Date of Award

Fall 2018

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

School

Ocean Science and Engineering

Committee Chair

Stephan Howden

Committee Chair School

Ocean Science and Engineering

Committee Member 2

David Wells

Committee Member 2 School

Ocean Science and Engineering

Committee Member 3

Paul Elmore

Committee Member 4

Juliette Ioup

Committee Member 5

Ian Church

Abstract

Robert Parker (1972) demonstrated the effectiveness of Fourier Transforms (FT) to compute gravitational potential anomalies caused by uneven, non-uniform layers of material. This important calculation relates the gravitational potential anomaly to sea-floor topography. As outlined by Sandwell and Smith (1997), a six-step procedure, utilizing the FT, then demonstrated how satellite altimetry measurements of marine geoid height are inverted into seafloor topography. However, FTs are not local in space and produce Gibb’s phenomenon around discontinuities. Seafloor features exhibit spatial locality and features such as seamounts and ridges often have sharp inclines. Initial tests compared the windowed-FT to wavelets in reconstruction of the step and saw-tooth functions and resulted in lower Root Mean Square (RMS) error with fewer coefficients. This investigation, thus, examined the feasibility of utilizing sparser base functions such as the Mexican Hat Wavelet, which is local in space, to first calculate the gravitational potential, and then relate it to sea-floor topography, with the aim of improving satellite derived bathymetry maps.

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