EPSRC Reference: 
GR/R93582/01 
Title: 
Faraday Fast Track Proposal: Reconstruction of an Interface in an Inhomogeneous Medium 
Principal Investigator: 
Kurylev, Professor V 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
School of Mathematics 
Organisation: 
Loughborough University 
Scheme: 
Faraday (PreFEC) 
Starts: 
31 January 2003 
Ends: 
30 January 2005 
Value (£): 
104,392

EPSRC Research Topic Classifications: 
Continuum Mechanics 
Numerical Analysis 
Oil & Gas Extraction 


EPSRC Industrial Sector Classifications: 

Related Grants: 

Panel History: 

Summary on Grant Application Form 
The mathematical model of oil exploration gives rise to an inverse problem of the reconstruction of the velocity distribution in a mutticomponent medium, e.g sediments, oil, water, etc. The principal method used in oil exploration is inversion of kinematic data. However, this method gives large error in the reconstruction of the interface location when the velocity profile above the interface is not known accurately. We intend to develop a probabilistic method to solve the kinematic inverse problem. We start with a probability space of assumed velocity profiles and interface locations. Further measurements of travel time made during the drilling of boreholes are used to decrease the size of the probability space. This follows from the random wave equation, using ideas of nonlinear filtering and SPDEs. It is now common in oil exploration to measure both dynamic and kinematic data. We will use the dynamic data to improve the reconstruction of the velocity profile and interface locations, by developing the boundary control method for nonlinear, timedependent, multicomponent problems. Measurements are only available over a midfrequency range, thus we will use the method of Gaussian beams in the reconstruction.Both the kinematic and dynamic methods incur errors of different nature, which limit the resolution of reconstruction. Thus we propose to combine these two methods into a hybrid scheme which will utilise the best features of each approach.

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Organisation Website: 
http://www.lboro.ac.uk 