A fundamental problem in wavelet analysis is the selection of the

A fundamental problem in wavelet analysis is the selection of the mother wavelet function. For analysing the echo envelope of the acoustic signal, Ostrovsky & Tęgowski (2010) applied six differently defined mother functions. The use of so many different functions did not yield a larger amount of information, however. In the present case, the number of wavelet mother functions was reduced to two: one symmetric and the other asymmetric. The Mexican Hat (mexh) Metformin manufacturer was selected as the symmetric wavelet mother function, while the family of Daubechies wavelets exemplifies the asymmetric mother functions. A wavelet

of the order of 7 (db7) was selected from this family. In order to account for wavelet asymmetry, profiles were analysed in both directions, in the same direction as the measurements according to (db7 +) and in the opposite direction (db7 −). The following parameters were determined for each of the transforms: – wavelet energies for a given scaling parameter (EMVj, wav, ELTj, wav, ESTj, wav): The use of a fractal dimension in the analysis of bottom bathymetry should result from the following assumptions (Herzfeld et al. 1995): – bathymetry has a non-trivial structure at every scale;

It is evident that the bathymetry of a water body formed by numerous geological processes has a non-trivial structure and that it cannot be described by simple geometric figures. The work involving the analysis of bathymetric profiles from the eastern Pacific (Herzfeld et al. 1995) indicates that bathymetry can be treated as a fractal because the assumption that DH > DT is fulfilled; selleck monoclonal antibody however, the assumptions of self-similarity are not satisfied when the image scale is being changed. The fractal dimension is considered to be an appropriate parameter for describing the morphological diversification of bottom surfaces ( Wilson et al. 2007).

In the case of a flat bottom, the fractal dimension calculated for the bathymetric Erastin profile should take a value equal to unity; as irregularities in the seafloor appear and their magnitudes change, its value will rise. In this work, the fractal dimension was determined using indirect methods, such as the box dimension, semivariogram analysis of spectral parameters and wavelet analysis. For determining the box fractal dimension of the deviations from the bathymetric profile segments (DMVbox, DLTbox, DSTbox), the definition given by Hastings & Sugihara (1994) was used: equation(14) Dbox=limΔs→0log10NΔs−log10Δs, where N(Δs) determines the number of squares covering a depth profile of a side length Δs. In case of the bathymetric profiles, both the length and depth have the same dimension. The proposed procedure for determining this parameter consists of four consecutive steps: – normalisation of the distance, taking the unit profile length to be 256 m; Application of a uniform standardisation is valid, taking a standard distance and depth of 256 m, equal to the length of the analysed section.

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