From the meaning of the question, we can know that the circle where ABCD is located is a small circle, the diagonal length is the root number 2, and the higher quarter of the pyramid is the root number 2.

Points S, A, B, C and D are all on the same sphere with a radius of 1. The distance from the center of the sphere to the center of the small circle is the root number 2, and the fixed point S is perpendicular to the distance from the center of the sphere.

On the plane bisected directly, and the distance from the vertex S to the center of the sphere is 1, so the distance from the center of the ground ABCD to the vertex S is 1.