A recipe for stability analysis of finite-difference wave equation computations

Laurence R. Lines, Raphael Slawinski and R. Phillip Bording

Finite-difference solutions to the wave equation are pervasive in the modeling of seismic wave propagation (Kelly and Marfurt, 1990) and in seismic imaging (Bording and Lines, 1997). That is, they are useful for the forward problem (modeling) and the inverse problem (migration). In computational solutions to the wave equation, it is necessary to be aware of conditions for numerical stability. In this short note, we examine a convenient recipe for insuring stability in our finite-difference solutions to the wave equation. The stability analysis for finite-difference solutions of partial differential equations is handled using a method originally developed by Von Neumann and described by Press et al. (1986, p. 827-830).

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