We demonstrate the existence of long-range field correlations in the seismic coda of regional records in Alaska. The cross correlations between the different components of coda records at two points are measured for a set of distant earthquakes. Remarkably, while individual correlations have a random character, the correlations averaged over source and time exhibit deterministic arrivals that obey the same symmetry rules as the Green tensor between the two points. In addition, the arrival times of these waves coincide with propagating surface waves between the two stations. Thus we propose to identify the averaged correlation signals with the surface wave part of the Green tensor. We observe the causal and anticausal parts of the Green function. However, we find experimentally that amplitudes at positive and negative times are not equal. We explain this observation by the long-lasting anisotropy of the diffuse field. We show that the flux of energy coming from the source can still dominate the late coda and result in nonsymmetric cross correlations when the distribution of earthquakes is not isotropic around the stations. The extraction of Green functions from coda waves allows new types of measurements with seismic waves along paths between stations that could not be obtained with the waves produced by earthquakes.