Intro; Preface; Contents; Neural Networks; 1 Artificial Neural Networks; 1.1 Introduction; 1.2 A Brief Review of ANN Applications in Geophysics; 1.3 Natural Neural Networks; 1.4 Definition of Artificial Neural Network (ANN); 1.5 From Natural Neuron to a Mathematical Model of an Artificial Neuron; 1.6 Classification into Two Groups as an Example; 1.7 Extracting the Delta-Rule as the Basis of Learning Algorithms; 1.8 Momentum and Learning Rate; 1.9 Statistical Indexes as a Measure of Learning Error; 1.10 Feed-Forward Back-Propagation Neural Networks

1.11 A Guidance Checklist for Step-by-Step Design of a Neural Network1.12 Important Factors in Designing a MLP Neural Network; 1.12.1 Determining the Number of Hidden Layers; 1.12.2 Determination of the Number of Hidden Neurons; 1.13 How Good Are Multi-layer Per Feed-Forward Networks?; 1.14 Under Training and Over Fitting; 1.15 To Stop or not to Stop, that Is the Question! (When Should Training Be Stopped?!); 1.16 The Effect of the Number of Learning Samples; 1.17 The Effect of the Number of Hidden Units; 1.18 The Optimum Number of Hidden Neurons; 1.19 The Multi-start Approach

1.20 Test of a Trained Neural Network1.20.1 The Training Set; 1.20.2 The Validation Set; 1.20.3 The Test Set; 1.20.4 Random Partitioning; 1.20.5 User-Defined Partitioning; 1.20.6 Partition with Oversampling; 1.20.7 Data Partition to Test Neural Networks for Geophysical Approaches; 1.21 The General Procedure for Testing of a Designed Neural Network in Geophysical Applications; 1.22 Competitive Networks-The Kohonen Self-organising Map; 1.22.1 Learning in Biological Systems-The Self-organising Paradigm; 1.22.2 The Architecture of the Kohonen Network; 1.22.3 The Kohonen Network in Operation

1.22.4 Derivation of the Learning Rule for the Kohonen Net1.22.5 Training the Kohonen Network; 1.22.5.1 The Kohonen Algorithm; 1.22.5.2 Learning Vector Quantisation (LVQ); 1.22.6 Training Issues in Kohonen Neural Nets; 1.22.6.1 Vector Normalisation; 1.22.6.2 Weight Initialisation; 1.22.6.3 Reducing Neighbourhood Size; 1.22.7 Application of the Kohonen Network in Speech Processing-Kohonen's Phonetic Typewrite; 1.23 Hopfield Network; 1.24 Generalized Regression Neural Network (GRNN); 1.24.1 GRNN Architecture; 1.24.2 Algorithm for Training of a GRNN; 1.24.3 GRNN Compared to MLP

1.25 Radial Basis Function (RBF) Neural Networks1.25.1 Radial Functions; 1.25.2 RBF Neural Networks Architecture; 1.26 Modular Neural Networks; 1.27 Neural Network Design and Testing in MATLAB; References; 2 Prior Applications of Neural Networks in Geophysics; 2.1 Introduction; 2.2 Application of Neural Networks in Gravity; 2.2.1 Depth Estimation of Buried Qanats Using a Hopfield Network; 2.2.1.1 Extraction of Cost Function for Hopfield Neural Network; 2.2.1.2 Synthetic Data and the Hopfield Network Estimator in Practical Cases; 2.2.1.3 Conclusions