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A person inside an underwater viewing pod in the hull of a catamaran watches bottlenose dolphins off the southern California coast on Jan. 30, 2012 near Dana Point, Calif.

By msnbc.com staff and news services - The lawsuit, filed in U.S. District Court in San Francisco, claims that the Navy's sonar use might be strong enough to kill the animals outright. But even if it doesn't, it claims, the repeated use of sonar in certain critical habitats is unwarranted.

The alliance said it wasn't seeking to stop the testing but to scale it back, especially at certain times and in waters important for feeding and giving birth.

Several studies have found that marine mammals can hear low-frequency sonar, which is magnified under water, and periodically dolphins and even whales have been found with perforated ear drums.