Università Roma Tre

Introduction to the course. Introduction to Matlab 1. Matricial Calculation; search for main components (eigenvalues, eigenvectors, ...).
Introduction to Matlab 2: rows, columns, matrix, figure, vectors, import data, ... Tensors; rigid rototranslations and associated matrix.
Rotation of a seismic signal to derive the radial and transverse component. Complex numbers and trigonometric functions. Polar representation. Phasor. Matlab exercise: representation in Cartesian-polar-spherical coordinates. Vector calculation. Waves. Stationary waves.
Signal analysis: linear time-invariant system, Convolution theorem.
Exercise on the impulse and step response. Fourier series. Fourier transform. Exercise on Fourier Analysis of mechanical waves. Solution of the wave equation in the frequency domain. Exercise: delay and phase.
Cross Correlation - Filtering of data in time and frequency domain.

Mathematical modelling for Earth sciences. Xin She Yang. Dunedin.