Mix a polyester resin with a filler, pigment and catalyst. Place in a mold. The catalyst initiates a chemical reaction that causes the resin to harden. The mixture comes together to become a solid piece of cultured marble. Coat the marble with a clear gel coat that produces the solid finish in whatever color or colors determined by the type of pigmet. You now have cultured marble that is harder than natural marble.
One choice for a rubbing compound is a car wax. The wax, or rubbing compound, comes in a paste or liquid. Its purpose is to restore the original luster to the gel coat. Using cleaning compounds does not restore the shine. A countertop wax also produces the same result as the automotive rubbing compound. Make sure the wax is non-abrasive.
Application of a rubbing compound on cultured marble requires an electric buffer. It is the quickest way to apply the rubbing compound. If you do not have access to a buffer or do not feel comfortable using one, then apply it by hand. A soft cloth is a substitute for the buffer pad. Careful application restores your cultured marble's original finish.
Use of a rubbing compound with or without an electric buffer is a project you can do by yourself. However, if there are deep scratches or chips, you may want to consider hiring a professional. Run your finger over the cultured marble. If you feel the scratch, it is probably deep enough to warrant a professional repair job.