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Hierarchical network approach to modeling natural complexities

Hierarchical network approach to modeling natural complexities. Ilya Zaliapin. Department of Mathematics and Statistics University of Nevada, Reno, USA. Co-authors: Yehuda Ben-Zion (USC), Michael Ghil (UCLA), Efi Foufoula-Georgiou (UM), Andrew Hicks (UNR), Yevgeniy Kovchegov (OSU).

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Hierarchical network approach to modeling natural complexities

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  1. Hierarchical network approach to modeling natural complexities Ilya Zaliapin Department of Mathematics and Statistics University of Nevada, Reno, USA Co-authors: Yehuda Ben-Zion (USC), Michael Ghil (UCLA), Efi Foufoula-Georgiou (UM), Andrew Hicks (UNR), Yevgeniy Kovchegov (OSU) ENHANS Workshop, Hatfield, Pretoria, South Africa 17-20 January, 2011 The research is supported by NSF grants DMS-0620838 and EAR-0934871

  2. Outline Natural disasters in Africa 1 1 Networks & trees: A unified approach to modeling natural complexities 2 2 Seismic clustering vs. physical properties of the crust 3 3 Conclusions 4 4

  3. Natural hazards in Africa

  4. Natural hazards in Africa Floods Algeria, 2001, 921 killed Volcanoes Congo, 2002, 200 killed Droughts Malawi, 2002, 500 killed Earthquakes Algeria, 2003, 2266 killed Wildfires Mozambique, 2008, 49 killed Heat waves Nigeria, 2002, 60 killed Cold waves South Africa, 2007, 22 killed Storms Magadascar, 2004, 363 killed Data according to AON Re

  5. Networks & trees

  6. Botanical trees Blood/Lungs systems River basins Valleys on Mars Snowflakes Neurons Hierarchies (trees) are ubiquitous in Nature...

  7. 1. Networks & trees = non-Eucledian metric Noyo basin, Mendocino county, California, US

  8. 1. Networks & trees = non-Eucledian metric • Branching structures (rivers, drainage networks, etc.) • [Horton, 1945; Shreve, 1966; Tokunaga, 1978, Peckham, 1995; Rodrigez-Iturbo & Rinaldo, 1997] • Interaction of climate system components • [Tsonis, 2006, Donges et al., 2009] • Structural organization of Solid Earth • [Turcotte, 1997; Keilis-Borok, 2002] • Spread of epidemics, diseases, rumors • [Newman et al. 2006] • Evolutionary relationships (phylogenetic trees) • [Maher, 2002] • etc. 2. Networks & trees = branching and aggregation (coalescence) • Environmental transport of rivers and hillslopes • [Zaliapin et al., 2010] • Fracture development is solids • [Kagan, 1982; Lawn, 1993; Baiesi, 2005; Davidsen et al., 2008] • Percolation phenomena • [Yakovlev et al., 2005] • Food webs • [Power, 2000] • Systems of interacting particles • [Gabrielov et al., 2008]

  9. 1. Horton laws: primary branching Power law relationship between size Mr and number Nr of objects. A counterpart of statistical “self-similarity”. Notably: a weak constraint on the hierarchy. 2. Tokunaga self-similarity: side-branching Provides a complete description of the hierarchy. Defines the “true”, structural self-similarity. 11 11 11 11 11 11 11 11 12 22 22 22 22 Primary branches 11 12 Side branches 11 33 33 23 11 23 11

  10. Why Horton-Strahler indexing? A: Naturally connects topology and geometry/physics of a hierarchy Noyo basin, Mendocino county, California, US See [Sklar et al., Water Resor. Res, 2006] for basin details

  11. Why Tokunaga self-similarity? A1: Very simple, two-parametric class of trees… A2: Very flexible class of trees, observed in unprecedented variety of modeled and natural systems: • Numerical studies • river stream networks • hillslope topography • earthquake aftershock clustering • vein structure of botanical leaves • diffusion limited aggregation • percolation • nearest-neighbor aggregation in Euclidean spaces • level-set tree of fractional Brownian motion • Theoretical results • critical Galton-Watson branching process [Burd at al., 2000] • Shreve random river network model [Shreve, 1966] • SOC-type general aggregation model [Gabrielov et al., 1999] • regular Brownian motion [Neveu and Pitman, 1989 + Burd at al., 2000] • symmetric Markov chains [Zaliapin and Kovchegov, 2011]

  12. Why Tokunaga self-similarity? Theorem 1 [Burd, Waymire, Winn, 2000] Critical Galton-Watson binary branching process corresponds to a Tokunaga self-similar tree (SST). Theorem 2 [Neveu and Pitman, 1989] The level set tree of a regular Brownian motion correspond to the critical Galton-Watson process. Theorem 3 [Zaliapin and Kovchegov, 2011] The level set tree of a symmetric homogeneous Markov chain is a Tokunaga SST. Conjecture [Webb2009; Zaliapin and Kovchegov, 2011] The level set tree of a fractional Brownian motion is a Tokunaga SST. Conjecture [Zaliapin et al., 2010; Zaliapin and Kovchegov, 2011] Nearest-neighbor aggregation in Euclidean space corresponds to a Tokunaga SST.

  13. Earthquake clustering & productivity Baiesi and Paczuski, PRE, 69, 066106 (2004) Zaliapin et al., PRL, 101, 018501(2008) Zaliapin and Ben-Zion, GJI (2011)

  14. World seismicity, NEIC, 1973-2010, M4

  15. Separation of clustered and homogeneous parts: NEIC, 1973-2010, M4 Homogeneous part (as in Poisson process) Theoretical prediction for a Poisson field [Zaliapin et al. 2008] Clustered part: events are much closer to each other than in the homogeneous part

  16. World seismicity, USGS/NEIC m ≥ 4.0; 223,600 events California, Shearer et al. (2005) m ≥ 2.0; 70,895 events Nevada, Nevada SeismoLab m > 1.0; 75,351 events Parkfield, Thurber et al. (2006) m > 0.0; 8,993 events

  17. Seismicity as a flow of clusters

  18. Identification of clusters: data driven Cluster #3 Cluster #1 Cluster #2 weak link strong link

  19. Identification of event types: problem driven Foreshocks Mainshock Aftershocks Time

  20. Clustering vs. physical properties of the crust

  21. Joint distribution of the number of fore/aftershocks

  22. Plate boundary types and seismic clustering • Thin hot lithosphere • in transform and especially divergent boundaries: • high clustering, • enhanced foreshock production Transform Divergent MOR, rift valleys Convergent subduction, orogenic belts • Thick cold lithosphere • in subduction and collision environments: • high proportion of isolated events, • enhanced aftershock production Illustration by Jose F. Vigil from This Dynamic Planet -- a wall map produced jointly by the U.S. Geological Survey, the Smithsonian Institution, and the U.S. Naval Research Laboratory. http://pubs.usgs.gov/gip/earthq1/plate.html

  23. Orogenic belt, Tethyan Zone Carlsberg ridge World proportion of aftershocks Philippine trench Manila trench Middle America trench Peru-Chile trench

  24. World proportion of aftershocks Red Sea rift + Aden ridge East Pacific rise Carlsberg ridge Mid-Atlantic Ridge

  25. Proportion of aftershocks Extremely hot places, with abnormally high foreshock productivity, similar to mid-oceanic ridges => enhanced possibility for earthquake forecast

  26. Summary Network approach to understanding natural complexities 1 1 Horton-Strahler,Tokunaga indexing Tokunaga self-similarity Earthquake clustering vs. physical properties of the crust 2 2 A unified approach to study aftershocks, foreshocks, swarms, etc. Notable deviation from self-similarity Objective non-parametric declustering Thin hot lithosphere  enhanced clustering, more foreshocks 3 3 Thick cold lithosphere  depressed clustering, more aftershocks Possibility for region-based forecasting strategies 4 4

  27. Thank you!

  28. Regions & catalogs analyzed World-wide (1973-present, m ≥4.0 ) USGS/NEIC http://earthquake.usgs.gov/earthquakes/eqarchives/epic/epic_global.php California (1984-present, m ≥ 2.0) ANSS, http://www.ncedc.org/anss/catalog-search.html Southern California (1981-2005, m ≥2.0) Shearer et al. (2005),BSSA, 95(3), 904–915. Lin et al. (2007), JGR, 112, B12309. Parkfield (1984-2005, m > 0.0) Thurber et al. (2006), BSSA, 96, 4B, S38-S49. 25 individual fault zones in CA (1984-2002) Powers and Jordan(2009), JGR, in press. Hauksson and Shearer (2005), BSSA, 95(3), 896–903. Shearer et al. (2005),BSSA,95(3), 904–915. Nevada (1990-present, m ≥1.0) Nevada Seismological Laboratory http://www.seismo.unr.edu/Catalog/search.html

  29. Cluster separation is time- & space-dependent

  30. World proportion of multiple-event clusters Nazca Plate -- South American Plate the Peru-Chile Trench Cocos Plate -- Caribbean Plate the Middle America Trench Pacific Plate -- Eurasian and Philippine Sea Plates the Mariana Trench Pacific Plate -- North American Plate the Aleutian Trench. Philippine Sea Plate -- Philippine Mobile Belt the Philippine Trench + the East Luzon Trench Eurasian Plate -- the Philippine Mobile Belt the Manila Trench Sunda Plate -- Philippine Mobile Belt the Negros Trench + the Cotobato Trench Pacific Plate -- Indo-Australian Plate Juan de Fuca, Gorda and Explorer -- North American plate South American Plate -- South Sandwich Plate the South Sandwich Trench East African Rift Mid-Atlantic Ridge East Pacific Rise Red Sea Rift Aden Ridge Carlsberg Ridge Gorda Ridge Explorer Ridge Juan de Fuca Ridge Chile Rise

  31. Measures of seismic clustering 1) Prop. of multiple-event clusters No. of clusters with fore/aftershocks = Total no. of clusters 2) Prop. of aftershocks No. of aftershocks = No. of foreshocks + aftershocks

  32. World proportion of multiple-event clusters

  33. World proportion of multiple-event clusters

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