Random inhomogeneities in an elastic half‐space generate scattered P and S waves when excited by a spherical P wave initiated at the surface. The scattered energy can be characterized by statistical correlations of the displacement components at two receivers on the free surface. Based on the assumptions of far‐field Rayleigh scattering, a simple perturbation theory, and the neglection of boundary effects, simple expressions can be obtained for the correlations. They are composed of weighted sums of partial correlations which are associated with combinations of P and S waves arriving at the two receivers. The partial correlations depend on the times at the two receivers, the distance between the source and the receivers, and the separation between the receivers. The weighting factors depend on the statistical properties of the random elastic parameters. Although the analysis is carried out for an impulsive source, the correlations for a more general source can be found by performing a single convolution. If the transient input pulse is appropriately prefiltered before convolution, the effects of energy loss during propagation can be taken into account, approximately.