Sarah A. Little

Wavelet analysis of a bathymetric profile reveals anomalous crust

A 200 km anomalous topographic zone was discovered using wavelet scale analysis in a 1600 km linear bathymetric profile taken northeast of Hawaii. A spectral analysis of the zone shows that the power in wavelengths shorter than 25 km averages 5–10 times lower than the surrounding topography. Conversely, wavelengths longer than 25 km have 2–3 times greater power than nearby topography. Further research reveals that this low-frequency zone correlates with the eastern flank of a regional bathymetric high which has been described by J. Mammerickx [1981]. Details of the features suggest that this zone is a small, abandoned, slow-spreading rift overprinted by a regional thermal swell. The magnitude of the feature is smaller than other, known, abandoned spreading centers, making it easy to overlook without the application of the wavelet transform.

Detecting nonlinear dynamics in spatio-temporal systems, examples from ecological models

Mathematical models of marine populations exhibit chaotic dynamics. However, we hypothesize that in moving water, Eulerian sampling of spatially heterogeneous populations may obscure any deterministic signal beyond the resolving capabilities of presently available nonlinear signal processing techniques. To examine this hypothesis we created two spatio-temporal models of population dynamics. To caricature actual ocean sampling limitations, we sampled the model output in two ways, random walks to simulate Eulerian sampling, and spatial averages to simulate population measurements from finite volumes. Results indicate that the ability to identify underlying nonlinear dynamics quickly degrades as the step size of a random walk sampling increases. On the other hand, the analysis techniques used are more robust in the face of spatial averaging.

Wavelet Analysis of Seafloor Bathymetry: An Example

Abstract 1-D wavelet analysis has been shown to be useful in studying bathymetric profiles [7]. 2-D bathymetric maps are less common than 1-D profiles, but offer immensely more information about seafloor generation processes. 2-D wavelet analysis is applied to swath-mapped bathymetric data from the Mid-Atlantic Ridge. Both image enhancement and feature identification are performed with excellent results in the identification of the location and scarp facing direction of ridge-parallel faulting. Wavelet image processing techniques enable computer analysis of distribution and spatial patterns in faults to be performed without the tedious job of transcribing hand picked and ruler-measured fault parameters from printed images to a digital data base.

Fault scarp identification in side-scan sonar and bathymetry images from the Mid-Atlantic Ridge using wavelet-based digital filters

Digital filters designed using wavelet theory are applied to high resolution deep-towed side-scan sonar data from the median valley walls, crestal mountains, and flanks of the Mid-Atlantic Ridge at 29°10′ N. With proper tuning, the digital filters are able to identify the location, orientation, length, and width of highly reflective linear features in sonar images. These features are presumed to represent the acoustic backscatter from axis-facing normal faults. The fault locations obtained from the digital filters are well correlated with visual geologic interpretation of the images. The side-scan sonar images are also compared with swath bathymetry from the same area. The digitally filtered bathymetry images contain nine of the eleven faults identified by eye in the detailed geologic interpretation of the side-scan data. Faults with widths (measured perpendicular to their strike) of less than about 150 m are missed in the bathymetry analysis due to the coarser resolution of these data. This digital image processing technique demonstrates the potential of wavelet-based analysis to reduce subjectivity and labor involved in mapping and analyzing topographic features in side-scan sonar and bathymetric image data.