Stability Analysis for Finite Difference Scheme Used for Seismic Imaging Using Amplitude and Phase Portrait

A finite difference scheme is produced when partial derivatives in the partial differential equation(s) governing a physical phenomenon like the propagation of seismic waves through real media are replaced by a finite difference approximation. The result is a single algebraic equation which, when solved, provide an approximation to the solution of the original partial differential equation at selected points of a solution grid. Stability of a numerical scheme like that of finite difference scheme in the solution of partial differential equations is crucial for correctness and validity and it means that the error caused by small perturbation in the numerical solution remains bound. This paper considers important concepts like the amplitude and phase portrait used to analyze the stability of finite difference scheme. Applying these concepts produces an amplification factor and celerity for the components of the numerical solution.