Acoustic and elastic wave equations. Finite difference, finite element and pseudo spectral methods of modelling the wave equation. Green’s functions, Representation and Reciprocity theorem. Forward and adjoint wave equations. Lippmann-Schwinger equation and Born approximation. Ray theory: Eikonal and Transport equations. Initial value ray tracing and upwind solutions to the Eikonal equation.   Seismic attenuation analysis, Kramers-Kronig relations, constant Q models, viscoacoustic wave equation. Waveform inversion: frequency and time domain implementations, adjoint state method, optimization algorithms, role of misfit functions. Introduction and applications of Seismic interferometry. Ambient noise tomography and waveform inversion for noise sources and earth structure.