The discrete wavenumber method is one of the techniques to simulate earthquake ground motions for a layered half-space. In the discrete wavenumber method, a seismic wave radiated from a source is expressed as an wavenumber integration. As long as the medium has no inelastic damping, however, the denominator of the integrand becomes zero for a particular wavenumber and the numerical integration becomes impossible. To solve this problem, a method to incorporate complex frequency was proposed as early as the proposal of the discrete wavenumber method itself. The numerical accuracy of a discrete wavenumber method with complex frequency, however, has not been fully verified. On the other hand, in the near-source region of an earthquake, the near-field term or the intermediate-field term often causes a displacement waveform with a residual displacement. Such a displacement waveform can theoretically be computed using a discrete wavenumber method with a complex wavenumber. The numerical accuracy of the residual displacement for such a case has not been fully verified either. The results of the verifications are reported in this technical note. The results can be summarized as follows.
1. The results of a discrete wavenumber method with complex frequency are compared with the results of a discrete wavenumbermethod with real frequency for a case including remarkable surfacewaves. A very good agreement was found both for the amplitude andthe phase, indicating the numerical accuracy of the discretewavenumber method with complex frequency.
2. The residual displacements computed using the discrete wavenumbermethod with complex frequency are compared with theoretical valuesfor a half-space. The values agree very well, indicating thenumerical accuracy of the residual displacements computed using thediscrete wavenumber method with complex frequency.
　A FORTRAN program newly developed for this research is available on the attached CD.