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Keywords:

  • Numerical solutions;
  • Numerical approximations and analysis;
  • Computational seismology;
  • Wave propagation

SUMMARY

As the first step towards a general analysis of the stability of optimally accurate predictor–corrector (P–C) time domain discretized schemes for solving the elastic equation of motion, we analyze the stability of two P–C schemes for a 1-D homogeneous case. Letting Δt be the time step, h be the spatial grid interval, β be the velocity of seismic wave propagation and inline image be the dimensionless Courant parameter, we find that each scheme has the following stability properties: stability for inline image, instability for inline image, stability for inline image and instability for inline image, where inline image. We refer to the region inline image as the second island of stability. The values of inline image, inline image and inline image are scheme-dependent. The existence of a second island of stability in a numerical scheme for solving the wave equation has not, to our knowledge, been previously reported.