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Reciprocity. Kees Wapenaar Evert Slob Jacob Fokkema. Review of reciprocity theorems Convolution type Correlation type Unified notation Acoustic Elastodynamic Electromagnetic Poroelastic Seismoelectric Review of boundary conditions Extension of reciprocity theorems Conclusions.
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Reciprocity Kees Wapenaar Evert Slob Jacob Fokkema
Review of reciprocity theorems • Convolution type • Correlation type • Unified notation • Acoustic • Elastodynamic • Electromagnetic • Poroelastic • Seismoelectric • Review of boundary conditions • Extension of reciprocity theorems • Conclusions
Review of reciprocity theorems • Convolution type • Correlation type • Unified notation • Acoustic • Elastodynamic • Electromagnetic • Poroelastic • Seismoelectric • Review of boundary conditions • Extension of reciprocity theorems • Conclusions
A B A B ‘State A’ ‘State B’
A B A B ‘State A’ ‘State B’
V V n n State A State B Wave fields Sources Medium PA, Vk,A QA,Fk,A kA, rA PB, Vk,B QB,Fk,B kB, rB kA, rA kB, rB PB QB QA PA ‘State B’ ‘State A’
V V n n 0 0 0 0 PB QB QA PA ‘State B’ ‘State A’
V V n n PB QB QA PA ‘State B’ ‘State A’ Convolution-type reciprocity theorem: forward problems
Review of reciprocity theorems • Convolution type • Correlation type • Unified notation • Acoustic • Elastodynamic • Electromagnetic • Poroelastic • Seismoelectric • Review of boundary conditions • Extension of reciprocity theorems • Conclusions
V V n n PB QB QA PA ‘State B’ ‘State A’ Correlation-type reciprocity theorem
V V n n Q Q P P ‘State B’ ‘State A’ Power-flux through boundary Power dissipated in medium Power radiated by sources
V V n n PB QB QA PA ‘State B’ ‘State A’ Correlation-type reciprocity theorem: inverse problems
Review of reciprocity theorems • Convolution type • Correlation type • Unified notation • Acoustic • Elastodynamic • Electromagnetic • Poroelastic • Seismoelectric • Review of boundary conditions • Extension of reciprocity theorems • Conclusions
V V n n PB QB QA PA ‘State B’ ‘State A’ Convolution-type reciprocity theorem
Review of reciprocity theorems • Convolution type • Correlation type • Unified notation • Acoustic • Elastodynamic • Electromagnetic • Poroelastic • Seismoelectric • Review of boundary conditions • Extension of reciprocity theorems • Conclusions
Electromagnetic: Acoustic: Poroelastic: Elastodynamic: Seismoelectric:
V V n n PB QB QA PA ‘State B’ ‘State A’ Correlation-type reciprocity theorem
V V n n PB QB QA PA ‘State B’ ‘State A’
Unified notation (convolution type): Unified notation (correlation type):
Review of reciprocity theorems • Convolution type • Correlation type • Unified notation • Acoustic • Elastodynamic • Electromagnetic • Poroelastic • Seismoelectric • Review of boundary conditions • Extension of reciprocity theorems • Conclusions
n n V V PB QB QA PA ‘State B’ ‘State A’ Perfectly coupled interfaces: No consequences for reciprocitytheorems of convolution type and correlation type Next: consider partially coupled interfaces
Review of linear slip model Displacement jump:
Review of linear slip model of Pyrak-Nolte et al. Frequency domain
diagonal Schoenberg, Pyrak-Nolte et al: Nakagawa et al.: full matrix, with Generalization: Review of linear slip model
Arbitrary interface: Horizontal interface:
Electromagnetic: Acoustic: Poroelastic: Elastodynamic: Seismoelectric:
Review of reciprocity theorems • Convolution type • Correlation type • Unified notation • Acoustic • Elastodynamic • Electromagnetic • Poroelastic • Seismoelectric • Review of boundary conditions • Extension of reciprocity theorems • Conclusions
n n V V PB QB QA PA ‘State B’ ‘State A’
0 0 0 n n V V PB QB QA PA ‘State B’ ‘State A’
n n V V PB QB QA PA ‘State B’ ‘State A’ Convolution-type reciprocity theorem: forward problems
n n V V PB QB QA PA ‘State B’ ‘State A’ Correlation-type reciprocity theorem
Q Q P P n n V V ‘State B’ ‘State A’ Power-flux through boundary Power dissipated in medium Power radiated by sources Power dissipated by interfaces
n n V V PB QB QA PA ‘State B’ ‘State A’ Correlation-type reciprocity theorem: inverse problems
Review of reciprocity theorems • Convolution type • Correlation type • Unified notation • Acoustic • Elastodynamic • Electromagnetic • Poroelastic • Seismoelectric • Review of boundary conditions • Extension of reciprocity theorems • Conclusions
Unified reciprocity theorems have been formulated of the convolution and correlation type
Unified reciprocity theorems have been formulated of the convolution and correlation type Valid for acoustic, elastodynamic, electromagnetic, poroelastic and seismoelectric waves
Unified reciprocity theorems have been formulated of the convolution and correlation type Valid for acoustic, elastodynamic, electromagnetic, poroelastic and seismoelectric waves Boundary condition for imperfectly coupled interface:
Unified reciprocity theorems have been formulated of the convolution and correlation type Valid for acoustic, elastodynamic, electromagnetic, poroelastic and seismoelectric waves Boundary condition for imperfectly coupled interface: No effects on source-receiver reciprocity
Unified reciprocity theorems have been formulated of the convolution and correlation type Valid for acoustic, elastodynamic, electromagnetic, poroelastic and seismoelectric waves Boundary condition for imperfectly coupled interface: No effects on source-receiver reciprocity Imaginary part of accounts for dissipation by interfaces