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4. Processing and visualisation of data

Characterising Noise in Archaeo-Geophysical Measurements

Armin Schmidt, Michel Dabas et Apostolos Sarris
p. 267-270

Résumé

– Noise can be characterised through geostatistical or spectral analysis.

– Under-sampled soil noise appears similar to random noise.

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Texte intégral

1To aid the archaeological interpretation of geophysical survey results it is desirable to minimise unwanted data (‘noise’). Geophysical measurements contain the sought after ‘signals’ and a ‘background’ against which the signals stand out as anomalies. The definition of what is considered to be the background usually depends on the context of a specific investigation. For example, the magnetic response of an ore body might be considered to be the background in an archaeological survey, but it could be the sought after signal in mineral exploration. Both of these components may be affected by noise, which can hence be considered to be the third contribution to geophysical measurements. It can be (i) internal, related to the instrumentation, (ii) caused by variations in the use of the instruments (e.g. while walking with a magnetometer), (iii) created by external signals entering the measurements (e.g. magnetic storms), or (iv) produced by the ground’s spatial variability, usually referred to as ‘soil noise’ (Schmidt et al., 2020). Once noise forms part of the measurement data it can be difficult to remove. Therefore, it should be attempted to minimise all avoidable sources (e.g. (ii) – poor use of instruments) during survey planning and execution.

2This paper describes ways of characterising noise in the data so that it can either be recognised and ignored during interpretation or, in the best case, removed. Some authors categorised unwanted data components as ‘errors’ that can be corrected and ‘noise’ that is unpredictable (Ghezzi et al., 2019; Schettino et al., 2019). Others preferred to base their discussion on the spatial appearance distinguishing between correlated and uncorrelated noise (Graham & Scollar, 1976; Scollar et al., 1990). For the current discussion we consider all unwanted signals to be noise and focus on four particular forms:

  1. Random noise is created in a stochastic process and there is no correlation between two subsequent noise measurements, other than all being governed by a statistical probability distribution. Random noise is typically generated in the measurement electronics of geophysical instruments (through thermal or quantum processes).

  2. Spatial noise is created by small inhomogeneities in the ground that produce their own weak anomalies, which are considered undesirable and hence often labelled soil noise. If exactly the same measurements were repeated, they would record the same spatial noise.

  3. Non-stationary noise is created by a time-varying process and superimposed on the recorded data. This can be synchronous with the spatial sampling of measurements (e.g. when walking with a magnetometer) or asynchronous (e.g. from external radio signals).

  4. Sampling noise results from a coarse sampling of spatial or non-stationary noise such that the existing correlation between adjacent data is unnoticed. According to the Shanno-Nyquist sampling theorem this occurs when the distance between measurements is bigger than half of the minimum wavelength of the underlying noise (Unser, 2000).

3In many instances sampling noise is mistaken as random noise and could be minimised by increasing the sampling frequency. Thus, for surveys that continuously move instruments over the ground, recording data with a higher resolution, rather than averaging them, may allow subsequent data processing to reveal patterns of spatial or non-stationary noise. By contrast, random noise can only be reduced when averaging stationary measurements. Such an improvement depends on the square-root of the number of averages (i.e. 100 averages improve data by a factor of 10) and therefore requires a considerable number of stationary readings.

4The mathematical discipline of geostatistics uses models of spatial data variation (‘variograms’) to estimate values at locations in between measurements (‘kriging’) (Matheron, 1969; Wackernagel, 2003). In addition to interpolation and data aggregation (Tamba, 2012) such variograms can also be used to examine the similarity of neighbouring measurements and estimate the average difference between repeat measurements at the same location (the ‘nugget effect’), in other words the level of random noise. Variograms also allow evaluating the ‘range’ of coherence, which is the distance at which measurements become independent of each other. For this study, such variograms were calculated for fluxgate gradiometer data from two sites (Table I).

Table I. Characteristic parameters for fluxgate gradiometer data from two sites.

Spatial Resolution

Area for Analysis

Data Range

Instrument

Site A

0.125 m × 0.5 m

30 m × 10 m

±2.8 nT

Geoscan FM256

Site B

0.25 × 0.5 m

60 m × 20 m

±0.3 nT

Bartington Grad 601

5The results in Figure 1 show that irrespective of the sampling resolution the variograms have a negligible nugget effect and a range value of 0.8 m and 1.4 m for sites A and B, respectively. It hence appears that the contribution of random instrument noise to the data is minimal for both surveys. Site A shows short-wavelength variability in the right half of the survey area, which may be one of the reason for the slightly shorter correlation range.

Figure 1. Variograms calculated along the horizontal (x-) axis for data from the two sites (see Table I).

Figure 1. Variograms calculated along the horizontal (x-) axis for data from the two sites (see Table I).

6A different approach to the analysis of noise is the well known calculation of spatial frequencies (Fig. 2), which started to be applied to archaeological geophysical data when the first computer processing of data became available (Scollar, 1970). Given sufficiently high sampling rates the small-scale variations of spatial noise can be seen as spikes of high wave-numbers and removed with a suitable low-pass filter. However, where spatial noise is under-sampled, even frequency analysis cannot distinguish it from random noise as the necessary high wavenumbers cannot be retrieved.

Figure 2. Spatial frequencies calculated along the horizontal (x-) axis for data from the two sites (see Table I).

Figure 2. Spatial frequencies calculated along the horizontal (x-) axis for data from the two sites (see Table I).

7As it is difficult to remove noise from recorded measurements, considerable efforts should be made during data acquisition to minimise it as far as possible. Of the remaining sources, modern instruments often create only low levels of random noise so that the main contribution originates from small-scale variations in the soil. This soil noise is often mistaken as random noise due to a spatial sampling resolution that is coarser than the typical wavelength of soil variations. Several methods exist for the evaluation of noise in geophysical data and a combination of geostatistics and spectral analysis can provide useful insights. Even if noise cannot be removed fully, such an analysis can help with the archaeological interpretation of survey results.

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Bibliographie

Ghezzi, A., Schettino, A., Tassi, L., Pierantoni, P.P., 2019. Magnetic modelling and error assessment in archaeological geophysics: the case study of Urbs Salvia, central Italy. Annals of Geophysics, 62(4): GM451.

Graham, I.D.G., Scollar, I., 1976. Limitations on Magnetic Prospection in Archaeology Imposed by Soil Properties. Archaeo-Physika, Technische und Naturwissenschaftliche Beiträge zur Feldarchäologie, 6: 1-124.

Matheron, G., 1969. Le krigeage universel. École nationale supérieure des mines de Paris, Fontainebleau.

Schettino, A., Ghezzi, A., Pierantoni, P.P., 2019. Magnetic field modelling and analysis of uncertainty in archaeological geophysics. Archaeological Prospection, 26(2): 137-153.

Schmidt, A., Dabas, M., Sarris, A., 2020. Dreaming of Perfect Data: Characterizing Noise in Archaeo-Geophysical Measurements. Geosciences, 10(10): 382.

Scollar, I., 1970. Fourier Transform Methods for the Evaluation of Magnetic Maps. Prospezioni Archeologiche, 8: 9-41.

Scollar, I., Tabbagh, A., Hesse, A., Herzog, I., 1990. Archaeological Prospecting and Remote Sensing. Cambridge University Press, Cambridge.

Tamba, R., 2012. Testing the Use of Geostatistics to Improve Data Visualization. Case Study on GPR Survey of Tarragona’s Cathedral. Archaeological Prospection, 19(3): 167-178.

Unser, M., 2000. Sampling-50 years after Shannon. Proceedings of the IEEE, 88(4): 569-587.

Wackernagel, H., 2003. Multivariate Geostatistics: An Introduction with Applications. Springer, Berlin, Heidelberg, New York.

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Table des illustrations

Titre Figure 1. Variograms calculated along the horizontal (x-) axis for data from the two sites (see Table I).
URL http://journals.openedition.org/archeosciences/docannexe/image/10014/img-1.jpg
Fichier image/jpeg, 1,4M
Titre Figure 2. Spatial frequencies calculated along the horizontal (x-) axis for data from the two sites (see Table I).
URL http://journals.openedition.org/archeosciences/docannexe/image/10014/img-2.jpg
Fichier image/jpeg, 2,1M
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Armin Schmidt, Michel Dabas et Apostolos Sarris, « Characterising Noise in Archaeo-Geophysical Measurements »ArcheoSciences, 45-1 | 2021, 267-270.

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Armin Schmidt, Michel Dabas et Apostolos Sarris, « Characterising Noise in Archaeo-Geophysical Measurements »ArcheoSciences [En ligne], 45-1 | 2021, mis en ligne le 16 août 2021, consulté le 29 janvier 2023. URL : http://journals.openedition.org/archeosciences/10014 ; DOI : https://doi.org/10.4000/archeosciences.10014

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Auteurs

Armin Schmidt

Corresponding author, GeodataWIZ, Remagen

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Michel Dabas

AOROC, UMR 8546, CNRS-PSL, École Normale Supérieure, Paris, France

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Apostolos Sarris

Department of History and Archaeology, University of Cyprus, Nicosia, Cyprus

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