Spectral Mapping Tools

Paper describing the use of the two-dimensional discrete Fourier transform and the two-dimensional continuous wavelet transform to automatically map deep-seated landslides:

Booth, A.M., Roering, J.J., Perron, J.T., 2009. Automated landslide mapping using spectral analysis and high-resolution topographic data: Puget Sound lowlands, Washington, and Portland Hills, Oregon. Geomorphology 109, 132-147. doi:10.1016/j.geomorph.2009.02.027

*Larger versions of Figs. 2 and 10: Figs2&10.pdf

Matlab m-files used in paper, with example DEM:

ALMtools.zip

File Descriptions:

dem.mat - Example 667x624 node digital elevation model (DEM) for part of the Carlyon Beach Peninsula, southern Puget Sound lowlands, WA, with 6ft (1.8m) point spacing. Available from the Puget Sound LiDAR Consortium.

lsmap.mat - 667x624 node array of 1s and 0s, with 1s indicating deep-seated landslide nodes as mapped by M. Polenz (Washington State Department of Natural Resources, personal communication, 2008), and 0s indicating unfailed terrain.

ALMexample.m - Example script that provides Matlab commands that use the m-files provided to create normalized power spectra (like Fig. 7 in Booth et al., 2009), generate maps of spectral power sums, and classify the spectral power sums into deep-seated landslide maps (like Figs. 8-10 in Booth et al., 2009).

conv2_mexh.m - Matlab function that computes the 2D CWT (Eq. 3 in Booth et al., 2009) of a data set at a specified wavelet scale using the Mexican hat wavelet.

conv2_mexh_var.m - Computes a 1D wavelet power spectrum of a data set.

detrend.m - Removes planar trend from a data set. Used by the fft functions.

envelope.m - Finds the data points that represent the upper envelope of a data series. Useful for highlighting peaks in 1D Fourier power spectra, such as in Booth et al. (2009) Figs. 10D-F.

fft_meanspec.m - Generates an average 2D Fourier power spectrum for a data set, as in Booth et al. (2009) Figs. 10A-C.

fft_normpower.m - Normalizes one 2D power spectrum by another 2D power spectrum, and generates both 2D and 1D normalized spectra. Booth et al. (2009) Figs. 10D-F.

fft_powsum.m - Sums the spectral power contained within the specified frequency band in a moving window centered at each point in the data set. Creates an array that can be classified into a deep-seated landslide map. Booth et al. (2009) Figs. 8A,B, 9A,B, and 10A,C.

hann2d.m - Windows a data set so that it tapers to 0 near the edges, necessary for using the fft algorithms.

hillshade.m - Creates hillshade view of a data set for easier visualization of features.

lsplane.m - Used by detrend.m to remove a data set's planar trend.

slide_optcurve.m - Computes the error indices (Carrara et al., 2009, Uncertainty in assessing landslide hazard and risk, ITC Journal 2, 172-183) of algorithm-generated landslide maps with different cutoff spectral power sums compared to a reference landslide map. Requires output of slide_stats.m.

slide_stats.m - Counts correctly and incorrectly classified landslide and unfailed nodes for a range of specified cutoff spectral power sums compared to a reference landslide map.

smooth2.m - Smooths a 2D data set by averaging within a circular window at each point.