scholarly journals A VARIATIONAL APPROACH FOR GEOACOUSTIC INVERSION USING ADJOINT MODELING OF A PE APPROXIMATION MODEL WITH NON LOCAL IMPEDANCE BOUNDARY CONDITIONS

2004 ◽  
Author(s):  
J.-C. LE GAC ◽  
Y. STEPHAN ◽  
M. ASCH ◽  
P. HELLUY ◽  
J.-P. HERMAND
Keyword(s):  
Boundary Conditions ◽  
Variational Approach ◽  
Approximation Model ◽  
Geoacoustic Inversion ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions ◽  
Non Local ◽  
Adjoint Modeling

scholarly journals Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions

1997 ◽  
Vol 20 (2) ◽  
pp. 397-402 ◽  
Author(s):  
E. M. E. Zayed
Keyword(s):  
Riemannian Manifold ◽  
Boundary Conditions ◽  
Finite Number ◽  
Spectral Function ◽  
Compact Riemannian Manifold ◽  
Smooth Boundary ◽  
Beltrami Operator ◽  
Smooth Functions ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions

The spectral functionΘ(t)=∑i=1∞exp(−tλj), where{λj}j=1∞are the eigenvalues of the negative Laplace-Beltrami operator−Δ, is studied for a compact Riemannian manifoldΩof dimension “k” with a smooth boundary∂Ω, where a finite number of piecewise impedance boundary conditions(∂∂ni+γi)u=0on the parts∂Ωi(i=1,…,m)of the boundary∂Ωcan be considered, such that∂Ω=∪i=1m∂Ωi, andγi(i=1,…,m)are assumed to be smooth functions which are not strictly positive.

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