Application of Soft Computing and Intelligent Methods in Geophysics

Description

Preface......Page 3 Contents......Page 6 --- Neural Networks......Page 15 1.1 Introduction......Page 16 1.2 A Brief Review of ANN Applications in Geophysics......Page 17 1.3 Natural Neural Networks......Page 19 1.4 Definition of Artificial Neural Network (ANN)......Page 20 1.5 From Natural Neuron to a Mathematical Model of an Artificial Neuron......Page 23 1.6 Classification into Two Groups as an Example......Page 29 1.7 Extracting the Delta-Rule as the Basis of Learning Algorithms......Page 31 1.8 Momentum and Learning Rate......Page 32 1.10 Feed-Forward Back-Propagation Neural Networks......Page 33 1.12 Important Factors in Designing a MLP Neural Network......Page 37 1.12.2 Determination of the Number of Hidden Neurons......Page 38 1.13 How Good Are Multi-layer Per Feed-Forward Networks?......Page 39 1.15 To Stop or not to Stop, that Is the Question! (When Should Training Be Stopped?!)......Page 40 1.16 The Effect of the Number of Learning Samples......Page 41 1.17 The Effect of the Number of Hidden Units......Page 42 1.19 The Multi-start Approach......Page 43 1.20.2 The Validation Set......Page 45 1.20.5 User-Defined Partitioning......Page 46 1.20.7 Data Partition to Test Neural Networks for Geophysical Approaches......Page 47 1.21 The General Procedure for Testing of a Designed Neural Network in Geophysical Applications......Page 48 1.22 Competitive Networks—The Kohonen Self-organising Map......Page 49 1.22.3 The Kohonen Network in Operation......Page 50 1.22.5.1 The Kohonen Algorithm......Page 52 1.22.6.1 Vector Normalisation......Page 53 1.23 Hopfield Network......Page 54 1.24.1 GRNN Architecture......Page 56 1.24.2 Algorithm for Training of a GRNN......Page 57 1.25.1 Radial Functions......Page 58 1.25.2 RBF Neural Networks Architecture......Page 59 1.26 Modular Neural Networks......Page 61 1.27 Neural Network Design and Testing in MATLAB......Page 63 References......Page 79 2.1 Introduction......Page 83 2.2 Application of Neural Networks in Gravity......Page 84 2.2.1.1 Extraction of Cost Function for Hopfield Neural Network......Page 85 2.2.1.2 Synthetic Data and the Hopfield Network Estimator in Practical Cases......Page 87 2.2.1.3 Conclusions......Page 90 2.2.2 Depth Estimation of Salt Domes Using Gravity Anomalies Through General Regression Neural Networks......Page 91 2.2.2.1 GRNN and MLP Design and Test......Page 92 2.2.2.2 Location of Field Data......Page 96 Modeling......Page 97 Training and Testing of GRNN......Page 100 Training and Testing of MLP......Page 102 2.2.3 Simultaneous Estimation of Depth and Shape Factor of Subsurface Cavities......Page 107 2.2.4 Modeling Anticlinal Structures Through Neural Networks Using Residual Gravity Data......Page 117 2.3 Application of ANN for Inversion of Self-potential Anomalies......Page 122 2.4 Application of ANN for Sea Level Prediction......Page 127 2.5 Application of Neural Network for Mineral Prospectivity Mapping......Page 133 2.6 Application of NN for SP Inversion Using MLP......Page 138 2.7 Determination of Facies from Well Logs Using Modular Neural Networks......Page 142 2.8 Estimation of Surface Settlement Due to Tunneling......Page 148 2.8.1 Introduction......Page 149 2.8.4 Soil and Rock Behavior Models......Page 153 2.8.5 The Studied Route of the Mashhad Subway Line 2 Project......Page 155 2.8.6 Characteristics of the Tunnel......Page 157 2.8.8 Surface Settlement Prediction Using ANN......Page 159 2.8.9 Surface Settlement Calculation Using FEM......Page 165 2.8.11 Conclusions......Page 166 2.9.1 Literature Review of the Prediction of the Penetration Rate of TBM......Page 168 2.9.2.1 Geotechnical Investigation of the Tunnel Route......Page 169 2.9.3 Geomorphology......Page 171 2.9.3.1 The Morphology of the Area......Page 172 2.9.6 A Static Model for Predicting the Penetration Rate......Page 173 2.9.7 Input Parameters......Page 175 2.9.8 ANN Topology......Page 176 2.10 Application of Neural Network Cascade Correlation Algorithm for Picking Seismic First-Breaks......Page 178 2.10.1 The Improvement of CC Algorithm......Page 180 2.10.2 Attribute Extraction for Neural Network Training......Page 182 2.11 Application of Neural Networks to Engineering Geodesy: Predicting the Vertical Displacement of Structures......Page 185 2.12 Attenuation of Random Seismic Noise Using Neural Networks and Wavelet Package Analysis......Page 188 2.12.1 Methodology......Page 190 2.12.2 Experimental Philosophy......Page 194 Appendix 1 of Chapter Two......Page 201 Appendix 2 of Chapter Two......Page 204 References......Page 205 --- Fuzzy Logic......Page 211 3.1 Introduction......Page 212 3.2.1 First Viewpoint......Page 213 3.2.2 The Second Viewpoint......Page 219 3.3 Fuzzy Sets......Page 221 3.3.1 The Concept of a Fuzzy Set......Page 222 3.3.2 Definition of a Fuzzy Set......Page 225 3.3.3.1 π-Shaped Fuzzy Sets......Page 230 3.3.3.2 Matlab Code for Non-conventional Pi-Shaped MF......Page 231 3.3.3.3 Matlab Code for a Triangular Membership Function (TRIMF)......Page 232 3.3.3.4 Matlab Command for a Trapezoidal Membership Function......Page 233 3.3.3.5 Matlab Code for Gaussian Curve Membership Function (GAUSSMF)......Page 236 3.3.3.7 Generalized Bell Curve Membership Function and Its Matlab Code......Page 237 3.3.3.9 Matlab Code for Z-Shaped Membership Function......Page 239 3.3.3.10 S Shaped Fuzzy Sets......Page 240 3.3.3.11 Matlab Code for S-Shaped Curve Membership Function (SMF)......Page 241 3.3.3.12 V Shaped Fuzzy Set......Page 242 3.3.4 Connecting Classical Set Theory to Fuzzy Set Theory......Page 243 3.3.4.2 Extension Principle......Page 244 3.4.1 Standard Union......Page 246 3.4.3 Standard Complement......Page 247 3.4.4 Applications of the Intersection of Fuzzy Set......Page 250 3.4.5 Fuzzy Averaging Operations......Page 251 3.4.7.1 Non-Joint Union......Page 252 3.4.7.5 Distance in Fuzzy Sets......Page 253 Euclidean Distance......Page 255 3.4.8 Cartesian Product......Page 256 3.5.1.1 Definition of a Classical Relationship......Page 257 3.5.1.2 Definition of a Fuzzy Relationship......Page 258 3.5.2 Domain and Range of Fuzzy Relationship......Page 259 3.5.3.3 Standard completion Is Defined as......Page 260 3.5.4.1 Projection of Fuzzy Relations......Page 261 3.5.4.2 Cylindrical Extension......Page 262 3.5.5 Composition of Fuzzy Relations......Page 263 3.5.6 Matlab Coding for Fuzzy Relations......Page 267 3.5.7 Properties of Fuzzy Relations......Page 268 3.5.7.2 Ordered Fuzzy Relation......Page 269 3.5.8 α-cut of a Fuzzy Relation......Page 270 3.5.9 α-cut of Equivalent Fuzzy Relationship......Page 271 3.6.1 Further Description of the Extension Principle......Page 272 3.6.2 Generalized Extension Principle or Multi-variate Extension Principle......Page 274 3.6.4 Definition of a Fuzzy Number......Page 275 3.6.5 LR Representation of Fuzzy Numbers......Page 277 3.6.6 Operations on LR Fuzzy Numbers......Page 279 3.6.8 \upalpha -cut of Fuzzy Number......Page 280 3.6.8.1 Operations on Domains......Page 281 3.6.8.3 Fuzzy Domain......Page 282 3.7 Definition of Some Basic Concepts of Fuzzy Sets......Page 283 3.8 T-Norm......Page 286 3.9 S-Norm......Page 287 3.12 Linguistic Variable......Page 288 3.13.1 Definition with Example in Geophysics......Page 289 3.13.2 Interpretation of Fuzzy if-then Rule......Page 291 3.14.1 Fuzzy Inference......Page 292 3.14.2 Fuzzy Extended Exceptional Deduction Rule......Page 294 3.15.2 FATI Method......Page 297 3.16.1 Center of Gravity (Centroid of Area) Defuzzification......Page 298 3.16.2 Center of Sum Method......Page 300 3.16.4 Height Method......Page 301 3.16.5 Bisector Defuzzification......Page 302 3.16.8 Weighted Average Defuzzification Method......Page 304 3.17.2 Triangular Fuzzifier......Page 305 3.18 Fuzzy Modeling Using the Matlab Toolbox......Page 306 3.18.2 Membership Function Editor......Page 307 3.18.3 Rule Editor......Page 308 3.18.5 Surface Viewer......Page 309 References......Page 310 4.2 Fuzzy Logic for Classification of Volcanic Activities......Page 312 4.3 Fuzzy Logic for Integrated Mineral Exploration......Page 313 4.4 Shape Factors and Depth Estimation of Microgravity Anomalies via Combination of Artificial Neural Networks and Fuzzy Rules Based System (FRBS)......Page 321 4.4.2 Extracting Suitable Fuzzy Sets and Fuzzy Rules for Cavities Shape Estimation......Page 323 4.4.4 Test of the Fuzzy Rule-Based Model with Real Data......Page 330 4.5.1 Introduction......Page 331 4.5.1.1 The Change Detection Process......Page 333 4.5.1.4 NDVI Differencing Method......Page 334 4.5.1.6 Image Differencing and NDVI Differencing Methods Applied to Case Study......Page 335 4.5.1.7 Fuzzy Applications Applied to Case Study......Page 336 4.6.1 Classical and Fuzzy Clustering......Page 341 4.6.2 Fuzzy Transitive Closure Method......Page 343 4.6.3 Fuzzy Equivalence Relations......Page 344 4.6.5 Application to for Geomagnetic Storm Data......Page 345 4.7 Geophysical Data Fusion by Fuzzy Logic to Image Mechanical Behavior of Mudslides......Page 350 4.8.1 Description of the Research......Page 359 4.8.2.1 The Goal of the Algorithm......Page 361 4.8.2.3 Potential Anomaly Domains Construction......Page 362 4.8.2.4 Genuine Anomaly Domain Construction......Page 365 4.8.3 Application of the DRAS Algorithm to Observational Data......Page 366 4.9 Operational Earthquake Forecasting Using Linguistic Fuzzy Rule-Based Models from Imprecise Data......Page 370 References......Page 378 --- Combination of NНs & Fuzzy Logic......Page 383 5.1.1 Introduction......Page 384 5.1.3 Concurrent Neuro-fuzzy Systems......Page 386 5.1.4 Hybrid Neuro-fuzzy Systems......Page 387 5.2.1 The Inference Engine......Page 389 5.2.4 The Neural Knowledge Base......Page 390 5.3 Neuro-fuzzy Systems......Page 392 5.3.1 Synergy of Neural and Fuzzy Systems......Page 393 5.3.2 Training of a Neuro-fuzzy System......Page 396 5.3.3 Good and Bad Rules from Expert Systems......Page 397 5.4.1 Structure of ANFIS......Page 398 5.4.2 Learning in the ANFIS Model......Page 401 5.4.2.2 The Over-Fitting Problem in ANFIS......Page 402 5.4.3 Function Approximation Using the ANFIS Model......Page 403 5.5.1 Introduction......Page 404 5.5.2 ANFIS Graphical User Interference......Page 406 References......Page 423 6.1.1 Why Use Neuro-Fuzzy Methods for Microgravity Interpretation?......Page 425 6.1.2 Multiple Adaptive Neuro Fuzzy Interference &!blank;SYSTEM (MANFIS)......Page 426 6.1.3 Procedure of Gravity Interpretation Using MANFIS......Page 428 6.1.4 Training Strategies and MANFIS Network Architecture......Page 429 6.1.5 Test of MANFIS in Present of Noise and for Real Data......Page 434 6.2.1 ANFIS Structure......Page 435 6.2.2 ANFIS Training and Testing......Page 437 6.2.3 Conclusion......Page 439 6.3.1 Introduction......Page 440 6.3.3 Geological Setting......Page 441 6.3.4 Data Set......Page 443 6.3.5 Preprocessing to Select the Most Suitable Attributes......Page 444 6.4.1 Introduction......Page 449 6.4.2 Training of the Neuro-Fuzzy Model......Page 450 6.4.4 Conclusion......Page 454 6.5.1 Introduction......Page 458 6.5.3 ANFIS Training......Page 459 6.5.4 ANFIS Performance Validation Using Real Data......Page 462 6.6.2 Feature Selection......Page 465 6.6.3 Spectral Characteristics......Page 466 6.6.4 Training and Test of ANFIS......Page 468 6.7.1 Literature......Page 469 6.7.2 Inputs-Output Structure of the Designed ANFIS......Page 470 6.7.4 Training of ANFIS Performance......Page 471 6.7.5 Validation of ANFIS Performance......Page 472 6.7.6 Application of ANFIS Methods to Real Borehole Geophysics Data......Page 473 6.8.1 Introduction......Page 474 6.8.3.1 Patterns for Polar Motions......Page 476 6.8.3.2 Patterns for LOD......Page 477 6.8.4 Design of ANFIS Structure......Page 478 6.8.5 Test of ANFIS for Real Data......Page 479 6.9.1 Literature Review......Page 481 6.9.2 Wiener-ANFIS Filtering......Page 483 6.9.3 Application to a Real Stacked Seismic Section......Page 484 6.9.4 Conclusions......Page 486 References......Page 488 --- Genetic Algorithm......Page 493 7.1 Introduction......Page 494 7.2 Optimization......Page 497 7.3.1 Model Representation......Page 499 7.3.3 Crossover and Mutation......Page 501 7.4.1 Multi-scale GA for Trans-Dimensional Inversion......Page 502 7.4.2 Multi-objective Optimization......Page 503 7.4.2.1 Multi-objective Optimization Methods in Geophysics......Page 507 7.4.2.2 General Overview of Multi-objective Optimization......Page 508 7.4.2.3 Geophysical Examples of Multi-objective Optimization......Page 511 7.4.3 The Future of Multi-objective Optimization in Geophysics......Page 526 Appendix of Chapter Seven: Pseudo Codes for GA......Page 532 References......Page 538