## The Boundary Element Method in Geophysics |

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### Contents

Basic Mathematical Preparation | 1 |

Isoparametric Elements and Gaussian Integration | 21 |

Potential Field Continuation and Transformation | 39 |

Modeling Magnetic and Gravity Anomalies | 71 |

Modeling Resistivity and IP Methods | 89 |

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### Common terms and phrases

3-D problems 3-D terrain angle subtended anomalous body apparent resistivity boundary conditions boundary element method boundary integral equation boundary value problem component computed constant coordinates curve derivative differential discretized displacement field divided elastic elastodynamic electromagnetic equa field values Fourier transform frequency domain fundamental solution Gaussian quadrature geoelectrical geophysical given Green’s formula Green’s function ground surface half-space Helmholtz equation homogeneous horizontal inhomogeneous body integral in equation integral over element isoparametric element Laplace equation linear interpolation Love wave magnetic anomaly magnetic field magnetic potential magnetotelluric node number of nodes obtain ohm-m polarization potential-field quadratic quadratic function region Q respectively right side shape functions shown in Figure side of equation source point Substituting equations sum of integrals system of equations system of linear terrain correction terrain effect tion topographic surface triangular element upward continuation vertical wavefield wavenumber yields