ISSN:
1573-8868
Keywords:
splines
;
scale transformation
;
surfaces
;
topography
;
rank coding
Source:
Springer Online Journal Archives 1860-2000
Topics:
Geosciences
,
Mathematics
Notes:
Abstract Addressing geophysical problems often implies the correct description of surfaces with large local variations. This problem is of interest in many areas of geophysics—for instance, for the description of topography when studying site effects in seismic wave propagation, or the propagation of lava or pyroclastic flows along the slopes of a volcano, or in the presence of geological structures with faults. However, surface fitting of rapidly varying data using classical functions like splines is known to be difficult. Without information about the location of the large variations in the data set, the usual approximation methods lead to instability phenomena or undesirable oscillations. We propose a new approach that uses scale transformations, and whose originality consists in a preprocessing and a postprocessing of the data. Variations of the unknown function are reduced using a scale transformation in the preprocessing phase. The transformed data do not exhibit large variations, and therefore we can use a usual approximant that will not create oscillations. An inverse scale transformation is subsequently applied. We discuss the convergence of the method when the number of data points tends to infinity. We show the efficiency of this technique by applying it to a Digital Elevation Model of the topography of the Piton de la Fournaise volcano (Réunion Island, France).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1007500624487
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