Integral equation method for the vector wavefield

In Chapter 13 we derived a general integral representation of the frequency domain wavefield (13.92), which can be written for an incident field as 

Note that we can show, by methods analogous to those used in deriving the reciprocity theorem 27 (formula (14.24)) for a scalar wavefield, that Gj satisfies the reciprocity relationship  

It can be also shown that G is a symmetric tensor (Morse and Feshbach, 1953) in other words  

Based on these properties of the Green s tensor, we can write expression (14.74) in the equivalent form  

Applying the integral representation (14.78) to the scattered field satisfying equation (14.73), we obtain 

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