Abstract:
The method of empirical orthogonal functions is commonly used in tomography to select a set of basis vectors to represent variations in the sound-speed profile. In this method, historical profiles are used to estimate a profile covariance matrix, and the eigenvectors corresponding to the largest eigenvalues of the covariance matrix are taken for the basis vectors. These basis vectors are the most efficient parametrization of the variations in the profile. They are NOT, however, the parametrization which leads to the most accurate post-measurement estimate of the profile, because, in a tomographic experiment, all profile variations cannot be measured with the same accuracy. In this paper, the set of basis vectors, which will yield the least error in the post-measurement estimate of the profile, are derived taking into account measurement resolution and measurement noise. These improved empirical orthogonal functions are applied to several canonical problems in ocean acoustic tomography, and the resulting enhancement in estimation accuracy is demonstrated. [Work supported by ONR.]