Abstract
Recent studies in the literature have introduced a new approach to earthquake forecasting based on representing the space-time patterns of localized seismicity by a time-dependent system state vector in a real-valued Hilbert space and deducing information about future space-time fluctuations from the phase angle of the state vector. While the success rate of this Pattern Informatics (PI) method has been encouraging, the method is still in its infancy. Procedural analysis, statistical testing, parameter sensitivity investigation and optimization all still need to be performed. In this paper, we attempt to optimize the PI approach by developing quantitative values for “predictive goodness” and analyzing possible variations in the proposed procedure. In addition, we attempt to quantify the systematic dependence on the quality of the input catalog of historic data and develop methods for combining catalogs from regions of different seismic rates.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aubrey, D.G. and Emery, K.O. (1983), Eigenanalysis of recent United States sea levels, Continental Shelf Res. 2, 21–33.
Bak, P. and Tang, C. (1989), Earthquakes as self-organized critical phenomena, J. Geophys. Res. 94, 15,635–15,637.
Bevington, P.R. and Robinson, D.K. (1992), Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill.
Bowman, D.D., Ouillon, G. Sammis, C.G., Sornette, A., and Sornette, D. (1998), An observational test of the critical earthquake concept. J. Geophys. Res. 103, 24,359–24,372.
Brehm, D.J. and Braile, L.W. (1999), Intermediate-term earthquake prediction using the modified time-to-failure method in Southern California, BSSA 89, 275–293.
Bufe, C.G. and Varnes, D.J. (1993), Predictive modeling of the seismic cycle of the greater San Francisco bay region, J. Geophys. Res. 98, 9871–9883.
Fukunaga, K., Introduction to Statistical Pattern Recognition, (Academic Press, New York (1970)).
Garcia, A. and Penland, C. (1991), Fluctuating hydrodynamics and principal oscillation pattern analysis, J. Stat. Phys. 64, 1121–1132.
Gross, S. and Rundle, J. B. (1998), A systematic test of time-to-failure analysis, Geophys. J. Int. 133, 57–64.
Holmes, P. Lumley, J.L., and Berkooz, G., Turbulence, Coherent Structures, Dynamical Systems and Symmetry, (Cambridge University Press, Cambridge, U.K. 1996).
Hotelling, H. (1993), Analysis of a complex of statistical variables into principal components, J. Educ. Psych. 24, 417–520.
Jaumé, S.C. and Sykes, L.R. (1999), Evolving towards a critical point: A review of accelerating seismic moment/energy release prior to large and great earthquakes, Pure Appl. Geophys. 155, 279–306.
Joliffee, I.T. and Stephenson, D.B., Forecast Verification (John Wiley. (2003)).
Kagan, Y.Y. and Jackson, D.D. (2000), Probabilistic forecasting of earthquakes, Geophys. J. Int. 143, 438–453.
Kanamori, H., The nature of seismicity patterns before large earthquakes. In Earthquake Prediction: An International Review, Geophys. Monogr. Ser., pp. 1–19, AGU (Washington, D. C. (1981)).
Moghaddam, B., Wahid, W., and Pentland, A. (1998) Beyond eigenfaces: Probabilistic matching for face recognition. In Third IEEE Intl. Conf. on Automatic Face and Gesture Recognition, pp. 1–6.
Mori, H. and Kuramoto, Y., Dissipative Structures and Chaos, (Springer-Verlag, Berlin. (1998)).
North, G.R. (1984), Empirical orthogonal functions and normal modes, J. Atm. Sci. 41 (5), 879–887.
Penland, C. (1989), Random forcing and forecasting using principal oscillation pattern analysis, Monthly Weather Rev. 117, 2165–2185.
Penland, C. and Magorian, T. (1993), Prediction of Niño 3 sea-surface temperatures using linear inverse modeling. J. Climate 6, 1067–1076.
Penland, C. and Sardeshmukh, P.D. (1995), The optimal growth of tropical sea surface temperature anomalies, J. Climate 8, 1999–2024.
Preisendorfer, R.W., Principle Component Analysis in Meteorology and Oceanography (Elsevier, Amsterdam. (1988)).
Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P., Numerical Recipes in C (Cambridge University Press, Cambridge, MA. (2002)).
Rundle, J.B. and Klein, W. (1995), New ideas about the physics of earthquakes, Rev. Geophys. Space Phys. Suppl. (July) 283, 283–286.
Rundle, J.B., Klein, W., Gross, S.J., and Tiampo, K.F., Dynamics of seismicity patterns in systems of earthquake faults. In Geocomplexity and the Physics of Earthquakes. Geophys. Monogr. Ser., vol. 120 (eds. by J.B. Rundle, D.L. Turcotte, and W. Klein), pp. 127–146 (AGU, Washington, D. C. 2000a).
Rundle, J.B., Klein, W., Tiampo, K.F., and Gross, S.J. (2000b), Linear pattern dynamics in nonlinear threshold systems, Phys. Rev. E. 61, 2418–2432.
Rundle, J.B., Tiampo, K.F., Klein, W., and Martins, J.S.S. (2002), Self-organization in leaky threshold systems: The influence of near-mean field dynamics and its implications for earthquakes, neurobiology, and forecasting. Proc. Natl. Acad. Sci. U. S. A. 99, 2514–2521: Suppl. 1.
Rundle, J.B., Turcotte, D.L., Shcherbakov, R., Klein, R., and Sammis, C. (2003), Statistical physics approach to understanding the multiscale dynamics of earthquake fault systems. Rev. Geophys. 41(4), 1019, doi:10.1029/2003RG000135.
Savage, J.C. (1988), Principal component analysis of geodetically measured deformation in long valley caldera, eastern California. 1983–1987, J. Geophys. Res. 93, 13,297–13,305.
Schorlemmer, D., Jackson, D.D., and Gerstenberger, M. (2003), Earthquake likelihood model testing. http://moho.ess.ucla.edu/~kagan/sjg.pdf.
Tiampo, K.F., Rundle, J.B., Klein, W., and Gross, S.J. (1999), Systematic evolution of nonlocal space-time earthquake patterns in Southern California. EOS Trans. AGU 80, 1013.
Tiampo, K.F., Rundle, J.B., McGinnis, S., Gross, S.J., and Klein, W., Observation of systematic variations in non-local seismicity patterns from southern California. In Geocomplexity and the Physics of Earthquakes, Geophys. Monogr. Ser. vol. 120 (eds. J.B. Rundle, D.L. Turcotte, and W. Klein), pp. 211–218 (AGU, Washington, D. C. 2000).
Tiampo, K.F., Rundle, J.B., McGinnis, S., Gross, S.J., and Klein, W. (2002a), Eigenpatterns in Southern California seismicity. J. Geophys. Res. 107(B12), 2354, doi:10.1029/2001JB000562.
Tiampo, K.F., Rundle, J.B., McGinnis, S., Gross, S.J., and Klein, W. (2002b), Mean field threshold systems and earthquakes: An application to earthquake fault systems. Europhys. Lett. 60 (3), 481–487.
Tiampo, K.F., Rundle, J.B., McGinnis, S., and Klein, W. (2002c), Pattern dynamics and forecast methods in seismically active regions. Pure Appl. Geophys 159, 2429–2467.
Vautard, R. and Ghil, M. (1989), Singular spectrum analysis in nonlinear dynamics, with applications to paleodynamic time series. Physica D 35, 395–424.
Walpole, R.E. and Myers, R.H., Probability and Statistics for Engineers and Scientists (Prentice Hall. 1993).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Birkhäuser Verlag
About this paper
Cite this paper
Holliday, J., Rundle, J., Tiampo, K., Klein, W., Donnellan, A. (2006). Systematic Procedural and Sensitivity Analysis of the Pattern Informatics Method for Forecasting Large (M > 5) Earthquake Events in Southern California. In: Yin, Xc., Mora, P., Donnellan, A., Matsu’ura, M. (eds) Computational Earthquake Physics: Simulations, Analysis and Infrastructure, Part II. Pageoph Topical Volumes. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8131-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-7643-8131-8_13
Received:
Revised:
Accepted:
Published:
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8130-1
Online ISBN: 978-3-7643-8131-8
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)