I Artificial Intelligence in Geophysical Data Analysis .......... 1
1 Dynamic and Fuzzy Logic Clustering and Classification ......... 1
1.1.Syntactic Algorithms for Time Series Classification ....... 1
1.1.1.Structural representation of waveforms: time-series
parametri-sation .................................... 1
1.1.2.Structural dissimilarity: Levenstein distance ....... 4
1.1.3."K-mean distances" decision rule. SPARS Algorithm ... 7
1.2.Fuzzy Logic Approach to Classification ................... 7
1.2.1.Basic Definitions ................................... 7
1.2.2.Operations on Fuzzy Sets ........................... 11
1.2.3.Fuzzy binary relations ............................. 14
1.2.4.The fuzzy logic approach to time series
classification ..................................... 15
1.2.5.Fuzzy version of SPARS algorithm (FSPARS) .......... 24
1.3.Clustering Algorithms .................................... 34
1.3.1."Lighting" and clustering in finite metric
spaces ............................................. 34
1.3.2.Algorithm "Rodin": ................................. 44
1.3.3.Fuzzy clustering ................................... 56
1.4.Linear and Circle Structures Recognition Algorithms ...... 64
1.4.1.Differential operations in GIS environment ......... 64
2 Applications to Physics of the Earth, Seismology and Engi
neering Seismology ........................................... 71
2.1.Syntactic Classification of Engineering Seismology
Data ..................................................... 71
2.1.1.Strong ground motion earthquake data base .......... 71
2.1.2.Classification of strong motion records
according to geotectonic regions ................... 74
2.2.Seismological Data Classification ........................ 78
2.2.1.Seismic observation networks and databases ......... 78
2.2.2.Syntactic classification of seismograms ............ 81
2.3.Recognition of Magnetic Anomalies along the
Mid-Atlantic Ridge ....................................... 88
2.3.1.Method ............................................. 88
2.3.2.Data, results and interpretation ................... 94
2.4.Clustering Analysis for Magnetic Field Studies ........... 99
2.4.1.Euler deconvolution ................................ 99
2.4.2.Magnetic Data Clustering .......................... 105
2.4.3.Euler solutions by clusterization in the gulf of
Saint Malo ........................................ 109
2.5.Linear and Circular Clustering of Bathymetric
Data in the Wharton Basin ............................... 114
3 Recognition of Earthquake-Prone Areas and Seismic Hazard
Assessment .................................................. 123
3.1.Earthquake-prone Areas in the Western Alps .............. 123
3.1.1.E.C. application to the neotectonic scheme ........ 135
3.1.2.CORA algorithm classification results ............. 137
3.1.3.Comparison of CORA-algorithm results with
E.C.-algorithm results ............................ 142
3.1.4.Control experiments ............................... 142
3.2.Seismically Dangerous Zones in the Pyrenees ............. 146
3.3.Comparison between Earthquake-prone areas in the
Pyrenees and the Alps ................................... 158
3.4.Strong Earthquakes Prone-areas in the Great Caucasus .... 163
II Fractals and Dynamic Systems ............................... 171
4 Fractals and Multifractals .................................. 173
4.1.A brief Review of Fractals and Multifractal Analysis .... 173
4.2.Geomorphology (Continental and Marine) Hydrology ........ 177
4.2.1.Continental Earth's Relief, Topography,
Self-affine Fractals .............................. 177
4.2.2.Bathymetry, Seafloor Roughness .................... 179
4.2.3.Fractal and Multifractal analysis applied to
river basins and to river flows ................... 184
4.3.Gravity Anomalies and Structural Inversion Modeling ..... 192
4.3.1.Fractal analysis of gravity anomalies ............. 193
4.4.Geomagnetism ............................................ 196
4.4.1.The Fractal Structure of the Interplanetary
Magnetic Field .................................... 196
4.4.2.Fractal dimension and power law for geomagnetic
time series ....................................... 197
4.5.Tectonics, Seismicity, Volcanology ...................... 199
4.5.1.Renormalization group theory ...................... 199
4.5.2.Fragmentation, Fracturation ....................... 202
4.5.3.Tectonics, Fractals and Multifractals ............. 213
4.5.4.Tectonics. Study of Surface Faults ................ 220
4.5.5.Multifractals and Wavelets applied to fault
fields ............................................ 223
4.5.6.Seismicity, Gutenberg and Richter Law,
Multifractals ..................................... 226
4.5.7.Power Law or Poisson Law? ......................... 229
4.6.Fragmentation, tectonics, seismicity, synthesis trial ... 236
5 Dynamic System Properties and Long Time Series .............. 239
5.1.Geomorphology, Hydrology ................................ 239
5.1.1.Correlation Function and Rivers Flows ............. 239
5.1.2.Wavelets Applied to Floods ........................ 240
5.2.Seismology .............................................. 243
5.2.1.Cantor Dust application ........................... 243
5.2.2.SOC applications to seismology .................... 245
5.3 Volcanology ............................................. 246
5.3.1.Application to Volcanic Eruptions ................. 246
5.3.2.Cantor Dust and Correlation Function
applications ...................................... 248
5.3.3.Volcano behaviour and Self Organized
Criticality ....................................... 253
5.3.4.Multifractal analysis ............................. 256
5.4 Geomagnetism Study at Different Time Scales ............. 258
5.4.1.Geomagnetic Reversals ............................. 258
5.4.2.Temporal Variations of the Magnetic Field
Vector ............................................ 262
5.4.3.Theoretical Modeling .............................. 270
5.5 Others .................................................. 282
5.5.1.Heat and Water Transport in an Underground cave ... 282
6 Conclusions and Perspectives ................................ 285
6.1 About Part I ........................................... 285
6.2 About Part II ........................................... 288
6.2.1.Intermittency and turbulence ...................... 289
6.2.2.The problem of short time series, slow and fast
dynamics in coupled systems ....................... 290
6.2.3.Self-Organised criticality, SOC ................... 292
6.2.4.Mastering and controlling Chaos ................... 292
III References ................................................ 295
IV Index ...................................................... 333
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