MIDW interpolation

In this chapter, the application of multifractal inverse distance weighted (MIDW) interpolation method and a fractal filtering technique, named spatial and spectral analysis or simply (S-A) method (Cheng, 2003), will be illustrated to evaluate geochemical background at the regional and local scale. For this purpose, two case studies will be discussed for two different Italian areas ... 

To decompose the MIDW interpolated map to obtain background/baseline and anomaly maps, a fractal filtering technique, named spatial and spectral analysis or simply (S-A) method, is applied. 

In theory decomposing the MIDW interpolated map, background and anomaly maps should be obtained but, often happens that the background map shows areas where concentration values are still affected by contaminations and they should hence be interpreted as baseline values. 

Figure 7 1 Pb (A) and U (B) geochemical maps compiled using MIDW interpolation method. Search distance is 3.5 km and map resolution 1 km. Pixel values have been reclassified by fractal C—A plot based on the frequency distribution of pixel values (Fig. 7.2A and B).

Figure 7.2 Fractal concentration-area (C-A) plots for Pb and U. The vertical axis represents cumulative pixel areas A(p), with element concentration values greater than p, and the horizontal axis the pixel values (p). Breaks between straight-line segments and corresponding values of p have been used as cutoffs to reclassify pixel values in the MIDW interpolated map (Fig. 7.1 A and B).

Comparing geological map (Fig. 7.3) of the Campania region with Pb (Fig. 7.1 A) and U (Fig. 7.IB) MIDW interpolated maps, it can be seen that the distribution of high Pb values reflects both a lithologic and an anthropogenic control, whereas U reflects mostly a lithologic control. 

Figure 8.4 Lead dot and interpolated data distribution maps of the municipal area of Avellino, Italy (Albanese et al., 2007). Histogram, frequency curve and C-A plot, respectively, used to reclassify dot intervals and MIDW interpolated grids are also shown in the map.

At an urban scale, in some cases (Albanese et al., 2007 Cicchella et al., in press Lima et al., 2007), the use of this technique has been unsuitable due to both the small dimensions of the contaminated zones, characterised by a weak environmental impact on the surroundings, and the uniformity of the underlying geology along the whole urban area. Application of the C—A method to the MIDW interpolated grids and a careful observation of concentration intervals applied to the interpolated surfaces have led to a satisfactory definition of both background/baseline and anomalous values in most cases. 

The MIDW (Cheng, 2003) interpolation method estimates the distribution of chemical values based on fitted power law trends between chemical values and the... 

The stream sediment geochemical maps (Fig. 7.1 A and B) of Campania have been interpolated by MIDW using the GeoDAS program (Cheng, 2003). Search distance and map resolution are 3.5 and 1 km, respectively. 

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