Discrimination of Bedform Scales Using Robust Spline Filters and Wavelet Transforms: Methods and Application to Synthetic Signals and the Rio Parana, Argentina

摘要

Currently, there is no standard nomenclature and procedure to systematically identify the scale and magnitude of bedforms such as bars, dunes and ripples that are commonly present in many sedimentary environments. This thesis proposes a standardization of the nomenclature and symbolic representation of bedforms, and details the combined application of robust spline filters and continuous wavelet transforms to discriminate these morphodynamic features, namely bedform hierarchies (BHs). The proposed methodology for bedform discrimination is applied to synthetic bedform signals, which are sampled at a Nyquist ratio interval of 5 to 100 and a signal-to-noise ratio interval of 1 to 20, and to a detailed 3D bed survey of the Rio Parana, Argentina, which exhibits large-scale dune bedforms with superimposed, smaller bedforms. After discriminating the synthetic bedform signals into 3 BHs that represent bars, dunes and ripples, the accuracy of the methodology is quantified by estimating the reproducibility, the cross correlation and the standard deviation ratio of the actual and retrieved signals. For the case of the field measurements, the proposed method is used to discriminate small and large dunes; and subsequently, obtain and statistically analyze the common morphological descriptors such as wavelength, slope, and amplitude for both stoss and lee sides of these different size bedforms. The analysis of the synthetic signals demonstrates that the Morlet wavelet function is the most efficient in retrieving smaller periodicities such as ripples and that the proposed methodology effectively discriminate the waves of different periodicities scales for Nyquist ratios higher than 50 and signal-to-noise ratios. The analysis of the bedforms of the Parana River reveals that in most cases, a Gamma probability distribution (with a positive skewness) best describes the dimensionless wavelength and amplitude for both the lee and stoss sides of large dunes. For the case of the smaller superimposed dunes, the dimensionless wavelength shows a discrete behavior governed by the sampling frequency of the data, and the dimensionless amplitude better fits the Gamma probability distribution, again with a positive skewness.