dorsal/arxiv
View SchemaFocusing inversion technique applied to radar tomographic data
| Authors | G. Vignoli, L. Zanzi |
|---|---|
| Categories | |
| ArXiv ID | physics/0606243 |
| URL | https://arxiv.org/abs/physics/0606243 |
Abstract
Traveltime tomography is a very effective tool to reconstruct acoustic, seismic or electromagnetic wave speed distribution. To infer the velocity image of the medium from the measurements of first arrivals is a typical example of ill-posed problem. In the framework of Tikhonov regularization theory, in order to replace an ill-posed problem by a well-posed one and to get a unique and stable solution, a stabilizing functional (stabilizer) has to be introduced. The stabilizer selects the desired solution from a class of solutions with a specific physical and/or geometrical property; e.g., the existence of sharp boundaries separating media with different petrophysical parameters. Usually stabilizers based on maximum smoothness criteria are used during the inversion process; in these cases the solutions provide smooth images which, in many situations, do not describe the examined objects properly. Recently a new algorithm of direct minimization of the Tikhonov parametric functional with minimum support stabilizer has been introduced; it produces clear and focused images of targets with sharp boundaries. In this research we apply this new technique to real radar tomographic data and we compare the obtained result with the solution generated by the more traditional minimum norm stabilizer.
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"date_created": "2026-03-02T18:01:11.490000Z",
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"abstract": "Traveltime tomography is a very effective tool to reconstruct acoustic,\nseismic or electromagnetic wave speed distribution. To infer the velocity image\nof the medium from the measurements of first arrivals is a typical example of\nill-posed problem. In the framework of Tikhonov regularization theory, in order\nto replace an ill-posed problem by a well-posed one and to get a unique and\nstable solution, a stabilizing functional (stabilizer) has to be introduced.\nThe stabilizer selects the desired solution from a class of solutions with a\nspecific physical and/or geometrical property; e.g., the existence of sharp\nboundaries separating media with different petrophysical parameters. Usually\nstabilizers based on maximum smoothness criteria are used during the inversion\nprocess; in these cases the solutions provide smooth images which, in many\nsituations, do not describe the examined objects properly. Recently a new\nalgorithm of direct minimization of the Tikhonov parametric functional with\nminimum support stabilizer has been introduced; it produces clear and focused\nimages of targets with sharp boundaries. In this research we apply this new\ntechnique to real radar tomographic data and we compare the obtained result\nwith the solution generated by the more traditional minimum norm stabilizer.",
"arxiv_id": "physics/0606243",
"authors": [
"G. Vignoli",
"L. Zanzi"
],
"categories": [
"physics.geo-ph",
"physics.comp-ph"
],
"title": "Focusing inversion technique applied to radar tomographic data",
"url": "https://arxiv.org/abs/physics/0606243"
},
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