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Acoustical tomography of the ocean (ATO) is the particular case of more general inverse problems. One of the methods which give the exact solution of inverse problem is the functional-analytical approach (FAA). For the first time this approach was developed for the purposes of quantum-mechanical inverse problems for the scattering on potentials. The method allows to find the exact solution of the inverse problem even in situation when the inhomoheneity to be reconstructed is so strong that approaches, based on the iteration procedures, don't work properly. Such a property makes the FAA to be interesting if it could be valid for ATO. Previously it was shown that Novikov algorithm can be effectively applied for medical problems when initial data are scattering amplitudes. In the proposed work we present functional-analytical method which is based on the data from vertical line arrays surrounding the investigated area in the ocean. The present work contains first estimations of the possibility for using FAA in purposes of ATO. Results of numerical reconstruction of scalar inhomogeneity in the regarded tomography scheme will be presented. INTRODUCTIONAcoustic tomography is the only approach that allows to implement full monitoring (in time scale close to real time) of spatial and temporal variability of large oceanic areas. From a mathematical point of view the problem of ocean tomography is usually ill-conditioned and, as result, ill-posed problem. There are some known ways [1] how to solve the problem of acoustic tomography of the ocean. All these ways are approximate. The linear approximation is generally applied which allows to establish a simple relationship between characteristics of the ocean area under investigation and parameters of acoustic signals that have passed through this area. If the linear approximation is not valid, iterative procedures can be considered. In this work the algorithm is considered which can be used to obtain the rigorous (not approximated) solution of mode ocean tomography problem.The main idea is that ocean tomography is a particular case of inverse problems so common methods of inverse problems solution can be applied for the ocean tomography purposes. There are rigorous methods for solving the inverse problems -so-called functional-analytical methods [2, 3, 4], which were initially developed for quantum-mechanical purposes. Since the Schrödinger equation in the monochromatic (isoenergetic) case is the same as the Helmholtz equation up to notation, it gives the simple idea to apply methods which were developed in quantum mechanics for ocean acoustic applications. In this paper we consider the possibility of application of one such a functional-analytical method -the algorithm of R.G. Novikov [2] -for the purpose of mode tomography of the ocean. This method is mathematically rigorous; it does not require both a linearity of the model and implementation of iteration procedures. In the paper [5] the previous version of this algorithm has been numerically implemented when initial dat...