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Fractal asperities, invasion of barriers, and interplate earthquakes

Earth, Planets and Space volume 55, pages 649–665 (2003)Cite this article

Abstract

I present a model to explain seismicity variations along consuming and transform fault plate boundaries. The basic assumptions of the model are: (1) plate boundary fault zones consist of asperities and barriers, which are defined as having negative and positive a-b values, respectively, of rate and state dependent friction laws, (2) circular-shaped asperities are distributed in a fractal manner, such that an asperity contains smaller asperities inside, (3) pore fluid pressure can be elevated almost to the lithostatic only in barriers (called invasion of barriers), and (4) a region whose barriers are invaded can rupture as an earthquake. Based on these assumptions, I re-estimate fault areas of interplate earthquakes along the San Andreas and near Japan. The derived relation between fault area and seismic moment for these earthquakes determines the fractal dimension of asperities to be 1.4, and nine smaller asperities are contained in a larger one of which the radius is 4.8 times those of the smaller ones. Various modes of invasion of barriers with a fractal distribution of asperities can explain the seismological phenomena such as variations of seismic coupling along plate boundaries, two types of earthquake families, and co-existence of the Gutenberg-Richter’s law and characteristic repeating earthquakes.

References

  • Abercrombie, R. E., Earthquake source scaling relationships from −1 to 5 ML using seismograms recorded at 2.5-km depth, J. Geophys. Res., 100, 24015–24036, 1995.

    Article  Google Scholar 

  • Aki, K., Characterization of barriers on an earthquake fault, J. Geophys. Res., 84, 6140–6148, 1979.

    Article  Google Scholar 

  • Aki, K., Asperities, barriers, characteristic earthquakes and strong motion prediction, J. Geophys. Res., 89, 5867–5872, 1984.

    Article  Google Scholar 

  • Ando, M., Source mechanisms and tectonic significance of historical earthquakes along the Nankai Trough, Japan, Tectonophysics, 27, 119–140, 1975.

    Article  Google Scholar 

  • Atwater, B. F. and E. Hemphill-Haley, Recurrence Interval for Great Earthquakes of the Past 3,500 Years at Northeastern Willapa Bay, Washington, U. S. Geol. Survey Prof. Paper 1576, 108 pp., 1997.

  • Bakun, W. H. and T. V. McEvilly, Recurrence models and Parkfield, California, earthquakes, J. Geophys. Res., 89, 3051–3058, 1984.

    Article  Google Scholar 

  • Beroza, G., Near-source imaging of seismic rupture, Ph.D. thesis, Mass. Inst. of Technol., Cambridge, 1989.

    Google Scholar 

  • Beroza, G. C., Near-source modeling of the Loma Prieta earthquake: Evidence for heterogeneous slip and implications for earthquake hazard, Bull. Seism. Soc. Am., 81, 1603–1621, 1991.

    Google Scholar 

  • Blanpied, M. L., D. A. Lockner, and J. D. Byerlee, An earthquake mechanism based on rapid sealing of faults, Nature, 358, 574–576, 1992.

    Article  Google Scholar 

  • Boatwright, J. and M. Cocco, Frictional constraints on crustal faulting, J. Geophys. Res., 101, 13895–13909, 1996.

    Article  Google Scholar 

  • Bouchon, M., The state of stress on some faluts of the San Andreas system as inferred from near-field strong motion data, J. Geophys. Res., 102, 11731–11744, 1997.

    Article  Google Scholar 

  • Byerlee, J., Model for episodic flow of high-pressure water in fault zones before earthquakes, Geology, 21, 303–306, 1993.

    Article  Google Scholar 

  • Cloos, M., Thrust-type subduction-zone earthquakes and seamount asperities: a physical model for seismic rupture, Geology, 20, 601–604, 1992.

    Article  Google Scholar 

  • Cockerham, R. S. and J. P. Eaton, The April 24, 1984 Morgan Hill earthquake and its aftershocks: April 24 through September 30, 1984, in The 1984 Morgan Hill, California Earthquake, CDMG Special Publication, 68, 1984.

  • Das, S. and K. Aki, Fault plane with barriers: A versatile earthquake model, J. Geophys. Res., 82, 5658–5670, 1977.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Dieterich, J. H. and B. D. Kilgore, Imaging surface contacts: power law contact distributions and contact stresses in quartz, calcite, glass and acrylic plastic, Tectonophysics, 256, 219–239, 1996.

    Article  Google Scholar 

  • Ellsworth, W. L. and L. D. Dietz, Repeating earthquakes: Characteristics and implications, U.S. Geol. Surv. Open File Rep., 90-98, 226–245, 1990.

    Google Scholar 

  • Fleitout, L., The sources of lithospheric tectonic stresses, Phil. Trans. R. soc. Lond. A, 337, 73–81, 1991.

    Article  Google Scholar 

  • Fujie, T., J. Kasahara, R. Hino, T. Sato, M. Shinohara, and K. Suyehiro, A significant relation between seismic activities and reflection intensities in the Japan Trench region, Geophys. Res. Lett., 29(7), doi:10.1029/20001GL013764, 2002.

  • Fukao, Y. and M. Furumoto, Hierarchy in earthquake size distribution, Phys. Earth Planet. Inter., 37, 149–168, 1985.

    Article  Google Scholar 

  • Geller, R. J. and C. S. Mueller, Four similar earthquakes in central California, Geophys. Res. Lett., 7, 821–824, 1980.

    Article  Google Scholar 

  • Gutenberg, B. and C. F. Richter, Frequency of earthquakes in California, Bull. Seism. Soc. Am., 34, 185–188, 1944.

    Google Scholar 

  • Hamaguchi, H. and A. Hasegawa, Recurrent occurrence of the earthquakes with similar wave forms and its related problems, Jisin, 28, 153–169, 1975 (in Japanese).

    Google Scholar 

  • Hartzell, S. H. and T. H. Heaton, Rupture history of the 1984 Morgan Hill, California, earthquake from the inversion of strong motion records, Bull. Seism. Soc. Am., 76, 649–674, 1986.

    Google Scholar 

  • Hartzell, S. H. 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. Seism. Soc. Am., 73, 1553–1583, 1983.

    Google Scholar 

  • Hellweg, M. and J. Boatwright, Mapping the rupture process of moderate earthquakes by inverting accelerograms, J. Geophys. Res., 104, 7319–7328, 1999.

    Article  Google Scholar 

  • Hickman, S., R. Sibson, and R. Bruhn, Introduction to special section: mechanical involvement of fluids in faulting, J. Geophys. Res., 100, 12831–12840, 1995.

    Article  Google Scholar 

  • Hubbert, M. K. and W. W. Rubey, Role of fluid pressure in mechanics of overthrust faulting 1. Mechanics of fluid-filled porous solids and its application to overthrust faulting, Bull. Geol. Soc. Am., 70, 115–166, 1959.

    Article  Google Scholar 

  • Hurukawa, N. and M. Imoto, Subducting oceanic crusts of the Philippine Sea and Pacific plates and weak-zone-normal compression in the Kanto district, Japan, Geophys. J. Int., 109, 639–652, 1992.

    Article  Google Scholar 

  • Hyndman, R. D., M. Yamano, and D. A. Oleskevich, The seismogenic zone of subduction thrust faults, The Island Arc, 6, 244–260, 1997.

    Article  Google Scholar 

  • Ide, S. and G. C. Beroza, Does apparent stress vary with earthquake size?, Geophys. Res. Lett., 28, 3349–3352, 2001.

    Article  Google Scholar 

  • Igarashi, T., T. Matsuzawa, and A. Hasegawa, Repeating earthquakes and interplate aseismic slip in the northeastern Japan subduction zone, J. Geophys. Res., 108(B5), doi:10.1029/2002JB001920, 2003.

  • Irwin, W. P. and I. Barnes, Effect of geologic structure and metamorphic fluids on seismic behavior of the San Andreas fault system in central and northern California, Geology, 3, 713–716, 1975.

    Article  Google Scholar 

  • Ito, A., R. Hino, M. Nishino, H. Fujimoto, S. Miura, S. Kodaira, and A. Hasemi, Deep crustal structure of the northeastern Japan fore arc by a seismic exploration, Jisin, 54, 507–520, 2002 (in Japanese).

    Google Scholar 

  • Izutani, Y. and H. Kanamori, Scale-dependence of seismic energy-to-moment ratio for strike-slip earthquakes in Japan, Geophys. Res. Lett., 28, 4007–4010, 2001.

    Article  Google Scholar 

  • Johnson, P. A. and T. V. McEvilly, Parkfield seismicity: Fluid-driven?, J. Geophys. Res., 100, 12937–12950, 1995.

    Article  Google Scholar 

  • Johnson, L. R. and R. M. Nadeau, Asperity model of an earthquake: Static problem, Bull. Seism. Soc. Am., 92, 672–686, 2002.

    Article  Google Scholar 

  • Kagan, Y. Y., Comments on “The Gutenberg-Richter or characteristic earthquake distribution, which is it?” by Steven G. Wesnousky, Bull. Seism. Soc. Am., 86, 274–285, 1996.

    Google Scholar 

  • Kanamori, H., Rupture process of subduction-zone earthquakes, Ann. Rev. Earth. Planet. Sci., 14, 293–322, 1986.

    Article  Google Scholar 

  • Kanamori, H. and D. L. Anderson, Theoretical basis of some empirical relations in seismology, Bull. Seism. Soc. Am., 65, 1073–1095, 1975.

    Google Scholar 

  • Kanamori, H. and T. H. Heaton, Microscopic and macroscopic physics of earthquakes, in Geocomplexity and the Physics of Earthquakes, Geophys. Monogr., AGU, 120, 147–163, 2000.

    Article  Google Scholar 

  • Kato, N. and T. Hirasawa, A model for possible crustal deformation prior to a coming large interplate earthquake in the Tokai district, central Japan, Bull. Seism. Soc. Am., 89, 1401–1417, 1999.

    Google Scholar 

  • Kawakatsu, H. and T. Seno, Triple seismic zone and the regional variation of seismicity along the northern Honshu arc, J. Geophys. Res., 88, 4215–4230, 1983.

    Article  Google Scholar 

  • Kikuchi, M., A hierarchy model of earthquake sources, Mem. Proc. Intern. Symp. on Earthquake Disaster Prevention, CENAPRED, JICA, IDNDR, 1, 170–177, 2000.

    Google Scholar 

  • Kikuchi, M., M. Nakamura, and K. Yoshikawa, Source rupture processes of the 1944 Tonankai earthquake and the 1945 Mikawa earthquake derived from low-gain seismograms, Earth Planets Space, 55, 159–172, 2003.

    Article  Google Scholar 

  • Kodaira, S., E. Kurashimo, N. Takahashi, A. Nakanishi, S. Miura, J.-O. Park, T. Iwasaki, N. Hirata, K. Ito, and Y. Kaneda, Structural factors in controlling a rupture process of a magathrust earthquake at the Nankai trough seismogenic zone: results from an onshore-offshore seismic study, Geophys. J. Inter., 149, 815–835, 2002.

    Article  Google Scholar 

  • Kostoglodov, V. and L. Ponce, Relationship between subduction and seismicity in the Mexican part of the Middle America trench, J. Geophys. Res., 99, 729–742, 1994.

    Article  Google Scholar 

  • Lachenbruch, A. H. and J. H. Sass, Heat flow from Cajon Pass, fault strength, and tectonic implications, J. Geophys. Res., 97, 4995–5015, 1992.

    Article  Google Scholar 

  • Lay, T. and H. Kanamori, An asperity model of large earthquake sequences, in Earthquake Prediction, an International Review, edited by D. Simpson and P. Richard, Maurice Ewing Series, 4, AGU, Washington, D.C., pp. 579–592, 1981.

    Google Scholar 

  • Lay, T., H. Kanamori, and L. Ruff, The asperity model and the nature of large subduction zone earthquakes, Earthquake Pred. Res., 1, 3–71, 1982.

    Google Scholar 

  • Liu, H.-L. and D. V. Helmberger, The near-source ground motion of the 6 August 1979 Coyote Lake, California, earthquake, Bull. Seism. Soc. Am., 73, 201–218, 1983.

    Google Scholar 

  • Lockner, D. A. and J. D. Byerlee, An earthquake instability model based on faults containing high fluid-pressure compartments, PAGEOPH, 145, 717–745, 1995.

    Article  Google Scholar 

  • Magee, M. E. and M. D. Zoback, Evidence for a weak interplate thrust fault along the northern Japan subduction zone and implications for the mechanics of thrust faulting and fluid expulsion, Geology, 21, 809–812, 1993.

    Article  Google Scholar 

  • Mareschal, J.-C., Fractal reconstruction of sea-floor topography, PAGEOPH, 131, 197–210, 1989.

    Article  Google Scholar 

  • Matsuzawa, T., T. Igarashi, and A. Hasegawa, Characteristic small-earthquake sequence off Sanriku, northeastern Honshu, Japan, Geophys. Res. Lett., 29(11), doi: 10.1029/200GL014632, 2002.

  • Mendoza, C. and S. H. Hartzell, Inversion for slip distribution using teleseismic P waveforms: North Palm Springs, Borah Peak, and Michoacan earthquake, Bull. Seism. Soc. Am., 78, 1092–1111, 1988a.

    Google Scholar 

  • Mendoza, C. and S. H. Hartzell, Aftershock patterns and main shock faulting, Bull. Seism. Soc. Am., 78, 1438–1449, 1988b.

    Google Scholar 

  • Mount, V. S. and J. Suppe, State of stress near the San Andreas fault: Implications for wrench tectonics, Geology, 15, 1143–1146, 1987.

    Article  Google Scholar 

  • Nadeau, R. M. and L. R. Johnson, Seismological studies at Parkfield VI: Moment release rates and estimates of source parameters for small repeating earthquakes, Bull. Seism. Soc. Am., 88, 790–814, 1998.

    Google Scholar 

  • Nadeau, R. M., W. Foxall, and T. V. McEvilly, Clustering and periodic recurrence of microearthquakes on the San Andreas fault at Parkfield, California, Science, 267, 503–507, 1995.

    Article  Google Scholar 

  • Nagai, R., M. Kikuchi, and Y. Yamanaka, Comparative study on the source processes of recurrent large earthquakes in Sanriku-oki Region: the 1968 Tokachi-oki earthquake and the 1994 Sanriku-oki earthquake, Jisin, 54, 267–280, 2001 (in Japanese).

    Google Scholar 

  • Okada, H., H. Watanabe, H. Yamashita, and I. Yokoyama, Seismological significance of the 1977–1978 eruptions and the magma intrusion process of Usu volcano, Hokkaido, J. Volcanol. Geotherm. Res., 9, 311–334, 1981.

    Article  Google Scholar 

  • Okada, T., T. Yamashita, A. Hasegawa, J. Koike, and S. Takahama, Source process of M5.8 earthquake off Fukushima in 2001, Abstr. Seismol. Soc. Jpn, C68, 2001 (in Japanese).

  • Oleskevich, D. A., R. D. Hyndman, and K. Wang, The updip and downdip limits to great subduction earthquakes: thermal and strucural models of Cascadia, south Alaska, SW Japan, and Chile, J. Geophys. Res., 104, 14965–14991, 1999.

    Article  Google Scholar 

  • Pacheco, J. F., L. R. Sykes, and C. H. Scholz, Nature of seismic coupling along simple plate boundaries of the subduction type, J. Geophys. Res., 98, 14133–14159, 1993.

    Article  Google Scholar 

  • Park, J.-O., T. Tsuru, N. Takahashi, T. Hori, S. Kodaira, A. Nakanishi, S. Miura, and Y. Kaneda, A deep strong reflector in the Nankai accretionary wedge from multichannel seismic data: Implications for under-plating and interseismic shear stress release, J. Geophys. Res., 107(B4), doi:10/1029/2001JB000262, 2002.

  • Parsons, B. and F. M. Richter, A relation between the driving force and geoid anomaly associated with mid-oceanic ridges, Earth Planet. Sci. Lett., 51, 445–450, 1980.

    Article  Google Scholar 

  • Peterson, E. T. and T. Seno, Factors affecting seismic moment release rates in subduction zones, J. Geophys. Res., 89, 10233–10248, 1984.

    Article  Google Scholar 

  • Rice, J. R., Fault stress states, pore pressure distributions, and the weakness of the San Andreas fault, in Fault Mechanics and Transport Propoerties of Rocks, edited by B. Evans and T. F. Wong, Academic Press, London, 476–503, 1992.

    Google Scholar 

  • Ruff, L. J., Do trench sediments affect great earthquake occurrence in subduction zones?, PAGEOPH, 129, 263–282, 1989.

    Article  Google Scholar 

  • Ruff, L. and H. Kanamori, Seismicity and the subduction process, Phys. Earth Planet. Inter., 23, 240–252, 1980.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Sacks, I. S. and P. A. Rydelek, Earthquake “Quanta” as an explanation for observed magnitudes and stress drops, Bull. Seism. Soc. Am., 85, 808–813, 1995.

    Google Scholar 

  • Sammis, C. G. and J. R. Rice, Repeating earthquakes as low-stress-drop events at a border between locked and creeping fault patches, Bull. Seism. Soc. Am., 91, 532–537, 2001.

    Article  Google Scholar 

  • Sammis, C. G., R. M. Nadeau, and L. R. Johnson, How strong is an asperity?, J. Geophys. Res., 104, 10609–10619, 1999.

    Article  Google Scholar 

  • Savage, J. C., J. D. Byerlee, and D. A. Lockner, Is internal friction friction?, Geophys. Res. Lett., 23, 487–490, 1996.

    Article  Google Scholar 

  • Scholz, C. H., The Mechanics of Earthquakes and Faulting, Cambridge Univ. Press, 439 pp., 1990.

  • Scholz, C. H. and J. Campos, On the mechanism of seismic decoupling and back arc spreading at subduction zones, J. Geophys. Res., 100, 22103–22115, 1995.

    Article  Google Scholar 

  • Scholz, C. H., M. Wyss, and S. W. Smith, Seismic and aseismic slip on the San Andreas fault, J. Geophys. Res., 74, 2049–2069, 1969.

    Article  Google Scholar 

  • Schwaltz, D. P. and K. J. Coppersmith, Fault behavior and characteristic earthquakes: Examples from the Wasatch and San Andreas fault zones, J. Geophys. Res., 89, 5681–5698, 1984.

    Article  Google Scholar 

  • Segall, P. and J. R. Rice, Dilatancy, compaction, and slip instability of a fluid-infiltrated fault, J. Geophys. Res., 100, 22155–22171, 1995.

    Article  Google Scholar 

  • Seno, T., Tsunami earthquakes as transient phenomena, Geophys. Res. Lett., 29(10), doi: 10.1029/2002GL014868, 2002.

  • Seno, T. and T. Eguchi, Seismotectonics of the western Pacific region, in Tectonics of the Western Pacific-Indonesian Region, edited by S. Uyeda and T. W. C. Hilde, Geodynamics Series, GSA/AGU, Washington D.C., 11, 5–40, 1983.

    Chapter  Google Scholar 

  • Seno, T., T. Sakurai, and S. Stein, Can the Okhotsk plate be discriminated from the North American plate?, J. Geophys. Res., 101, 11305–11315, 1996.

    Article  Google Scholar 

  • Shimamoto, T., T. Seno, and S. Uyeda, Rheological framework for comparative subductology, in Relating Geophysical Structures and Processes: The Jeffreys Volume, Geophys. Monogr., edited by K. Aki and R. Dmowska, IUGG/AGU, 76, 39–52, 1993.

  • Shipley, T. H., G. F. Moore, N. L. Bang, J. C. Moore, and P. L. Stoffa, Seismically inferred dilatancy distribution, northern Barbados Ridge decollement: Implications of fluid migration and fault strength, Geology, 22, 411–414, 1994.

    Article  Google Scholar 

  • Sibson, R. H., Fluid flow accompanying faulting: Field evidence and models, in Earthquake Prediction, Maurice Ewing Series, AGU, 4, 593–603, 1981.

    Google Scholar 

  • Sibson, R. H., Implications of fault-value behaviour for rupture nucleation and recurrence, Tectonophysics, 211, 283–893, 1992.

    Article  Google Scholar 

  • Sleep, N. H., Ductile creep, compaction, and rate and state dependent friction within major fault zones, J. Geophys. Res., 100, 13065–13080, 1995.

    Article  Google Scholar 

  • Sleep, N. H. and M. L. Blanpied, Creep, compaction and the weak rheology of major faults, Nature, 359, 687–692, 1992.

    Article  Google Scholar 

  • Tobin, H. J., J. C. Moore, and G. F. Moore, Fluid pressure in the frontal thrust of the Oregon accretionary prism: Experimental constraints, Geology, 22, 979–982, 1994.

    Article  Google Scholar 

  • Tse, S. T. and J. R. Rice, Crustal earthquake instability in relation to the depth variation of frictional slip properties, J. Geophys. Res., 91, 9452–9472, 1986.

    Article  Google Scholar 

  • Turcotte, D. L., Fractals in geology and geophysics, PAGEOPH, 131, 171–196, 1989.

    Article  Google Scholar 

  • Utsu, T., Space-time pattern of large earthquakes occurring off the Pacific coast of the Japanese islands, J. Phys. Earth, 22, 325–342, 1974.

    Article  Google Scholar 

  • Uyeda, S. and H. Kanamori, Back-arc opening and the mode of subduction, J. Geophys. Res., 84, 1049–1061, 1979.

    Article  Google Scholar 

  • Wald, D. J., D. V. Helmberger, and S. H. Hartzell, Rupture process of the 1987 Superstition Hills earthquake from the inversion of strong-motion data, Bull. Seism. Soc. Am., 80, 1079–1098, 1990.

    Google Scholar 

  • Wald, D. J. and P. G. Somerville, Variable-slip rupture model of the great 1923 Kanto, Japan, earthquake: Geodetic and body-waveform analysis, Bull. Seism. Soc. Am., 85, 159–177, 1995.

    Google Scholar 

  • Wallace, R. E., Earthquake recurrence intervals on the San Andreas fault, Geol. Soc. Am. Bull., 81, 2875–2890, 1970.

    Article  Google Scholar 

  • Wesnousky, S. G., The Gutenberg-Richter or characteristic earthquake distribution, which is it?, Bull. Seism. Soc. Am., 84, 1940–1959, 1994.

    Google Scholar 

  • Wiens, D. A. and S. Stein, Implications of oceanic intraplate seismicity for plate stresses, driving forces and rheology, Tectonophysics, 116, 143–162, 1985.

    Article  Google Scholar 

  • Yagi, Y. and M. Kikuchi, Source process of the Chi-Chi, Taiwan earthquake of Sept. 21, 1999, 2002 (in preparation).

  • Yamanaka, Y. and M. Kikuchi, Asperity map along the subduction zone in northeastern Japan inferred from regional seismic data, J. Geophys. Res., 2003 (submitted).

  • Yamanaka, Y., M. Kikuchi, and K. Yoshikawa, Source processes of the 1946 Nankai earthquake (M 8.0) and the 1964 Niigata earthquake (M 7.5) inferred from JMA strong motion records, Abstr. Seism. Soc. Jpn, C68, 2001 (in Japanese).

  • Zoback, M. D., M. L. Zoback, V. S. Mount, J. Suppe, J. P. Eaton, J. H. Healy, D. Oppenheimer, P. Reasenberg, L. Jones, C. B. Raleigh, I. G. Wong, O. Scotti, and C. Wentworth, New evidence on the state of stress of the San Andreas fault system, Science, 238, 1105–1111, 1987.

    Article  Google Scholar 

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    Tetsuzo Seno

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Seno, T. Fractal asperities, invasion of barriers, and interplate earthquakes. Earth Planet Sp 55, 649–665 (2003). https://doi.org/10.1186/BF03352472

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