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Table of Contents
Intro; Preface; Contents; List of Accepted Abbreviations and Symbols; Chapter 1: Introduction; References; Chapter 2: Mathematical Background; 2.1 Elements of Potential Theory for LaplaceÂś Equation; 2.2 Elements of Integral Equation Theory; 2.3 Fourier and Hankel Transforms; 2.3.1 The Fourier Transform; 2.3.2 The Hankel Transform; References; Chapter 3: Electrical Survey Technique and Mathematical Models; 3.1 Electrical Arrays, Field Measurements, and the Electrical Resistivity Tomography Method; 3.1.1 Types of Arrays; 3.1.2 Apparent Resistivity; 3.1.3 Different Types of Resistivity Methods
3.1.4 Electroprofiling3.1.5 Electrical Sounding; 3.1.6 Circular (Azimuthal) Measurements (Profiling and Sounding); 3.1.7 Electrical Resistivity Tomography; 3.2 Mathematical Model of the Resistivity Method; 3.3 Direct and Inverse Problems in the Resistivity Method; 3.4 The Electric Field of a Point Source Above a Horizontally Layered Medium; 3.4.1 Introduction; 3.4.2 Statement of the Problem and Its Solution in General Form; 3.4.3 Algorithm of Linear Filtration; 3.5 Introduction to the Integral Equations Method and the Boundary Element Method; 3.6 Methods of Solving Inverse Problems
4.3 The BEM for Solving Direct Sounding Problems Above a Medium with Buried Relief, with Numerical Examples4.3.1 Statement of the Direct Problem and Solvability of the Integral Equation; 4.3.2 Solvability of the Integral Equation in the 3D Case; 4.3.3 Numerical Examples; References; Chapter 5: The Boundary Element Method in the Sounding of Media with Ground Surface Relief; 5.1 The BEM for a Homogeneous Medium with Surface Relief; 5.1.1 Mathematical Basics for 2D Relief; 5.1.2 Application of the BEM to Solve the Integral Equation
5.1.3 The Influence of Different Relief Forms on the Results of Interpretation5.2 The BEM for a Two-Layered Medium with a Ground Surface Relief; 5.2.1 Mathematical Model; 5.2.2 The Numerical Method; 5.2.2.1 Test 1: Reciprocity Principle; 5.2.2.2 Test 2: Two Horizontally Layered Media; 5.2.3 Influence of a Second Layer on the Measured Data and Inversion Results; 5.3 The BEM for 3D Media: Influence of the Third Coordinate on Measuring Data and Interpretation Results; 5.3.1 Triangulation and Approximation of the Ground Surface; 5.3.1.1 Triangulation of a 3D Surface; 5.3.2 Numerical Results
3.1.4 Electroprofiling3.1.5 Electrical Sounding; 3.1.6 Circular (Azimuthal) Measurements (Profiling and Sounding); 3.1.7 Electrical Resistivity Tomography; 3.2 Mathematical Model of the Resistivity Method; 3.3 Direct and Inverse Problems in the Resistivity Method; 3.4 The Electric Field of a Point Source Above a Horizontally Layered Medium; 3.4.1 Introduction; 3.4.2 Statement of the Problem and Its Solution in General Form; 3.4.3 Algorithm of Linear Filtration; 3.5 Introduction to the Integral Equations Method and the Boundary Element Method; 3.6 Methods of Solving Inverse Problems
4.3 The BEM for Solving Direct Sounding Problems Above a Medium with Buried Relief, with Numerical Examples4.3.1 Statement of the Direct Problem and Solvability of the Integral Equation; 4.3.2 Solvability of the Integral Equation in the 3D Case; 4.3.3 Numerical Examples; References; Chapter 5: The Boundary Element Method in the Sounding of Media with Ground Surface Relief; 5.1 The BEM for a Homogeneous Medium with Surface Relief; 5.1.1 Mathematical Basics for 2D Relief; 5.1.2 Application of the BEM to Solve the Integral Equation
5.1.3 The Influence of Different Relief Forms on the Results of Interpretation5.2 The BEM for a Two-Layered Medium with a Ground Surface Relief; 5.2.1 Mathematical Model; 5.2.2 The Numerical Method; 5.2.2.1 Test 1: Reciprocity Principle; 5.2.2.2 Test 2: Two Horizontally Layered Media; 5.2.3 Influence of a Second Layer on the Measured Data and Inversion Results; 5.3 The BEM for 3D Media: Influence of the Third Coordinate on Measuring Data and Interpretation Results; 5.3.1 Triangulation and Approximation of the Ground Surface; 5.3.1.1 Triangulation of a 3D Surface; 5.3.2 Numerical Results