Geographically Distributed Data


Display and Identification

Gridding is required to put irregularly spaced data into a rectangular coordinate system. Methods include:

Gridding

Triangulation (Delauney)

Inverse distance weighted averaging

For 3 points, with distances d and values z

In general,

Advantages

Disadvantages

Bi-linear interpolation

Simple, conservative

Smoothing

Polynomial trend surface

Designed degree of smoothing

Unstable near edges

Inverse square distance weighting

Preserves high frequencies

Outliers

Kriging (variogram)

Uses variance of data

Directional effects

Spline interpolation

Optimal fit

Strong edge effects

Laplacian fitting

Good fitting, smooth decay at edges

Smoothing


Display methods

  1. Contour maps

  2. Shaded relief

    1. Grey-level coding

    2. Isoline

    3. Isoline with grey-level coding

  3. False color imagery

  4. 3-D mapping

    1. Isometric

    X = k1 (x cos 30° - y cos 30°)

    Y = k1 (x sin 30° - y sin 30°) + k2 z

    k1 , k2 = scaling constants

    1. Oblique

    X = k1 x + (k1/2) y cos 45°

    Y = k2 x + (k2/2) y sin 45°

    1. Perspective

Smoothing

  1. Splines

  2. Trend surface analysis


Artifacts and spurious effects

Methods of testing surface estimates


Image analysis of geophysical data

  1. Filtering (high pass, low pass, band pass, averaging)

  2. Wavelength filtering, deconvolution

  3. Derivative mapping

  4. Residual-regional separation


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