| Numerical Source Analysis (NSA) in Use for Forensic Geochemistry |
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A Procedure to Evaluate Water Chemistry Data on a Source-Related Basis.
- Reconstruction of Source Waters
- Recognition of Flow Patterns
- Independent Control of Flow- and Transport Models
- A Solution to Multiple Source Contamination in Water Systems.
- Mass Balance Calculations and Quantification of Contaminants Originating from Individual Contamination Sources
Numerical Source Analysis (NSA) is an innovative computer-based procedure of special interest for Forensic Geochemistry (ForGeo HC, ForGeo CHC, ForGeo SM). Originally applied to answer specific questions in exploration geochemistry, CTI of Canada has further developed the system for quantitative reconstruction of mixing processes involving contamination.
The illustration below, Figure 1, exemplifies a common problem in contamination assessments: Samples from a heavily contaminated area may point to multiple sources of contamination, however, the exact source character (A, B and C) and individual contributions to the main contamination site remain unknown. NSA provides the means to solve this problem. The NSA procedure transfers measured chemical water data such as Na, Ca, and HCO3 etc. into a vector matrix associated with linear unmixing equations. The goal of the procedure is to mathematically decipher and reconstruct mixed systems such as groundwater mixtures sourced from different types of groundwater, crude oils, natural gas, magma chambers fed from various sources at depth etc. NSA is strictly based on measured data with no assumptions required. Instead of describing a sample by its components or listed contamination profile, the field samples are now classified in terms of their source relationship: for instance, a field sample # 3 may be composed of 25% A, 45% B, and 30% C contamination source.
Figure 1
The result of NSA is the numerically reconstructed chemical composition of (previously unknown) sources, and the contribution of individual sources in every field sample. In essence, NSA provides detailed insights into mixing processes by reconstructing source components. NSA is, therefore, a corner stone in Forensic Geochemistry. NSA allows us to allocate and define source contamination, previously impossible from conventional data analysis. NSA is problem-oriented, very cost-effective, and provides results of high confidence, a prime requirement in Forensic Geochemistry (ForGeo HC, ForGeo CHC, ForGeo SM).
Concept, Method, and Advantage of NSA
The concept of this numerically derived process of source allocation from mixed samples is best explained in the conceptual illustration Figure 2, by considering the opposite situation of known source waters with defined compositions, which form a mixing system in the centre part of the illustration Figure 2.
Figure 2
In case four source waters of differently defined composition (as indicated by base colours in Fig.2) contribute to a mixing system from water flow towards the centre of the above illustration, all 25 field samples taken in the centre part, the work area, are, by definition, mixed samples with contributions from at least one, at most four source waters. Since four source waters in Figure 2 are the sources for the mixed waters in the centre part, it is obvious that three factors control and define the composition of all mixed samples:
- The number of source waters
- The composition of the source waters
- The portions of the different source waters in each field sample.
This fundamental relation allows us to draw the reverse conclusion: The complete information on (unknown) sources can be provided by the mixed samples themselves, because the (unknown) sources define the data structure of the mixed samples! In fact, each field sample contains a "genetic" fingerprint of each source water. The "strength" of this "source water fingerprint" in each sample is reflected by the portion of the respective source water in that sample. This portion may range from 0% (absence of a source water in a sample) to 100% (sample being, in fact, a source water).
The NSA procedure is the opposite step of the conceptual illustration in Figure 2: instead of calculating compositions of mixed samples from known sources, NSA calculates unknown sources from (measured) mixed sample populations. This information on unknown source waters can be numerically "extracted" from the mixed field sample information as discussed above.
It is also obvious that the NSA procedure of source water reconstruction is independent from any geologic or hydro-geologic situation. In case a particular groundwater flow pattern prevails or flow patterns change, the "colour pattern" of the field samples in Figure 2 would change accordingly. For instance, if a flow were established from NE to SW in Figure 2, the NSA result would be three source waters with waters #1, 2, and 4. Due to the major source contribution of water #2 the majority of field samples would turn into a "reddish" colour corresponding to the source input from this water.
In mathematical terms mixing processes induce a number of numerical characteristics in sample data sets:
- Mixing induces a linear variance in data sets. The variance increases with the number of sources and with increased chemical source differences.
- Source waters are, by definition, extreme samples; mixed field samples, participating in the mixing system, cannot exhibit more extreme characters.
- Source waters are independent from each other; each source water forms an eigenvector in data sets obtained from mixing processes.
The important advantage of NSA is the view of measured data in terms of source – mixing relationships. Table 1 is a partial list of measured ion concentration data in a groundwater. Table 2 is the numerically derived composition of source waters; based on the data provided, four distinct source waters participate in the groundwater mixing system.
Table 1: Raw, measured field data (section)
| Date | Station | Na mg/l |
K mg/l |
Mg mg/l |
Ca mg/l |
NO3 mg/l |
SO4 mg/l |
Cl mg/l |
HCO3 mg/l |
| 01. Jan. 04 | B 312 | 226.00 | 45.00 | 71.30 | 372.00 | 0.08 | 434.00 | 402.00 | 945.60 |
| 01. Jan. 04 | B 313 | 175.00 | 55.00 | 78.00 | 365.00 | 0.62 | 378.79 | 336.03 | 945.50 |
| 01. Jan. 04 | B 314 | 201.00 | 23.00 | 74.00 | 400.00 | 1.03 | 456.06 | 353.18 | 963.80 |
Table 2: Internal composition (%) of numerically determined source waters from Table 1
| Variable in Gew. % | Water 1 | Water 2 | Water 3 | Water 4 |
| Na | 2.1 | 22.0 | 3.3 | 3.5 |
| K | 0.8 | 0.8 | 0.7 | 0.4 |
| Mg | 3.2 | 0.4 | 3.0 | 6.1 |
| Ca | 18.2 | 9.5 | 20.5 | 15.0 |
| NO3 | 0.0 | 0.0 | 0.0 | 2.7 |
| SO4 | 1.2 | 12.2 | 45.4 | 16.1 |
| Cl | 1.9 | 33.5 | 6.5 | 11.5 |
| HCO3 | 72.6 | 20.4 | 20.5 | 44.7 |
Table 3 provides the % list of each source water in the groundwater field samples. For instance, sample # B 312 is composed of 32% source water 1, 37% of source water 2, 25% of source water 3, and 6% of source water 4.
Table 3: Proportions (%) of source waters in field samples
| Date | Station | % Water 1 | % Water 2 | % Water 3 | % Water 4 |
| 01. Jan. 04 | B 312 | 32 | 37 | 25 | 6 |
| 01. Jan. 04 | B 313 | 36 | 32 | 25 | 7 |
| 01. Jan. 04 | B 314 | 32 | 28 | 30 | 10 |
An important aspect in the understanding and significance of this numerical approach is the fact of the information in Tables 2 & 3 being identical with the information of Table 1. The numerically constructed data of Tables 2 & 3 can be used to re-calculate the Table 1 data. In case of pure mixing with no errors involved the re-calculated data perfectly match measured data. Thus, the difference between Table 1 data and Tables 2 & 3 data relates to a data transformation from concentration-data (with obscured information on sources) to source-related data:
Convoluted information Table 1 = Explicit, source-related information Tables 2 & 3
Instead of a list of measured data of limited diagnostic value, NSA determines source waters and their mixing relationships. This provides for a superior interpretation of hydro-chemical and hydrodynamic processes. Because these numerical source reconstructions are data based and unique, the NSA results are of considerable significance when it comes to the assessment and evaluation of individual contamination source contributions in cases of multiple source contamination.
This numerical data transformation and reconstruction of source types is successful as long as mixing is a prominent process, or reactions within the mixing system follow semi-linear kinetics.
Application of NSA:
- Identification of flow regimes solely based on water chemistry data
- Mass balance calculations for economic problems associated with groundwater:
- River-filtrate mass balance approaches
- Investigations on basic regional hydro-chemical and hydrodynamic relationships.
- Volume calculations on ground waters of different origins.
- Efficient and cost-effective evidence in case of complex contamination from (suspected) multiple sources.
- Control and optimization of conventional groundwater monitoring programs.
- Avoidance of costly, additional programs by fast and reliable source-related analysis of hydro-chemical data.
- Quantification of point source and diffuse emissions into the groundwater system.
- Quantification of individual contamination contributions.
- Prognosis and projection of the fate of contamination.
- Critical assessment and optimization of groundwater modelling.
- Clarification on contaminant migration and age-determination of contamination.
- Supplement and control of emission pump tests and flow/transport models
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