In order to improve the computational efficiency of algorithms while exploring the method to overcome the ambiguity problems in underwater geo-acoustic inversion, we use the data of transmission losses at the broadband sound frequencies and multiple propagating distances with the matrix of polynomial chaos expansion coefficients of transmission losses to invert the speed (c), attenuation (a) of compression sound wave and the density ratio of seabed to seawater (r) in their prior searching

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... als. When approximating the transmission loss with the polynomial chaos expansion, the expansion coefficients are the functions of parameters including sound frequency, source and hydrophone's position while the polynomial bases are functions of the above geoacoustic parameters which are uniformly distributed in their respective intervals. The expansion coefficients are calculated by embedding the orthogonal polynomial bases into the acoustic wide-angle parabolic equation model. After that, the coefficients are deduced using the Galerkin projection and least angel regression. Under the situations of low sound frequency, short or medium sound propagation distance and short or medium length of intervals of geo-acoustic parameters, the polynomial chaos expansion can approximate the transmission losses accurately with the relatively error less than 1%. In the simulation case, with the high signal to noise ratio and the low errors of relative distances between source and receivers, the geo-acoustic parameters can be inverted accurately when the appropriate truncated powers are chosen. And the time cost is reduced by at least an order of magnitude compared with that of traversal grids searching procedure.