oa Reciprocity, Elastic GRT Inversion, Caustics, Multipathing

Linearized inversion can be derived from the reciprocity theorems of the time-convolution and the time-correlation types. The convolution-type theorem defines a mapping from medium contrast to scattered field, while the correlation type theorem defines its adjoint, viz. a mapping from scattered field to a quantity that relates to medium contrast. The time-correlation provides an error criterion for the data misfit as well as an imaging condition. The image is nothing else then the gradient of the error function (Tarantola 1984).