Forensic soil provenancing in an urban/suburban setting: A sequential multivariate approach

2.1 The North Canberra soil geochemical survey

The North Canberra soil geochemical survey was initiated in 2017 and focused on the northern part of Canberra city and surrounding suburban areas, in the Australian Capital Territory (ACT) (Figure 1). The total area covered by the survey was ~260 km² sampled at an average density of 1 site/km² [35]. In addition to the 268 samples in this survey, three “blind” samples (Blind 1, Blind 2, and Blind 3 hereafter) were collected from sites within the survey area (but away from the survey's grid samples), the geographical coordinates or even approximate locations of which were unknown to the lead researcher until the project had concluded all data analysis and map production.

General background, results, and interpretations of the geochemical mapping of the ACT, including the investigation of the effects of lithology and land use on soil geochemistry, will be presented elsewhere (upcoming paper in preparation). A simple description of the blind sample sites is, however, warranted here as it will have a bearing on the interpretation of the provenance analysis we focus on (see Fig. S1 in Appendix S1). Blind 1 is a Kurosol soil (all soil types from the Australian Soil Classification (ASC) [36]) collected over the Mount Ainslie Volcanics Formation, a Wenlockian (Early Silurian) dacitic ignimbrite with minor ashstone, agglomerate and shale, and porphyry, within the Hawkins Volcanic Suite (all stratigraphic units from the Australian Stratigraphic Units Database https://asud.ga.gov.au/). We note here that Blind 1 was deliberately collected from a local environment not representative of the broader landscape to test the limit of soil provenancing. Blind 2 is Kurosol/Rudosol (Alluvial) soil collected over undifferentiated Quaternary alluvium and fluvial deposits of gravel, sand, silt, and clay along Ginninderra Creek. Blind 3 is a Kurosol soil collected over a thin, folded Acton Shale Member, an Early Ordovician black graptolitic siliceous shale within the broader turbiditic (sandstone, mudstone, shale) Adaminaby Group.

In this paper, the analytical focus is directed to both (i) soil mineralogy via infrared spectroscopy (informing on, e.g., hydrated minerals such as clay minerals, carbonates, and sulfates) and magnetic susceptibility (informing on, e.g., ferrimagnetic minerals such as maghemite or magnetite, and their grain sizes); and (ii) soil geochemistry via major oxides and organic matter concentrations as well as trace element concentrations after two chemical extractions of different strengths. Sample collection, preparation, and analysis methods are detailed in the Appendix S1, as are data analysis, spatial analysis, quality control, and detailed uncertainty analysis procedures.

2.2 Uncertainty analysis

Uncertainty arises from any attempt to quantify natural phenomena, from sampling through to analysis. In this project, two main types of uncertainty were specifically quantified: measurement uncertainty (U_m) and interpolation uncertainty (U_i). They were quantified as three standard deviations of field triplicates (SD_m) and of residuals (SD_i), respectively. Residuals are the differences between the interpolated (modeled) values and the measured values at each sampled site. The combined uncertainty (U_c), which applies to the generated property raster surfaces, is calculated using the root sum of squares method (e.g., [37, 38]) as follows:

(1)

The standard deviations (SD_m, SD_i) and uncertainties (U_m, U_i, U_c) of each analyte are given in Table S3 in the Appendix S1.

2.3 Determination of search ranges

For each variable, the Search Range (SR) for a blind (evidentiary) sample was set to the measured value of that variable in that blind sample (Target Value or TV) with a buffer reflecting the sum of the uncertainty in the analytical data (U_m) and of the uncertainty in the raster surface (U_c), according to:

(2)

This accounts for uncertainty in both the interpolated surface (which is derived from measured values in the database and a smoothing interpolation algorithm), via U_c, and the measured value in the blind sample, via U_m, as illustrated in Figure 2. The graphic illustrates that the interpolated grid value for a particular soil property needs to fall within the uncertainty envelope (U_m + U_c) around that soil property for the evidentiary sample to count as a match and score a 1 in the provenance raster computation (see below and Appendix S1).

2.4 Raster generation and clipping

Interpolation rasters for each available variable were prepared by inverse distance weighting (IDW), clipped, and analyzed in QGIS as explained in the Spatial Analysis section of the Appendix S1.

2.5 Provenancing methodology

A sequential multivariate approach to soil provenancing based on an empirical database of soil properties is developed in this contribution. The first step in this approach is to measure and map a number of mineralogical (e.g., FTIR, MS) and geochemical (e.g., XRF and ICP-MS) soil properties at the sampled sites. The next step is the interpolation of those properties between sampled sites, here performed using IDW (power 3; 12 neighbors; 250 m cells) as detailed elsewhere. The final step of this method is to select raster cells from those grids that match the Target Value ± Search Range of the evidentiary sample of interest. This is akin to drawing contours on a topographic map that follow a given elevation with allowance for some slack or uncertainty in that elevation value; this essentially yields a corridor (or corridors) of locations (cells) that satisfy the elevation ± uncertainty criterion. A raster calculation in QGIS assigns a value of 1 to cells that satisfy a given criterion (i.e., those whose soil property value fall within the Search Range), and a value of 0 to those that do not (i.e., those whose soil property value fall outside the Search Range). Once the cells that satisfy the Search Range for one composition variable are established, those for one or many more variables can be added to it. This generates a map over the area of interest with cells having values ranging from 0 to N (the number of soil properties under consideration). Such maps can be colored to produce “heat maps” that readily draw attention to those areas with most criteria being satisfied and thus more likely to include the potential origin for the evidentiary sample. It is noted that the provenancing methodology presented here is not intended to be used at the exclusion of other provenancing avenues such as soil microbiome or palynology, but rather complement those by providing a geochemical/mineralogical perspective. Once areas of enhanced provenance potential are identified, further resources can be allocated to these focussed regions with a lower failure risk.

3.1 Validation

Standard deviations and uncertainties derived for each parameter as described above are given in the Appendix S1 (Table S3). The Target Values and Search Ranges for the Blind 1, Blind 2, and Blind 3 evidentiary samples collected as part of this project are shown in Tables 2, 3, and 4, respectively. The results of soil provenancing investigations using the sequential multivariate approach are discussed below.

The maps of provenance prediction for samples Blind 1, Blind 2, and Blind 3 based on three FTIR principal components and two MS parameters (for a total of five parameters) are shown in Figure 3. Results indicate that for these three blind samples, 3 of (a theoretical maximum of) 5, 2 of 5, and 3 of 5 parameters match the Search Ranges for Blind 1, Blind 2, and Blind 3, respectively. If the three PCs from FTIR are removed from the analysis and only MS data are considered (not shown), the match rates for these three blind samples change to 1 of 2 for all three blind samples.

The soil provenance rasters generated by the present sequential multivariate provenancing method can be interpreted like “heat maps” where raster grid cells with hotter colors are a better match to the evidentiary sample under investigation than cooler colored cells. In Figure 3A, grid cells colored light, medium, and dark red (scores of 3, 4, or 5) indicate a match equivalent or superior to the cell from which simulated evidentiary sample Blind 1 actually comes from (which has score of 3). Provenancing grids computed from the cumulative results from more variables yield smoother, more gradational spatial patterns than those generated from fewer variables, as demonstrated by subsequent figures. In a separate section (Performance Assessment), we will discuss metrics to quantify how good the provenance predictions are.

The maps of provenance prediction for samples Blind 1, Blind 2, and Blind 3 based on 11 compositional XRF parameters are shown in Figure 4. Results indicate that for these three blind samples, 6 of 11, 3 of 11, and 5 of 11 parameters match the Search Ranges for Blind 1, Blind 2, and Blind 3, respectively. If the 8 first PCs are included in the analysis (not shown), the match rates for these three blind samples change to 10 of 19, 6 of 19, and 5 of 19 for Blind 1, Blind 2, and Blind 3, respectively.

The maps of provenance prediction for samples Blind 1, Blind 2, and Blind 3 based on 38 compositional Total ICP-MS parameters are shown in Figure 5. Results indicate that for these three blind samples, 13 of 38, 31 of 38, and 17 of 38 parameters match the Search Ranges for Blind 1, Blind 2, and Blind 3, respectively. If the 8 first PCs are included in the analysis (not shown), the match rates for these three blind samples change to 17 of 46, 39 of 46, and 29 of 46 for Blind 1, Blind 2, and Blind 3, respectively.

The maps of provenance prediction for samples Blind 1, Blind 2, and Blind 3 based on 19 compositional AR ICP-MS parameters are shown in Figure 6. Results indicate that for these three blind samples, 4 of 19, 15 of 19, and 6 of 19 parameters match the Search Ranges for Blind 1, Blind 2, and Blind 3, respectively. If the 8 first PCs are included in the analysis (not shown), the match rates for these three blind samples change to 9 of 27, 20 of 27, and 10 of 27 for Blind 1, Blind 2, and Blind 3, respectively.

The maps of provenance prediction for samples Blind 1, Blind 2, and Blind 3 based on the 97 combined FTIR, MS, XRF, Tot, and AR ICP-MS parameters (including PCs) are shown in Figure 7. Results indicate that for these three blind samples, 39 of 97, 67 of 97, and 39 of 97 parameters match the Search Ranges for Blind 1, Blind 2, and Blind 3, respectively. If the 27 PCs are removed from the analysis (not shown), the match rates for these three blind samples change to 26 of 70, 51 of 70, and 31 of 70 for Blind 1, Blind 2, and Blind 3, respectively.

3.2 Performance assessment

The performance statistics of the sequential method of provenancing soil samples are summarized in Table 5. Two performance indicators are calculated. First “precision” (Prc) is defined as the ratio of cells in a grid that have scores equivalent to, or lower than, the score of the cell containing the Blind (evidentiary) sample over the total number of cells. If Prc is 99%, only 1% of cells are identified as provenance matches, a highly precise result. Thus for instance, Blind 1 for FTIR +MS (5 variables) has a score of 3; there are 3634 cells of the total 4638 cells of the FTIR +MS grid that has a score of 3 or less (0, 1, or 2), giving Prc = 3634/4638 or 78.4%. Second “accuracy” (Acc) is defined as the ratio of the score for the cell containing the Blind (evidentiary) sample in a particular provenancing grid over the (actual) maximum score obtained at any cell within the grid. If Acc is 100%, all variables making up the provenance grid correctly identify the cell containing the evidentiary sample as a match, a highly accurate result. Thus for instance, Blind 1 for the FTIR +MS grid (maximum recorded score of 5) has a score of 3, giving Acc = 3/5 or 60%.

Each Blind sample behaves slightly differently in terms of provenancing performance (Table 5). The most precise and accurate results for Blind 1 were obtained for the XRF with PCs method (Prc = 93.6%; Acc = 66.7%). The next highest Prc came from XRF without PCs (86.6%), while the next highest Acc was obtained for both XRF without PCs and FTIR + MS with PCs (60%).

For Blind 2, the most precise results came from FTIR + MS without PCs (Prc = 99.8%), while the most accurate results were obtained for Total ICP-MS with PCs (Acc = 86.7%). The next highest Prc came from Total ICP-MS with PCs (94%), while the next highest Acc was obtained for ALL variables with PCs (84.8%).

The most precise and accurate results for Blind 3 were obtained for FTIR + MS with PCs (Prc = 92.2%; Acc = 60%). The next highest Prc came from XRF without PCs (88.7%), while the next highest Acc was obtained for ALL variables with PCs (52.7%) then Total ICP-MS with PCs (51.2%).

Considering average rather than maximum (or next highest) precision and accuracy, provenancing performance improved from Blind 1 (50.1% and 45.4%), to Blind 3 (70.6% and 46.6%), to Blind 2 (86.2% and 66.1%). The authors believe that the poorer results for Blind 1 are due to the fact that this sample was collected in a non-representative location for that grid cell (see above).

In terms of the best-suited analytical method for deterministic provenancing across all Blind samples, FTIR + MS without PCs has the highest precision of any method (Prc = 99.8% for Blind 2), followed by Total ICP-MS with PCs (94.0% for Blind 2), while Total ICP-MS with PCs has the highest accuracy of any method (Acc = 86.7% for Blind 3), followed by ALL variables with PCs (84.8% for Blind 2) then AR ICP-MS without PCs (83.3% for Blind 2).

Across all three Blind samples, FTIR + MS with PCs has the highest average precision (80.7%), closely followed by XRF without PCs (80.0%) then XRF with PCs (76.9%); ALL methods with PCs have the highest average accuracy (61.3%), followed by Total ICP-MS with PCs (59.1%) then ALL methods without PCs (56.2%).

Inclusion of principal components (PCs) in the provenancing workflow provides a marginal advantage in terms of provenancing performance (Table 5). For all Blind samples confounded, both average Prc and Acc are higher with PCs (70.3% and 54.5%) than without (67.6% and 50.9%). From those figures, one can also observe that of the two performance metrics, Prc (ranges from 28.4% to 94.0% with PCs, and from 25.6% to 99.8% without PCs) tends to have higher values than Acc (ranges from 33.3% to 86.7% with PCs, and from 21.1% to 83.3% without PCs).

The performance of individual analytes, such as specific major oxides or trace elements, can be deduced from the sequential multivariate approach presented here. The following analytes were successful at matching all three Blind samples’ Search Ranges and can thus be put forward as the most effective soil provenancing indicators in the present study: Ba, Cu, Ge, Nb, Pb, Ta, and V by total ICP-MS; Pb and Zn by aqua regia ICP-MS; and two PCs for each of these analytical methods. However, seeing that analytical methods such as XRF or ICP-MS are commonly available as packages of analytes rather than oxide-by-oxide or element-by-element analyses, realistically, comprehensive analyte packages are probably the most practical and cost-effective requests to submit to institutional or commercial laboratories.

3.3 Sensitivity analysis

The sequential multivariate soil provenancing method developed here suggests a number steps to take for identifying regions within a search area (i.e., cells within a raster) that are more likely to contain the source of an evidentiary (blind) sample being provenanced. In this section, we test a number of variations on the previously described workflow to identify how sensitive the results are to parameterization choices. In particular, we measure the effect on the performance metrics Prc and Acc of (i) using an IDW algorithm with power of 2 (instead of 3) for the interpolation step, (ii) shifting the origin of the interpolation raster grids by 125 m to the west and south, (iii) using raster grid cells of 500 × 500 m (instead of 250 × 250 m), and (iv) applying an uncertainty multiplier of 6 (instead of 3) in calculating and propagating uncertainty (Equation 1). Table 6 shows the impact of these scenarios relative to the base scenario for XRF and Total ICP-MS analyses.

The sensitivity analysis (Table 6) reveals that performance metrics can vary by up to ±~40% relative to the reference scenario for Blinds 1, 2, and 3 combined and that Prc tends to deteriorate (−41% to +17%; i.e., negative bias) when parameters are changed, whereas Acc tends to improve (−20% to +39%; i.e., positive bias). Median changes in Prc relative to the base scenario are −10% and −7% with and without PCs, respectively. Median changes in Acc relative to the base scenario are +12% and +8% with and without PCs, respectively. The dependency of provenancing performance on parameter choices is relatively significant: performance across all three Blind samples and five scenarios averages 61.5% and 64.4% for Prc when PCs are and are not included, respectively, and 61.8% and 59.4% for Acc when PCs are and are not included, respectively. Therefore, we recommend that values of 60% be used for both Prc and Acc as minimum thresholds for accepting a provenance prediction. On this basis, Table 5 clearly shows that provenancing of Blind 1 largely failed (4 out of 20 performance metrics ≥60%), most likely because of the uncharacteristic choice of location of this blind sample as discussed above, whereas provenancing of Blind 3 (10 out of 20) and especially Blind 2 (16 out of 20) was (more) successful.

3.4 Limitations and future research

The present study focussed specifically on data analysis workflows for the provenancing of soil trace evidence. It did not address the (acknowledged) issues of (i) sample size available for analysis in a geochemical survey situation vs a crime scene forensic casework; (ii) soil transfer and persistence from the crime scene to the point where soil is sampled for forensic assessment; (iii) the potential for a questioned soil sample from an urban/suburban environment being impacted by human activity (e.g., transported soil for landscaping or engineering purpose); and (iv) the choice of interpolation method to predict the values of a soil property between survey grid points. The latter point has been the focus of investigations in the past (e.g., [39-42]), though perhaps not specifically with a forensic application in mind. Other limitations to this provenancing approach, such as contamination, are common to all forensic traces, for example, fingerprinting, biological tissues, fibers, and not specific to soil provenancing; they are of course an important concern and need to be managed by appropriate protocols.

Future research could thus include expanding the present investigation to include (i) micro-analysis techniques, and (ii) quantitative mineralogical and geochemical assessment of soil transfer and persistence (e.g., as footsteps are taken with dirty boots, a car is driven with muddied tires, or a shovel is subjected to drying and shaking to simulate transport in a vehicle).

Despite the acknowledged limitations to the empirical soil provenancing approach developed herein and the recognition that additional research is recommended, it is concluded that empirical soil provenancing based on soil mineralogical and geochemical surveys can play an important role in forensic and intelligence applications.