DOI: https://doi.org/10.26089/NumMet.v16r112

A stochastic modification of the spherical block-and-fault model of lithosphere dynamics and seismicity

Authors

  • L.A. Melnikova
  • V.L. Rozenberg

Keywords:

block-and-fault models of lithosphere dynamics and seismicity
synthetic earthquake catalogs
scalability of parallel algorithms
parallel computing
stochastic analysis
stochastic differential equations

Abstract

A brief description of the last version of the spherical block-and-fault model is discussed. This version takes into account random factors essentially influencing the dynamics of model parameters. Two variants of introducing stochasticity into the procedures for calculating the forces acting on a block and determining the model earthquakes are tested. This stochasticity consists in (i) adding a noise to the differential equations describing the dynamics of elastic forces and inelastic displacements and in (ii) using random quantities when specifying strength thresholds for the medium of tectonic faults. Numerical experiments demonstrate the perspectivity of introducing stochasticity into the model.

New computational technologies

Downloads

Published

2015-03-12

Issue

Vol. 16 (2015): Issue 1.

Section

Section 1. Numerical methods and applications

Author Biographies

L.A. Melnikova

N.N. Krasovskii Institute of Mathematics and Mechanics of UB RAS (IMM UB RAS)
• Chief Programmer

V.L. Rozenberg

N.N. Krasovskii Institute of Mathematics and Mechanics of UB RAS (IMM UB RAS)
• Senior Researcher

References

  1. A. Gabrielov and W. I. Newman, “Seismicity Modeling and Earthquake Prediction: A Review,” in Nonlinear Dynamics and Predictability of Geophysical Phenomena (Am. Geophys. Union, Washington, 1994), pp. 7-13.
  2. V. Keilis-Borok and A. A. Soloviev (Eds.), Nonlinear Dynamics of the Lithosphere and Earthquake Prediction (Springer, Berlin, 2003).
  3. A. M. Gabrielov, V. I. Keilis-Borok, T. A. Levshina, and V. A. Shaposhnikov, “A Block Model of Lithosphere Dynamics,” in Mathematical Methods in Seismology and Geodynamics: Computational Seismology (Nauka, Moscow, 1986), Issue 19, pp. 168-178.
  4. A. Peresan, I. Vorobieva, A. Soloviev, and G. F. Panza, “Simulation of Seismicity in the Block-Structure Model of Italy and its Surroundings,” Pure Appl. Geophys. 164 (11), 2193-2234 (2007).
  5. D. V. Rundquist and A. A. Soloviev, “Numerical Modeling of Block Structure Dynamics: An Arc Subduction Zone,” Phys. Earth Planet. Inter. 111 (3-4), 241-252 (1999).
  6. L. A. Melnikova and V. L. Rozenberg, “Spherical Block Model of Lithosphere Dynamics and Seismicity: Different Modifications and Numerical Experiments,” Tr. Inst. Mat. Mekh. Akad. Nauk 13 (3), 95-120 (2007).
  7. L. A. Melnikova and V. L. Rozenberg, “High Performance Computing in Modeling the Dynamics and Seismicity of Tectonic Plate Systems,” Vychisl. Metody Programm. 13, 280-289 (2012).
  8. L. A. Melnikova and V. L. Rozenberg, “A Spherical Block Model: Optimization of Computational Load and New Results of Simulation,” in Proc. Int. Conf. on Parallel Computational Technologies, Chelyabinsk, Russia, April 1-5, 2013 (South Ural Univ., Chelyabinsk, 2013), pp. 467-472.
  9. V. L. Rozenberg, P. O. Sobolev, A. A. Soloviev, and L. A. Melnikova, “The Spherical Block Model: Dynamics of the Global System of Tectonic Plates and Seismicity,” Pure Appl. Geophys. 162 (1), 145-164 (2005).
  10. B. Oksendal, Stochastic Differential Equations: An Introduction with Application (Springer, New York, 1998; Mir, Moscow, 2003).
  11. K. Aki and P. G. Richards, Quantitative Seismology: Theory and Methods (Freeman, San Francisco, 1980; Mir, Moscow, 1983).
  12. D. L. Wells and K. J. Coppersmith, “New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement,” Bull. Seism. Soc. Am. 84 (4), 974-1002 (1994).
  13. A. E. Gripp and R. G. Gordon, “Young Tracks of Hotspots and Current Plate Velocities,” Geophys. J. Int. 150 (2), 321-361 (2002).
  14. Global Hypocenters Data Base, NEIC/USGS. Denver, CO, 2015.
    http://earthquake.usgs.gov/. Cited January 29, 2015.
  15. V. P. Gergel’, Theory and Practice of Parallel Computing (Binom, Moscow, 2007) [in Russian].
  16. I. Foster, Designing and Building Parallel Programs: Concepts and Tools for Parallel Software Engineering (Addison-Wesley, Reading, 1995).