HR: 1340h
AN: S33A-0310    [Abstracts]
TI: Regularization and L-curve in Cross-hole and VSP Diffraction Tomography
AU: * Bassrei, A
EM: bassrei@ufba.br
AF: IF/UFBA and CPGG/UFBA, Instituto de Geociencias, Campus Universitario de Ondina, Salvador, BA 40170-290 Brazil
AU: Santos, E T
EM: eduardot@ufba.br
AF: CEFET-BA and IGEO/UFBA, Instituto de Geociencias, Campus Universitario de Ondina, Salvador, BA 40170-290 Brazil
AB: The main objective of exploration geophysics for hydrocarbons is to provide trustworthy images of the subsurface, which could indicate potential hydrocarbons reservoirs. Exploration seismology, known better as seismics is the area of applied geophysics most employed for the subsurface imaging. And within seismics, tomography was incorporated as a method of data inversion. Inverse problems have some limitations in such a way that they are said to be ill-posed. Ill-posedness has several causes, and it is present in all geophysical applications. Acoustical tomography, either travel time or diffraction tomography, is not an exception. In this work we deal with geophysical diffraction tomography where the input data is the scattered acoustic field measured at the receivers, and the velocity of the 2-D medium is the inversion output. Since geophysical diffraction tomography is an ill-posed inverse problem, it is necessary to use some tool to reduce this deficiency. The tool that we choose is the regularization of the inverse problem by derivative matrices, known in the literature by several names, specially as Tikhonov regularization. Regularization has an input parameter with crucial role known as regularization parameter or factor, which choice is already a problem. L-curve was reintroduced in the literature of inverse problems by Hansen. The L-curve knee represents a trade-off between smoother solutions with higher errors and rougher solutions with smaller errors. Thus, the knee detection (maximum curvature point) at the L-curve is a heuristic criterium to select the most appropriate solution. Solutions near to the curve knee are also acceptable and possibly more physically meaningful. We studied two acquisition geometries in diffraction tomography using the matrix formulation: well to well (cross hole) and well to surface (vertical seismic profiling). From the sets of overdetermined synthetic examples with ill-conditioned kernel matrix we have shown that the algorithm in question is feasible for a regularization solution in geophysical diffraction tomography.
DE: 0902 Computational methods: seismic
DE: 0935 Seismic methods (3025, 7294)
DE: 3260 Inverse theory
DE: 3285 Wave propagation (0689, 2487, 4275, 4455, 6934)
DE: 7270 Tomography (6982, 8180)
SC: Seismology [S]
MN: Fall Meeting 2005