( ( ( ( The ( displacement vector ) ) and ) ( the ( radiation pattern ) ) ) ( ( defined ( as ( ( ( a modulus ) ( of ( ( the amplitude ) ( of ( ( the ( displacement vector ) ) ( measured ( on ( ( a ( unit sphere ) ) ( around ( the source ) ) ) ) ) ) ) ) ) ) ( ( are both ) ( proportional ( to ( ( the ratio ) ( of ( ( ( the ( directivity function ) ) and ) ( the ( geometrical spreading ) ) ) ) ) ) ) ) ) ) ) . ) )
(ROOT (S (NP (NP (DT The) (JJ displacement) (NN vector)) (CC and) (NP (DT the) (NN radiation) (NN pattern))) (VP (VBD defined) (SBAR (IN as) (S (NP (NP (DT a) (NNS modulus)) (PP (IN of) (NP (NP (DT the) (NN amplitude)) (PP (IN of) (NP (NP (DT the) (JJ displacement) (NN vector)) (VP (VBN measured) (PP (IN on) (NP (NP (DT a) (NN unit) (NN sphere)) (PP (IN around) (NP (DT the) (NN source))))))))))) (VP (VBP are) (DT both) (ADJP (JJ proportional) (PP (TO to) (NP (NP (DT the) (NN ratio)) (PP (IN of) (NP (NP (DT the) (JJ directivity) (NN function)) (CC and) (NP (DT the) (JJ geometrical) (NN spreading))))))))))) (. .)))
The displacement vector and the radiation pattern defined as a modulus of the amplitude of the displacement vector measured on a unit sphere around the source are both proportional to the ratio of the directivity function and the geometrical spreading.
(ROOT (S (NP (NNP Vector)) (VP (VBZ is) (NP (NP (DT a) (NN measure)) (SBAR (WHNP (WDT that)) (S (VP (VBZ has) (NP (DT both) (NN size) (CC and) (NN direction))))))) (. .)))