In shallow waters, it is physically possible to fix a platform to the sea floor. This is what is called a fixed platform rig. The 'legs' are structures made of concrete or steel, extending down from the platform, and fixed to the seafbed with piles. With some of the concrete fixed platform structures, the weight of the legs and seafloor platform is so great, that they do not have to be physically attached to the seafloor, but instead simply rest on their own mass. These are called gravity based fixed platforms.  There are many possible designs for these fixed, permanent platforms. The advantages of these types of fixed platforms are their good stability, as they are permanantly fixed to the sea floor there is no  movement due to wind and water forces. These platforms cannot be used in very deep water, it is not economical or practical to build legs that long.