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Lazy D-map

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SEM image of fault rock: light gray: K-spar, dark gray: quartz.

D-map indicating high (dark) and low (bright) D values ('fractal dimension') of grain size distribution.

INTRODUCTION

The purpose of the Lazy D-Map macro is to visualize the spatial distribution of the D-value of the grain size distribution (GSD) such as occur in fragmented rocks and fault gouge (see Heilbronner & Keulen, 2006).

The D-value is the (negative) slope of the GSD represented on a log-log plot of number (N) versus size (r). In the context of fractal interpretations, the D-value is often called the "fractal dimension".

Using the Lazy D-map macro, it is possible to to map the distribution of D-values, i.e., regions of different fragmentation intensity

References:

Heilbronner, R.; Keulen, N., 2006. Grain size and grain shape analysis of fault rocks. Tectonophysics, Volume 427, 199-216.

GETTING STARTED

The object of this set of macros is

to convert a bitmap of a cataclastic rock to a matrix density map
to convert a matrix density map to a D-map
to visualize / color code matrix density maps and D-maps

Reducing gray level contrast between quartz/plagioclse and K-feldspar

PREPARING THE IMAGE

If more than one phase is present on an SEM micrograph (such as the one shown here), the command [C] may be used to collapse the peak at GV=56 (K-feldspar) and the one at GV=90 (quartz and plagioclase) into one intermediate grey value (GV=73). This ensures that during the subsequent gray thresholding, fragment size does not depend on brightness of fragment.

Original gray value histogram

Histogram of grayvalues after [C]

Note: Only one peak (one gray level)

for both quartz/plagioclase and K-spar grains

Map created by [C]

Bitmap of SEM micrograph

Histogram of bitmap

CREATING THE BITMAP

Using the Image SXM toolbox (with or without the Lazy Erode Dilate macro), the image is thresholded. The histogram indicates that 58% of the image are matrix (black pixels)

Filtered bitmap

CONVERTING TO MATRIX DENSITY MAPS

Using the command [0] the bitmap is smoothed using a Gauss filter. The radius of the filter can be adapted to the size of the bitmap

Gauss filter

Dialogue window recommending a Gauss filter radius of 10% of image height.

Color coded matrix density map

Color coding from 20% to 70% (5% intervals): < 20% = white, > 70% = black

CALIBRATION AND COLORING

Using the command [M] the matrix density map is calibrated to 100%. Color stepping (command [Z]) may be used to color code matrix density

Matrix density map visualized as D-map using LUT3

CONVERTING TO D-MAPS

Using one of the look-up tables ([1] to [5]) the matrix density map is visualized as D-map (0.00 ≤ D ≤ 2.00) where D is the slope of the log-log grain size distribution. After applying the LUT3, the D-values are stretched between 1.00 and 2.00 ([E]). Using [Y] 20 levels of D at interval of 0.05 ar shown.

Other coloring schemes may be used, as shown, e.g., at beginning of this page.