[Funny Math Art] Guess what's inside?

The surface in above image is a portion of the graph of
some mathematical equation.

Let's do some brainstorming:
Can you guess what's inside the surface?

Hint:
Consider the intersection of a horizontal plane with
the surface.
.

Hint:

Consider the intersection of a horizontal plane with the surface.

The intersection consists of a family of funny curves.
(An example curve is shown below. It has nothing to do with the answer.)

Cut off the upper surface above the horizontal plane to get a funny 3D image.


(This curve is obtained from another surface.)

Answers:

A funny 3D image:


A funny curve:


The above graphics were created completely using math formulas and math softwares.