Multifractional splines: from seismic singularities to geological transitions
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HERRMANN.PDF
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Author(s)
Herrmann, Felix
de Hoop, Martijn V.
Date Issued
2002
Publisher
Massachusetts Institute of Technology. Earth Resources Laboratory
Series/Report no.
Earth Resources Laboratory Industry Consortia Annual Report;2002-10
Abstract
A matching pursuit technique in conjunction with an imaging method is used to obtain quantitative
information on geological records from seismic data. The technique is based on a greedy, non-linear
search algorithm decomposing data into atoms. These atoms are drawn from a redundant dictionary
of seismic waveforms. Fractional splines are used to define this dictionary, whose elements are not only
designed to match the observed waveforms but also to span the appropriate family of geological patterns.
Consequently, the atom’s parameterization provides localized scale, order and direction information that
reveals the stratigraphy and the type of geological transitions. Besides a localized scaling characterization,
the atomic decomposition allows for an accurate denoised reconstruction of data with only a small number
of atoms. Application of this approach to angles gathers allows us to track geological singularities from
seismic data. Our characterization bridges the gap between the analysis of the main features within
geologic processes, i.e. the geologic patterns, and the interpretation of their associated seismic response.
A case study of Valhall data is presented.
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