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Stratigraphic Analysis and The Matrix: connecting and reusing digital records and archives of archaeological investigationsOpen Materials

Keith May, James S. Taylor and Ceri Binding

Cite this as: May, K., Taylor, J.S. and Binding, C. 2023 Stratigraphic Analysis and The Matrix: connecting and reusing digital records and archives of archaeological investigations, Internet Archaeology 61.

Appendix A – Stratigraphic rules and checks used in a Matrix diagram and incorporated in Phaser software

The Matrix project found that the drawing, layout and symbology of a Matrix diagram can vary somewhat between different archaeological practitioners, depending upon how the stratigraphic analyst chooses to depict certain basic 'rules'. Nevertheless, the most common approaches that were adopted by practitioners in the UK have been incorporated in a set of basic validation checks that are implemented in the Phaser software to enable these rules to be checked.

A.1. Checking of basic stratigraphic rules in the Matrix and Phaser

As outlined in Section 7.4, the Phaser software includes the functionality for the stratigraphic analyst to check, and to some extent choose, how rigidly to implement certain basic stratigraphic rules that need to be in place for their Matrix diagram to be consistent. This checking is enabled in the 'validation' tab in the prototype.

To maintain internal data consistency the software includes a series of checks of things such as 'every group must contain at least one context' and highlights any inconsistencies that may occur during the data entry and analysis updates. Every new context that is entered is included in this 'validation' checking and the relationships can be cross-checked at appropriate points in the analysis process. Examples of the basic internal checks that can be monitored in the 'Validation' tab are shown in Figure 17.

Figure 17: Video capture showing example use of Phaser 'Validation' tab. This example initially displays that contexts (NFE) (10000) and (+) have not been allocated to a phase and then shows in detail the process of validation checking of a context (1076) that is moved below another context (1067) and no longer reflects its recorded stratigraphic alignment.

These rules as implemented in Phaser are summarised in the simplified steps set out below (see also Appendix B).

A.1.1. Need for consistency in how to record 'Top' and 'Bottom' of the Matrix

One of the parameters to be checked is the denoting of the top of the stratigraphic sequence. In examples of datasets we worked with, it was not always clear if a convention had been used for this. The most commonly occurring example was the use of the '+' symbol to denote the uppermost context (e.g. in MOLA archives). In some archives, this '+' corresponds to a 'top of sequence'. In other examples (mostly from rural excavations), the term 'Topsoil' denoted the uppermost context in the stratigraphic sequence. Similar issues occurred with the terms used for the bottom of the sequence although, as explained below, it emerged these could involve further ambiguities.

A common expression for the bottom of the stratigraphic sequence was the term 'NFE', which is an abbreviation for 'No Further Excavation'. Other terms that were encountered were 'limit of excavation', 'excavation extent' and variations on a similar theme. Again the question of how widely these are used remains open. What seems clear is that it would be useful to adopt a uniform way of representing the bottom of an excavation in a Matrix diagram and the associated data records, once archaeologists have finished excavating (Recommendation 4.4). Similarly, various terms were used for where the surface of underlying geological layers and non-anthropogenic strata were encountered. Most commonly 'Natural', or 'Surface of Natural' is used, but it is not always clear if archaeologists are consistent in distinguishing between 'NFE' and 'SoN', and more often than not, archaeologists finish at NFE and do not feel it necessary to record whether SoN has been encountered.

The importance of this 'Surface of Natural' (SoN) is also highlighted by Matt Edgeworth in various publications on anthropocene studies where it is labelled as 'Boundary A'.

Few disciplines have any rigorous way of measuring depth of anthropogenic ground. Soil science and geology for example do not generally recognize or record the division between natural ground and human-modified ground. But archaeologists routinely find and follow along an interface in the ground known in the UK as 'the surface of the natural' – which I call Boundary A (Edgeworth et al. 2015). It is not always clear-cut or easy to discern. But where found it can be mapped in three-dimensional space. A simple set of recording protocols (to be added on to existing recording procedures) could focus on documenting this interface - its approximate depth below ground surface over the whole site, and some general characterisation and dating of it (Edgeworth pers. comm.).

'Boundary A' can also be equated to something described elsewhere as the 'Jinji':

Archaeologists sometimes informally refer to it as 'the surface of the natural'. Geologists in Japan call it the Jinji unconformity, which when loosely translated means the conjunction of human and natural' (Edgeworth 2018).

Understanding the significance of attempts to trace this Boundary A at scale across the whole of the Anthropocene using multiple excavation records, might emphasise and underline to other archaeologists the importance of consistency in their records to enable better reuse by others. Experience so far on the Matrix project seems to show only limited consistency in how archaeologists from different organisations actually document the 'top of natural' and not much better for Limits of Excavation/NFE. That said, most excavators do have some convention for how the extents of excavation are documented, so it ought to be possible to locate and semantically join those up across different excavations by different organisations.

There may also be considerable public benefit in incorporating non-archaeological approaches to this information along with archaeological records. For example, once construction is underway, often the footprints of excavations for most development sites go much deeper or wider than where the archaeologists decide the 'earlier archaeology' stops. It would be advantageous to future archaeologists, as well as others who come after, to tie in the bottom of the recorded archaeological horizons (e.g. NFE by construction teams) with any subsequent development activity. Some forms of Building Information Modelling (BIM) are now used on major infrastructure projects, and these would be worth more investigation with construction firms who often change or extend the Jinji boundary much deeper when digging their new foundations after all the older archaeology has been excavated. Also geoscientists have plenty to offer on how to record 'natural' stratigraphic boundaries most effectively (Coe 2022), although attempts to find whether geoscientists use anything like a Harris matrix to analyse their stratigraphic data seems to have proved less fruitful so far.

A.2. Expressing Allen operators for temporal relations and using the implicit temporal relationships between the matrix data fields

It has been demonstrated previously (May 2020) that commonly expressed versions of stratigraphic Harris Matrix diagrams (Harris 1989) contain not only the explicitly recorded stratigraphic relationships of Before, After and Equals, but also an implicit set of temporal relationships (Figure 18) as defined by J.F. Allen and commonly known as the Allen Temporal Operators (Allen 1983).

Allen temporal operators annotated on an original Excel spreadsheet to show the temporal relationships implicitly in Harris Matrix diagram of Silbury Hill
Figure 18: Allen temporal operators annotated on original Excel spreadsheet to show the temporal relationships implicitly in Harris Matrix diagram of Silbury Hill, downloaded from ADS archive.

One aim in developing Phaser is to increase the explicit expression and more consistent use of the temporal relationships implicit in Matrix diagrams. This has been shown in the Phaser software by highlighting where the temporal relationships between contexts and (sub)groups correspond to the Allen temporal operators, derived by comparing the date ranges in the dating records for each context (or group). The temporal relationships between the different contexts with dating evidence are shown in tables expressing the 'derived temporal relationships' between each element within a chosen phase. In current practice, much of the analysis work undertaken, particularly use of the Harris Matrix diagram as the tool to 'work out' stratigraphic and phasing relationships (temporal relations), does not result in the temporal reasoning and relationships being recorded in the final data records. Often a paper copy of the matrix results, but this (or even a digital PDF copy) is not reusable without an inordinate amount of work to re-key individual data items back into a usable database format. Although those interested can view a Matrix diagram, it is not easy to navigate (especially a large complex example) without a very detailed knowledge of the individual site that each different diagram represents (Paice 1991).

A.3. Use of Allen operators for checking the Matrix as implemented in Phaser

The Harris matrix covers all stratigraphic relationships between stratigraphic units (contexts) as recorded by observation and excavation during fieldwork. The analysis work of grouping and phasing those stratigraphic units involves, indeed requires, the stratigraphic analyst to sequence the matrix using the stratigraphic relationships but also by incorporating any dating evidence that results from analysis of finds, and scientific dating by other experts working on such material recovered from the stratigraphic units. The stratigraphic analyst must deduce and incorporate additional interpretation of the temporal relationships, alongside inferred spatial relationships that are derived from checking the spatial records, more often these days using a GIS alongside the matrix tools (Taylor 2016; and see Figure 10).

The Matrix project has formulated a method for recording a comprehensive temporal model, based upon the Harris matrix methodology, for all the possible stratigraphic (spatio-temporal) and temporal relationships that can hold between a sequence of stratigraphic units recorded in the field (Figure 12). This method has been incorporated in the Phaser software tool (see discussion in section 7.5) and the Allen relationships have been implemented using a set of functions to determine the relationship between any two ranges of years (start year/end year). These functions are coded according to the rules detailed in Binding 2010.

A.4. Making the Allen Temporal Relationships explicit using stratigraphic relations and dating evidence

Including the Allen relationships more explicitly in the matrix analysis makes the reliance upon the dating evidence also more explicit. This brings to the surface the varying degrees of (un)certainty in the dating evidence, which is to some degree masked when the matrix is presented as a purely stratigraphic record. Yet we would argue that without the role of the dating evidence explicit in the grouping and phasing dating processes then the fundamental evidence underpinning the interpretative outputs remains 'buried' in the archive.

Where dating evidence is available for finds within a single context, the Phaser software will calculate a derived date for the overall context, based upon the earliest 'minimum' date entered for any find from that context and the latest 'maximum' date entered for any find from the same context. This results in a derived overall duration – earliest start date to latest end date – for each context.

A.5. Incorporation of Terminus Post Quem (TPQ) and Terminus Ante Quem (TAQ)

During development, the project team considered building in TPQ and TAQ functionality to Phaser but did not have clear guidance to follow on how best to do so. Therefore it remained on the 'nice to have' list of requirements. After the final project workshop, correspondence with MOLA staff provided the following piece of feedback that might form the basis for how to incorporate TPQ and TAQ functionality when managing the dating evidence.

'The TPQ and TAQ dates are assigned to the context, and the E_Date and L_Date are assigned to each specific finds category from that context, so they can and do differ if there are residual/intrusive finds, or if one finds category has particularly tight and convincing dating.'
'It might help to explain how the form is completed. The specialists enter the data, and the first specialist using the form (usually ceramics) will assign TPQ and TAQ dates to the context based on their assemblage. As other specialists add dates for their material they can review and revise the TPQ and TAQ dates for the context manually – the form is updated as the project progresses. Our regular finds specialists usually prefer for the dates and phasing to be driven by the overall phasing for the site (and use this information to assign dates to their objects), so that's why they haven't assigned E_Date or L_Date to their material – but the capacity is there for them to do so if it was relevant for a particular site' (Louise Fowler - MOLA pers. comm.).

In Phaser we did build in the functionality to 'exclude' any single item of dating evidence from the Min Year & Max Year derived calculations. In effect, the stratigraphic analyst has the ability in Phaser to exclude any dates and add their own TPQ or TAQ date to a context, but this will, and should, be shown explicitly and preserved in the data record.

A.6. Checking of derived dating evidence against stratigraphic relative dating (above/below/equals)

Phaser compares the derived duration of any stratigraphic units that have stratigraphic relationships recorded as part of the matrix (Figure 19). If the duration of the context is consistent with the stratigraphic record (i.e. Above/Below/Equals) then it will return green in the table of 'derived temporal relationships', but if there is an inconsistency between the stratigraphic record and the temporal duration recorded in the dating evidence then this will be highlighted in one of a number of ways by the software using a colour key.

In the second window (see Figure 20), this comparison of stratigraphic order against temporal duration is displayed with a different colour key to highlight the different possible matches or discrepancies. This is not meant to suggest these are definite errors in the data, but rather to highlight any discrepancies to the stratigraphic analyst so that they can check the relevant dating evidence against the stratigraphic record and decide whether there is a problem either in the dating, or possibly some error in how the stratigraphy has been entered in the matrix record.

Figure 19: Video capture showing example of checking derived temporal relationships displayed in Phaser 'Temporal' tab

The (Allen) temporal relationships are derived from dating evidence entered from existing XSM10 dating evidence taken from XSM10_coins_data01.csv and compared against stratigraphic relationships (as recorded in Stratify archived file XSM10_prebg_matrix01.lst) entered for all stratigraphic entities within a Phase 5.01 (as recorded in XSM10_iaa01.csv )

Colour coded discrepancies between stratigraphic relationships and temporal relationships derived from the dating evidence within each context
Figure 20: Colour coded discrepancies between stratigraphic relationships and temporal relationships derived from the dating evidence within each context

Limited dating evidence means many relationships remain unsubstantiated – i.e. there simply was no evidence to derive a temporal relationship. In this case, the matrix stratigraphic relationships still enable the basic checking, i.e. that the stratigraphic units are sequenced accurately.

A.7. Temporal validation in Phaser and potential user interface enhancement work

Adding in the Allen operators to express the complexity of the temporal relationships at a human interaction level has added a considerable degree of additional information for the archaeological user to work with. This enables the archaeologist to see more explicitly where there may be discrepancies between the stratigraphic relationships recorded for stratigraphic units and the dating evidence recorded for the objects retrieved from those stratigraphic units. We found, as we developed the Phaser application, that this additional information, although highly useful for checking dating correlations, needed some management through the user interface, to enable the nature of any discrepancies to be mediated and highlighted most helpfully to the user. In the prototype we have used various colour bandings to show different degrees of mis-match or agreement between the temporal relationships and the stratigraphic relationships (Figure 20). It would be feasible to give a user more control in choices of colours and rule expression as part of further software development, if considered useful.

Appendix B. Data Validation rule checks used in the prototype

We have provided the following list of the main examples of the rule checks used in the prototype software.

Stratigraphic Unit/Context

Group/Feature (group is more common)



Period/Level ('level' more common in Ancient Near Eastern context i.e. Tells).

Diagram showing 3 possible matrix relationships
Figure 21: Possible relationships (Harris 1989, 36, fig.9)

The matrix system admits to only three possible relationships between two given units of stratification. In Harris' figure A, the units have no direct stratigraphic (physical) relationship; in B, they are in superposition; and in C, the units are correlated (equated by the = sign) as separate parts (given different numbers in the field) of a once whole deposit or feature interface (Harris 1989, 36).

Diagram showing stratigraphic relation inheritance between contexts, sub-groups, groups
Figure 22: Stratigraphic relation inheritance between contexts, sub-groups, groups

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