The role of Moonquake hazard distribution (peak ground acceleration, PGA; instrumental intensity Moonquakes scale, IIM) on the co-seismic moment is critical for understanding the lunar quake (including the shallow and deep lunar quakes). Here, we use Lagrangian analysis methods and lunar surface image extraction-calibration technologies to investigate the relationship between the co-seismic induced ground motion (PGA and IIM) and the rolling trajectories of the lunar boulder on the lunar slope. First, the inverse algorithm, the validation of IIM (00.18g_m), the certain critical rolling condition between the PGA and the IIM, and the falling boulder are obtained. Then, the correlation between IIM scale (scale I, ~ 0 m⁄s^2 ; scale II, ~ 0.0017g_m; scale III, 0.0017g_m0.014g_m; scale IV, 0.014 g_m0.039g_m; scale V, 0.039 g_m0.092g_m; scale VI, 0.092g_m0.18g_m) and different parameters (e.g., lunar slope 1°44°; lasting time, t, 0.12s ; fixed PGA coefficient, the ratio of the vertical component to the horizontal component of PGA amplitude, A_y0⁄A_x0 =2) is simulated and discussed. All these results play an important role in understanding lunar quakes' mechanism and the internal structure evolution. The elevation extraction-calibration technologies with the particular software for automatically recognizing lunar-terrain observational images and data (e.g., high-resolution satellite lunar imagery from NASA's lunar reconnaissance orbiter narrow-angle camera) driven IIM with observational trajectories of the lunar boulder are presented in Part II and Part III of this three-paper series studies, respectively. We anticipate our studies to be a key point, give new insights for understanding the role of PGA and IIM, and help assess the stabilities of the rovers (e.g., Zhurong rover, Chang'e series rover) in China's Moon and Mars exploration program.