Abstract: In this paper, the general expressions of long-range average revedberation intensity in shallow water have been developed on the basis of the normal-mode thoery. Because the effects of the complex eigenvalues on the mode incident field have been considered, the results are more accurate than those in the former normal-mode theories of reverberation. In addition, for the sake of simplifying the calculations and making the results convenient to compare with the experiments, the reverberation intensity was smooth-averaged in space. The obtained expressions have obvious physical meaning and concise form so that they can be used for numerical calculation and analytical discussion. These expressions are suitable for wider types of velocity-profile, bottom-reflection and scattering coefficients.
When the source and receiver are at the same position, the reverberation intensity is expressed as I_R=\fracc_0\pi E_0r \int_a^c^x/2 \frac\sin (2a)\sigma (a)\exp - 2\beta (a)rdaS'(a)|V(a)|D(z) + sin ^2a(z)1/2D(h) + sin ^2a1/2^2
As an example, the average reverberation intensity in shallow-water with the thermocline is evaluated. The result shows that when both the source and receiver are located above the thermocline, the long-range revedberation intensity is proportional to r^-5. This result is in agreement with the experimental data.