Application of Computational Mechanics to the Analysis of Seismic Time-series via Numerical Optimisation

We apply the Computational Mechanics approach to the analysis of time-series representative of geophysical measurements. The algorithm employed is the Causal-State Splitting Reconstruction (CSSR) algorithm. We address a number of data pre-processing steps which are necessary when analysing complex time-series and specific to symbolised time-series analysis tools such as CSSR. We cast the choice of input parameters for the CSSR algorithm and time-series symbolisation, into an optimisation problem, with the aim of maximising the predictability of events of specific interest. Our approach is problem independent and can be easily extended to other applications. This research highlights the challenges to be overcome when analysing complex time-series using the Computational Mechanics approach. We also discuss further developments necessary to extend the approach to real data applications.

[1]  Cosma Rohilla Shalizi,et al.  Blind Construction of Optimal Nonlinear Recursive Predictors for Discrete Sequences , 2004, UAI.

[2]  C. Shalizi,et al.  Causal architecture, complexity and self-organization in time series and cellular automata , 2001 .

[3]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[4]  Cosma Rohilla Shalizi,et al.  Quantifying self-organization in cyclic cellular automata , 2003, SPIE International Symposium on Fluctuations and Noise.

[5]  J. P. Crutchfield,et al.  From finite to infinite range order via annealing: the causal architecture of deformation faulting in annealed close-packed crystals , 2004 .

[6]  Cosma Rohilla Shalizi.  Optimal Nonlinear Prediction of Random Fields on Networks , 2003, DMCS.

[7]  J. Crutchfield.  The calculi of emergence: computation, dynamics and induction , 1994 .

[8]  Dion Weatherley,et al.  Long-range Automaton Models of Earthquakes: Power-law Accelerations, Correlation Evolution, and Mode-switching , 2002 .

[9]  Y. Lai,et al.  What symbolic dynamics do we get with a misplaced partition? On the validity of threshold crossings analysis of chaotic time-series , 2001 .

[10]  Asok Ray,et al.  Anomaly prediction in mechanical systems using symbolic dynamics , 2003, Proceedings of the 2003 American Control Conference, 2003..

[11]  L. R. Sykes,et al.  Evolving Towards a Critical Point: A Review of Accelerating Seismic Moment/Energy Release Prior to Large and Great Earthquakes , 1999 .

[12]  B. Gutenberg,et al.  Seismicity of the Earth and associated phenomena , 1950, MAUSAM.

[13]  Matthew B Kennel,et al.  Estimating good discrete partitions from observed data: symbolic false nearest neighbors. , 2003, Physical review letters.

[14]  A. Mees,et al.  Context-tree modeling of observed symbolic dynamics. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  William H. Press,et al.  Numerical Recipes: FORTRAN , 1988 .

[16]  William H. Press,et al.  Numerical Recipes in Fortran 77 , 1992 .

[17]  David J. Varnes,et al.  Predictive modeling of the seismic cycle of the Greater San Francisco Bay Region , 1993 .

[18]  James P. Crutchfield,et al.  Computational Mechanics: Pattern and Prediction, Structure and Simplicity , 1999, ArXiv.

[19]  Young,et al.  Inferring statistical complexity. , 1989, Physical review letters.

[20]  F. Boschetti,et al.  Inversion of seismic refraction data using genetic algorithms , 1996 .

[21]  Asok Ray,et al.  Symbolic dynamic analysis of complex systems for anomaly detection , 2004, Signal Process..

[22]  C. Finney,et al.  A review of symbolic analysis of experimental data , 2003 .