| EPSRC Reference: |
GR/S79664/01 |
| Title: |
Inverse Problems in a Laterally Varying Multicomponent Layered Medium |
| Principal Investigator: |
Kurylev, Professor V |
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| Department: |
School of Mathematics |
| Organisation: |
Loughborough University |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 May 2004 |
Ends: |
31 July 2005 |
Value (£): |
3,566
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| EPSRC Research Topic Classifications: |
| Continuum Mechanics |
Non-linear Systems Mathematics |
| Numerical Analysis |
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Summary on Grant Application Form |
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Describe the proposed research using (about 200) words geared to the non-specialist reader.In many models in oil-exploration and seismology, the elastic parameters depend mainly on the depth - z, with only slow dependence on the horizontal coordinates. Using acoustic approximation, this means that the governing wave equation isutt -C2(Ext) u=O, E<<1, Z>0 We intend to develop a perturbation type method of solving an inverse problem of reconstruction of velocity and interfaces from measured dynamic data on the ground surface z=0. Chosen anzatz will be based on an exact solution of the fully non-linear inverse problem for a layered media . To this end Blagovestchenskii method which reduces the one-dimensional inverse problem in the time-domain to non-linear Volterra type integral equations will be used. Being convenien t for numerical implementations and applicable to the multicomponent case, we believe that Blagovestchenskii method can be used as a basis for a perturbation scheme to solve inverse problem for laterally varying multicomponent layered media. We will.analyse stability properties of the recurrent equations of the perturbation scheme. We expect to achieve Holder type stability estimates dramatically improving on logarithmic type estimates traditional for multidimensional inverse problems. We will develop an algorithm for numerical solution of the inverse problem under consideration and test it on several model examples.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.lboro.ac.uk |