Yes, that is exactly what I meant by "elephant tracks", the finisher usually tapes the joints and applies only one coat of compound, maybe not even sanding that first coat. They put a little extra water in a bucket of joint compound, roll it on the ceiling with a heavy nap roller, then "stomp" the pattern in the compound with a round window brush on an extension pole.
To get rid of it: use a garden sprayer with water, wet a small space at a time to soften the compound and scrape it off with a scrapping hoe (blade in line with the handle) being careful not to gouge the sheetrock or get it too wet. After you scrape off all you can, use a pole sander to smooth it as much as possible (forget electric sanders, they'll choke you to death with dust), then apply a skim coat of compound with a 12" or longer concrete trowell, keep retrowelling until it is completely smooth without adding more compound. When you have done your best trowell job you will still have some hair like swirls which you can sand off with the pole sander after it is cured out well.