Summary
Theory of Potential Field Methods in Geophysics
Prerequisites
1
Introduction
Mathematical foundations
2
Fields
Newton potential
3
The gravity potential function
4
Point mass
5
Mass distribution
6
Newton’s shell theorem
7
PREM - Preliminary Reference Earth Model
8
Potential and gravitational attraction of a sphere
9
Circular Disc
Two-dimensional problems
10
2-D mass distributions
11
Gravitational attraction of a prism
12
Implementation of the TALWANI approach
13
Introduction to Complex Analysis
14
Hilbert Transform
15
Implementation of the Hilbert transform
Three-dimensional problems
16
Gravitational Field Caused by a Density Distribution in
\(\mathbb{R}^3\)
Dipole potential
17
Potential of an electrical dipole
18
Potential of a magnetic dipole
19
Equation of a dipole field line
Spherical harmonics
20
Introduction to Spherical Harmonic Analysis
21
Legendre Polynomials
22
Numerical computation of Legendre polynomials
23
Solution of the Laplace equation in spherical coordinates
24
Mathematical description of the Earth’s global magnetic field
Boundary value problems
25
Introduction
26
Dirichlet problems
27
Neumann problems
28
Robin problems
29
The uniqueness theorem
30
Domains
31
Examples
32
Green’s identities
33
Applications
Summary
References
Summary
WIP
33
Applications
References