We quantify the effects of spatially heterogeneous noise sources and seismic processing on noise correlation measurements and their sensitivity to Earth structure. Using numerical wavefield simulations and adjoint techniques, we calculate interstation correlations and sensitivity kernels for arbitrarily distributed noise sources where—as in the real Earth—different frequencies are generated in different locations. While both heterogeneous noise sources and processing can have profound effects on noise correlation waveforms, narrow-band traveltime measurements are less affected, in accord with previous analytical studies. Sensitivities to Earth structure depend strongly on the source distribution and the processing scheme, and they reveal exotic frequency dependencies that go beyond the well-known frequency scaling of the Fresnel zone width. Our results indicate that modern full waveform inversion applied to noise correlations is not possible unless one of the following measures is taken: (1) properly account for noise source distribution and processing, or (2) limit measurements to phase or time shifts in narrow frequency bands. Failure to do so can lead to erroneous misfits, tomographic artefacts, and reduced resolutio
