# Optimised Extraction of Archaeological Features from Full 3-D GPR Data
## 3 Methods
On MO data, several precise methods can be exploited, with most of them based on the shape of the reflectors of common midpoint gathers (CMP). Unfortunately, as reported in the Introduction section, the most common GPR acquisition strategy encompasses CO surveys even when array antennas are adopted. On CO data, the velocity analysis can be completed by exploiting the scattering events (diffractions); the most common analysis methods are diffraction hyperbola fitting and migration velocityscans [20]. The overall accuracy of such techniques and the spatial resolution of the reconstructed velocity field are often limited, since usually only a few diffractors are present and they are not regularly distributed within the investigated area. The number of diffractions usable for the velocity analysis by hyperbola fitting was not relevant; however, we combined all the obtained analyses (after a careful check evaluating the reliability of strong lateral variations) and used the obtained velocity field for 3-D Stolt time migration and depth conversion. The Stolt algorithm was selected as it requires low computational resources and produces acceptable results for smoothed EM velocity fields, as in the present case. A direct calibration was further conducted thanks to an outcropping drainage pipe in the western portion of the area (Figure 2), at a measured depth of 1.31 m. A velocity of 9 cm/ns was obtained by the fitting of that hyperbola, thus giving an estimated depth for the pipe of 1.35 m. Therefore, there was a depth error equal to 4 cm (3%), which is considered to be within the intrinsic accuracy limits of the applied method. On the processed data we calculated various GPR attributes. GPR attribute analysis can enhance the GPR performance, because attributes are potential indicators of subsurface changes of physical properties of archaeological interest [18; 39], thus emphasizing features and patterns not apparent in the amplitude data. Attributes are increasingly applied to reveal archaeological targets for 2-D and 2.5-D datasets (e.g., [40; 41]) but, as far as we know, there are only a few recent examples of their application on full 3-D data in  
Figure 2: (**A**) Exemplary time-slice of the GPR data volume processed and the location of the areas reported in Figures 3–9; (**B**) Portion of a GPR profile crossing an outcropping pipe (its location is highlighted in A by the yellow arrow) and the result of the hyperbola fitting analysis. archaeology [42]. For GPR attribute calculation we used software originally developed for reflection seismic data analysis and interpretation (Petrel--Schlumberger and OpenDect--dGB Earth Sciences). Calculation details and the performance of some selected attributes are reported in the next paragraph. We further used the Petrel platform for the semi-automatic extraction of isosurfaces, i.e., zones in which an attribute has values higher or lower than a set threshold. Our approach was quite different (and simpler) from the one proposed by [43], which exploited a structuring element strategy in which linear predefined templates are used to extract walls. In our test, only some of the targets were linear (typically this is the case of walls) but many others were planar elements, localized features, or exhibited complex shapes (circular, semi-circular, irregular). We adopted an autotracking function implemented in Petrel: After just a few control points (seeds) with values considered typical for the desired feature are manually picked by the operator, our function is able to automatically extract all the cells (or voxels) with predefined values for a specific attribute. From such points the algorithm is able to select within a predefined search space, which can be either the entire dataset or a portion of it, all the cells having values close to the ones of the seeds and matching pre-set thresholds. An intrinsic advantage of this strategy is that each attribute can be independently used and, by integrating the results, an improved extraction can be achieved.