A self-normalized statistic the modified modal scintillation index MMSI is proposed and defined as the variance of the modulus of modal excitation normalized by the square of its expected value over some observation intervals.It is proved in an analytical form that the MMSI is a depth dependent signature and independent of the source level and the source range under the condition of the ideal waveguide while the classical modal scintillation index MSI depends on both the source level and the source range.The MSI and the MMSI in the Pekeris waveguide at 70 Hz are simulated with different source levels and source ranges by the Kraken normal mode model.The simulation results are consistent with the theoretical deduction.The MMSI probability density functions PDFs of different normal modes for surface and submerged sources are calculated using the mode filtering methods with the same variations of vertical motions.It is indicated that the PDFs can be used to separate the submerged and the surface sources except for the fourth mode.
