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Spatial Sampling

Introduction - Samples, Models, Errors & Trends

All survey is essentially a modelling process & the more representative the data of whatever is being measured, the better the model. It can be assumed that every physical property can be modelled as a curving shape or surface, whether of the ground, a magnetic anomaly, a distribution of items or sites or anything else. The accuracy of the model is the smallest curve that is represented in the data. Decreasing accuracy is accompanied by the introduction of ambiguities & spurious curves.

Any one sample of a curve is of limited value & the smallest trend that is apparent is twice the sampling interval so a spot reading every 10m merely informs of trends 20m long. At the same time, without knowing how precise the measurement is we cannot know whether that sample is truly representative. Each is associated with a random & a systematic error & although the systematic may not be important (as it is common to all the data) the random error is. To revisit the 20m trend, this is only apparent if it exceeds the magnetitude of the random error of all three points defining it. Without measuring the size of this error the only way of assessing the validity of a trend is to compare it with neighbouring ones, at which point the effective resolution of the data has decreased again to perhaps 30m or 40m.

Finally, all models make assumptions about the spaces between the samples & the nature & variability of this space is entirely dependent upon what was measured. Consequently, a model built from samples is only as valid as the knowledge of what might be between those samples. A sampling strategy therefore has to account for the probability of change between samples. For example, the magnetic field will change by a reasonable but not excessive amount across an interval of 0.25m & therefore samples need not be any closer than this.

This is straightforward because the properties of magnetic fields are known. What about archaeological features? How variable is the landscape of the past, how close together do evaluation trenches need to be? How do you know? Would coverage by geophysical survey allow trenches to be better positioned than a random 2% scatter?

Landscape survey

Landscapes are usually surveyed by walking in parallel lines across them, observing & recording relevant features. The line separation needs to match the visibility of the target features which is affected by their size, whether they are obscured by vegetation, whether they are upstanding & the available light. For low earthworks visibility is also a function of the angle they make with the sunshine & the observer & it is frequently best to seek elevated views from different angles to be sure of their identification.

In general, if vegetation is tall enough to obscure features but low enough to see over then a line separation of 30m seems to work. For short vegetation this can be increased to 50m while still able to detect low earthworks. For discrete level features (e.g., shafts & pits) the line separation needs to be reduced to around 10m unless there is no vegetation. Small isolated features like standing stones cannot easily be recognised from more than about 100m away. Features hidden within bushes or small stands of trees can be missed by someone only 10m away & the best strategy is to search these separately.

Geophysical survey

The table below summarises sampling for some common geophysical methods. It is biased towards archaeological studies because the low target size makes adequate resolution paramount to success. That said, there will always be cases where an innovative approach may be necessary or where conditions prevent the best resolution from being acheived.

Method	Maximum Spacing	Ideal Spacing	Variables	Preferred Orientation
Magnetometry (archaeology)	0.5m x 1.0m	0.25m x 0.5m		Narrowest interval orientated towards magnetic north
Magnetometry (UXO)	1.0m x 1.0m	0.5m x 0.5m	Depends on target type & expected depth	Narrowest interval orientated towards magnetic north
Electrical Conductivity (agriculture)	5.0m x 5.0m	variable	Depth of soil, instrument used, weather conditions & current crop
Electrical Resistance (archaeology)	1.0m x 1.0m	0.5m x 0.5m	Soil type, recent weather & expected feature size	Slightly angled relative to known structures
Magnetic Susceptibility (archaeology - continuous survey)	2.0m x 2.0m	1.0m x 1.0m	Recent land use & coil separation of instrument (1.0m for EM38)
Magnetic Susceptibility (archaeology - point sample)	10m x 10m	5m x 5m	Recent land use & vegetation cover
Magnetic Susceptibility (archaeology - pedogenesis)	0.25m x 0.25m	0.1m x 0.1m	Nature of sediment
Radar (archaeological)	1.0m line spacing	0.5m spaced orthogonal lines	Size, depth & separation of targets	Slightly angled relative to known structures
Radar (sand & gravels)	10m line spacing		Exact purpose of survey

Topographic survey

Topographic survey is in some ways more straightforward as there is only one variable which is the scale at which the result is meant to be viewed. As long as sufficient points are measured along a feature or across a surface for the shape to be reconstructed at that scale in theory this is enough. However, the days of surveying straight onto paper plans are over & the advent of CAD & GIS mean that data can be viewed at a wide variety of scales. Surveys therefore need to catch the nuances of a shape as well as the overall form so that the model retains integrity at all relevant scales.

This is usually guided by a common sense notion of purpose. For example, it is frequently important to record the position of a gate post or telegraph pole, but its size is irrelevant & hence a single measurement is sufficient. In the same way as smooth curves were once modelled by drawing a curve through a scatter of points CAD can do the same - there is no need to create smooth lines of measurements in the field. Many asset management & restoration-driven surveys require the scale of vegetation to be measured & it is common to provide trunk & crown diameters of trees, the extent of bushes, etc.

For 3D surveys the situation is more complex as the curves of the ground need to be accurately modelled in all directions & while smooth surfaces can be interpolated between points sudden changes of slope cannot be modelled in this way. Break lines, lines of measurements that supply the 3D co-ordinates of edges, should be provided. Abrupt changes of level, e.g. at tops of retaining walls, need to be recorded as fault lines so that the interpolation process accurately renders the break.