Short answer. Yes. Article 512 provides that explorations for subterranean waters on lands of public dominion may be made only with the permission of the administrative authorities — so digging on public land to search for underground water requires that permission first.
What the law says
Explorations for subterranean waters on lands of public dominion may be made only with the permission of the administrative authorities.
Civil Code, Article 512 — Exploring For Subterranean Waters. Read the full provision →
Private land needs the owner's permission
Article 512 first sets the rule for privately owned land: only the owner of a piece of land, or another person with his permission, may make explorations thereon for subterranean waters, except as provided by the Mining Law. On private property, the person controlling access is the landowner, and exploring without that owner's consent is not authorized by this article at all.
Public land requires permission from administrative authorities
The article then addresses land that belongs to the public rather than a private owner: explorations for subterranean waters on lands of public dominion may be made only with the permission of the administrative authorities. There is no private landowner to ask on public land, so the article substitutes the administrative authorities as the body whose permission is required before anyone may explore there for underground water.
The Mining Law carve-out
The article's rule for private land expressly yields to a separate body of law: the Mining Law. Where mining activity is involved, that specific law may set its own rules for exploration rather than this general Civil Code provision. If your digging touches on mining rather than simply searching for water, it is worth checking whether that separate framework applies to your situation instead, since it can impose its own permitting requirements distinct from the ones this article sets out.
What this means before you dig
Because the land in your question is public rather than private, the rule that applies is the one requiring permission from the administrative authorities, not the landowner-consent rule that governs private property. Digging to explore for subterranean water on public land without first securing that administrative permission is not something Article 512 authorizes, and proceeding without it leaves the exploration outside what this article permits regardless of your intentions.
Why the rule shifts from consent to permission on public land
Private land has an owner who can decide, case by case, whether to allow someone onto the property to explore for water. Land of public dominion has no equivalent private decision-maker, so Article 512 substitutes the administrative authorities as the body that exercises that same gatekeeping role on the public's behalf. The underlying idea in both branches of the article is the same — you need someone with actual authority over the land to say yes before exploring it for subterranean water — the only thing that changes is who that authority is.