The mathematical definition of solid earths' surface,geoid and earth ellipsoid

According to the relation between solid earth X1 and air X2,vegetation X3and water body X4 existed border at different place,the author deduced the definition of land surface Sland and seabed surface Ssea,proceed to the next step deduced the definition of earths' surface Ssurface.Because geoid S0 is an equipotential surface of gravity,it has the same gravity potential value Wo,and according to this physical specific property we may give the definition of geoid S0.In the course of computatiom of inquire into optimal earth ellipsoid we must use a group of separation of geoid from ellipsoid,according to big or small of geographic value field of used data decide computational result is reference ellipsoid or sum earth ellipsoid,then give the mathematical expression for two earth ellipsoids.