On the geometric complexity of earthquake focal zone and fault systems: A statistical study

Physics of the Earth and Planetary Interiors

Volumn 173, Issue 3-4, 2009, Pages 254-268

  Kagan, Yan Y ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

CLVD; Double couple; Earthquake focal mechanism; Geometric barriers; Quaternion; Statistical analysis

Indexed keywords

FOCUSING;

CLVD; DOUBLE COUPLE; EARTHQUAKE FOCAL MECHANISM; GEOMETRIC BARRIERS; QUATERNION; STATISTICAL ANALYSIS;

EARTHQUAKES;

EARTHQUAKE CATALOGUE; FOCAL MECHANISM; GEOMETRY; MOMENT TENSOR; SEISMIC MOMENT; SEISMIC SOURCE; STATISTICAL ANALYSIS;

EID: 62749113379     PISSN: 00319201     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.pepi.2009.01.006     Document Type: Article

References (80)

1. Aki K., and Richards P. Quantitative Seismology. 2nd ed. (2002), University Science Books, Sausalito, CA 700 pp
2. Alberti M. Spatial structures in earthquakes and faults: quantifying similarity in simulated stress fields and natural data sets. J. Struct. Geol. 28 6 (2006) 998-1018
3. Altmann S.L. Rotations, Quaternions and Double Groups (1986), Clarendon Press, Oxford pp. 317
4. Amelung F., and King G. Large-scale tectonic deformation inferred from small earthquakes. Nature 386 (1997) 702-705
5. Anderson T.L. Fracture Mechanics: Fundamentals and Applications. 3rd ed. (2005), Taylor and Francis, Boca Raton 621 pp
6. Backus G.E. Interpreting the seismic glut moments of total degree two or less. Geophys. J. R. Astr. Soc. 51 (1977) 1-25
7. Backus G.E. Seismic sources with observable glut moments of spatial degree two. Geophys. J. R. Astr. Soc. 51 (1977) 27-45
8. Backus G., and Mulcahy M. Moment tensor and other phenomenological descriptions of seismic sources. I. Continuous displacements. Geophys. J. R. Astr. Soc. 46 (1976) 341-361
9. Backus G., and Mulcahy M. Moment tensor and other phenomenological descriptions of seismic sources. II. Discontinuous displacements. Geophys. J. R. Astr. Soc. 47 (1976) 301-329
10. Bailey, I.W., Becker, T.W., Ben-Zion, Y., 2009. Patterns of co-seismic strain computed from southern California focal mechanisms, Geophys. J. Int., in press.
11. Brudzinski M.R., Thurber C.H., Hacker B.R., and Engdahl E.R. Global prevalence of double Benioff zones. Science 316 5830 (2007) 1472-1474 doi:10.1126/science.1139204
12. Burridge R., and Knopoff L. Body force equivalents for seismic dislocations. Bull. Seismol. Soc. Am. 54 (1964) 1875-1888
13. Chang T., Stock J., and Molnar P. The rotation group in plate tectonics and the representation of uncertainties of plate reconstruction. Geophys. J. Int. 101 (1990) 649-661
14. Chen P., Jordan T.H., and Zhao L. Finite-moment tensor of the 3 September 2002 Yorba Linda earthquake. Bull. Seismol. Soc. Am. 95 3 (2005) 1170-1180
15. w magnitude scale, style of faulting, and automation of the method. Bull. Seismol. Soc. Am. 96 5 (2006) 1689-1705
16. Dreger, D.S., 2003. TDMT_INV: Time Domain Seismic Moment Tensor INVersion. In: Lee, W.H.K., Kanamori, H., Jennings, P.C., Kisslinger, C. (Eds.), International Handbook of Earthquake and Engineering Seismology, vol. B, p. 1627 (Chapter 85.11).
17. Dziewonski A.M., Ekström G., and Maternovskaya N.N. Centroid-moment tensor solutions for October-December, 1998. Phys. Earth Planet. Int. 115 (1999) 1-16
18. Dziewonski A.M., and Woodhouse J.H. An experiment in systematic study of global seismicity: centroid-moment tensor solutions for 201 moderate and large earthquakes of 1981. J. Geophys. Res. 88 (1983) 3247-3271
19. Dziewonski A.M., Chou T.-A., and Woodhouse J.H. Determination of earthquake source parameters from waveform data for studies of global and regional seismicity. J. Geophys. Res. 86 (1981) 2825-2852
20. Ekström G., Dziewonski A.M., Maternovskaya N.N., and Nettles M. Global seismicity of 2003: centroid-moment-tensor solutions for 1087 earthquakes. Phys. Earth Planet. Int. 148 2-4 (2005) 327-351
21. Frohlich C. Note concerning non-double-couple source components from slip along surfaces of revolution. J. Geophys. Res. 95 B5 (1990) 6861-6866
22. Frohlich C. Deep Earthquakes (2006), Cambridge University Press, New York 573 pp
23. Frohlich C., and Davis S.D. How well constrained are well-constrained T, B, and P axes in moment tensor catalogs?. J. Geophys. Res. 104 (1999) 4901-4910
24. Frohlich C., Riedesel M.A., and Apperson K.D. Note concerning possible mechanisms for non-double-couple earthquake sources. Geophys. Res. Lett. 16 6 (1989) 523-526
25. Gabrielov A., Keilis-Borok V., and Jackson D.D. Geometric incompatibility in a fault system. Proc. Natl. Acad. Sci. U.S.A. 93 (1996) 3838-3842
26. Hanson A.J. Visualizing Quaternions (2005), Elsevier, San Francisco, CA pp. 498
27. Hardebeck J.L. Homogeneity of small-scale earthquake faulting, stress, and fault strength. Bull. Seismol. Soc. Am. 96 5 (2006) 1675-1688
28. Huc, M., Main, I.G., 2003. Anomalous stress diffusion in earthquake triggering: Correlation length, time dependence, and directionality. J. Geophys. Res. 108 (B7), ESE-1, pp. 1-12, art. no. 2324.
29. Jaeger J.C., and Cook N.G.W. Fundamentals of Rock Mechanics. 3rd ed. (1979), Chapman and Hall, London 593 pp
30. Julian B.R., Miller A.D., and Foulger G.R. Non-double-couple earthquakes. 1. Theory. Rev. Geophys. 36 4 (1998) 525-549
31. Kagan Y.Y. Stochastic model of earthquake fault geometry. Geophys. J. R. Astr. Soc. 71 (1982) 659-691
32. Kagan Y.Y. Point sources of elastic deformation: elementary sources, static displacements. Geophys. J. R. Astr. Soc. 90 (1987) 1-34 (Errata, Geophys. J. R. Astron. Soc. 93 (1988) 591)
33. Kagan Y.Y. Static sources of elastic deformation in homogeneous half-space. J. Geophys. Res. 93 (1988) 10560-10574
34. Kagan Y.Y. Random stress and earthquake statistics: spatial dependence. Geophys. J. Int. 102 (1990) 573-583
35. Kagan Y.Y. 3D rotation of double-couple earthquake sources. Geophys. J. Int. 106 (1991) 709-716
36. Kagan Y.Y. On the geometry of an earthquake fault system. Phys. Earth Planet. Int. 71 1-2 (1992) 15-35
37. Kagan Y.Y. Correlations of earthquake focal mechanisms. Geophys. J. Int. 110 (1992) 305-320
38. Kagan Y.Y. Temporal correlations of earthquake focal mechanisms. Geophys. J. Int. 143 (2000) 881-897
39. Kagan Y.Y. Modern California earthquake catalogs and their comparison. Seism. Res. Lett. 73 6 (2002) 921-929
40. Kagan Y.Y. Accuracy of modern global earthquake catalogs. Phys. Earth Planet. Int. 135 2-3 (2003) 173-209
41. Kagan Y.Y. Double-couple earthquake focal mechanism: random rotation and display. Geophys. J. Int. 163 3 (2005) 1065-1072
42. Kagan, Y.Y., 2006. Why does theoretical physics fail to explain and predict earthquake occurrence? In: Bhattacharyya, P., Chakrabarti, B.K. (Eds.), Lecture Notes in Physics, vol. 705. Springer Verlag, Berlin/Heidelberg, pp. 303-359. http://scec.ess.ucla.edu/ ykagan/india_index.html.
43. Kagan Y.Y. Earthquake spatial distribution: the correlation dimension. Geophys. J. Int. 168 3 (2007) 1175-1194
44. Kagan Y.Y. Simplified algorithms for calculating double-couple rotation. Geophys. J. Int. 171 1 (2007) 411-418
45. Kagan Y.Y., and Jackson D.D. Long-term probabilistic forecasting of earthquakes. J. Geophys. Res. 99 (1994) 13685-13700
46. Kagan, Y.Y., Knopoff, L., 1984. A stochastic model of earthquake occurrence. In: Proceedings of the 8th International Conference on Earthquake Engineering, vol. 1. Prentice-Hall, Englewood Cliffs, New Jersey, pp. 295-302.
47. Kagan Y.Y., and Knopoff L. The first-order statistical moment of the seismic moment tensor. Geophys. J. R. Astr. Soc. 81 (1985) 429-444
48. Kagan Y.Y., and Knopoff L. The two-point correlation function of the seismic moment tensor. Geophys. J. R. Astr. Soc. 83 (1985) 637-656
49. Kaverina A.N., Lander A.V., and Prozorov A.G. Global creepex distribution and its relation to earthquake-source geometry and tectonic origin. Geophys. J. Int. 125 (1996) 249-265
50. King G. The accommodation of large strains in the upper lithosphere of the Earth and other solids by self-similar fault systems: the geometrical origin of b-value. Pure Appl. Geophys. 121 (1983) 761-815
51. King G.C.P. Speculations on the geometry of the initiation and termination processes of earthquake rupture and its relation to morphology and geological structure. Pure Appl. Geophys. 124 3 (1986) 567-585
52. Klein, F., 1932. Elementary Mathematics from an Advanced Standpoint. Vol. I. Arithmetic, Algebra, Analysis, translated by E.R. Hedrick and C.A. Noble, Macmillan, London, pp. 274.
53. Knopoff L., and Randall M.J. The compensated linear vector dipole: a possible mechanism for deep earthquakes. J. Geophys. Res. 75 (1970) 4957-4963
54. Kubo A., Fukuyama E., Kawai H., and Nonomura K. NIED seismic moment tensor catalogue for regional earthquakes around Japan: quality test and application. Tectonophysics 356 (2002) 23-48
55. Kuffner, J., 2004. Effective sampling and distance metrics for 3D rigid body path planning. In: Proceedings 2004 IEEE International Conference on Robotics and Automation, vol. 4. New Orleans, LA, pp. 3993-3998.
56. Kuipers J.B. Quaternions and Rotation Sequences: a Primer with Applications to Orbits. Aerospace and Virtual Reality (2002), Princeton University Press, Princeton 400 pp
57. Le Pichon X., Francheteau J., and Bonnin J. Plate Tectonics (1973), Elsevier, London pp. 300
58. Marder M., Deegan R.D., and Sharon E. Crumpling, buckling, and cracking: elasticity of thin sheets. Phys. Today 60 2 (2007) 33-38
59. Marsaglia G. Choosing a point from the surface of a sphere. Ann. Math. Stat. 43 (1972) 645-646
60. MathWorks, 2006. Aerospace Toolbox-Quaternion Math. http://www.mathworks.com/access/helpdesk/help/toolbox/aerotbx/ (see Functions-By Category, then Quaternion Math).
61. MathWorld, 2004. http://mathworld.wolfram.com/Quaternion.html.
62. Matsumoto T., Ito Y., Matsubayashi H., and Sekiguchi S. Spatial distribution of F-net moment tensors for the 2005 West Off Fukuoka Prefecture Earthquake determined by the extended method of the NIED F-net routine. Earth Planet. Space 58 1 (2006) 63-67
63. McGuire J.J., Zhao L., and Jordan T.H. Teleseismic inversion for the second-degree moments of earthquake space-time distributions. Geophys. J. Int. 145 (2001) 661-678
64. Miller A.D., Foulger G.R., and Julian B.R. Non-double-couple earthquakes. 2. Observations. Rev. Geophys. 36 4 (1998) 551-568
65. Moran, P.A.P., 1975. Quaternions, Haar measure and estimation of paleomagnetic rotation. In: Gani, J. (Ed.), Perspectives in Probability and Statistics. Academic Press, pp. 295-301.
66. Pasyanos M.E., Dreger D.S., and Romanowicz B. Toward real-time estimation of regional moment tensors. Bull. Seismol. Soc. Am. 86 (1996) 1255-1269
67. Pondrelli S., Salimbeni S., Ekström G., Morelli A., Gasperini P., and Vannucci G. The Italian CMT dataset from 1977 to the present. Phys. Earth Planet. Int. 159 (2006) 286-303
68. Richardson E., and Jordan T.H. Low-frequency properties of intermediate-focus earthquakes. Bull. Seismol. Soc. Am. 92 6 (2002) 2434-2448
69. Shen Y.-Z., Chen Y., and Zheng D.-H. A quaternion-based geodetic datum transformation algorithm. J. Geodyn. 80 (2006) 233-239 10.1007/s00190-006-0054-8
70. Silver P.G., and Jordan T.H. Total-moment spectra of fourteen large earthquakes. J. Geophys. Res. 88 (1983) 3273-3293
71. Silver P., and Masuda T. Source extent analysis of the Imperial Valley earthquake of October 15, 1979, and the Victoria earthquake of June 9, 1980. J. Geophys. Res. 90 (1985) 7639-7651
72. Smith G.P., and Ekström G. Interpretation of earthquake epicenter and CMT centroid locations, in terms of rupture length and direction. Phys. Earth Planet. Int. 102 (1997) 123-132
73. Snoke, J.A., 2003. FOCMEC: FOcal MEChanism determinations. In: Lee, W.H.K., Kanamori, H., Jennings, P.C., Kisslinger, C. (Eds.), International Handbook of Earthquake and Engineering Seismology. Academic Press, San Diego (Chapter 85.12, pp. 1629-1630). http://www.geol.vt.edu/outreach/vtso/focmec/.
74. Snyder, J.P., 1987. Map Projections-A Working Manual. U.S. Geological Survey Professional Paper, 1395; Washington, 383 pp.
75. Wang Y.C., Abe S., Latham S., and Mora P. Implementation of particle-scale rotation in the 3D Lattice Solid Model. Pure Appl. Geophys. 163 9 (2006) 1769-1785
76. Ward J.P. Quaternions and Cayley Numbers: Algebra and Applications (1997), Kluwer Academic Publications, London pp. 237
77. Weeks J.R. The Shape of Space. 2nd ed. (2002), CRC Press 382 pp
78. Witten T.A. Stress focusing in elastic sheets. Rev. Modern Phys. 79 2 (2007) 643-675
79. Wolfram, S., 1999. The Mathematica Book, 4th ed. Wolfram Media/Cambridge University Press, Champaign, IL/Cambridge, New York, pp. 1470.
80. Yershova, A., LaValle, S.M., 2004. Deterministic sampling methods for spheres and SO(3). In: Proceedings 2004 IEEE International Conference on Robotics and Automation, vol. 4. New Orleans, LA, pp. 3974-3980.