As long as there is no specific prohibition that says "no metal detectors", then ........ there you go. It's not a prohibited acitivity. You wouldn't need "explicit consent from the parks dept", any more so than you would need "explicit consent" to fly a frisbee, for instance. To find out if there's any specific verbage, you can check the city website, and find the menus for city charter, laws, codes, etc.... There may even be a subsection specfically for the park's dept, with any rules they may have (dogs on leash, parks close at sunset, no alcahol, etc...). If you see nothing there about detectors, then there's your answer.
The issue (if one were to come up), is going to be about "digging", we all know. And any text you can find to that extent ("alterations", "defacement", etc....) all refer to the end result, when you think about it. Ie.: if you leave utterly no trace of your presence, then by definition, you have not "altered" or "defaced" anything! Sure *anyone* can take exception to these semantics, and anyone can be a kill-joy. You simply can not stop that. So you'll have to use a little discretion on your timing, and simply go at low-traffic odd hours, so as not be a "sore thumb". Or put another way: simply because there may not be an express disallowance of a certain activity, does not mean that, ergo, we can go at high traffic times and waltz over people's beach blankets. I mean, a certain level of sense to avoid persons who might draw connotations, is in order.