Linear shallow-water wave theory applied to step topography

A planar monochromatic wave, h_{I} incident on a ridge, produces a transmitted wave, h_{T} and a reflected wave, h_{R}

The dispersion relation is w / k = c where c = (gh) for normal incidence

The transmissivity is defined as the ratio of amplitudes T = | AT | / | AI |

Effects of Cross-Ridge Phase q = kL

Minimum transmission (Tmin) occurs when q = 90°, 270°, 450°,...

100% transmission occurs when the cross-ridge phase shift q = kL is exactly q = 180°, 360°,...

Effects of Ridge Depth on Transmissivity

The actual transmissivity is close to Tmin when q < 90° , i.e. for ridges that are narrower than a quarter wavelength as computed from the ridge-top depth h

At higher frequencies w, rapid fluctuations occur between and T=Tmin << 100% as w varies (T~100% when e << 1 is a highly idealized result)

Smoothing Smith/Sandwell Topography

• 2-D orthogonal wavelet transform (LA8) was performed on the gridded topography

• The shorter-scale wavelet amplitudes were then set to zero with a tapered cutoff in scale

• Finally, the amplitudes were back-transformed to produce the smoothed topography