Miscellanea 553 ANNALS OF GEOPHYSICS, VOL. 51, N. 4 August 2008 Key words geomagnetism – magnetic dating – relo- cation 1. Introduction The geomagnetic field is commonly de- scribed through its potential, which can be rep- resented by a spherical harmonic series. A se- ries of coefficients (that are referred to as Gauss coefficients) of the spherical functions are enough to accurately depict the features of the field for a given time. The International Associ- ation of Geomagnetism and Aeronomy (IAGA) publishes regularly estimates of the Gauss coef- ficients at five-yearly intervals (Maus et al., 2005) these constitute the so-called IGRF mod- els that cover the evolution of the geomagnetic field from 1900 up to present. Another set of time-dependent Gauss coefficients, covering the interval from 1590 to 1990, compose the GUFM1 model by Jackson et al. (2000). The historical part of the model is essentially based on ship log books. Recently, both geomagnetic models (IGRF- 9 and GUFM1) have been used to compute the distribution of errors due to relocation of geo- magnetic data (Casas and Incoronato, 2007). Relocation is routinely carried out by archaeo- magnetists and consists on reducing data to a central location. This procedure permits to compare geomagnetic data from different loca- Application of the relocation-error distribution on geomagnetic databases. Analyses on the «Historical Italian Geomagnetic Data Catalogue» Lluís Casas (1) and Alberto Incoronato (2) (1) Departament de Geologia, Universitat Autònoma de Barcelona, Spain (2) Dipartimento di Scienze della Terra, Università degli Studi di Napoli, Italy Abstract The reliability of the Historical Italian Geomagnetic Data Catalogue, comprising 536 directions and 393 inten- sities, has been assessed by comparing the historical geomagnetic measurements with the GUFM1 model pre- dictions. Such measurements were assessed at three selected relocation centres. For all the data contained in the Catalogue it has been calculated the discrepancy between the relocated data and the GUFM1-model prediction at the relocation centres. There is a correlation between relocation distance and the mean discrepancy. The up- per limit of discrepancy assumable as relocation error has been selected using error distributions previously cal- culated using geomagnetic field models. Angular and intensity threshold lines have been slightly shifted upwards to account for the estimated error of GUFM1 model itself at the considered region, mainly due to the crustal field. The Italian database proved to contain reliable data, as only a very low percentage of data (namely 14 di- rections and 20 intensities) can be considered anomalous. Possible explanations for such questionable data are suggested. All the remaining data of this catalogue could thus be added to the databases used to produce region- al or global geomagnetic models. Mailing address: Dr. Lluís Casas, Departament de Geologia, Universitat Autònoma de Barcelona, Edifici C, Campus de la UAB, 08193 Bellaterra (Cerdanyola del Val- lès), Spain; e-mail: lluis.casas@uab.cat Miscellanea 9-03-2009 14:41 Pagina 553 554 L. Casas and A. Incoronato tions. The relocation process is usually per- formed using the «conversion via pole» method (CVP) and assumes a purely dipolar field with- in the area where the relocation is done. As is stated in Casas and Incoronato (2007) the distri- bution of relocation errors can be used by ar- chaeomagnetists as an indication of the maxi- mum error induced by such a practice. Howev- er, this conclusion is restricted to periods with similar or lower values of the ratio between di- pole to non-dipole contributions than in the present geomagnetic field; this could cover at least the last 7000 years (Korte and Constable, 2005). Fig. 1. Map of Italy and neighbouring areas with indication of several data locations: solid dots (•) indicate dec- lination and inclination data at a given time from the Historical Italian Geomagnetic Data Catalogue (Cafarella et al., 1992a); open dots (�) indicate declination and inclination data at a given time from the database used to compute GUFM1 model; small dots (·) indicate single data values (declination or inclination) from the database used to compute GUFM1 model and finally open diamonds (�) indicate the three locations selected as reloca- tion centres. Miscellanea 9-03-2009 14:41 Pagina 554 555 Relocation-error distribution to analyse the «Historical Italian Geomagnetic Data Catalogue» Another possible application of the distribu- tion of relocation errors can be found on obser- vatory data from historical periods (last 400 years). The error distribution can be used to de- tect spurious data within historical geomagnet- ic databases. The historical Italian geomagnet- ic data catalogue (Cafarella et al., 1992a) has been used as a demonstrative example. This database, fully available at the cited reference (Cafarella et al., 1992a) is an excellent compi- lation of declination, inclination and intensity data (both isolate and simultaneous determina- tions essentially from the 19th century) from many locations in Italy obtained from libraries of old institutes and universities, as well as da- ta from Italian observatories (Cafarella et al., 1992b). The limited resolution of historical (and older) models that often results in an imperfect representation of the non-dipole field structure, brings a worthy motive to apply the relocation- error distribution, which checks the self-consis- tency of data assemblies, instead of founding decisions on data quality solely on a geomag- netic field model. Moreover, the methodology used and presented in this paper allows a quick survey on long lists of geomagnetic data with- out the need of computing the «true» values (from a global model) at every single location but only at a few selected relocation centres. 2. Analysis on the Historical Italian Geomagnetic Data Catalogue 2.1. Methodology The geomagnetic field for the time period of the data from the Italian catalogue is well de- scribed by the GUFM1 model (Jackson et al., Fig. 2. Comparison between the Neapolitan geomagnetic data, circles, from the Historical Italian Geomagnet- ic Data Catalogue (Cafarella et al., 1992a) and the GUFM1 (Jackson et al., 2000) field model, grey line, in Naples. Inset: angular mismatch between data from the Catalogue and the corresponding values computed us- ing GUFM1 model. Miscellanea 9-03-2009 14:41 Pagina 555 556 L. Casas and A. Incoronato 2000). It is worth to note that data from the Ital- ian catalogue were not used to build the GUFM1 model (see fig. 1), one of the authors of this model (A. Jackson) kindly provided us with the entire database used in his model and he also confirmed in a personal communication with the authors that the Italian catalogue was not used to develop GUFM1. However, the con- sistency between the Italian catalogue and the model can be assessed by comparing the his- torical geomagnetic measurements made in Naples (which is the most represented location within the Italian catalogue) with the model predictions for this location (fig. 2), coefficient R2 is 0.995. The calculation of the relocation error for any given geomagnetic datum requires the knowledge of the «true» value of the magnitude considered (direction or intensity) at the reloca- tion centre. Relocation error distributions pre- sented in Casas and Incoronato (2007) were calculated considering a grid of relocation cen- tres. For each of them, geomagnetic data from neighbouring sites (within a radius of 1200 km) obtained from a model (IGRF or GUFM1) were relocated. The relocation error was calculated as the difference between the relocated data and the data predicted by the model at the relocation centre. Relocation error distributions calculated using the historical database were computed similarly. The «true» values at the relocation centres were calculated using the GUFM1 geo- magnetic field model. Data containing both declination and incli- nation of a given site and time were selected from the Italian catalogue to carry out the direc- tional analysis. For the intensity analysis, data containing both inclination and the horizontal Fig. 3. Angular discrepancy between the relocated Italian-catalogue data and GUFM1 values at Viterbo as a function of relocation distance. Correlation is apparent. Miscellanea 9-03-2009 14:42 Pagina 556 557 Relocation-error distribution to analyse the «Historical Italian Geomagnetic Data Catalogue» projection (H) of the magnetic vector were se- lected. All the selected data (536 directions and 393 intensity values) were relocated to each one of three central locations distributed along the Italian latitude range (La Spezia, Viterbo and Naples) and their alleged relocation error was evaluated as the discrepancy between the relo- cated values and the ones predicted according to the GUFM1 model. The correlation between relocation distance and the mean «discrepancy» is the same found in Casas and Incoronato (2007). As an example the angular discrepancy between relocated data from the Italian cata- logue and GUFM1 values at Viterbo as a func- tion of relocation distance is plotted in fig. 3. The correlation is apparent, R2 parameter is 0.167. To cancel out the dispersion effect the correlation parameter can be computed averag- ing the data at 10 km intervals, then R2 raises to 0.454 and using only data with a relocation dis- tance lower than 450 km is already 0.815. How- ever some data exhibit discrepancy values that cannot be explained as solely due to relocation error. The upper limit of discrepancy assumable as relocation error has been selected using error distributions presented in Casas and Incoronato (2007). Figure 4 shows the evolution of the maximum values of relocation errors (both an- gular and intensity errors) through time accord- ing to the models. Three types of maximum val- ues have been plotted: the absolute global max- ima, the maxima for the range of latitudes of Italy and finally the actual Italian maxima. The absolute global errors have kept increasing for the last 200 years, this is due to the decline of the dipole to non-dipole field ratio although it might be also partially due to the increasing res- olution of the model for the most modern years. In any case, the local maximum errors (those across the Italian latitude or simply those of the Italian area) are similar and relatively constant through the time period analyzed. Therefore, the upper limits of assumable discrepancy for Fig. 4. Evolution of the maximum values of (a) angular and (b) intensity relocation errors through time accord- ing to the GUFM1 and IGRF-9 models (dashed and continuous lines respectively). Bold (Italian maxima), dark grey (Italian latitude maxima), light grey (global maxima). Miscellanea 9-03-2009 14:42 Pagina 557 558 L. Casas and A. Incoronato the Italian region have been selected as 0.35º and 300 nT per every relocated hundred of kilo- metres. Threshold lines have been shifted up- wards 0.5º and 300 nT to account for the esti- mated error of GUFM1 model itself at the con- sidered region, which is mainly due to the crustal field (Jackson, et al., 2000). This methodology allows a quick survey on long lists of geomagnetic data without the need of computing the «true» values (from a global model) at every single location but only at some relocation centres. 2.2. Results Figure 5 shows the discrepancy between re- located and predicted values at Viterbo as a function of relocation distance. The shifted and unshifted upper limits have been plotted to re- veal the outliers, though they show discrepancy values well above the average ones. The shift of the threshold lines reduces the number of out- liers and can be considered as a cautious filter to avoid the exclusion of appropriate data. Ta- bles I and II show the assembly of data that be- ing relocated fail to lie below the line of assum- able relocation error for at least one of the three relocation centres. These are 14 directions and 20 intensity data that could be regarded as anomalous. They only represent the 2.6% and the 5.1% of the total amount of directions and intensity values respectively. 3. Discussion Although some data are revealed as erro- neous for any relocation centre considered, it is noticeable that every relocation centre has a higher sensitivity to detect outliers from nearby locations. For instance, spurious data from northern Italy (Milano, Moncalieri…) are espe- cially detected from La Spezia, whereas spuri- ous data from Sicily (Palermo, Caltanissetta…) are particularly detected from Naples. This in- dicates that the defined threshold could actual- ly be logarithmic instead of linear. However, systematic evaluations described in Casas and Incoronato (2007) point to a linear dependence of the maximum errors up to relocation dis- tances of 1200km. Anyhow, this non-uniform sensitivity advises to perform this kind of analysis from a grid of relocation centres in- stead of a single central point. The anomalous values could be due to local- ly important crustal disturbances, for instance 50% of the spurious directional data comes from Moncalieri and Lanzo Torinese (two loca- tions from the Piedmont only 30 km away from each other). These data were published by a single author (Boddaert, 1907). However, most Fig. 5. Angular (a) and intensity (b) discrepancy between relocated data from the Italian catalogue and GUFM1 values at Viterbo as a function of relocation distance. Shifted line of maximum assumable relocation error has been plotted to identify anomalous data. Miscellanea 9-03-2009 14:42 Pagina 558 559 Relocation-error distribution to analyse the «Historical Italian Geomagnetic Data Catalogue» of the data in the Italian database from these two locations and from Superga, spelled as Soperga in the database, (~10 km away from Moncalieri) published by several authors lie just below the defined threshold. In fact, situat- ing Moncalieri and its surrounding locations on an aeromagnetic anomaly map of Italy (Cara- tori-Tontini et al., 2004) one notices that they lie in a zone with important positive and nega- tive magnetic anomalies and thus with impor- tant anomaly gradients which can result in high relocation errors. Concerning the anomalous di- rectional data from other locations, we could presume instrumental errors for one datum from Naples (1829.5) and two data from Rome (1640.5 and 1833.1) as they are the oldest measurements (comprising both declination and inclination) from these two locations. The correlation between time and angular mismatch observed in fig. 2 (inset) supports the signs of lower quality for the oldest data. Although not being that old, possibly instrumental errors are also affecting the anomalous values registered in Bormio and Castelnuovo because they are detected for any of the three selected relocation centres and their associated relocation errors are several times the average relocation error values and thus the discrepancy cannot be merely attributed to the combined effect of re- location procedure and crustal field. Anomalous intensity values can be partly explained by the low quality of their associated directional data which is fundamental to com- pute the relocation of intensity. For a significant part of the anomalous intensity data (40%) the associated declination values were not available and thus, for the relocation of the intensity, the position of the virtual pole obtained from a Table I. Directional data from the Historical Italian Geomagnetic Data Catalogue (Cafarella et al., 1992a) that fail to lie below the line of assumable relocation error for at least one of the three relocation centres: La Spezia (S), Viterbo (V) or Naples (N). Failure is indicated by ✓ sign. References are labelled according to Cafarella et al. (1992a). LOCATION TIME Reference S V N Roma 1640.5 Kircher*(1643) ✓ ✓ ✓ Napoli 1829.5 Fisher1 ✓ Roma 1833.1 Pianciani1 ✓ Milano 1863.8 Buzzetti*(1864) ✓ Bormio 1887.0 Chistoni*(1888) ✓ ✓ ✓ Castel Piano 1889.6 Palazzo10 ✓ Castelnuovo 1890.0 Kesslitz10 ✓ ✓ ✓ Moncalieri 1905.5 Boddaert*(1907) ✓ Moncalieri 1905.5 Boddaert*(1907) ✓ Lanzo Torinese 1906.0 Boddaert*(1907) ✓ Moncalieri 1906.5 Boddaert*(1907) ✓ Moncalieri 1906.5 Boddaert*(1907) ✓ Moncalieri 1906.5 Boddaert*(1907) ✓ Lanzo Torinese 1907.0 Boddaert*(1907) ✓ ✓ Miscellanea 9-03-2009 14:42 Pagina 559 560 L. Casas and A. Incoronato Table II. Intensity data from the Historical Italian Geomagnetic Data Catalogue (Cafarella et al., 1992a) that fail to lie below the line of assumable relocation error for at least one of the three relocation centres: La Spezia (S), Viterbo (V) or Naples (N). Failure is indicated by ✓ sign. Values in italics indicate that the corresponding direc- tional data (table I) also failed. References are labelled according to Cafarella et al. (1992a). LOCATION TIME Reference S V N NAPOLI 1805.0 Humboldt33 & Humboldt1 ✓ ✓ ✓ a NAPOLI 1829.5 Fisher1 ✓ MILANO 1834.9 von Waltershansen1 ✓ ✓ ✓ a FIRENZE 1835.0 Listing1 ✓ ✓ ✓ a PALERMO 1836.0 Listing1 ✓ ✓ ROMA 1838.4 Bache1 ✓ a MANTOVA 1846.6 Kreil1 ✓ ✓ ✓ NAPOLI 1859.5 Fox1 ✓ a RUTA 1859.5 Fox1 ✓ a SPOLETO 1859.5 Fox1 ✓ a NAPOLI 1860.3 Quetelet1 ✓ ✓ a MILANO 1863.8 Buzzetti*(1864) ✓ ROMA 1870.6 Braun1 ✓ NAPOLI 1871.0 Secchi1 ✓ TRAPANI 1881.0 Chistoni*(1881) ✓ PALERMO 1881.9 Chistoni*(1881) ✓ CATANIA 1882.0 Chistoni10 ✓ ✓ ✓ CATANIA 1882.0 Chistoni10 ✓ ✓ ✓ ARENZANO 1885.9 Chistoni10 ✓ CALTANISETTA 1890.6 Chistoni10 ✓ aDeclination values were not available. nearby location datum of similar age was used. The higher incidence of such kind of values compared with their occurrence (9%) within the general database of intensity values is evidence for the additional source of error due to the lack of knowledge of declination. Two more data have directional values already detected as anomalous and thus the corresponding relocat- ed intensity could lack of meaning. It is worth noting that in these cases the original (non-relo- cated) intensity values could be in fact not erro- neous at all. Finally, from the 9 remaining anomalous intensity values it is remarkable the high rate of data from Sicily (6 values from 5 Miscellanea 9-03-2009 14:42 Pagina 560 561 Relocation-error distribution to analyse the «Historical Italian Geomagnetic Data Catalogue» different locations) although it is difficult to ex- plain this geographical concentration in terms of crustal anomalies as the Sicilian directional data does not appear as doubtful. 4. Conclusions The distribution of relocation errors calcu- lated using IGRF-9 and GUFM1 models has been applied to a historical geomagnetic data- base (the Historical Italian Geomagnetic Data Catalogue) to detect abnormal data. Specific conclusions (on the Italian database) and gener- al conclusions (on the approach used) can be drawn. The Italian database has proven to contain reliable data, only a very low percentage of da- ta (14 directions and 20 intensities) can be con- sidered anomalous. This catalogue could thus be added to the databases used to produce re- gional or global geomagnetic models. Some reasons can be hypothesized to explain some of the outliers: i) poor quality of the measure- ments, this appears to correlate with the oldest data, ii) intensity data can appear anomalous as a consequence of the poor quality of their asso- ciated directional data, iii) local crustal distur- bances of the internal field, grounds for this ef- fect are found for several data from the Pied- mont area. The latter reason implies that not all anom- alous values are actually erroneous; discrepan- cies can arise from the fact that GUFM1 model was devised as a model for the core-mantle boundary and its extrapolation to the Earth’s surface disregards crustal contributors. The described methodology takes advan- tage of the higher resolution of the geomagnet- ic models that describe the present field to de- fine the limits to decide whether a value is con- sistent or requires additional explanation. Sim- ple comparison between the historical geomag- netic database values and its corresponding val- ues computed from a model would evade an overview on the global structure of the field and it would be difficult to establish acceptance lim- its as there are no uncertainty indications relat- ed to the values predicted by the model. A secondary advantage of the described methodology over the simple comparison be- tween every single data and its value computed from a model is precisely the fact that it is not necessary to compute all the data through the model. This could be important whenever the model is difficult to compute or simply not computable for some areas (e.g. when using a non-global model to evaluate data that lie out- side the application limits of the model, the da- ta could be relocated to a centre within the ap- plication area). Finally, even without any mod- el at all, the approach presented here could be used as a way to check the self-consistency of any assembly of data by relocating contempora- neous data to every neighbouring available data location. This should be helpful in areas where the existing models predict the field based on only a few historical records and specially when dealing with assemblies of archaeomag- netic data from a given area. 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(received March 26, 2008; accepted April 23, 2008) Miscellanea 9-03-2009 14:42 Pagina 562