Resistivity Probability Tomography Imaging at the Castle of Zena, Italy
© Vincenzo Compare et al. 2009
Received: 27 January 2009
Accepted: 8 October 2009
Published: 23 November 2009
We present the results of an electrical resistivity investigation performed at Castle of Zena (Castello di Zena), a 13th-century fortress located between the towns of Fiorenzuola and Piacenza in the Emilia Romagna Region (Northern Italy), in the frame of a project of restoration. Dipole-dipole resistivity tomographies were planned in three areas suspected of containing buried archaeo-architectural remnants. Data analysis has been made using a 3D tomography imaging approach based on the concept of occurrence probability of anomaly sources in the electrical resistivity distribution. The 3D tomography has allowed three interesting anomaly source areas to be identified in the 1-2 m depth range below ground level. Subsequent excavations have brought to light a giacciara, that is, a brickwork room for food maintenance, a furnace, and the basement of a wing of the castle destroyed in the 18th century, exactly in correspondence with the anomaly sources detected by the resistivity tomography.
Geoelectrics is one of the most reliable prospecting tools in the field of Cultural Heritage, thanks to the technological and methodological developments in recent years, which have made it a fast target-oriented method. The electrical resistivity parameter, on which the method is based, has such a large variability so as to allow the great majority of the structures and bodies of archaeologic and architectural interest to be readily distinguished, in principle, from the hosting material. To enhance the resolution power of the method, a great help is provided by the recently developed electrical resistivity tomography (ERT) approach, which involves the acquisition and processing of large datasets.
The ERT survey was planned in the framework of the SOCRATES project, sponsored by institutional subjects and finalised to the study and preservation of the castle and surrounding areas. The ERT survey was addressed to study the nature of the subsoil in three different zones, which the historians involved in the project suspected to contain remnants of great archaeo-architectural interest.
2. Outline of the Geoelectrical Method
The solution for the electrical potential arising from an electrical current flowing into the ground from a point source of current (a grounded electrode) is the starting theoretical point for the resistivity prospecting method. In practice, there is always a device of four electrodes used to measure the ground resistivity: two are used for injecting a current of intensity I and two for detecting a voltage (potential difference) .
For all of the devices the theoretical solution is basically a superposition of the fundamental equations for the potential from a current point source with appropriate sign for the current. The formulae for evaluating the resistivity of the ground are a product of the impedance and a geometric factor with the units of length which depends on the geometry of the four electrodes. However, as the resistivity is an intrinsic property of a homogeneous material and the subsoil is generally a complex distribution of different materials with different resistivities, the key concept of apparent resistivity, , is defined. In simple terms, is a volumetric average of a heterogeneous half-space, except that the averaging is not done arithmetically but by a complex weighting function dependent on the 4-electrode device and how it is used.
To investigate the resistivity distribution along a profile, a dataset is collected from a linear array of dipoles coupled to a transmitter/receiver unit through a series of solid state relays. Measurements are realised from predefined arrays of dipoles selected by the relays.
The plotting convention is to attribute the values of at the intersection point of two lines descending from the current dipole and from the voltage dipole. The resulting maps of are contoured at constant (usually logarithmic) intervals. The contoured sections are called pseudosections because they look somewhat like resistivity cross-sections of the ground, but actually they are simply a graphical representation of the dataset. The vertical scale is not depth but some function of the array spacing. For simplest geological models the relative pseudosections do have an intuitive relationship to the actual section but mostly they do not. For a layered earth the contour lines are horizontal and rise and fall in value in the same sense as the actual resistivity, but for the case of even a single vertical contact between dissimilar resistivities the pseudosection is a complex map with no direct relationship to the actual model.
A numerical inversion is used to convert measured apparent resistivity distributed along a pseudosection to electrical resistivity values displayed as a function of depth below surface.
The geoelectric resistivity tomography (ERT) approach comes from taking many determinations at as many locations as possible and involves the joint inversion of many independent tests, using an algorithm to discern subtle details from differences which would otherwise not be seen in any one test. The inversion of a dataset collected by the described DD profiling field technique gives rise to a two-dimensional (2D) DD ERT. If one assembles a set of parallel DD profiles, as we did in the Castle of Zena survey, the inversion of the whole dataset provides a three-dimensional (3D) DD ERT.
Resistivity inversion is a typical nonlinear, ill-posed, and underdetermined problem [1–4]. Furthermore, mainly in 3D cases, the number of the model parameters to be inverted is so high that the large computer time required to solve the problem makes the approach almost unpractical in routine applications. An efficient way of dealing with 2D and 3D inversion derives from a linearised form of the nonlinear problem. One-step and iterative linear methods have been proposed; see for example, [5–8]. The main advantage of such methods is that they can greatly reduce the computer time needed to generate an approximate model.
Following the one-step linearised strategy, a probability-based ERT method has also been developed in more recent years as a simple and fast anomaly source imaging tool [9–11]. It has been proven to be very useful in highlighting shape and position of the most probable sources responsible of the anomalies detected on the free surface. An outline of the probability-based ERT method is given below, since it was used to interpret the ERT survey performed in the Castle of Zena area.
3. Outline of the Probability Tomography
The probability tomography method consists in the analysis of an occurrence probability function ranging between −1 and +1, defined as a normalised cross-correlation product of the dataset by a suitably digitised scanner function, derived from the electric potential theory by a perturbation technique under Born approximation .
In practice, since the source pattern generating the observed anomalies is unknown, an elementary source of unitary strength is ideally used to scan the volume beneath the surveyed area, called the tomospace, and search where the sources are most probably located. From the analytical point of view, this ideal process corresponds to calculating the occurrence probability function in a grid of points in the tomospace. A positive value of this function will give the occurrence probability of an increase of resistivity with respect to a reference resistivity value, whereas a negative value will give the occurrence probability of a decrease of resistivity. By scanning the tomospace, a full 3D image reconstruction of the anomaly sources distribution can at last be obtained in a probabilistic sense.
A suitable reference resistivity can be either the true background resistivity, if it is known, or simply the average apparent resistivity, as we did in this study. At the end of the scanning procedure, one can draw sections or, more efficaciously, 3D images of the probability distribution pattern in the tomospace.
Besides this primary scope of the method, worthy of mention is a second, not less important peculiarity, which makes the 3D probability tomography a versatile and objective imaging approach. Since the algorithm can deal even with multiple datasets, independently of the acquisition technique, it also works as an intrinsic filter. The result is a simultaneous smoothing of the uncorrelated noise and suppression of any correlated phantom effects. In principle, this peculiarity derives from the circumstance that such types of disturbances have zero probability to be generated by true anomaly sources within the context of the geoelectrical theory.
Concluding, we think that it is useful to point out that the probability-based ERT approach cannot give estimates of the true resistivity contrasts which characterise the sources of anomalies. Therefore, it appears to be more appropriate in those circumstances in which the resistivity contrast of the targets is either known in advance or relatively less relevant than the discovery of their existence and retrieval of their shape. This is usually the case in target-oriented applications to archaeology. Otherwise, the method can be considered a valuable support to the classical interpretation. Its results can in fact be used as a priori robust geometrical constraints in anyone of the inversion routines.
4. The Survey Planning
Zone B: it covers an area of 620 m2, located south of the castle, where the construction of a swimming pool had been planned. 21 parallel profiles, 31 m long and spaced 1 m apart, were investigated. Each profile consisted of 185 measurements, thus totalling 3885 data points.
Zone C: it covers an area of about 600 m2, located inside the southwestern portion of the ditch that surrounds the fortress, where part of the destroyed southern wing of the castle was founded. Due to logistic difficulties, 18 profiles spaced 1 m apart, but with different lengths ranging between 15 m and 31 m, were measured. The total number of data points was 3560.
5. The 3D Probability Tomography
In the A-zone 4 holes (S1-S4) located as in Figure 11 were also bored. The results from the S2 hole, bored down to 5 m of depth in correspondence with the top right alignment of small positive nuclei, showed the only significant anomalies. In S2, a layer with significant signs of human activity was in fact detected at about 1.65 m of depth. A slimy-sandy-clayey layer, rich of bricks and carbonaceous frustules, was found . This fertile layer has, however, not yet been confirmed by direct archaeological excavations. It may reasonably extend over the whole top third of the A-zone, likely as patches separated by sterile zones. A support to this interpretation derives from the discontinuous nature of the dark nuclei and the circumstance that the hole S1, located a little outside the large horizontal sequence of nuclei in the top left-hand side of the area, did not meet any remnants. No interesting archaeological data came also out of the S3 and the S4 holes, thus confirming the absence of resistivity anomaly source nuclei in those areas.
The hole S6 was bored down to 5 m of depth, in correspondence with the small positive nucleus located at the centre of the lower half of the zone. The most significant archaeological layer was found between 0.7 and 1.47 m of depth with abundant brick fragments. In particular, the first strata are worthy of note because remnants similar to those found in the S5 hole were detected in the same depth range, allowing for a connection between them. The S7 hole, instead, was bored down to 5 m of depth in an area where the geoelectrical tomography did not put in evidence any relevant positive nucleus. The hole confirmed such a result, since only very rare fragments were there detected .
The C-zone is almost totally dominated by a positive pattern of source occurrence probabilities, composed of a double set of parallel positive nuclei, which appear to conform at right angle to the southwestern corner of the castle. The internal sequence of nuclei may reasonably attest the presence underground of the foundations of the fourth wing, including the tower, as indicated in the drawing of Figure 2, both destroyed in the 18th century. The outer sequence of positive nuclei may, instead, be associated to traces of structural elements connected to the castle, likely the base of the former embankment of the ancient ditch.
We have shown the results from an application of the 3D probability-based ERT imaging approach to a case-study of great importance from both the historical and architectural points of view, consisting in the mapping of some structural remains of the medieval Castle of Zena in three adjacent areas destined to restoration and renovation.
As outlined in previous applications [14, 15], the 3D probability-based ERT method can be considered a self-sufficient procedure, useful to delineate location and shape of the most probable sources of the anomalies detected on the ground surface. In this study, and more generally in the field of Cultural Heritage, the exact knowledge of the true resistivity is not so essential as the location and shape delineation of the expected targets. The rationale for this assumption is that, generally speaking, buried stone remnants or metal bodies of archaeo-architectural interest are characterised by true resistivities higher or lower, respectively, than the resistivity of the hosting environment, which normally consists of medium-to-low resistivity sediments. This, of course, facilitates the detection of meaningful anomalies on the measurement surface. It must also be stressed that the knowledge of the resistivity of the targets generally does not give any added value to the immediate interest of the historians, archaeologists, or architects. This is the reason why the 3D probability tomography approach has not required in this application a further step, aimed at associating true resistivity values to the revealed anomaly sources.
The subsequent ground-truth excavations are to be considered a further successful confirmation of the full validity of the 3D probability-based ERT imaging in detecting the targets location underground and of its resolving power. For a more detailed discussion on this aspect and examples of comparison with the results of inversion-based ERT approaches, the reader is referred to [9, 14, 15].
The authors wish to thank for the fruitful collaboration the Archaeology Service of Parma and Piacenza and the Institute of Technologies for Cultural Heritage, National Research Council (CNR), Italy. Thanks are also to Dr. P. Mancioppi, GEONORD Company, Piacenza, Italy, who has kindly provided them with the stratigraphic results from the boreholes, and to Professor. A. Augenti and his group, Department of Archaeology, Ravenna branch, University of Bologna, Italy, who has supervised the archaeological excavations in the areas indicated by the geoelectrical probability tomography.
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