classes

This repository contains matlab codes for the classes on: Numerical modeling and Inverse theory.

To download this repository: git clone https://github.com/vsilwal/classes

Numerical Modeling in Geophysics

Theory and Lab Schedule

S. No	Theory	Lab	Theory Hours	Lab Hours
1	Intro to forward and inverse problems	Intro to MATLAB and GitHub	2	2
2	Discretization	Projectile motion example	4	2
	- Projectile motion example
	- Overdetermined-underdetermined
	- Seismic tomography example
3	Interpolation and linear regression	(1) Polynomial interpolation (2) Lagrange and spline interpolation	4	6
4	Taylor series and Newton's method	Taylor series example	2	2
5	Numerical differentiation, Generalized matrix method for numerical derivatives	Solutions to ODE using Euler and RK4	4	2
6	Numerical integration	Difference in trapezoidal and Simpson’s solutions	2	2
7	Iterative solvers	Jacobi and Gauss-Seidel method	2	2
Mid Sem
8	Basic elements of Finite difference method (explicit, implicit, Crank-Nicolson)	-	4	0
9	Heat equation using Finite difference method	Example 1: Numerical solution to heat equation using FDM	3	4
10	Acoustic equation using Finite difference method	Example 2: Numerical solution to acoustic equation using FDM	3	4
End Sem
Total			30	26

Geophysical Inversion

Theory and Lab Schedule

S. No	Theory	Lab	Theory Hours	Lab Hours
1	Intro to forward and inverse problems	Treasure hunt problem, Intro to MATLAB and GitHub	2	0
2	Revision of linear algebra (null space, rank, eigenvectors)	Properties of eigenvalues and eigenvectors	2	2
3	Taylor series (gradient and Hessian)	Linear regression problem	4	2
4	Linear and non-linear inverse problems	Example 1: Vertical Seismic Profiling (VSP) linear vs non-linear	4	4
5	Iterative methods	Gradient vs Newton method	2	2
6	Earthquake location problem	Example 2: Hypocenter Inversion	2	2
Mid Sem
7	Probabilistic viewpoint: Weighted least-square and Gaussian PDF	-	4	0
8	Regularization and Lagrange multiplier	An example of Lagrange multipliers	2	2
9	SVD, Truncated SVD, Damped SVD	Properties of SVD, Image compression	4	4
10	Tomography inversion	Example 3: Crosswell Borehole tomography	2	2
11	Global Optimization Technique	Particle Swarm Optimization	2	2
12	Inverse problems using basis functions	Shaw Problem	2	2
End Sem
Total			32	24