Magnetic field modelling and analysis of uncertainty in archaeological geophysics

Abstract

One of the major problems in the forward modelling of magnetic anomalies is the assessment of a minimum level of acceptable accuracy in the fit between observed and theoretical anomalies. We present a new approach to the analysis and interpretation of archaeological magnetic anomalies, based on classical algorithms of forward modelling and a new technique of error assessment. This approach allows us to determine geometry, physical properties, and location of buried archaeological features, as well as the occurrence of fires or other historical events that may have affected the observed magnetic signal. Our method starts from the acquisition of total field data, usually in a regular grid arrangement, and proceeds through their reduction to archaeological magnetic anomalies. This reduction is performed subtracting from the observed total field data a polynomial representation of the regional field, on the basis of a rigorous criterion that tries to separate archaeological anomalies from geological (crustal) contributions. At the next step, a map of the maximum allowed misfit is built, which depends from the estimated uncertainty at each point of the magnetic anomaly field. This map specifies the maximum allowed deviation of theoretical anomalies from the observed values. The last step is the analysis of these anomalies through a new forward modelling tool, with the objective to reconstruct the three-dimensional arrangement of buried features and possibly obtain some information about the history.

Magnetic modelling and error assessment in archaeological geophysics: The case study of Urbs Salvia, central Italy

“…First, even the sophisticated knitting algorithms discussed above could not remove completely the edge effect. Secondly, the best results in the reduction of total field data to magnetic anomalies using the method of Schettino et al [2018] are obtained performing the analysis at the scale of the whole survey area, not on the individual much smaller regions. Therefore, we believe that the correct approach to the knitting of total field data should start with a procedure of equalization of the survey regions, which shifts each data set except one reference region by a constant value depending on the rms error of the difference grids along overlapped edges.…”

“…x , e 2 y , e 2 z ) 1/2 /2 1/3 . We can estimate the local uncertainty, e P , associated with positioning errors by the following expression (Schettino et al, 2018): (3)…”

“…Given that the greatest observable wavelength for a squared survey area of size L is l max = L, the core contribution is simply a constant F(x,y,z) = F 0 at the scale of archaeological survey areas (up to 100-200 m). Regarding the separation between crustal and archaeological anomalies, Schettino et al [2018] have shown that the maximum wavelength of archaeological features is between 80 and 100 m and that there are no wavelengths in the observed magnetic field between this threshold and the maximum observable wavelength for a survey area of size L, which is generally of the order of few hundreds m. Consequently, the reduction of total field data to archaeological anomalies by subtraction of a reference field F coincides with a HP filtering, where the cutoff wavelength l c depends from the polynomial degree N. This observation implies that the choice of N in Equation 1is critical for obtaining an accurate representation of the archaeological anomalies. Schettino et al [2018] noted that in many situations a value N = 1 is the correct choice for the polynomial representation of the reference field in areas not exceeding 50 m. Larger areas, up to 200 m width, could require a value of N between 4 and 5.…”

“…A new interactive forward modelling software, Ar-chaeoMag, has been designed at the University of Camerino for the specific needs of magnetic data modelling in archaeological geophysics [Schettino et al, 2018]. It can be freely downloaded at: http://www.serg.unicam.it/Downloads.htm.…”

“…To reduce the total field readings to magnetic anomalies, we used the comparative procedure proposed by Schettino et al [2018]. This procedure allows to select rigorously the polynomial degree N in Equation 1.…”