Abstract: Two simple noise models, namely isotropic noise and surface noise, are discussed regarding the spatial correlation of a noise vector field in this paper. Given that the interference noises of different sonar systems have different bandwidths and according to acoustic geometric theory and the Euler formula satisfied by harmonic plane waves, time-domain modeling is used to establish spatial correlation models of the vector fields of isotropic noise and surface noise, and their frequency bands are adjustable. An integral expression for the correlation function of the noise field and an analytical expression for the vertical correlation coefficient of the noise field are given. With the analytical solutions of the normalized spatial correlation functions, the single-frequency or narrowband results are obtained by calculation while taking the appropriate limit, and they are the same as those already presented in the literature. The results show that the change of the radiation noise spectrum structure of noise source affects the spatial correlation radius of broadband noise vector field. And the directivity of the noise source has a significant effect on the spatial correlation of the surface noise field in the vertical direction. Compared with the existing method for calculating the spatial correlation coefficient of broadband noise, the model can directly obtain the spatial correlation function of broadband noise through time domain modeling without requiring a numerical Fourier synthesis of the frequency domain formulations to do so.