Ocean Bottom Node (OBN) acquisition is becoming popular in the exploration of challenging marine environments. A major advantage over conventional streamer acquisition is its ability of capturing converted wave by recording both P-and S-wave on the solid seabed. Thus, to study and process OBN data, modeling of seismic wave propagation in fluid-solid coupled media needs to be taken into account. In this study, we apply a partitioned approach to fluid-solid coupled media. Fluid and solid domains are divided explicitly and handled with the acoustic-wave and (visco)elastic-wave equation, respectively. The mutual interaction between these two wave-equations is modeled by boundary conditions at the fluid-solid interface. This leads to a coupled acoustic-(visco)elastic wave-equation system. According to the wavefield variables used in the acoustic-wave equation, we compare 4 acoustic-(visco)elastic coupled formulations in terms of pressure, velocity potential, displacement potential and displacement, respectively. The spectral-element method (SEM) is used as a numerical modeling tool to reveal their pros and cons from the aspects of complexity, accuracy and computational efficiency. Finally, we present various fluid-solid coupled modeling examples including isotropic elastic, anisotropic elastic (VTI and TTI) and anelastic media on the Cartesian-based hexahedral mesh. They are all implemented with the displacement potential formulation which achieves the best trade-off compared with the other three.