We carried out benchmark tests for the strong motion simulation methods using various theoretical methods (the wavenumber integration method, the discrete wavenumber method, and the thin layer method). All the results generally show good agreements, but the results for damping media show large discrepancies, especially in the later phases at very far stations. This is because the most methods used the quality factors of the complex parts of the medium velocities, whereas one method used the factors not only in the complex parts, but also in the real parts, in order to satisfy the causality condition in the waveforms.
