The results of cross-correlation of seismic records depend on both the distribution of seismic sources and the structure in the vicinity of the path between the stations being correlated. The differences between the segments of the correlograms corresponding to opposite senses of propagation between the stations provide information on source excitation, while the properties of the dominant arrivals are mainly sensitive to structure.These properties can be exploited in inversion of the correlation wavefield, to extract both noise sources and Earth structure.

Descent methods of optimisation depend on calculating the derivatives of the composite function with respect to the large number of model parameters. Adjoint techniques allow the computation of derivatives in such complex models, with much less calculation than direct methods, and so enable practical non-linear inversion.Adjoint methods also allow effective computation of sensitivity kernels associated with the variation of critical parameters for both structure and sources. Sensitivity kernels can provide insight into the nature of Earth structure and the potential resolution of seismic tomography.