Abstract Signal-to-Noise SKew Ratio (SNSKR) is defined and its mathematical formula is obtained. A novel analysis based on the SNSKR is presented. When ambient noise is asymmetrical distributed noise, the SNSKR is equal to or greater than the original Signal-to-Noise Ratio(SNR); whereas the SNSKR is theoretically infinite value if ambient noise is symmetrical distributed noise. Theoretic analysis and simulation results have shown that the analysis is valid and that it is unnecessary to assume that the ambient noise is Gaussian distribution or asymmetrical distribution when employing third-order cumulant slices extracts the underwater target-radiated quadratic phase dynamic coupling signals. These conclusions are significance in engineering.