Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Ubiquitous weakening of faults due to thermal pressurization

Abstract

Laboratory simulations of earthquakes show that at high slip rates, faults can weaken significantly, aiding rupture1,2,3. Various mechanisms, such as thermal pressurization and flash heating, have been proposed to cause this weakening during laboratory experiments1,4,5,6, yet the processes that aid fault slip in nature remain unknown. Measurements of seismic radiation during an earthquake can be used to estimate the frictional work associated with fault weakening, known as an event’s fracture energy7,8,9. Here we compile new and existing8,9 measurements of fracture energy for earthquakes globally that vary in size from borehole microseismicity to great earthquakes. We observe a distinct transition in how fracture energy scales with event size, which implies that faults weaken differently during small and large earthquakes, and earthquakes are not self-similar. We use an elastodynamic numerical model of earthquake rupture to explore possible mechanisms. We find that thermal pressurization of pore fluid by the rapid shear heating of fault gouge can account for the observed scaling of fracture energy in small and large earthquakes, over seven orders of fault slip magnitude. We conclude that thermal pressurization is a widespread and prominent process for fault weakening.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Cascade of weakening at the tip of a dynamic shear rupture.
Figure 2: Fault fracture energy and gradual fault weakening with slip.
Figure 3: Variation of inferred event fracture energy with event slip.

Similar content being viewed by others

References

  1. Han, R., Shimamoto, T., Hirose, T., Ree, J. H. & Ando, J. I. Ultralow friction of carbonate faults caused by thermal decomposition. Science 316, 878–881 (2007).

    Article  Google Scholar 

  2. Goldsby, D. L. & Tullis, T. E. Flash heating leads to low frictional strength of crustal rocks at earthquake slip rates. Science 334, 216–218 (2011).

    Article  Google Scholar 

  3. Di Toro, G. et al. Fault lubrication during earthquakes. Nature 471, 494–498 (2011).

    Article  Google Scholar 

  4. Lachenbruch, A. H. Frictional heating, fluid pressure, and the resistance to fault motion. J. Geophys. Res. 85, 6097–6112 (1980).

    Article  Google Scholar 

  5. Rice, J. R. Heating and weakening of faults during earthquake slip. J. Geophys. Res. 111, B05311 (2006).

    Article  Google Scholar 

  6. Beeler, N. M., Tullis, T. E. & Goldsby, D. L. Constitutive relationships and physical basis of fault strength due to flash heating. J. Geophys. Res. 113, B01401 (2008).

    Article  Google Scholar 

  7. Kanamori, H. & Heaton, T. H. Microscopic and macroscopic physics of earthquakes. Geophys. Monogr. Ser. 120, 147–163 (2009).

    Google Scholar 

  8. Abercrombie, R. E. & Rice, J. R. Can observations of earthquake scaling constrain slip weakening? Geophys. J. Int. 162, 406–424 (2005).

    Article  Google Scholar 

  9. Tinti, E., Spudich, P. & Cocco, M. Earthquake fracture energy inferred from kinematic rupture models on extended faults. J. Geophys. Res. 110, B12303 (2005).

    Article  Google Scholar 

  10. Dieterich, J. Modeling of rock friction 1. Experimental results and constitutive equations. J. Geophys. Res. 84, 2161–2168 (1979).

    Article  Google Scholar 

  11. Fulton, P. M. et al. Low coseismic friction on the Tohoku-Oki fault determined from temperature measurements. Science 342, 1214–1217 (2013).

    Article  Google Scholar 

  12. Ujiie, K. et al. Low coseismic shear stress on the Tohoku-Oki megathrust determined from laboratory experiments. Science 342, 1211–1214 (2013).

    Article  Google Scholar 

  13. Simons, M. et al. The 2011 magnitude 9.0 Tohoku-Oki earthquake: Mosaicking the megathrust from seconds to centuries. Science 332, 1421–1425 (2011).

    Article  Google Scholar 

  14. Ide, S., Baltay, A. & Beroza, G. C. Shallow dynamic overshoot and energetic deep rupture in the 2011 Mw 9.0 Tohoku-Oki earthquake. Science 332, 1426–1429 (2011).

    Article  Google Scholar 

  15. Faulkner, D. R., Mitchell, T. M., Behnsen, J., Hirose, T. & Shimamoto, T. Stuck in the mud? Earthquake nucleation and propagation through accretionary forearcs. Geophys. Res. Lett. 38, L18303 (2011).

    Article  Google Scholar 

  16. Noda, H. & Lapusta, N. Stable creeping fault segments can become destructive as a result of dynamic weakening. Nature 493, 518–521 (2013).

    Article  Google Scholar 

  17. Zheng, G. & Rice, J. R. Conditions under which velocity-weakening friction allows a self-healing versus a cracklike mode of rupture. Bull. Seismol. Soc. Am. 88, 1466–1483 (1998).

    Google Scholar 

  18. Noda, H., Dunham, E. M. & Rice, J. R. Earthquake ruptures with thermal weakening and the operation of major faults at low overall stress levels. J. Geophys. Res. 114, B07302 (2009).

    Google Scholar 

  19. Heaton, T. H. Evidence for and implications of self-healing pulses of slip in earthquake rupture. Phys. Earth Planet. Inter. 64, 1–20 (1990).

    Article  Google Scholar 

  20. Mase, C. W. & Smith, L. Effects of frictional heating on the thermal, hydrologic, and mechanical response of a fault. J. Geophys. Res. 92, 6249–6272 (1987).

    Article  Google Scholar 

  21. Garagash, D. I. Seismic and aseismic slip pulses driven by thermal pressurization of pore fluid. J. Geophys. Res. 117, B04314 (2012).

    Article  Google Scholar 

  22. Rempel, A. W. & Rice, J. R. Thermal pressurization and onset of melting in fault zones. J. Geophys. Res. 111, B09314 (2006).

    Article  Google Scholar 

  23. Chester, F. M. & Chester, J. S. Ultracataclasite structure and friction processes of the Punchbowl fault, San Andreas system, California. Tectonophysics 295, 199–221 (1998).

    Article  Google Scholar 

  24. Boullier, A.-M., Yeh, E.-C., Boutareaud, S., Song, S.-R. & Tsai, C.-H. Microscale anatomy of the 1999 Chi-Chi earthquake fault zone. Geochem. Geophys. Geosyst. 10, Q03016 (2009).

    Article  Google Scholar 

  25. Kuo, L.-W., Hsiao, H.-C., Song, S.-R., Sheu, H.-S. & Suppe, J. Coseismic thickness of principal slip zone from the Taiwan Chelungpu fault Drilling Project-A (TCDP-A) and correlated fracture energy. Tectonophysics 619–620, 29–35 (2014).

    Article  Google Scholar 

  26. Wibberley, C. A. J. Hydraulic diffusivity of fault gouge zones and implications for thermal pressurization during seismic slip. Earth Planet. Space 54, 1153–1171 (2002).

    Article  Google Scholar 

  27. Brantut, N. & Rice, J. R. How pore fluid pressurization influences crack tip processes during dynamic rupture. Geophys. Res. Lett. 38, L24314 (2011).

    Article  Google Scholar 

  28. Andrews, D. J. Rupture dynamics with energy loss outside the slip zone. J. Geophys. Res. 110, B01307 (2005).

    Article  Google Scholar 

  29. Zoback, M. D. & Healy, J. H. In situ stress measurements to 3.5 km depth in the Cajon Pass scientific research borehole: Implications for the mechanics of crustal faulting. J. Geophys. Res. 97, 5039–5057 (1992).

    Article  Google Scholar 

  30. Zoback, M. D. & Harjes, H.-P. Injection-induced earthquakes and crustal stress at 9 km depth at the KTB deep drilling site, Germany. J. Geophys. Res. 102, 18477–18491 (1997).

    Article  Google Scholar 

  31. Causse, M., Dalguer, L. A. & Mai, P. M. Variability of dynamic source parameters inferred from kinematic models of past earthquakes. Geophys. J. Int. 196, 1754–1769 (2013).

    Article  Google Scholar 

  32. Madariaga, R. Dynamics of an expanding circular fault. Bull. Seismol. Soc. Am. 66, 639–666 (1976).

    Google Scholar 

  33. Madariaga, R. On the relation between seismic moment and stress drop in the presence of stress and strength heterogeneity. J. Geophys. Res. 84, 2243–2250 (1979).

    Article  Google Scholar 

  34. Cocco, M. & Tinti, E. Scale dependence in the dynamics of earthquake propagation: Evidence from seismological and geological observations. Earth Planet. Sci. Lett. 273, 123–131 (2008).

    Article  Google Scholar 

  35. Lay, T. et al. Depth-varying rupture properties of subduction zone megathrust faults. J. Geophys. Res. 117, B04311 (2012).

    Article  Google Scholar 

  36. Venkataraman, A. & Kanamori, H. Observational constraints on the fracture energy of subduction zone earthquakes. J. Geophys. Res. 109, B05302 (2004).

    Google Scholar 

  37. Choy, G. L. & Dewey, J. W. Rupture process of an extended earthquake sequence: Teleseismic analysis of the Chilean earthquake of March 3, 1985. J. Geophys. Res. 93, 1103–1118 (1988).

    Article  Google Scholar 

  38. Lay, T., Ammon, C. J., Kanamori, H., Xue, L. & Kim, M. J. Possible large near-trench slip during the 2011 Mw 9.0 off the Pacific coast of Tohoku earthquake. Earth Planets Space 63, 687–692 (2011).

    Article  Google Scholar 

  39. Lay, T. et al. The 25 October 2010 Mentawai tsunami earthquake (Mw 7.8) and the tsunami hazard presented by shallow megathrust ruptures. Geophys. Res. Lett. 38, L06302 (2011).

    Google Scholar 

  40. Lin, Y. et al. Coseismic and postseismic slip associated with the 2010 Maule Earthquake, Chile: Characterizing the Arauco Peninsula barrier effect. J. Geophys. Res. 118, 3142–3159 (2013).

    Article  Google Scholar 

  41. Konca, O. et al. Partial rupture of a locked patch of the Sumatra megathrust during the 2007 earthquake sequence. Nature 456, 631–635 (2008).

    Article  Google Scholar 

  42. Lay, T., Ammon, C. J., Hutko, A. R. & Kanamori, H. Effects of kinematic constraints on teleseismic finite-source rupture inversions: Great Peruvian earthquakes of 23 June 2001 and 15 August 2007. Bull. Seismol. Soc. Am. 100, 969–994 (2010).

    Article  Google Scholar 

  43. Kanamori, H., Miyazawa, M. & Mori, J. Investigation of the earthquake sequence off Miyagi prefecture with historical seismograms. Earth Planet. Space 58, 1533–1541 (2006).

    Article  Google Scholar 

  44. Konca, O. et al. Rupture kinematics of the 2005 Mw 8.6 Nias–Simeulue earthquake from the joint inversion of seismic and geodetic data. Bull. Seismol. Soc. Am. 97, S307–S322 (2007).

    Article  Google Scholar 

  45. Rhie, J., Dreger, D., Burgmann, R. & Romanowicz, B. Slip of the 2004 Sumatra–Andaman earthquake from Joint inversion of long-period global seismic waveforms and GPS static offsets. Bull. Seismol. Soc. Am. 97, S115–S127 (2007).

    Article  Google Scholar 

  46. Honda, R. et al. Ground motion and rupture process of the 2003 Tokachi-oki earthquake obtained from strong motion data of K-NET and KiK-net. Earth Planet. Space 56, 317–322 (2004).

    Article  Google Scholar 

  47. Swenson, J. L. & Beck, S. L. Source characteristics of the 12 November 1996 Mw 7.7 Peru subduction zone earthquake. Pure Appl. Geophys. 154, 731–751 (1999).

    Article  Google Scholar 

  48. Tanioka, Y. & Gonzalez, F. I. The Aleutian earthquake of June 10, 1996 (Mw 7.9) ruptured parts of both the Andreanof and Delarof segments. Geophys. Res. Lett. 25, 2245–2248 (1998).

    Article  Google Scholar 

  49. Ihmle, P. F., Gomez, J.-M., Heinrichand, P. & Guibourg, S. The 1996 Peru tsunamigenic earthquake: Broadband source process. Geophys. Res. Lett. 25, 2691–2694 (1998).

    Article  Google Scholar 

  50. Carlo, D. L., Lay, T., Ammon, C. J. & Zhang, J. Rupture process of the 1995 Antofagasta subduction earthquake (Mw = 8.1). Pure Appl. Geophys. 154, 677–709 (1999).

    Article  Google Scholar 

  51. Sato, T., Imanishi, K. & Kosuga, M. Three-stage rupture process of the 28 December 1994 Sanriku-Oki earthquake. Geophys. Res. Lett. 23, 33–36 (1996).

    Article  Google Scholar 

  52. Wald, D. J. & Heaton, T. H. Spatial and temporal distribution of slip for the 1992 Landers, California, earthquake. Bull. Seismol. Soc. Am. 84, 668–691 (1994).

    Google Scholar 

  53. Asano, K. & Iwata, T. Source process and near-source ground motions of the 2005 west off Fukuoka Prefecture earthquake. Earth Planet. Space 58, 93–98 (2006).

    Article  Google Scholar 

  54. Yoo, S., Rhie, J., Choi, H. & Mayeda, K. Evidence of non-self-similarity and transitional increment of scaled energy in the 2005 west off Fukuoka seismic sequence. J. Geophys. Res. 115, B08308 (2010).

    Google Scholar 

  55. Custodio, S., Page, M. T. & Archuleta, R. J. Constraining earthquake source inversions with GPS data: 2. A two-step approach to combine seismic and geodetic data sets. J. Geophys. Res. 114, B01315 (2009).

    Article  Google Scholar 

  56. Ma, S., Custodio, S., Archuleta, R. J. & Liu, P. Dynamic modeling of the 2004 Mw 6.0 Parkfield, California, earthquake. J. Geophys. Res. 113, B02301 (2008).

    Google Scholar 

  57. Asano, K., Iwata, T. & Irikura, K. Estimation of source rupture process and strong ground motion simulation of the 2002 Denali, Alaska, earthquake. Bull. Seismol. Soc. Am. 95, 1701–1715 (2005).

    Article  Google Scholar 

  58. Choy, G. L. & Boatwright, J. Radiated energy and the rupture process of the Denali fault earthquake sequence of 2002 from broadband teleseismic body waves. Bull. Seismol. Soc. Am. 94, S269–S277 (2004).

    Article  Google Scholar 

  59. Choy, G. L. & Boatwright, J. Differential energy radiation from two earthquakes in Japan with identical Mw: The Kyushu 1996 and Tottori 2000 earthquakes. Bull. Seismol. Soc. Am. 99, 1815–1826 (2009).

    Article  Google Scholar 

  60. Ji, C., Wald, D. J. & Helmberger, D. V. Source description of the 1999 Hector Mine, California, earthquake, part II: Complexity of slip history. Bull. Seismol. Soc. Am. 92, 1208–1226 (2002).

    Article  Google Scholar 

  61. Venkataraman, A., Rivera, L. & Kanamori, H. Radiated energy from the 16 October 1999 hector mine earthquake: Regional and teleseismic estimates. Bull. Seismol. Soc. Am. 92, 1256–1265 (2002).

    Article  Google Scholar 

  62. Boatwright, J., Choy, G. & Seekins, L. Regional estimates of radiated seismic energy. Bull. Seismol. Soc. Am. 92, 1241–1255 (2002).

    Article  Google Scholar 

  63. Hernandez, B. et al. Rupture history of the 1997 Umbria-Marche (Central Italy) main shocks from the inversion of GPS, DInSAR and near field strong motion data. Ann. Geophys. 47, 1355–1376 (2004).

    Google Scholar 

  64. Pino, N. A., Mazza, S. & Boschi, E. Rupture directivity of the major shocks in the 1997 Umbria-Marche (Central Italy) sequence from regional broadband waveforms. Geophys. Res. Lett. 26, 2101–2104 (1999).

    Article  Google Scholar 

  65. Wald, D. J. Slip history of the 1995 Kobe, Japan earthquake determined from strong motion, teleseismic, and geodetic data. J. Phys. Earth 44, 489–503 (1996).

    Article  Google Scholar 

  66. Wald, D. J., Heaton, T. H. & Hudnut, K. W. The slip history of the 1994 Northridge, California, earthquake determined from strong ground motion, teleseismic, GPS, and leveling data. Bull. Seismol. Soc. Am. 86, S49–S70 (1996).

    Google Scholar 

  67. Kanamori, H. et al. Determination of of earthquake energy release and M L using TERRAscope. Bull. Seismol. Soc. Am. 83, 330–346 (1993).

    Google Scholar 

  68. McGarr, A. & Fletcher, J. A method for mapping apparent stress and energy radiation applied to the 1994 Northridge earthquake fault zone. Geophys. Res. Lett. 27, 1953–1956 (2000).

    Article  Google Scholar 

  69. Hartzell, S. H. & Heaton, T. H. Rupture history of the 1984 Morgan Hill, California, earthquake from the inversion of strong motion records. Bull. Seismol. Soc. Am. 76, 649–674 (1986).

    Google Scholar 

  70. Bolt, B. A. Seismic energy release over a broad frequency band. Pure Appl. Geophys. 124, 919–930 (1986).

    Article  Google Scholar 

  71. Archuleta, R. A faulting model for the 1979 Imperial Valley earthquake. J. Geophys. Res. 89, 4559–4585 (1984).

    Article  Google Scholar 

  72. Smith, K. D., Brune, J. N. & Priestley, K. F. The seismic spectrum, radiated energy, and the Savage and Wood inequality for complex earthquakes. Tectonophysics 188, 303–320 (1991).

    Article  Google Scholar 

  73. Lamb, S. Shear stresses on megathrusts: Implications for mountain building behind subduction zones. J. Geophys. Res. 111, B07401 (2006).

    Google Scholar 

  74. Seno, T. Determination of the pore fluid pressure ratio at seismogenic megathrusts in subduction zones: Implications for strength of asperities and Andean-type mountain building. J. Geophys. Res. 114, B05405 (2009).

    Article  Google Scholar 

  75. Tinti, E., Spudich, P. & Cocco, M. Correction to “Earthquake fracture energy inferred from kinematic rupture models on extended faults”. J. Geophys. Res. 113, B07301 (2008).

    Article  Google Scholar 

  76. Hernandez, B., Cotton, F. & Campillo, M. Contribution of radar interferometry to a two-step inversion of the kinematic process of the 1992 Landers earthquake. J. Geophys. Res. 104, 13083–13099 (1999).

    Article  Google Scholar 

  77. Franceschina, G., Gentili, S. & Bressan, G. Source parameters scaling of the 2004 Kobarid (Western Slovenia) seismic sequence. Phys. Earth Planet. Inter. 222, 58–75 (2013).

    Article  Google Scholar 

  78. Viegas, G., Abercrombie, R. E. & Kim, W.-Y. The 2002 M5 Au Sable Forks, NY, earthquake sequence: Source scaling relationships and energy budget. J. Geophys. Res. 115, B07310 (2010).

    Article  Google Scholar 

  79. Franceschina, G., Kravanja, S. & Bressan, G. Source parameters and scaling relationships in the Friuli-Venezia Giulia (Northeastern Italy) region. Phys. Earth Planet. Inter. 154, 148–167 (2006).

    Article  Google Scholar 

  80. Fletcher, J. B. & Boatwright, J. Source parameters of Loma Prieta aftershocks and wave propagation characteristics along the San Francisco Peninsula from a joint inversion of digital seismograms. Bull. Seismol. Soc. Am. 81, 1783–1812 (1991).

    Google Scholar 

  81. Kwiatek, G. et al. Frequency-magnitude characteristics down to magnitude −4.4 for induced seismicity recorded at Mponeng Gold Mine, South Africa. Bull. Seismol. Soc. Am. 100, 1165–1173 (2010).

    Article  Google Scholar 

  82. Venkataraman, A. et al. Measurements of spectral similarity for microearthquakes in western Nagano, Japan. J. Geophys. Res. 111, B03303 (2006).

    Article  Google Scholar 

  83. Ide, S., Beroza, G. C., Prejean, S. G. & Ellsworth, W. L. Apparent break in earthquake scaling due to path and site effects on deep borehole recordings. J. Geophys. Res. 108, 2271 (2003).

    Article  Google Scholar 

  84. Jost, M. L., Bubelberg, T., Jost, O. & Harjes, H.-P. Source parameters of injection-induced microearthquakes at 9 km depth at the KTB Deep Drilling Site, Germany. Bull. Seismol. Soc. Am. 88, 815–832 (1998).

    Google Scholar 

  85. Ide, S. & Beroza, G. C. Does apparent stress vary with earthquake size? Geophys. Res. Lett. 28, 3349–3352 (2001).

    Article  Google Scholar 

  86. Stork, A. L. & Ito, H. Source parameter scaling for small earthquakes observed at the Western Nagano 800-m-deep borehole, Central Japan. Bull. Seismol. Soc. Am. 94, 1781–1794 (2004).

    Article  Google Scholar 

  87. Mori, J., Abercrombie, R. E. & Kanamori, H. Stress drops and radiated energies of aftershocks of the 1994 Northridge, California, earthquake. J. Geophys. Res. 108, 2545 (2003).

    Article  Google Scholar 

  88. Boatwright, J. The effect of rupture complexity on estimates of source size. J. Geophys. Res. 89, 1132–1146 (1984).

    Article  Google Scholar 

  89. Thio, H. K. & Kanamori, H. Source complexity of the 1994 Northridge earthquake and its relation to aftershock mechanisms. Bull. Seismol. Soc. Am. 86, S84–S92 (1996).

    Google Scholar 

  90. Poliakov, A., Dmowska, R. & Rice, J. R. Dynamic shear rupture interactions with fault bends and off-axis secondary faulting. J. Geophys. Res. 107, 2295 (2002).

    Article  Google Scholar 

  91. Dor, O., Ben-Zion, Y., Rockwell, T. K. & Brune, J. Pulverized rocks in the Mojave section of the San Andreas fault zone. Earth Planet. Sci. Lett. 245, 642–654 (2006).

    Article  Google Scholar 

  92. Mitchell, T. M. & Faulkner, D. R. The nature and origin of off-fault damage surrounding strike-slip fault zones with a wide range of displacements: A field study from the Atacama fault system, northern Chile. J. Struct. Geol. 31, 802–816 (2009).

    Article  Google Scholar 

  93. Templeton, E. L. & Rice, J. R. Off-fault plasticity and earthquake rupture dynamics: 1. Dry materials or neglect of fluid pressure changes. J. Geophys. Res. 113, B09306 (2008).

    Article  Google Scholar 

  94. Templeton, E. L. Effects of Inelastic Off-Fault Deformation on the Dynamics of Earthquake Rupture and Branch Fault Activation PhD thesis, Univ. Harvard (2009)

  95. Townend, J. & Zoback, M. D. Regional tectonic stress near the San Andreas fault in central and southern California. Geophys. Res. Lett. 31, L15S11 (2004).

    Article  Google Scholar 

  96. Cocco, M., Tinti, E., Marone, C. & Piatanesi, A. Fault-Zone Properties and Earthquake Rupture Dynamics Vol. 273, 163–186 (Academic Press, 2009).

    Book  Google Scholar 

  97. Ruina, A. Slip instability and state variable friction laws. J. Geophys. Res. 88, 10359–10370 (1983).

    Article  Google Scholar 

  98. Rice, J. R. Constitutive relations for fault slip and earthquake instabilities. Pure Appl. Geophys. 121, 443–475 (1983).

    Article  Google Scholar 

  99. Marone, C. Laboratory-derived friction laws and their application to seismic faulting. Annu. Rev. Earth Planet. Sci. 26, 643–696 (1998).

    Article  Google Scholar 

  100. Garagash, D. I. On fracture energy of flash heating. EOS Trans. Am. Geophys. Union 92, T13A–2360 (2011).

    Google Scholar 

  101. Andrews, D. J. A fault constitutive relation accounting for thermal pressurization of pore fluid. J. Geophys. Res. 107, 2363 (2002).

    Article  Google Scholar 

  102. Weertman, J. Unstable slippage across a fault that separates elastic media of different elastic constants. J. Geophys. Res. 85, 1455–1461 (1980).

    Article  Google Scholar 

  103. Erdogan, F., Gupta, G. D. & Cook, T. S. Numerical Solution of Singular Integral Equations Vol. 1, Ch. 7 368–425 (Noordhoff International Publ., 1973).

    Google Scholar 

  104. Berrut, J. & Trefethen, L. Barycentric Lagrange interpolation. SIAM Rev. 46, 501–517 (2004).

    Article  Google Scholar 

  105. King, F. W. Hilbert Transforms Vol. I (Cambridge Univ. Press, 2009).

    Book  Google Scholar 

Download references

Acknowledgements

This study was supported by the Natural Science and Engineering Research Council of Canada (Discovery grant 371606), the National Science Foundation (grant EAR-1344993), and the Southern California Earthquake Center (SCEC; contribution No. 6004). SCEC is funded by NSF Cooperative Agreement EAR-1033462 and USGS Cooperative Agreement G12AC20038.

Author information

Authors and Affiliations

Authors

Contributions

Both authors contributed to developing the main ideas, interpreting the results and producing the manuscript.

Corresponding authors

Correspondence to Robert C. Viesca or Dmitry I. Garagash.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 1354 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Viesca, R., Garagash, D. Ubiquitous weakening of faults due to thermal pressurization. Nature Geosci 8, 875–879 (2015). https://doi.org/10.1038/ngeo2554

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/ngeo2554

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing