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Abstract We develop a linearized boundary control method for the inverse boundary value problem of determining a potential in the acoustic wave equation from the Neumann-to-Dirichlet map. When the linearization is at the zero potential, we derive a reconstruction formula based on the boundary control method and prove that it is of Lipschitz-type stability. When the linearization is at a nonzero potential, we prove that the problem is of Hölder-type stability in two and higher dimensions. The proposed reconstruction formula is implemented and evaluated using several numerical experiments to validate its feasibility.
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Linearized boundary control method for density reconstruction in acoustic wave equations
Abstract We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the linearized Neumann-to-Dirichlet map. A key ingredient in the derivation is a linearized Blagoves̆c̆enskiĭ’s identity with a free parameter. When the linearization is at a constant background density, we derive two reconstructive algorithms with stability estimates based on the boundary control method. When the linearization is at a non-constant background density, we establish an increasing stability estimate for the recovery of the density perturbation. The proposed reconstruction algorithms are implemented and validated with several numerical experiments to demonstrate the feasibility.
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- PAR ID:
- 10559873
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Inverse Problems
- Volume:
- 40
- Issue:
- 12
- ISSN:
- 0266-5611
- Format(s):
- Medium: X Size: Article No. 125031
- Size(s):
- Article No. 125031
- Sponsoring Org:
- National Science Foundation
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