A numerical tour of wave propagation |

**Pengliang Yang**

Xi'an Jiaotong University, Xi'an, China, 710049

This tutorial is written for beginners as an introduction to basic wave propagation using finite difference method, from acoustic and elastic wave modeling, to reverse time migration and full waveform inversion. Most of the theoretical delineations summarized in this tutorial have been implemented in Madagascar with Matlab, C and CUDA programming, which will benefit readers' further study.

- Basic wave equation

- Forward modeling
- Taylor and Páde expansion
- Approximate the wave equation
- Absorbing boundary condition (ABC)
- Perfectly Matched Layer (PML)
- Discretization

- Reverse time migration (RTM)
- Brief overview
- RTM implementation
- Imaging condition
- Computation strategies and boundary saving
- Numerical examples

- Full waveform inversion (FWI)
- The Newton, Gauss-Newton, and steepest-descent methods
- Conjugate gradient (CG) implementation
- Fréchet derivative
- Gradient computation

- Numerical results
- Acknowledgement
- Bibliography
- About this document ...

2014-05-30