A brief construction£º NMPQ,the MATLAB version underwater sound field program is used to calculate the complex wavenumbers and eigen functions of the normal modes. The bottom is charactered by reflection phase-shift parameter P and attenuation parameter Q, which are information concentrated compared with the geoacoustic parameters. The main function is NMPQ.m, and all the environment parameters are inputed in the main function. The detailed instructions can be found in the xx.m files. For more details of the PQ-characterazation of the sea bottom firstly proposed by prof.E.C.Shang, several references is provided here: [1] T.C. Wang and E.C. Shang, ¡°Underwater Acoustics¡±, Ch.4, Science Press, Beijing, 1981 (in Chinese). [2] E.C.Shang et al, ¡°Numerical program of normal mode in shallow water,¡±Acta Ocean. 7, 212-224, 1985. [3] E.C. Shang, T.F. Gao and J.R. Wu, ¡°A shallow-water reverberation model based on perturbation theory,¡± IEEE-JOE, 33, pp.451-461, 2008. [4] Shi-hong Zhou, et al, ¡°Propagation modeling in shallow-water based on characteristic bottom reflection parameters and its application to source localization¡°, Proceedings of ICTCA2005 (II), pp.314-322, China, 2005 [5] H.L. Ge et al, ¡°Bottom reflection phase-shift estimation from ASIAX data,¡± IEEE-JOE, 29, No.4, pp. 1045-1049, (2004). [6] E.C. Shang, J.R. Wu and Z.D. Zhao, ¡°Relating waveguide invariant and bottom reflection phase-shift parameter P in a Pekeris waveguide,¡± JASA, 131, pp. 3691-3697, 2012. [7] Z.D. Zhao, Li Ma and E.C. Shang, Modeling of Green's Function with bottom reflection parameter (P, Q) instead of GA parameters, Journal of Computational Acoustics. 22(1), 1-16, 2014 For more information or any advice, please contact: shangerchang32@aol.com zhaozhendong@aliyun.com