Effects of tool positions on borehole acoustic measurements : a stretched grid finite difference approach

This dissertation made three contributions to numerical simulation and borehole acoustic logging. The first one is a novel finite difference time domain algorithm that features non- uniform grid, wavelet-based difference operator and anisotropic perfectly matched layer. This algorithm reduces numerical reflections and wave distortions introduced by grid change to a minimum by sampling the physical space with gradually varying mesh. By coordinate stretching, the algorithm discretizes the physical space with variable grid, while solving the wave equation on a uniform mesh. That approach helps retain the advantages pertaining to uniform mesh. Further improvement in efficiency is achieved without losing accuracy by the development of a wavelet-based difference operator. By using a family of compactly supported wavelet function, the wavelet- based finite difference time domain algorithm allows less grid point per wavelength. Coordinate stretching is also employed in deriving an anisotropic perfectly matched layer, superior to currently available perfectly matched layer formulation which re quires field splitting, a process that results in more computer memory requirement for the storage of extra variables. Validations of the algorithm include comparison with analytical solutions, uniform grid FDTD solutions and discrete wavenumber results. The second contribution is a time domain investigation of wave propagations in the logging while drilling situation. Logging while drilling is an emerging downhole acoustic acquisition method. The investigation is focused on soft formations where formation shear velocity is slower than borehole fluid velocity, because shear velocity measurement, one of the key measurements that acoustic logging is designed

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Earth, Atmospheric, and Planetary Sciences.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2003

Author dc:creator

• Huang, Xiaojun, 1970-

Advisor dc:contributor.advisor

• M. Nafi Toksöz.

• Earth, Atmospheric, and Planetary Sciences.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/7962

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/7962