/2018).
[134] H. Olsson, K. Åström, C. C. de Wit, M. Gäfvert, and P. Lischinsky, “Friction
models and friction compensation,” Nov. 1997. [Online]. Available: http://catsfs.
rpi.edu/~wenj/ECSE4962S04/astrom_friction.pdf.
[135] C. Marone, “Laboratory-derived friction laws and their application to seismic
faulting,” Annu Rev Earth Planet Sci, vol. 26, no. 1, pp. 643–696, 1998. doi:
10.1146/annurev.earth.26.1.643. [Online]. Available: https://doi.org/10.
1146/annurev.earth.26.1.643 (visited on 10/11/2018).
[136] J. Fréne and T. Cicone, “SECTION 8.4 - Friction in lubricated contacts,” in
Handbook of Materials Behavior Models, J. Lemaitre, Ed., Burlington: Academic
Press, Jan. 2001, pp. 760–767, isbn: 978-0-12-443341-0. doi: 10 . 1016 / B978 -
012443341-0/50076-4. [Online]. Available: http://www.sciencedirect.com/
science/article/pii/B9780124433410500764 (visited on 11/22/2018).
[137] C. C. de Wit, H. Olsson, K. J. Astrom, and P. Lischinsky, “A new model for control
of systems with friction,” IEEE Trans Autom Control, vol. 40, no. 3, pp. 419–425,
Mar. 1995, issn: 0018-9286. doi: 10.1109/9.376053.
[138] R. A. Fisher, “Theory of statistical estimation,” Math Proc Cambridge Philos Soc,
vol. 22, no. 5, pp. 700–725, Jul. 1925, issn: 1469-8064, 0305-0041. doi: 10.1017/
S0305004100009580. [Online]. Available: https://www.cambridge.org/core/
journals/mathematical- proceedings- of- the- cambridge- philosophicalsociety/
article/theory-of-statistical-estimation/7A05FB68C83B36C0E91D42C76AB177D4
(visited on 12/18/2018).
[139] B. R. Frieden, “Fisher information, disorder, and the equilibrium distributions of
physics,” Phys Rev A, vol. 41, no. 8, pp. 4265–4276, Apr. 1990. doi: 10.1103/
PhysRevA.41.4265. [Online]. Available: https://link.aps.org/doi/10.1103/
PhysRevA.41.4265 (visited on 12/18/2018).
[140] D. C. Marinescu and G. M. Marinescu, “CHAPTER 3 - Classical and quantum
information theory,” in Classical and Quantum Information, D. C. Marinescu
and G. M. Marinescu, Eds., Boston: Academic Press, Jan. 1, 2012, pp. 221–344,
isbn: 978-0-12-383874-2. doi: 10.1016/B978- 0- 12- 383874- 2.00003- 5. [Online].
Available: https : / / www . sciencedirect . com / science / article / pii /
B9780123838742000035 (visited on 04/01/2024).
[141] B. R. Frieden, Physics from Fisher Information: A Unification. Cambridge: Cambridge
University Press, Dec. 1998. doi: 10.1017/CBO9780511622670. [Online].
Available: /core/books/physics-from-fisher-information/EAD061980A31B012779A6BC5D7F93822
(visited on 02/11/2019).
[142] N. Grzywacz and H. Aleem, “Does amount of information support aesthetic values?”
Frontiers in Neuroscience, vol. 16, p. 805 658, Mar. 1, 2022. doi: 10.3389/
fnins.2022.805658.
[143] L. Devroye, A course in density estimation. Birkhauser Boston Inc., 1987, isbn:
0-8176-3365-0.
[144] A. Janicki and A. Weron, “Simulation and chaotic behavior of alpha-stable stochastic
processes,” Hugo Steinhaus Center, Wroclaw University of Technology, HSC
Books, 1994. [Online]. Available: https://econpapers.repec.org/bookchap/
wuuhsbook/hsbook9401.htm (visited on 12/18/2018).
[145] L. Telesca and M. Lovallo, “On the performance of Fisher Information Measure
and Shannon entropy estimators,” Physica A, vol. 484, pp. 569–576, 2017, issn:
0378-4371.
[146] A. B. Chelani, “Irregularity analysis of CO, NO2 and O3 concentrations at traffic,
commercial and low activity sites in Delhi,” Stochastic environmental research and
risk assessment, vol. 28, no. 4, pp. 921–925, 2014, issn: 1436-3240.
[147] B. D. Fath, H. Cabezas, and C. W. Pawlowski, “Regime changes in ecological
systems: An information theory approach,” J Theor Biol, vol. 222, no. 4, pp. 517–
530, Jun. 2003, issn: 0022-5193.
[148] M. Troudi, A. M. Alimi, and S. Saoudi, “Analytical plug-in method for kernel
density estimator applied to genetic neutrality study,” EURASIP Journal on Advances
in Signal Processing, vol. 2008, no. 1, p. 739 082, May 2008, issn: 1687-6180.
doi: 10.1155/2008/739082. [Online]. Available: https://doi.org/10.1155/
2008/739082 (visited on 05/14/2019).
[149] V. C. Raykar and R. Duraiswami, “Fast optimal bandwidth selection for kernel
density estimation,” in Proceedings of the 2006 SIAM International Conference
on Data Mining, Society for Industrial and Applied Mathematics, Apr.
2006, pp. 524–528, isbn: 978-0-89871-611-5 978-1-61197-276-4. doi: 10.1137/1.
9781611972764 . 53. [Online]. Available: https : / / epubs . siam . org / doi / 10 .
1137/1.9781611972764.53 (visited on 12/18/2018).
[150] G. Di Toro, R. Han, T. Hirose, et al., “Fault lubrication during earthquakes,”
Nature, vol. 471, no. 7339, pp. 494–498, 7339 Mar. 2011, issn: 1476-4687. doi: 10.
1038/nature09838. [Online]. Available: https://www.nature.com/articles/
nature09838 (visited on 01/18/2024).
[151] K. Mizoguchi, T. Hirose, T. Shimamoto, and E. Fukuyama, “Reconstruction of
seismic faulting by high-velocity friction experiments: An example of the 1995
Kobe earthquake,” Geophysical Research Letters, vol. 34, no. 1, 2007, issn: 1944-
8007. doi: 10.1029/2006GL027931. [Online]. Available: https://onlinelibrary.
wiley.com/doi/abs/10.1029/2006GL027931 (visited on 01/21/2024).
[152] A. Tsutsumi and T. Shimamoto, “High-velocity frictional properties of gabbro,”
Geophysical Research Letters, vol. 24, no. 6, pp. 699–702, 1997, issn: 1944-8007.
doi: 10.1029/97GL00503. [Online]. Available: https://onlinelibrary.wiley.
com/doi/abs/10.1029/97GL00503 (visited on 01/21/2024).
[153] E. Spagnuolo, O. Plümper, M. Violay, A. Cavallo, and G. Di Toro, “Fast-moving
dislocations trigger flash weakening in carbonate-bearing faults during earthquakes,”
Scientific Reports, vol. 5, no. 1, p. 16 112, 1 Nov. 10, 2015, issn: 2045-2322. doi:
10.1038/srep16112. [Online]. Available: https://www.nature.com/articles/
srep16112 (visited on 07/28/2023).
[154] H. Kanamori and L. Rivera, “Energy partitioning during an earthquake,” pp. 3–
13, 2006. doi: 10.1029/170GM03. [Online]. Available: https://onlinelibrary.
wiley.com/doi/abs/10.1029/170GM03 (visited on 09/23/2021).
[155] T.-H. Wu, C.-C. Chen, M. Lovallo, and L. Telesca, “Informational analysis of
Langevin equation of friction in earthquake rupture processes,” Chaos: An Interdisciplinary
Journal of Nonlinear Science, vol. 29, no. 10, p. 103 120, Oct. 1,
2019, issn: 1054-1500. doi: 10 . 1063 / 1 . 5092552. [Online]. Available: https :
//aip.scitation.org/doi/full/10.1063/1.5092552 (visited on 12/10/2019).
[156] M. P. Zorzano, H. Mais, and L. Vazquez, “Numerical solution of two dimensional
Fokker—Planck equations,” Applied Mathematics and Computation, vol. 98, no. 2,
pp. 109–117, Feb. 1999, issn: 0096-3003. doi: 10.1016/S0096-3003(97)10161-8.
[157] “Fundamentals,” in Nonlinear Fokker-Planck Equations: Fundamentals and Applications,
ser. Springer Series in Synergetics, T. D. Frank, Ed., Berlin, Heidelberg:
Springer, 2005, pp. 19–30, isbn: 978-3-540-26477-4. doi: 10.1007/3-540-26477-
9_2. [Online]. Available: https://doi.org/10.1007/3-540-26477-9_2 (visited
on 03/22/2020).
[158] G. A. Pavliotis, “The Fokker–Planck equation,” in Stochastic Processes and Applications:
Diffusion Processes, the Fokker-Planck and Langevin Equations, ser. Texts
in Applied Mathematics, G. A. Pavliotis, Ed., New York, NY: Springer, 2014,
pp. 87–137, isbn: 978-1-4939-1323-7. doi: 10 . 1007 / 978 - 1 - 4939 - 1323 - 7 _ 4.
[Online]. Available: https://doi.org/10.1007/978-1-4939-1323-7_4 (visited
on 03/22/2020).
[159] K. K. S. Thingbaijam and P. M. Mai, “Evidence for truncated exponential probability
distribution of earthquake slip,” Bulletin of the Seismological Society of
America, vol. 106 (4), no. 4, pp. 1802–1816, Jul. 2016, issn: 0037-1106, 1943-3573.
doi: 10.1785/0120150291.
[160] H. Kanamori and E. E. Brodsky, “The physics of earthquakes,” Reports on Progress
in Physics, vol. 67, no. 8, p. 1429, 2004, issn: 0034-4885. doi: 10.1088/0034-
4885/67/8/R03. [Online]. Available: http://stacks.iop.org/0034-4885/67/
i=8/a=R03 (visited on 07/13/2017).
[161] S. Ide, “A Brownian walk model for slow earthquakes,” Geophysical Research
Letters, vol. 35, no. 17, p. L17301, Sep. 2008, issn: 1944-8007. doi: 10.1029/
2008GL034821.
[162] S. Cyganowski, P. Kloeden, and J. Ombach, From elementary probability to stochastic
differential equations with MAPLE®. Springer Science & Business Media, 2001,
isbn: 3-540-42666-3.
[163] H.-J. Chen, T.-H. Wu, C.-C. Chen, L.-W. Kuo, L. Telesca, and M. Lovallo, “Informational
analysis of experimental seismic slip rate history and implication for
fault ruptures,” Preprint. Submitted for publication., 2024.
[164] L. R. Moreno-Torres, A. Gomez-Vieyra, M. Lovallo, A. Ramírez-Rojas, and L.
Telesca, “Investigating the interaction between rough surfaces by using the Fisher–
Shannon method: Implications on interaction between tectonic plates,” Physica A,
2018, issn: 0378-4371.
[165] M. Nosonovsky, “Entropy in tribology: In the search for applications,” Entropy,
vol. 12, no. 6, pp. 1345–1390, Jun. 2010. doi: 10.3390/e12061345. [Online]. Available:
https://www.mdpi.com/1099-4300/12/6/1345 (visited on 12/18/2018).
[166] G. W. Drake, Entropy | definition & equation | Britannica, in Mar. 28, 2024.
[Online]. Available: https://www.britannica.com/science/entropy-physics
(visited on 04/13/2024).
[167] K. Aki, “Scaling law of seismic spectrum,” Journal of Geophysical Research (1896-
1977), vol. 72, no. 4, pp. 1217–1231, 1967, issn: 2156-2202. doi: 10 . 1029 /
JZ072i004p01217. [Online]. Available: https://agupubs.onlinelibrary.wiley.
com/doi/abs/10.1029/JZ072i004p01217 (visited on 07/13/2020).
[168] T. Utsu, “44 - Relationships between magnitude scales,” in International Geophysics,
ser. International Handbook of Earthquake and Engineering Seismology,
Part A, W. H. K. Lee, H. Kanamori, P. C. Jennings, and C. Kisslinger,
Eds., vol. 81, Academic Press, Jan. 1, 2002, pp. 733–746. doi: 10.1016/S0074-
6142(02 ) 80247 - 9. [Online]. Available: https : / / www . sciencedirect . com /
science/article/pii/S0074614202802479 (visited on 07/17/2024).
[169] H. Kanamori, “Magnitude scale and quantification of earthquakes,” Tectonophysics,
Quantification of Earthquakes, vol. 93, no. 3, pp. 185–199, Apr. 10, 1983, issn:
0040-1951. doi: 10.1016/0040- 1951(83)90273- 1. [Online]. Available: https:
//www.sciencedirect.com/science/article/pii/0040195183902731 (visited
on 07/17/2024).
[170] N. A. Haskell, “Total energy and energy spectral density of elastic wave radiation
from propagating faults. Part II. A statistical source model,” Bulletin of the
Seismological Society of America, vol. 56, no. 1, pp. 125–140, Feb. 1, 1966, issn:
0037-1106. [Online]. Available: https://pubs.geoscienceworld.org/ssa/bssa/
article-abstract/56/1/125/101428/Total-energy-and-energy-spectraldensity-
of (visited on 07/24/2020).
[171] P. M. Shearer, Introduction to Seismology, 2nd ed. Cambridge: Cambridge University
Press, 2009. doi: 10.1017/CBO9780511841552. [Online]. Available: https://
www.cambridge.org/core/books/introduction-to-seismology/D2CE729616AD16EFA417BE683273B562
(visited on 07/19/2024).
[172] J. Boatwright, “A spectral theory for circular seismic sources; simple estimates
of source dimension, dynamic stress drop, and radiated seismic energy,” Bulletin
of the Seismological Society of America, vol. 70, no. 1, pp. 1–27, Feb. 1, 1980,
issn: 0037-1106. [Online]. Available: https://pubs.geoscienceworld.org/ssa/
bssa/article/70/1/1/101951/A-spectral-theory-for-circular-seismicsources
(visited on 07/19/2020).
[173] M. Furumoto and I. Nakanishi, “Source times and scaling relations of large earthquakes,”
Journal of Geophysical Research: Solid Earth, vol. 88, no. B3, pp. 2191–
2198, 1983, issn: 2156-2202. doi: 10.1029/JB088iB03p02191.
[174] Y. Tanioka and L. J. Ruff, “Source time functions,” Seismological Research Letters,
vol. 68, no. 3, pp. 386–400, May 1997, issn: 0895-0695. doi: 10.1785/gssrl.68.
3.386.
[175] H. Houston, “Influence of depth, focal mechanism, and tectonic setting on the
shape and duration of earthquake source time functions,” Journal of Geophysical
Research: Solid Earth, vol. 106, no. B6, pp. 11 137–11 150, 2001, issn: 2156-2202.
doi: 10.1029/2000JB900468.
[176] S. Michel, A. Gualandi, and J.-P. Avouac, “Similar scaling laws for earthquakes
and Cascadia slow-slip events,” Nature, vol. 574, no. 7779, pp. 522–526, Oct. 2019,
issn: 1476-4687. doi: 10.1038/s41586-019-1673-6.
[177] S. Ide, G. C. Beroza, D. R. Shelly, and T. Uchide, “A scaling law for slow earthquakes,”
Nature, vol. 447, no. 7140, pp. 76–79, May 2007, issn: 0028-0836. doi:
10.1038/nature05780.
[178] A. C. Aguiar, T. I. Melbourne, and C. W. Scrivner, “Moment release rate of
Cascadia tremor constrained by GPS,” Journal of Geophysical Research: Solid
Earth, vol. 114, no. B7, 2009, issn: 2156-2202. doi: 10.1029/2008JB005909.
[179] H. Gao, D. A. Schmidt, and R. J. Weldon, “Scaling relationships of source parameters
for slow slip events,” Bulletin of the Seismological Society of America, vol. 102,
no. 1, pp. 352–360, Feb. 2012, issn: 0037-1106. doi: 10.1785/0120110096.
[180] J. Gomberg, A. Wech, K. Creager, K. Obara, and D. Agnew, “Reconsidering
earthquake scaling,” Geophysical Research Letters, vol. 43, no. 12, pp. 6243–6251,
2016, issn: 1944-8007. doi: 10.1002/2016GL069967.
[181] J.-H. Wang, “A review on scaling of earthquake faults,” Terrestrial, Atmospheric
and Oceanic Sciences, vol. 29, no. 6, pp. 589–610, 2018, issn: 1017-0839. doi:
10.3319/TAO.2018.08.19.01. [Online]. Available: http://tao.cgu.org.tw/
index.php/articles/archive/geophysics/item/1612 (visited on 06/08/2024).
[182] S. Ide, K. Imanishi, Y. Yoshida, G. C. Beroza, and D. R. Shelly, “Bridging the
gap between seismically and geodetically detected slow earthquakes,” Geophysical
Research Letters, vol. 35, no. 10, May 2008, issn: 0094-8276. doi: 10 . 1029 /
2008GL034014.
[183] W. B. Frank, B. Rousset, C. Lasserre, and M. Campillo, “Revealing the cluster
of slow transients behind a large slow slip event,” Science Advances, vol. 4, no. 5,
eaat0661, May 2018, issn: 2375-2548. doi: 10.1126/sciadv.aat0661.
[184] K. Thøgersen, H. A. Sveinsson, J. Scheibert, F. Renard, and A. Malthe-Sørenssen,
“The moment duration scaling relation for slow rupture arises from transient rupture
speeds,” Geophysical Research Letters, vol. 46, no. 22, pp. 12 805–12 814, 2019,
issn: 1944-8007. doi: 10.1029/2019GL084436.
[185] K. Aki, “Earthquake mechanism,” in Developments in Geotectonics, ser. The Upper
Mantle, A. R. Ritsema, Ed., vol. 4, Elsevier, Jan. 1972, pp. 423–446. doi:
10.1016/B978-0-444-41015-3.50029-X.
[186] Y. Iio, “Frictional coefficient on faults in a seismogenic region inferred from earthquake
mechanism solutions,” Journal of Geophysical Research: Solid Earth, vol. 102,
no. B3, pp. 5403–5412, 1997, issn: 2156-2202. doi: 10.1029/96JB03593. [Online].
Available: https://onlinelibrary.wiley.com/doi/abs/10.1029/96JB03593
(visited on 06/21/2024).
[187] Z. Reches, G. Baer, and Y. Hatzor, “Constraints on the strength of the upper
crust from stress inversion of fault slip data,” Journal of Geophysical Research:
Solid Earth, vol. 97, no. B9, pp. 12 481–12 493, 1992, issn: 2156-2202. doi: 10.
1029/90JB02258. [Online]. Available: https://onlinelibrary.wiley.com/doi/
abs/10.1029/90JB02258 (visited on 06/21/2024).
[188] S. Ji, S. Sun, Q. Wang, and D. Marcotte, “Lamé parameters of common rocks
in the Earth’s crust and upper mantle,” Journal of Geophysical Research: Solid
Earth, vol. 115, no. B6, 2009JB007134, Jun. 2010, issn: 0148-0227. doi: 10.1029/
2009JB007134. [Online]. Available: https://agupubs.onlinelibrary.wiley.
com/doi/10.1029/2009JB007134 (visited on 06/21/2024).
[189] J. Von Plato, “Boltzmann’s ergodic hypothesis,” Archive for History of Exact Sciences,
vol. 42, no. 1, pp. 71–89, 1991, issn: 0003-9519. doi: 10.1007/BF00384333.
[190] K. Aki, “Scaling law of earthquake source time‐function,” Geophysical Journal
International, vol. 31, pp. 3–25, 1‐3 1972, issn: 1365-246X.
[191] P. S. Dysart, J. A. Snoke, and I. S. Sacks, “Source parameters and scaling relations
for small earthquakes in the Matsushiro region, southwest Honshu, Japan,” Bulletin
of the Seismological Society of America, vol. 78, no. 2, pp. 571–589, Apr. 1,
1988, issn: 0037-1106. doi: 10.1785/BSSA0780020571. [Online]. Available: https:
//doi.org/10.1785/BSSA0780020571 (visited on 07/16/2024).
[192] I. Selwyn Sacks and P. A. Rydelek, “Earthquake “Quanta”as an explanation
for observed magnitudes and stress drops,” Bulletin of the Seismological Society
of America, vol. 85, no. 3, pp. 808–813, Jun. 1, 1995, issn: 0037-1106. doi:
10 . 1785 / BSSA0850030808. [Online]. Available: https : / / doi . org / 10 . 1785 /
BSSA0850030808 (visited on 07/16/2024).
[193] Z. L. Wu, Y. T. Chen, and S. G. Kim, “Physical significance of earthquake quanta,”
Bulletin of the Seismological Society of America, vol. 86, no. 5, pp. 1623–1626, Oct.
1996, issn: 0037-1106.
[194] D. P. Hess and A. Soom, “Friction at a lubricated line contact operating at oscillating
sliding velocities,” J Tribol, vol. 112, no. 1, pp. 147–152, Jan. 1990, issn:
0742-4787. doi: 10.1115/1.2920220. [Online]. Available: http://dx.doi.org/
10.1115/1.2920220 (visited on 05/07/2019).
[195] E. E. Brodsky and H. Kanamori, “Elastohydrodynamic lubrication of faults,”
Journal of Geophysical Research: Solid Earth, vol. 106, no. B8, pp. 16 357–16 374,
2001, issn: 2156-2202. doi: 10.1029/2001JB000430. [Online]. Available: https:
//agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2001JB000430 (visited
on 05/07/2019).
[196] D. Kilb and J. Gomberg, “The initial subevent of the 1994 Northridge, California,
earthquake: Is earthquake size predictable?” J Seismolog, vol. 3, no. 4, pp. 409–420,
Oct. 1999, issn: 1573-157X. doi: 10.1023/A:1009890329925. [Online]. Available:
https://doi.org/10.1023/A:1009890329925 (visited on 05/06/2019).
[197] W. L. Ellsworth and G. C. Beroza, “Observation of the seismic nucleation phase in
the Ridgecrest, California, Earthquake sequence,” Geophys Res Lett, vol. 25, no. 3,
pp. 401–404, 1998, issn: 1944-8007. doi: 10.1029/97GL53700. [Online]. Available:
https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/97GL53700
(visited on 05/06/2019).
[198] J. N. Brune, “Implications of earthquake triggering and rupture propagation for
earthquake prediction based on premonitory phenomena,” Journal of Geophysical
Research: Solid Earth, vol. 84, no. B5, pp. 2195–2198, 1979, issn: 2156-
2202. doi: 10.1029/JB084iB05p02195. [Online]. Available: https://agupubs.
onlinelibrary.wiley.com/doi/abs/10.1029/JB084iB05p02195 (visited on
05/06/2019).
[199] E. L. Olson and R. M. Allen, “The deterministic nature of earthquake rupture,”
Nature, vol. 438, no. 7065, pp. 212–215, Nov. 2005, issn: 0028-0836, 1476-4687.
doi: 10 . 1038 / nature04214. [Online]. Available: http : / / www . nature . com /
articles/nature04214 (visited on 05/02/2019).
[200] Y.-M. Wu and L. Zhao, “Magnitude estimation using the first three seconds Pwave
amplitude in earthquake early warning,” Geophys Res Lett, vol. 33, no. 16,
2006, issn: 1944-8007. doi: 10.1029/2006GL026871. [Online]. Available: https:
/ / agupubs . onlinelibrary . wiley . com / doi / abs / 10 . 1029 / 2006GL026871
(visited on 05/03/2019). |
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