A complex network model for seismicity based on mutual information

Seismicity is the product of the interaction between the different parts of the lithosphere. Here, we model each part of the Earth as a cell that is constantly communicating its state to its environment. As a neuron is stimulated and produces an output, the different parts of the lithosphere are constantly stimulated by both other cells and the ductile part of the lithosphere, and produce an output in the form of a stress transfer or an earthquake. This output depends on the properties of each part of the Earth’s crust and the magnitude of the inputs. In this study, we propose an approach to the quantification of this communication, with the aid of the Information Theory, and model seismicity as a Complex Network. We have used data from California, and this new approach gives a better understanding of the processes involved in the formation of seismic patterns in that region.

[1]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[2]  Ilya Zaliapin,et al.  Colliding cascades model for earthquake prediction , 2000 .

[3]  Kristy F. Tiampo,et al.  Small world in a seismic network: the California case , 2008 .

[4]  D. Wells,et al.  New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement , 1994, Bulletin of the Seismological Society of America.

[5]  M. Baiesi,et al.  Scale-free networks of earthquakes and aftershocks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Funabashi,et al.  Small-world structure of earthquake network , 2004 .

[7]  K. Tiampo,et al.  Analysis of complex networks associated to seismic clusters near the Itoiz reservoir dam , 2009 .

[8]  K. Kaski,et al.  Intensity and coherence of motifs in weighted complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Y. Lai,et al.  Characterization of weighted complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Wenxu Wang,et al.  Mutual selection model for weighted networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Antonio M. Posadas,et al.  A probabilistic seismic hazard model based on cellular automata and information theory , 2005 .

[12]  K. Yakubo,et al.  Generalized strength of weighted scale-free networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  K. Tiampo,et al.  An Ising model for earthquake dynamics , 2007 .

[14]  Javier Martín Hernández,et al.  Betweenness centrality in a weighted network. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  K. Tiampo,et al.  Describing Seismic Pattern Dynamics by Means of Ising Cellular Automata , 2008 .

[16]  Funabashi,et al.  Scale-free network of earthquakes , 2002 .

[17]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[18]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[20]  Norikazu Suzuki,et al.  Complex-network description of seismicity , 2006 .

[21]  K. Tiampo,et al.  Testing the persistence in earthquake catalogs: The Iberian Peninsula , 2006 .

[22]  Peter Grassberger,et al.  Networks of recurrent events, a theory of records, and an application to finding causal signatures in seismicity. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Mikko Kivelä,et al.  Generalizations of the clustering coefficient to weighted complex networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Kristy F. Tiampo,et al.  Seismicity-based earthquake forecasting techniques: Ten years of progress , 2012 .

[25]  Maya Paczuski,et al.  Complex networks of earthquakes and aftershocks , 2004, physics/0408018.

[26]  K. Tiampo,et al.  The Stress Accumulation Method and the Pattern Informatics Index: Complementary Approaches to Earthquake Forecasting , 2008 .

[27]  Bruce D. Malamud,et al.  Earthquakes as a Complex System , 2002 .

[28]  D. Garlaschelli.  The weighted random graph model , 2009, 0902.0897.

[29]  B. Bollobás.  The evolution of random graphs , 1984 .

[30]  A. Jiménez.  Comparison of the Hurst and DEA exponents between the catalogue and its clusters: The California case , 2011 .

[31]  J. Dieterich.  A constitutive law for rate of earthquake production and its application to earthquake clustering , 1994 .

[32]  K. Tiampo,et al.  Eigenpatterns in southern California seismicity , 2002 .

[33]  F. Luzón,et al.  Weighted complex networks applied to seismicity: the Itoiz dam (Northern Spain) , 2011 .

[34]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[35]  P. Rapp,et al.  Statistical validation of mutual information calculations: comparison of alternative numerical algorithms. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Charles F. Hockett,et al.  A mathematical theory of communication , 1948, MOCO.

[37]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.