On the inverse gravimetry problem with minimal data
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Victor Isakov
Abstract
The inverse problem in gravimetry is to find a domain đ· inside the reference domain Ω from measurements of gravitational force outside Ω.
We consider the problem in three dimensions where we found that a few parameters of the unknown đ· can be stably determined given data noise in practical situations.
An ellipsoid is the best approximation of đ·.
We prove uniqueness of recovering an ellipsoid in a particular case for the inverse problem from minimal amount of data which are the approximated gravitational force at nine boundary points.
In the proofs, we derive and use simple systems of linear and nonlinear algebraic equations for the parameters of an ellipsoid.
Similarly, a rectangular parallelepiped đ· is considered.
To support our theory, we use numerical examples with different location of measurements points on
Funding source: National Science Foundation
Award Identifier / Grant number: DMS 20-08154
Funding statement: This research is supported in part by the Emylou Keith and Betty Dutcher Distinguished Professorship and the NSF grant DMS 20-08154.
References
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Articles in the same Issue
- Frontmatter
- Parameter identification for portfolio optimization with a slow stochastic factor
- Simultaneous inversion of a fractional order and a space source term in an anomalous diffusion model
- On the inverse gravimetry problem with minimal data
- On stable parameter estimation and short-term forecasting with quantified uncertainty with application to COVID-19 transmission
- Uniqueness for inverse source problems of determining a space-dependent source in thermoelastic systems
- Convergence analysis of iteratively regularized GaussâNewton method with frozen derivative in Banach spaces
- Identification of an unknown flexural rigidity of a cantilever EulerâBernoulli beam from measured boundary deflection
- Hadamardâs example and solvability of the mixed Cauchy problem for the multidimensional Gellerstedt equation
- Ill-posed problems and the conjugate gradient method: Optimal convergence rates in the presence of discretization and modelling errors
- Simultaneous determination of mass density and flexural rigidity of the damped EulerâBernoulli beam from two boundary measured outputs
