## UE Wave physics

Degrees incorporating this pedagocial element :

### Description

An important part of Geophysics concerns the imaging of the Earth with waves. This lecture aims at providing students with a solid background of the mechanisms of wave propagation and scattering. The main concepts of wave physics are introduced from a theoretical point of view and are illustrated with various exercices and lab works.

Content
- Chapter 1 Fundamentals of Acoustics

governing equations of acoustics; impedance; sound power; acoustic intensity; Poynting's vector

- Chapter 2 Acoustic ducts and waveguides

closed / open ducts; Kundt's tube; stationary wave, acoustic waveguides, dispersion; phase and group velocities

- Chapter 3 Basic signal processing for wave physics

correlation; convolution; Fourier and Laplace transforms; time-space Fourier transforms; sampling theorem

- Chapter 4 Green's functions

causality; reciprocity; free-space Green's functions; monopoles; dipoles; integral representation of wave field

- Chapter 5 Fundamental of elastodynamics

constitutive relationships; Hooke's law; wave equation and its solutions; wave polarization; Christoffel's tensor; reflection and refraction

- Chapter 6 Single scattering

Huygen's principle; Rayleigh-Sommerfeld and Kirchhoff diffraction; Fraunhofer and Fresnel approximations

- Chapter 7 Surface, guided and interface waves

Rayleigh wave; Love wave; Lamb waves; Scholte waves; Stoneley waves

- Chapter 8 Electromagnetic et gravity waves

Field equations; Maxwell's relations; gravity waves

Lab work 1: ultrasonic wave propagation in homogeneous and heterogenous steel. Imaging with migration method

Lab work 2: Measure and inversion of Lamb wave dispersion curves

Lab work 3: Kundt's tube

This lecture is highly recommended to follow the Quantitative Seismology class in semester 9, and mandatory for the students of the Geophysics master.

### Prerequisites

- Linear algebra fundamental

- Basic spectral analysis

- Cartesian, cylindrical and spherical coordinates systems

- homogeneous and inhomogeneous differential equations

- Bessel and Hankel functions

### Targeted skills

In-depth analysis of a wave field (refraction, dispersion, attenuation, modal analysis...)

time-space and frequency-wavenumber analysis

wave propagation modeling