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A hierarchical generalization of the acoustic reciprocity theorem involving higher-order derivatives and interaction
Ju Lin1, Jie Li1, Xiaolei Li1
1College of Information Science and Engineering, Ocean University of China, 238 Song Ling Road, Qingdao 266100, China julin97@gmail.com, jennyprc89@gmail.com, 1241137284@qq.com, wangyu@public.qd.cn.
Abstract:
An acoustic reciprocity theorem is generalized, for a smoothly varying perturbed medium, to a hierarchy of reciprocity theorems including higher-order derivatives of acoustic fields. The standard reciprocity theorem is the first member of the hierarchy. It is shown that the conservation of higher-order interaction quantities is related closely to higher-order derivative distributions of perturbed media. Then integral reciprocity theorems are obtained by applying Gauss's divergence theorem, which give explicit integral representations connecting higher-order interactions and higher-order derivative distributions of perturbed media. Some possible applications to an inverse problem are also discussed.
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