# Optimised Extraction of Archaeological Features from Full 3-D GPR Data
## 4 Results
Coherence is defined by waveform similarity in both the inline and crossline directions, considering patterns with various extensions and shapes. In general, by increasing the number of traces considered in the coherency calculation, more stable results can be obtained but with a lower resolution  
Figure 3: Comparison of time migration computed using different constant velocity values (**(A)**: 7 cm/ns; **(B)**: 9 cm/ns; **(C)**: 10 cm/ns; **(D)**: 12 cm/ns) on a portion of the 3-D volume (location in Figure 2). Red arrows point to EM features with specific circular and semi-circular shapes. level. This attribute can be calculated within a fixed length sliding window, usually defined by a lower- and upper-time boundary with respect to a central value lying on a time-slice or a specific horizon; another approach is to compute the attribute over the entire data volume then visualize the coherence along any arbitrary surface [47]. The number of vertical samples of the sliding window is another crucial parameter for coherence calculation (Figure 7). In general, a few (or just one) sample windows produce more detailed results but are more prone to both random and coherent noises, while with larger windows the overall resolution becomes lower, but results are much more stable. In our tests, 16 samples seem to have the best trade off (Figure 7). By considering a velocity of 9 cm/ns for this area and a central frequency of 300 MHz (slightly lower than the nominal one due to the filtering effect of the ground), it is possible to calculate the dominant wavelength, which is equal to 30 cm. The data sampling interval is equal to 0.24 ns, so 16 samples correspond to a time length of 3.84 ns, which can be converted into a thickness of 34.56 cm. These are general results and can be used as a guide when setting the time window length for coherence calculation: a length corresponding or close to the dominant wavelength of the data is a reasonable choice, but the target's dimensions and lateral variability also play an important role. Figure 4: Comparison between a 2-D profile (**A**) and 3-D analysis of the time-slice at 35 ns of the 3-D GPR volume (**B**) (location in Figure 2). An example of semi-automatic extraction of isosurfaces is provided in Figure 8 in which the trace envelope attribute is exploited, but the same approach can be applied to any attribute independently or to combined attributes (a.k.a., meta-attributes). One of the advantages of the procedure is that it is able to \"search\" in the entire data volume (or portions of it) for values within the set thresholds, making the entire process fast since the operators do not need to analyse single slices, as they do in the traditional picking procedures. In Figure 8B, isosurfaces highlight both localized, linear and planar elements within a depth range from 100 to 200 cm below the topographic surface. The lateral continuity of the automatically extracted structures is in general high, demonstrating that the approach is robust, but some \"holes\" are present, especially within planar targets. In any case, such artifacts do not limit the interpretability and do not misrepresent the archaeological potential of the extracted features. Figure 5: Comparison between a 2-D section and 3-D analysis of a portion of the 3-D GPR volume (location in Figure 2): (**A**) 2-D GPR profile across a high amplitude sub-horizontal feature and (**B**) time-slice at 30 ns, where the same elements can be better classified in terms of shape and dimension. Figure 6: Example of texture attributes calculated on the same depth-slice. See text for details. Figure 7: Coherency attribute calculation using the same 5 by 5 matrix pattern, but with different numbers of vertical samples: 4 (**A**), 16 (**B**), 32 (**C**). Yellow arrows point to two structures, while question marks refer to situations in which the coherence is low.