Guide to programming using RSF

Introduction

This section presents time-domain finite-difference modeling written with the RSF library. The program is demonstrated with the C, C++ and Fortran 90 interfaces.

The acoustic wave-equation

$$\Delta U - \frac{1}{v^2} \frac{\partial^2 U}{\partial t^2} = f(t)$$ (1)

can be written as

$$\left[ \Delta U - f(t) \right] v^2 = \frac{\partial^2 U}{\partial t^2} \;.$$ (2)

$\Delta$ is the Laplacian symbol, $f(t)$ is the source wavelet, $v$ is the velocity, and $U$ is a scalar wavefield.

A discrete time-step involves the following computations:

$$U_{i+1} = \left[ \Delta U -f(t) \right] v^2 \Delta t^2 + 2 U_{i} - U_{i-1} \;,$$ (3)

where $U_{i-1}$, $U_{i}$ and $U_{i+1}$ represent the propagating wavefield at various time steps.