What will happen, where water or oil has been removed from under land near or adjacent to the sea, is that sea water will flow into the underground formation. Unless, of course, someone builds a desalinization plant and puts fresh water into the formation instead. (Yes, rivers can do this away from the sea, and if you can pipe in fresh water, great. Now apply this thinking to Los Angeles.)
Putting on my economist hat, there may be people pulling water or oil out of the ground, who may not like the idea of adding sea water. Some cases, you get secondary recovery by adding (salt or fresh) water to an oil producing formation. In those cases though, you don't have to worry about doing it, it is already being done.
Would it be worthwhile to study what is happening near cities like LA and Houston? If you can get the data, go right ahead. Hmm. Two sets of seismic data from the same location, several years apart, and you should be all set.