Summary
Theory of Potential Field Methods in Geophysics
Prerequisites
1
Introduction
Mathematical foundations
2
Fields
Newton potential
3
Point mass
4
Mass distribution
5
Newton’s shell theorem
6
PREM - Preliminary Reference Earth Model
7
Potential and gravitational attraction of a sphere
8
Circular Disc
Two-dimensional problems
9
2-D mass distributions
10
Gravitational attraction of a prism
11
Implementation of the TALWANI approach
12
Introduction to Complex Analysis
13
Hilbert Transform
14
Implementation of the Hilbert transform
Three-dimensional problems
15
Gravitational Field Caused by a Density Distribution in
\(\mathbb{R}^3\)
Dipole potential
16
Potential of an electrical dipole
17
Potential of a magnetic dipole
18
Equation of a dipole field line
Spherical harmonics
19
Introduction to Spherical Harmonic Analysis
20
Legendre Polynomials
21
Numerical computation of Legendre polynomials
22
Solution of the Laplace equation in spherical coordinates
23
Mathematical description of the Earth’s global magnetic field
Boundary value problems
24
Introduction
25
Dirichlet problems
26
Neumann problems
27
Robin problems
28
The uniqueness theorem
29
Domains
30
Examples
31
Green’s identities
32
Applications
Summary
References
Summary
WIP
32
Applications
References