Mathematical Geosciences

, Volume 48, Issue 5, pp 487–510 | Cite as

Smoothing Three-Dimensional Manifold Data, with Application to Tectonic Fault Detection

  • Carlo Grillenzoni


Three-dimensional manifold data arise in many contexts of geoscience, such as laser scanning, drilling surveys and seismic catalogs. They provide point measurements of complex surfaces, which cannot be fitted by common statistical techniques, like kriging interpolation and principal curves. This paper focuses on iterative methods of manifold smoothing based on local averaging and principal components; it shows their relationships and provides some methodological developments. In particular, it develops a kernel spline estimator and a data-driven method for selecting its smoothing coefficients. It also shows the ability of this approach to select the number of nearest neighbors and the optimal number of iterations in blurring-type smoothers. Extensive numerical applications to simulated and seismic data compare the performance of the discussed methods and check the efficacy of the proposed solutions.


Bandwidth selection Kernel splines Local averaging Principal surfaces New Madrid earthquakes Sliced scanning Stopping criteria 



A sincere thank to the Editors and Reviewers for their useful comments.


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Copyright information

© International Association for Mathematical Geosciences 2016

Authors and Affiliations

  1. 1.Institute of ArchitectureUniversity of VeniceVeneziaItaly

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