Surface-generalized ambient noise in a shallow ocean waveguide with a sediment layer possessing a specific class of density and sound speed distributions capable of describing a realistic seabed environment is considered in this analysis. This class of non-uniform sediment layer has the density and sound speed distributions varying with respect to depth as a genearlized-exponential and an inverse-square function, respectively. The study invokes a formulation developed by Kuperman and Ingenito for surface noise generation, in conjunction with the analytical solutions for the Helmholtz equation corresponding to the sediment layer, to arrive at an analytical expression convenient for numerical implementation. The intensity and spatial correlation of the noise sound field are analyzed with respect to the variations of the system parameters, including frequency, sediment layer thickness, sound speed gradient, with emphasis on the effects of sediment properties on the ambient noise field. The results have demonstrated that the intensity of the noise field is relatively sensitive to the variations of the paramters, while the spatial correlation is not, suggesting that the energy distribution, rather than the spatial structure, of the noise field is susceptible to the environmental variation.