Density distribution functions of faults and scaling relations

  • Authors

    • Riccardo Caputo Dept. Physics and Earth Sciences,Univ. Ferrara, Italy
    • Michele Caputo Texas A&M University, College Station, Texas
    2016-07-25
    https://doi.org/10.14419/ijag.v4i2.6330
  • Seismic Parameters, Statistical Analysis, Stress Drop.
  • In the present note, we analyse various seismological datasets collected in different geological and tectonic settings as well as at different time and space scales, like seismic sequences, regional background seismicity, aftershock sequences, microseismic data, and swarms and induced seismicity. We investigate these datasets in terms of statistical distribution of single parameters focusing on stress drop (Δσ), scalar seismic moment (M0) and fault's dimension (often referred to as faults' radius, r0). In particular, we systematically obtain the density distribution functions (ddfs) of each parameter verifying the possible extension of the regression curves. We also analyse the correlations between the investigated parameters by comparing the slopes of the ddf for each dataset. Another goal of this investigation is to verify a possible similarity between comparable and different datasets (i.e. collected in similar or different geological and tectonic settings and range of magnitudes), to verify the stability of the ddf when using different methods as well as the variability of the stress drop even in the same seismological region. We suggest that even more accurate data covering wider ranges of values would be desirable in order to be of practical use like seismotectonic characterization, ground motion prediction and seismic hazard analyses, while the representation of the seismicity for any seismogenic region should be not limited to the b (or b0) value of the Gutenberg-Richter curve.

  • References

    1. [1] Abercrombie R (1995) Earthquake source scaling relationships from -1 to 5 ML using seismograms recorded at 2.5-km depth. J. Geophys. Res. 100, 24,015-24,036, http://dx.doi.org/10.1029/95JB02397.

      [2] Abercrombie RE & Rice JR (2005) Can observations of earthquake scaling constrain slip weakening? Geophys. J. Int. 162, 406-424, http://dx.doi.org/10.1111/j.1365-246X.2005.02579.x.

      [3] Aki K (1972) Scaling law of earthquake source time-function. Geophys. J. R. astr. Soc. 31, 3-25.

      [4] Allen TI, Gibson G, Brown A & Cull JP (2004) Depth variation of seismic source scaling relations: implications for earthquake hazard in southeastern Australia. Tectonophys. 390, 5-24, doi: 10.1019/j.tecto.2004.03.018.

      [5] Allmann BP & Shearer PM (2007) Spatial and temporal stress drop variations in small earthquakes near Parkfield, California. J. Geophys. Res. 112, B04305, http://dx.doi.org/10.1029/2006JB004395.

      [6] Allmann BP & Shearer PM (2009) Global variations of stress drop for moderate to large earthquakes. J. Geophys. Res. 114, B01310, http://dx.doi.org/10.1029/2008JB005821.

      [7] Ameri G, Oth A, Pilz M, Bindi D, Parolai S, Luzi L, Mucciarelli M & Cultrera G (2011) Separation of source and site effects by generalized inversion technique using the aftershock recordings of the 2009 L’Aquila earthquake. Bull Earthquake Eng. 9, 717-739, http://dx.doi.org/10.1007/s10518-011-9248-4.

      [8] Andrews DJ (1986) Objective determination of source parameters and similarity of earthquakes of different size. In Das S, Boatwright J & Scholz CH (Eds.), Earthquake Source Mechanics, 259-267, American Geophysical Union, Washington DC, http://dx.doi.org/10.1029/GM037p0259.

      [9] Asano K & Iwata T (2011) Characterization of stress drops on asperities estimated from the heterogeneous kinematic slip model for strong motion prediction for inland crustal earthquakes in Japan. Pure Appl. Geophys. 168, 105-116, http://dx.doi.org/10.1007/s00024-010-0116-y.

      [10] Baltay AS, Ide S, Prieto G & Beroza GC (2011) Variability in earthquake stress drop and apparent stress. Geophys. Res. Lett. 38, L06303, http://dx.doi.org/10.1029/2011GL046698.

      [11] Baltay AS, Beroza GC & Ide S (2014) Radiated energy of great earthquakes from teleseismic empirical Green's function deconvolution. Pure Appl. Geophys. 171, 2841-2862, http://dx.doi.org/10.1007/s00024-014-0804-0.

      [12] Baltay AS, Hanks TC & Beroza GC (2013) Stable stress-drop measurements and their variability: implications for ground-motion prediction. Bull. Seismol. Soc. Am. 103(1), 211-222, http://dx.doi.org/10.1785/0120120161.

      [13] Bilek SL, Lay T & Ruff LJ (2004) Radiated seismic energy and earthquake source duration variations from teleseismic source time functions for shallow subduction zone thrust earthquakes. J. Geophys. Res. 109, B09308, http://dx.doi.org/10.1029/2004JB003039.

      [14] Boore DM (1983) Stochastic simulation of jhigh-frequency ground motions based on seismological models of the radiated spectra. Bull. Seismol. Soc. Am. 73(6), 1865-1894.

      [15] Bora DK, Baruah S, Biswas R & Gogoi NK (2013) Estimation of source parameters of local Earthquakes originated in Shillong-Mikir Plateau and its adjoining region of Northeastern India. Bull. Seismol. Soc. Am. 103(1), 437-446, http://dx.doi.org/10.1785/0120120095.

      [16] Calderoni G, Rovelli A, Cultrera G, Azzara RM & Di Giulio G (2005) Assessment of ground motion in Palermo, Italy, during the 6 September 2002 Mw 5.9 earthquake using source scaling law. Bull. Seismol. Soc. Am. 95(6), 2342-2363, http://dx.doi.org/10.1785/0120050063.

      [17] Calderoni G Rovelli A & Singh SK (2013) Stress drop and source scaling of the 2009 April L’Aquila earthquakes. Geophys. J. Int. 192, 260-274, http://dx.doi.org/10.1093/gji/ggs011.

      [18] Caputo M (1976) Properties of earthquake statistics. Ann. matematica pura e applicata, Ser. IV, CXI, 186-193. http://dx.doi.org/10.1007/bf02411818.

      [19] Caputo M (1981) Earthquake-induced ground accelerations. Nature 51(5810), 51-53, http://dx.doi.org/10.1038/291051a0.

      [20] Caputo M (1982) On the reddening of the spetra of Earthquake parameters, Earthquake prediction research 1, 173-181,

      [21] Caputo M (1987) the interpretaion of the b and b0 values and its implications on the regional deformation of the crust. Geophys. J. R. astr. Soc. 990, 551- 573.

      [22] Caputo M (1998) the density distribution of the fractured asperities on the surfaces of a fault. Phys. Earth Planet. Int. 109, 9-23. http://dx.doi.org/10.1016/S0031-9201(98)00109-5.

      [23] Caputo M, Gasperini P, Keilis-Borok V, Marcelli L & Rotwain I (1977) Earthquake's swarms as forerunners of strong earthquakes in Italy, Ann. Geophys. 30(3-4), 269-283.

      [24] Cocco M & Rovelli A (1989) Evidence for the variation of stress drop between normal and thrust faulting earthquakes. J. Geophys. Res. 94, 9399-9416. http://dx.doi.org/10.1029/JB094iB07p09399.

      [25] Cotton F, Archuleta R & Causse M (2013) what is sigma of the stress drop? Seismol. Res. Letts. 84(1), http://dx.doi.org/10.1785/0220120087.

      [26] Escudero CR & Doser DI (2012) Relative source-time function studies and stress drop of earthquakes in Southeastern Alaska-Northwestern Canada. Bull. Seismol. Soc. Am. G102G (4), 1820-1828, http://dx.doi.org/10.1785/0120110252.

      [27] Eshelby JD (1957) the determination of the elastic field of an ellipsoidal inclusion and related problems. Proc. R. Soc London, a 241, 376-396. http://dx.doi.org/10.1098/rspa.1957.0133.

      [28] Gabrielov A, Keilis-Borok V, Sinai Ya & Zaliapin I (2008) Statistical Properties of the Cluster Dynamics of the Systems of Statistical Mechanics. In Boltzmann's Legacy, ESI Lectures in Mathematics and Physics, EMS Publishing House, 203-216. http://dx.doi.org/10.4171/057-1/13.

      [29] Garcìa-Garcìa JM, Vidal F, Romacho MD, Martìn-Marfil JM, Posadas a & Luzòn F (1996) Seismic source parameters for microearthquakes of the Granada basin (southern Spain). Tectonophys. 261, 51-66. http://dx.doi.org/10.1016/0040-1951(96)00056-x.

      [30] Giampiccolo E, D’Amico S, Patanè D & Gresta S (2007) Attenuation and Source Parameters of Shallow Microearthquakes at Mt. Etna Volcano, Italy. Bull. Seismol. Soc. Am. 97(1B), pp. 184-197, http://dx.doi.org/10.1785/0120050252.

      [31] Giampiccolo E, Musumeci C, Falà F & Gresta S (2008) Seismological investigations in the Gioa Tauro Basin (southern Calabria, Italy). Ann. Geophys. 51(5/6), 184-197.

      [32] Gibowicz SJ, Young RP, Talebi S & Rawlence DJ (1991) Source parameters of seismic events at the underground research laboratory in Manitoba, Canada: scaling relations for events with moment magnitude smaller than -2. Bull. Seismol. Soc. Am. 81(4), 1157-1182.

      [33] Hanks TC (1977) Earthquake stress drops, ambient tectonic stresses and stresses that drive plate motions. Pure Appl. Geophys. 115, 441-458. http://dx.doi.org/10.1007/BF01637120.

      [34] Hanks TC & Wyss M (1972) the use of body-wave spectra in the determination of seismic-source parameters. Bull. Seismol. Soc. Am. 62(2) 561-589.

      [35] Hardebeck JL & Hauksson E (1997) Static stress drop in the 1994 Northridge, California, aftershock sequence. Bull. Seismol. Soc. Am. 87(6), 1495-1501.

      [36] Hauksson E. (2015) Average stress drops of Southern California earthquakes in the context of crustal geophysics: implications for fault zone healing. Pure Appl. Geophys. 172, 1359-1370, http://dx.doi.org/10.1007/s00024-014-0934-4.

      [37] Hauksson E, Stock J, Bilham R, Boese M, Chen X, Fielding EJ, Galetzka J, Hudnut KW, Hutton K, Jones LM, Kanamori H, Shearer PM, Steidl J, Treiman J, Wei S & Yang W (2013) Report on the August 2012 Brawley earthquake swarm in Imperial Valley, Southern California. Seismol. Res. Letts. 84(2), 177-189, http://dx.doi.org/10.1785/0220120169.

      [38] Hough SE & Dreger DS (1995) Source parameters of the 23 April 1992 M 6.1 Joshua Tree, California, earthquake and its aftershocks: empirical Green's function analysis of GEOS and TERRAscope data. Bull. Seismol. Soc. Am. 85(6), 1576-1590.

      [39] Ide S & Beroza GC. (2001) Does apparent stress vary with earthquake size? Geophys. Res. Lett. 28(17), 3349-3352. http://dx.doi.org/10.1029/2001GL013106.

      [40] Ide S, Beroza GC, Prejean SG & Ellsworth WL (2003) apparent break in earthquake scaling due to path and site effects on deep borehole recordings. J. Geophys. Res. 108(B5), 2271, http://dx.doi.org/10.1029/2001JB001617.

      [41] Jin A, Moya CA & Ando M (2000) Simultaneous determination of site responses and source parameters of small earthquakes along the Atotsugawa Fault Zone, Central Japan. Bull. Seismol. Soc. Am. 90(6), 1430-1445. http://dx.doi.org/10.1785/0119990140.

      [42] Jost ML, Büsselberg T, Jost Ö & Harjes H-P (1998) Source parameters of injection-induced microearthquakes at 9 km depth at the KTB deep drilling site, Germany. Bull. Seismol. Soc. Am. 88(3), 815-832.

      [43] Kagan YT (1991) 3-D rotation of double-couple earthquake sources, Geophys. J. Int. 106, 709-716. http://dx.doi.org/10.1111/j.1365-246X.1991.tb06343.x.

      [44] Kanamori H & Anderson DL (1975) Theoretical basis of some empirical relations in seismology. Bull. Seismol. Soc. Am. 65(5), 1073-1095.

      [45] Kanamori H & Rivera L (2004) Static and dynamic scaling relations for earthquakes and their implications for rupture speed and stress drop. Bull. Seismol. Soc. Am. 94(1), 314-319. http://dx.doi.org/10.1785/0120030159.

      [46] Kato N (2009) A possible explanation for difference in stress drop between intraplate and interplate earthquakes. Geophys. Res. Lett. 36, L23311, http://dx.doi.org/10.1029/2009GL040985.

      [47] Knopoff L (1958) Energy release in earthquakes. Geophys. J. R. astr. Soc. 1(1), 44-52, doi: 10.1111/j.1365-246X.1958.Cb00033.x.

      [48] Kumar N, Yadav DK, Mondal SK & Roy PNS (2013) Stress drop and its relations to tectonic and structural elements for the meizoseismal region of great 1905 Kangra earthquake of the NW Himalaya. Nat. Hazards 69, 2021-2038, doi: 10.1007/s11069-013-0793-9.

      [49] Kwiatek G, Plenkers K, Dresen G & JAGUARS Research Group (2011) Source parameters of picoseismicity recorded at Mponeng deep gold mine, South Africa: implications for scaling relations. Bull. Seismol. Soc. Am. 101(6), 2592-2608, http://dx.doi.org/10.1785/0120110094.

      [50] Lindley GT (1994) Source parameters of the 23 April 1992 Joshua tree, California, earthquake, ita largest foreshock, and aftershocks. Bull. Seismol. Soc. Am. 84, 1051-1057.

      [51] Malagnini L, Mayeda K, Nielsen S, Yoo S-H, Munafò I, Rawles C & Boschi E (2014a) Scaling transition in earthquake sources: a possible link between seismic and laboratory measurements. Pure Appl. Geophys. 171, 2685-2707, http://dx.doi.org/10.1007/s00024-013-0749-8.

      [52] Malagnini L, Munafò I, Cocco M, Nielsen S, Mayeda K & Boschi E (2014b) Gradual fault weakening with seismic slip: inferences from the seismic sequences of L'Aquila, 2009, and Northridge, 1994. Pure Appl. Geophys. 171, 2709-2730, http://dx.doi.org/10.1007/s00024-013-0752-0.

      [53] Mayeda K. & Walter W.R. (1996) Moment, energy, stress drop, and source spectra of western United States earthquakes from regional coda envelopes. J. Geophys. Res. 101(B5), 11,195-11,208. http://dx.doi.org/10.1029/96JB00112.

      [54] Mayeda K, Gök R, Walter WR & Hofstetter A (2005) Evidence for non-constant energy/moment scaling from coda-derived source spectra. Geophys. Res. Lett. 32, L10306, http://dx.doi.org/10.1029/2005GL022405.

      [55] McGarr A (1984) Scaling of ground motion parameters, state of stress, and focal depth. J. Geophys. Res. 89, B8, 6969-6979, http://dx.doi.org/10.1029/jb089ib08p06969.

      [56] McGarr A (1999) on relating apparent stress to the stress causing earthquake fault slip. J. Geophys. Res. 104(B2), 3003-3011. http://dx.doi.org/10.1029/1998JB900083.

      [57] Mori J, Abercrombie RE & Kanamori H (2003) Stress drop and radiated energies of aftershocks of the 1994 Northridge, California, earthquake. J. Geophys. Res. 1089(B11), 2545, http://dx.doi.org/10.1029/2001JB000474.

      [58] Oth A (2013) on the characteristics of earthquake stress release variations in Japan. Earth Planet. Sc. Letts. 377-378, 132-141, http://dx.doi.org/10.1016/j.epsl.2013.06.037.

      [59] Oth A & Kaiser AE (2014) Stress release and source scaling of the 2010-2011 Canterbury, New Zealand earthquake sequence from spectral inversion of ground motion data. Pure Appl. Geophys. 171, 2767-2782, http://dx.doi.org/10.1007/s00024-013-0751-1.

      [60] Patanè D, Ferrucci F, Giampiccolo E & Scaramuzzino L (1997) Source scaling of microearthquakes at Mt. Etna volcano and in the Calabrian Arc (southern Italy). Geophys. Res. Lett. 24(15), 1879-1882. http://dx.doi.org/10.1029/97GL01745.

      [61] Perez-Campos X & Beroza GC (2001) an apparent mechanism dependence of radiate seismic energy. J. Geophys. Res. 106 (B6), 11,127-11,136. http://dx.doi.org/10.1029/2000JB900455.

      [62] Prejean SG & Ellsworth WL (2001) Observations of earthquake source parameters at 2 km depth in the Long Valley Caldera, Eastern California. Bull. Seismol. Soc. Am. 91(2), 165-177. http://dx.doi.org/10.1785/0120000079.

      [63] Rovelli A & Calderoni G (2014) Stress drop of the 1997-1998 Colfiorito, Central Italy earthquake: hints for a common behaviour of normal faults in the Apennines. Pure Appl. Geophys. 171, 2731-2746, http://dx.doi.org/10.1007/s00024-014-0856-1.

      [64] Ruff LJ (1999) Dynamic stress drop of recent earthquakes: variations within subduction zones. Pure Appl. Geophys. 154, 309-431. http://dx.doi.org/10.1007/978-3-0348-8679-6_2.

      [65] Senatorskt P (2012) Effect of seismic moment-area scaling on apparent stress-seismic moment relationship. Pyhs. Earth Planet. Int. 196-197, 14-22, http://dx.doi.org/10.1016/j.pepi.2012.02.001.

      [66] Shearer PM, Prieto GA & Hauksson E (2006) Comprehensive analysis of earthquake source spectra in southern California. J. Geophys. Res. 111, B06303, http://dx.doi.org/10.1029/2005JB003979.

      [67] Somei K, Asano K, Iwata T & Miyakoshi K (2014) Source scaling of inland crustal earthquake sequences in Japan using the S-wave coda spectral ratio method. Pure Appl. Geophys. 171, 2747-2766, http://dx.doi.org/10.1007/s00024-014-0774-2.

      [68] Stork AL & Ito H (2004) Source parameter scaling for small earthquakes observed at the Western Nagano 800-m-deep borehole, Central Japan. Bull. Seismol. Soc. Am. 94(5), 1781-1794. http://dx.doi.org/10.1785/012002214.

      [69] Tomic J, Abercrombie RE & do Nascimento AF (2009) Source parameters and rupture velocity of small M ≤2:1 reservoir induced earthquakes. Geophys. J. Int. 179, 1013-1023, http://dx.doi.org/10.1111/j.1365-246X.2009.04233.x.

      [70] Tusa G, Brancato A & Gresta S (2006a) Source parameters of microearthquakes in Southeastern Sicily, Italy. Bull. Seismol. Soc. Am. 96(3), 968-983, http://dx.doi.org/10.1785/0120050071.

      [71] Tusa G, Brancato A, Gresta S & Malone SD (2006b) Source parameters of microearthquakes at Mount St. Helens (USA). Geophys. J. Int., 166, 1193-1223 http://dx.doi.org/10.1111/j.1365-246X.2006.03025.x.

      [72] Wang L, Zöller G & Hainzl S (2015) Joiont determination of slip and stress drop in a Bayesian inversion approach: a case study for the 2010 M8.8 Maule earthquake. Pure Appl. Geophys. 172, 375-388, http://dx.doi.org/10.1007/s00024-014-0868-x.

      [73] Yamada T, Mori JJ, Ide S, Abercrombie RE, Kawakata H, Nakatani M, Iio Y. & Ogasawara H (2007) Stress drops and radiated seismic energies of microearthquakes in a South African gold mine. J. Geophys. Res. 112, B03305, http://dx.doi.org/10.1029/2006JB004553.

      [74] Zaliapin I, Gabrielov A, Keilis-Borok V & Wong H (2008) Clustering analysis of seismicity and aftershock identification. Phys. Rev. Letters 101, 018501, http://dx.doi.org/10.1103/PhysRevLett.101.018501.

  • Downloads

  • How to Cite

    Caputo, R., & Caputo, M. (2016). Density distribution functions of faults and scaling relations. International Journal of Advanced Geosciences, 4(2), 42-53. https://doi.org/10.14419/ijag.v4i2.6330