This is a hazard, so you are right to resolve the situation.

Trace the cable back to where it's fed inside the house, and disconnect it at that point. Ideally you'd remove the cable entirely. However, once it's disconnected, you can abandon it in place by cutting it off short enough that it can't be reconnected.

If you can't find where the cable terminates inside, call a pro for help.

If it's buried that shallowly, you can probably just get a good grip on it and rip it up. I'd look around the exterior of the house for possible emergence of the wire (either bare or through some ersatz piece of conduit or a pipe). Possibly it's tapped into an existing exterior light or receptacle.

I don't think that the wire itself is buried that shallow, it seems to be coming up vertically - this is just the end point where the post used to be. I can't find where it exits the house.. There aren't any light switches that don't do anything so I figure it was either an automatic post or tied in with the other exterior lights.

Is it possible just to terminate the wire in some sort of underground rated box?

I wouldn't want to handle any wire if I didn't know the power was off. Perhaps that pop you heard tripped a breaker or blew a fuse. If you know how, check your circuit box and that may identify the branch for you. If so, put in a new fuse or throw the breaker and see if the line is now live by using a device that senses an electric field (HD). Now you know how to deactivate the line and you can safely terminate it by whatever means seems safest to you. I hope you might be able to trace it from the circuit box to where it heads off through a wall into the yard and cut the line at that point rather than living a live wire in the yard to hurt someone in the future.

If you are unsure of any of this, call a pro. No sense in killing yourself over a couple of hundred dollars.

Uh, how can a live wire be grounded in the soil and not either throw the circuit breaker or run up a huge power bill?

"Uh, how can a live wire be grounded in the soil and not either throw the circuit breaker or run up a huge power bill?"

At 120 V the soil is often not that good a conductor.

Unless you manage to have enough current flowing to trip a breaker (normally at least 15 A, and possibly 20 A) the breaker is not going to repsond since no over-current condition exists.

The same for power dissipation.

Even if you had 10 A leakage, that is only 1,200 W, or 1.2 kW.
While you might see a rise on your bill since you are using 28.8 kW-hr per day, depending on the electric rate it might not be that high.

At $0.07 per kW-hr it is only about $2 a day, or about $60 a month.

Many bills wander around that much from heating and cooling.

To even pull 10 amps requires a resistance of 12 ohms, not likely long term.

If a GFCI device was present the odds are it would have tripped since they are sensitive down to about 6 mA (0.006 A) of current imbalance.

Thanks, Brickeye.

Say, could he very carefully (with rubber gloves, not standing in water -etc) hook a light bulb or tester to the wire and turn off breakers till he found the right circuit?

A non-contact tester would probably be easiest. While these aren't foolproof, they'll be good enough to tell when the right breaker was tripped.
You can get them for under $20 at the home center.

How someone could have left a land mine like that in a yard and sleep at night is beyond me.