B M Brown et al 2005 Inverse Problems 21 1953 doi:10.1088/0266-5611/21/6/010
A variational approach to an elastic inverse problem
B M Brown1, M Jais1 and I W Knowles2
Show affiliationsWe present a variational approach to the seismic inverse problem of determining the coefficients C and ρ of the hyperbolic system of partial differential equations 
from traction and displacement data measured on the surface. A crucial point of our approach will be a transformation of the above system to an elliptic system of partial differential equations 
Thus, we transform the inverse problem for a hyperbolic system to an inverse problem for an elliptic system. We give a definition of the direct and inverse seismic problem, where we distinguish between the isotropic and anisotropic cases. Further, we develop the theoretical results that we need for a successful recovery procedure of the coefficients C and ρ in the isotropic case. Our approach consists of a minimization procedure based on a conjugate gradient descent algorithm. Finally, we present various numerical results that show the effectiveness of our approach.
- PACS
- MSC
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35J50 Variational methods for elliptic systems
65K10 Optimization and variational techniques (See also 49Mxx, 93B40)
35R30 Inverse problems (undetermined coefficients, etc.) for PDE
- Subjects
- Dates
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Issue 6 (December 2005)
Received 14 April 2005, in final form 4 October 2005
Published 28 October 2005
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A variational approach to an elastic inverse problem
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