We consider modeling seismic wave propagation in fluid-solid coupled media, in the perspective of seismic exploration in marine environments. The spectral element method is used for the spatial discretization due to its high accuracy in relatively smooth media and high computational efficiency through a domain-decomposition based parallelization. During the implementation, fluid and solid domains are divided explicitly and handled with the acoustic-wave and elastic-wave equation, respectively. The mutual interaction between these two wave equations is modeled by coupling conditions at the fluid-solid interface. The weak forms of 4 existing coupling formulations in terms of pressure, velocity potential, displacement potential and displacement are constructed respectively. Several benchmark tests are carried out to analyze their pros and cons in the spectral element method, from the aspects of complexity, accuracy and computational efficiency.