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Efforts to characterize environmental parameters from ambient noise must contend with uncertainty introduced by stochastic fluctuations of the noise itself. This Letter calculates the Fisher information and Cramer-Rao bound of an unbiased correlated ambient noise parameter estimate. As an illustration, lower bounds on the error covariance of medium speed and attenuation parameters are obtained for a two-dimensional isotropic ambient noise scenario. The results demonstrate that an optimal sensor separation exists for obtaining the minimum error and the predictions are validated using simulated parameter inversions. The influences of record length, bandwidth, signal-to-noise, and spatial resolution are discussed.

Using Fisher information to quantify uncertainty in environmental parameters estimated from correlated ambient noise