Acoustic tomography is now a well known method for remote estimation of water column properties. The problem is ill-conditioned and computationally intensive, if each spatial point varies freely in the inversion. Empirical orhogonal functions (EOFs) efficiently regularize the inversion, leading to a few (2, 3) coefficients to be estimated, giving a coherent estimate of the field. At small scales, EOFs are typically depth-dependent basis functions. The extension of the concept to larger-scale anisotropic fields requires horizontal discretization into cells, with corresponding coefficients. This becomes unstable and computationally intensive, having been overcome by two-dimensional depth-range EOFs, in the past. The present work extends the empirical orthogonal function concept to three dimensions, assessing the performance of the inversion for an instantaneous sound speed field constructed from dynamical predictions for Cabo Frio, Brazil. The results show that the large-scale features of the field are correctly estimated, though with strong ambiguity, using an acoustic source tens of km from an acoustic hydrophone array. Work is under progress, to remove the ambiguity and estimate finer details of the three-dimensional field, via the addition of multiple acoustic arrays.