## 4 Discussion  
### The Meaning of the Equations  
In general, the fitting equations obtained (Tables 3-5) required few elementary terms (11 equations with one element term, 11 equations with two terms, and 5 equations with three terms) to obtain satisfactory approximations for the target elements (average r = 0.959 for all the equations). The element most involved the most times in the equations in Tables 3-5 was Fe(m). It was present as the most important term in the fitting equations for Cr and Ni in compost, as a negative secondary term for Ni and Se in sludges, and as the most important term for As, Ni, and Se in organic fertilizers. Oxides and hydroxides of Fe and Mn are relatively common constituents in soils and they are closely related to trace metal behavior [29; 30]. [PERSON] et al. [23] observed a Cr-Ni-Fe relationship of geogenic origin when studying 17 compost samples of varied sources using PCA. Thus, the significant influence of  
Figure 4: Relative differences (RDs) of the predicted aqua regía concentrations of the target elements. Fe could be due to the variable proportion of soil mineral particles in the different samples, which would greatly affect the concentrations of the target trace elements. The second most included element in the equations was Zr(m). It influenced As, Cd, and Se in compost and As and Ni in organic fertilizers. Zirconium occurs in several complex silicates that are frequently associated with Ti and Hf minerals. It does not accumulate in plants (levels in food plants vary from 0.005 to 2.6 mg kg\({}^{-1}\)), but the crustal abundance of Zr varies from 100 to 200 mg kg\({}^{-1}\)[29]. Therefore, this element is also an indicator of the contribution of soil or mineral material in each sample. [PERSON] et al. [31] also suggested that the presence of Zr (as well as Fe, Ca, Ti, Rb, Sr) in samples of organic compost suggests that the compost was mixed into the soil in the composting process. The relevance of Fe and Zr is not only because they are a clue of the presence of soil in the samples, but it may also be related to their low LOD (see [PERSON] et al. [31] for LODs), allowing for good precision and time stability in their pXRF measurements (see Table 2). The Si(m) readings are included for As in the compost equations and for Cd in the organic fertilizer equations. Arsenic is abundant in argillaceous sediments [29]; hence, its influence is likely related to the presence of soil clay particles in the amendments. The readings of Ti(s) are included in Cr and Ni equations for sludges. As indicated before, Ti is also indicative of the presence of soil particles because it is an abundant element in the Earth's crust. [PERSON] et al. [23] defined the Cr-Ni grouping as being of geogenic origin. Nevertheless, as Ti is used in many industrial applications, it cannot be ruled out that the Ti-Cr-Ni relationship in sludge may have another cause. [PERSON] [22] indicated that in Austrian composts, a factor including Ni-Cr might have a common source, namely, the abrasion of tools. The Cr and Ni elements could also come from plastic films, textiles, footwear, paper, cardboard, glass, and packaging waste that can appear in municipal solid waste [32]. The elements Zn and Pb showed wide representation as they are the main predictors of As, Cd, Hg, and Se in compost, and for As, Cd, and Hg in sludge. All these elements (Zn, Pb, As, Cd, Hg, and Se) are commonly considered as being of anthropogenic origin [33] and generally accumulate in the fine size fractions [23]. The concentrations of Zn and Pb in the amendments (Table 1) were generally higher than their LOD for pXRF (\(<\)10 mg kg\({}^{-1}\)[31]) such that these elements, when measured with good precision, can be considered good predictors. Phosphorus appeared as a predictor of Se in sludge. In a study covering 68 rock phosphates and 162 P-containing fertilizers sold in Germany, [PERSON] et al. [34] found up to 12.1 mg kg\({}^{-1}\) of Se. Kabata-Pendias and Pendias [29] indicated that there was up to 25 mg Se kg\({}^{-1}\) in P fertilizers.