E0-190-2008_(10)1D_Shear_Propagation(SHAKE)

That is j 32 uj ujzj0 j zjdj2 j zj dj jjzjdj2

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Unformatted text preview: j=0) ( j) zj=dj/2 ( j) Zj dj Γj=Γj(zj=dj/2) ( j+1) dU j ( z j ) dz j = ik j {E j e Uj+1=Uj+1(zj+1=0) Zj+1 z j = d j / 2 i( k j d j / 2 ) − Fj e ( j+1) − i( k j d j / 2 ) } (33) In Eq.(29): (29) putting j=n, then: {Cn +1 } = [ A n ]{Cn } (34) Furthermore, putting j=n-1, {Cn } = [ A n −1 ]{Cn −1 } (35) Substituting Eq.(35) into Eq.(34), then: (36) Repeating the calculations from Eq.(34) to Eq.(36) up to j=1, {Cn +1 } = [ A n ]{Cn } {Cn } = [ A n −1 ]{Cn −1 } (34) (35) (36) we obtain: {Cn +1 } = [ A n ][ A n −1 ]{Cn −1 } = ⋅⋅⋅ (37) Putting, (38) then, Eq.(37) can be rewritten by: (39) Expressing Eq.(39) : (39) by the elements in the vectors and the matrix, then (40) where, (41) EO: the amplitude of incident wave Eq.(39) or Eq.(40) : G.L (40) express the relation of the displacement amplitudes between {En+1(=EO) F n+1}T of the waves in the deepest stratum (n+1) and {E1 F1}T in the shallowest stratum 1. (1) E1 F1 (2) E2 F2 . . . (j) Fj . . . (n) In Eq.(40),...
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