The vertical accelerogram recorded at the IWTH25 site located just above the earthquake fault of the 2008 Mw 6.9 Iwate–Miyagi inland earthquake showed nonlinear dynamics because of intrawave frequency modulation with a maximum amplitude close to 4g, due to the nonlinear response of the near-surface layer at the site. In the present paper, a stochastic second-order model is proposed to explain these observations. The dynamics of the model are determined by the configuration of three pairs of complex conjugated poles in the z-transform domain, and the dynamics of these poles are interpreted in terms of the instantaneous frequency of the recorded acceleration signal. The results of simulations using the proposed model show overall agreement with the recorded accelerogram, including its maximum amplitude and its time of appearance. The physical mechanism producing the displacement waveform is found to be analogous to a ball bouncing on a vibrating surface. From the simulated and recorded seismograms, it was apparent that at least two consecutive high bounces are required to produce extremely high accelerations of close to 4g.