Constraining Euler Deconvolution Solutions Through Combined Tilt Derivative Filters
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Pure and Applied Geophysics
Constraining Euler Deconvolution Solutions Through Combined Tilt Derivative Filters FABRI´CIO R. CASTRO,1 SAULO P. OLIVEIRA,2
JEFERSON
Abstract—Local phase filters as the tilt derivative (TDR) and the horizontal tilt derivative (TDX) are extensively used to interpret magnetic data. We use two combinations of these filters, namely TDR - TDX and TDR ? TDX, to design a constraining mask that guides the Euler deconvolution moving data window. The TDR - TDX filter produces sharp peaks over the centers of the sources, while the TDR ? TDX filter generates plateaus over them. Motivated by previous approaches that make use of the Laplacian filter or the analytic signal to constrain the Euler deconvolution window, we compute the solutions for windows centered at points that (1) have positive values of TDR - TDX and (2) are contained in the plateaus of TDR ? TDX. The use of both criteria improves the selection of source-related points while reducing the number of spurious ones. Our method is tested in synthetic anomalies due to interfering dike-like sources and field data from southeast Brazil. The experiments show that the use of a constraining mask based on combined tilt filters produce Euler solutions that are more contiguous and less sensitive to noise than the traditional located-Euler deconvolution. Keywords: Potential methods, Euler deconvolution, tilt derivative, magnetic anomaly.
1. Introduction In the last decades several semi-automatic interpretation techniques have been proposed to process and interpret large potential field data sets. A frequently used method is Euler deconvolution introduced by Thompson (1982) and generalized to gridded magnetic data by Reid et al. (1990). The
1 Department of Geology and Laboratory for Research in Applied Geophysics, Federal University of Parana´, Curitiba, PR 81531-980, Brazil. E-mail: [email protected]; [email protected]; [email protected] 2 Department of Mathematics, Federal University of Parana´, Caixa Postal 19096, Curitiba, PR 81531-980, Brazil. E-mail: [email protected] 3 ´ gua Verde, Parana´ State Secretary of Education, Av. A 2140, Vila Izabel 19096, Curitiba, PR 80240-900, Brazil.
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SOUZA,1,3 and FRANCISCO J. F. FERREIRA1
earliest Euler deconvolution algorithms make use of a moving window that scans the whole dataset to estimate the depths and commonly yield a high number of spurious solutions. The successful application of Euler deconvolution depends on the effective separation of meaningful from unphysical solutions, among other factors such as the appropriate selection of the structural index and window size. Thompson (1982) suggested an acceptance criterion where the normalized depth solutions which are under a tolerance value are removed. Barbosa et al. (1999) proposed removing also the solutions whose residual norms are smaller than a maximum prescribed value. In both criteria suitable parameters are selected by try-and-error. FitzGerald et al. (2004) provides a comprehensive list of related acceptance criteria.
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