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Title Algorithms and Software for Large-Scale Geophysical Reconstructions
Author Bruun, Christian Eske
Nielsen, Trine Brandt
Supervisor Hansen, Per Christian (Scientific Computing, Informatics and Mathematical Modelling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Institution Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
Thesis level Master's thesis
Year 2007
Abstract The main focus of the thesis is algorithms and software for large-scale geophysical reconstructions. Throughout the project we deal with a special Toeplitz structure of the coeffecient matrix that enables a significant loss-less compression. The geophysical surveying problems dealt with in the thesis are by nature ill-posed. For this reason we use regularization methods to perform the reconstuctions. The methods used in the paper are TSVD, Tikhonov, and CGLS. We will describe the constraints in the surveying problems that need to be met in order to achieve the Toeplitz structures. Aside from enabling compression the Toeplitz structures makes it possible to use a FFT matrix-vector multiplication to achieve fast multiplications in the regularization methods. Multi-level observation sets are used to meet the constraints and a Fourier based upward continuation method can be used to achieve the multi-levels, however, for forward problems we are able to compute levels at different altitudes. The performance of the upward continuation method is investigated. The result of this thesis is a Matlab object-oriented package implemented within the frameworks of MOOReTools and expands the existing GravMagTools package. The package is tested and reconstructions are performed.
Series IMM-Thesis-2007-29
Keywords Toeplitz structures; Large-scale inversions; Ill-posed problems; Compression; FFT matrix-vector multiplication; Regularization methods; Upward continuation; Object-oriented implementation; MOOReTools
Original PDF imm5257.pdf (5.50 MB)
Admin Creation date: 2007-06-11    Update date: 2007-09-21    Source: dtu    ID: 200689    Original MXD