For this reason, the maximum difference in depth of all segments was used as the depth normalisation. The other methods used for determining the fractal dimension of bathymetric profile deviations from the mean, linear and quadratic trend were the analyses of (i) the semivariogram (DMVsem, DLTsem, DSTsem), (ii) the power spectral density (DMVFFT, DLTFFT, DSTFFT)and(iii)thewavelet transform (DMVwav, DLTwav, DSTwav). The following relationships can be derived from them: equation(15) Dsem=2−αw, where α is the semivariogram regression coefficient in the log-log scale
( Wen & Sinding-Larsen 1997); equation(16) DFFT=5−β2, where β is the regression coefficient of the spectral density in the log-log scale ( Mandelbrot, 1982 and Wornell and Oppenheim, 1992); equation(17) Dwav=32−γ, where γ is the regression coefficient of the wavelet transform coefficient C(a, b) averaged over the VX-809 molecular weight parameter b determining the location depending on the scaling parameter a in the log-log scale ( Mandelbrot 1982). A median filter was also used to analyse the diversity of bottom forms. Operation of the filter resulted in replacement of all the values by the median of the nearest
values to each of them (White, 2003 and White and Hodges, 2005). This filter is used to separate different sizes of morphological forms (e.g. Wessel, 1998, Adam et al., 2005, Kim, 2005, Hiller and Smith, 2008 and Kim and Wessel, 2008). A window of width 2d with d increasing in geometric progression was used in the study: d = 2 (MF1MV, MFLT1, MFST1), 4 (MF2MV, MF2LT, MF2ST), 8 (MFMV3, DAPT chemical structure MFLT3, MFST3), 16 (MFMV4, MFLT4, MFST4), 32 (MFMV5, MFLT5, MFST5) and
64 (MFMV6, MFLT6, MFST6) metres. The next filter, which cuts the size forms up to 128 m, could not be applied to a 256 m long profile segment. This parameter was determined by averaging the absolute values of the residue after filtering. All the parameters defined above were identified for every profile. Some of them were correlated or their shape was chaotic, providing no information that could define the seabed morphological diversity. The discussion includes all the parameters used, based on an example Ribonucleotide reductase bathymetric profile. This profile is characterised by including varied morphology (Figure 3b). The profile’s depth varies within the range of 10–120 m. The maximum depth of 120 m was found in the central part of Brepollen, and the profile end is positioned close to the Hyrne glacier calving front. The following profile sections were identified: – Section 1 – an almost flat seabed 1 km long with depths between 115–120 m. Analysis of the statistical parameters for the example bathymetric profile indicates that its diversity is reflected by the variability in parameters De, σ, SLR for every type of deviation and CMV0. Analysis of the other parameters does not reflect this diversity, however: the variations are mostly chaotic.