Analytic expressions are derived for the spatial covariance of the field from a point source after forward propagation though a waveguide containing random surface and volume inhomogeneities. It is shown that the depth-averaged second moment and expected power of the forward propagated field can be obtained analytically. The mean forward propagated field has also been obtained analytically in terms of modal attenuation and dispersion coefficients in a waveguide [P. Ratilal and N. C. Makris 112, 2403 (2002)]. The covariance between two receiver depths of the forward propagated field through the entire random medium can then be determined by invoking the equi-partition of modal energy after significant multiple scattering. It is expressible as a sum of modal covariance terms. Each term depends on (1) the modal extinction cross-section [P. Ratilal and N. C. Makris, 110, 2924-2945 (2001)] of an expected elemental inhomogeneity of the medium, and (2) the scatter function variance of an elemental inhomogeneity which couples each mode to all the other modes.