HR: 1340h
AN: S23B-1378    [Abstracts]
TI: Application of the L-curve in geophysical inverse problems: methodologies for the extraction of the optimal parameter
AU: * Bassrei, A
EM: bassrei@cpgg.ufba.br
AF: Institute of Physics/UFBA and CPGG/UFBA, Campus Universitario de Ondina, Salvador, BA 40170-290, Brazil
AU: Terra, F A
EM: fat@cpgg.ufba.br
AF: Institute of Geosciences/UFBA, Campus Universitario de Ondina, Salvador, BA 4017-290, Brazil
AU: Santos, E T
EM: eduardo.telmo@terra.com.br
AF: CEFET-BA and Stanford University, Campus Universitario de Ondina, Salvador, BA 40170- 290, Brazil
AB: Inverse problems in Applied Geophysics are usually ill-posed. One way to reduce such deficiency is through derivative matrices, which are a particular case of a more general family that receive the name regularization. The regularization by derivative matrices has an input parameter called regularization parameter, which choice is already a problem. It was suggested in the 1970's a heuristic approach later called L-curve, with the purpose to provide the optimum regularization parameter. The L-curve is a parametric curve, where each point is associated to a λ parameter. In the horizontal axis one represents the error between the observed data and the calculated one and in the vertical axis one represents the product between the regularization matrix and the estimated model. The ideal point is the L-curve knee, where there is a balance between the quantities represented in the Cartesian axes. The L-curve has been applied to a variety of inverse problems, also in Geophysics. However, the visualization of the knee is not always an easy task, in special when the L-curve does not the L shape. In this work three methodologies are employed for the search and obtainment of the optimal regularization parameter from the L curve. The first criterion is the utilization of Hansen's tool box which extracts λ automatically. The second criterion consists in to extract visually the optimal parameter. By third criterion one understands the construction of the first derivative of the L-curve, and the posterior automatic extraction of the inflexion point. The utilization of the L-curve with the three above criteria were applied and validated in traveltime tomography and 2-D gravity inversion. After many simulations with synthetic data, noise- free as well as data corrupted with noise, with the regularization orders 0, 1, and 2, we verified that the three criteria are valid and provide satisfactory results. The third criterion presented the best performance, specially in cases where the L-curve has an irregular shape.
DE: 0902 Computational methods: seismic
DE: 0920 Gravity methods (1219)
DE: 0935 Seismic methods (3025, 7294)
DE: 3260 Inverse theory
DE: 7270 Tomography (6982, 8180)
SC: Seismology [S]
MN: 2007 Fall Meeting