The dynamic characteristics and structural responses of operation and grid loss offshore wind turbines (OWTs) under onshore and seafloor earthquakes are analyzed based on the established coupled seismic analysis model. In addition to the remarkable influence of the rotor system on the responses of the operation OWT under earthquakes, interactions among the natural modes of the grid loss OWT in the fore-aft and side-to-side directions are revealed. By comparing with the onshore earthquakes, the more significant differences of structural response are observed under the selected seafloor earthquakes, due to the longer duration and more abundant energy distribution around the natural frequencies of OWT. Concurrently, a multiple tuned mass damper (MTMD) is designed and applied to the operation and grid loss OWTs. Then, the comparisons of the mitigation effects under onshore and seafloor ground motions are carried out, and the necessity of applying seafloor ground motions to OWTs are proved. Moreover, in comparison to the operation OWT, more effective reductions are observed for the grid loss OWT under onshore and seafloor earthquakes using the designed MTMD. Therefore, the combined shutdown procedures and MTMD vibration control strategy is suggested for OWTs under earthquakes. [ABSTRACT FROM AUTHOR]