## 2 Materials and Methods
### Data Processing and Interpretation  
The principle of GPR operation is conceptually simple and involves directing an electromagnetic radio energy (radar) pulse into the subsurface, followed by measurement of the elapsed time taken by the signal as it is travels downwards from the transmitting antenna, partially reflects off a buried feature, and is eventually returned to the surface, where it is recorded by a receiving antenna. For each point of measurement along a GPR transect, reflections from different depths produce a signal trace,  
Figure 4: GPR measurement transects (yellow lines) and locations of physical RTK/GNSS base stations (orange squares): (**a**) Site 1; (**b**) Site 2; (**c**) Site 3.  
which is a function of the radar wave amplitude (and energy) versus two-way travel time. (Note: As previously indicated, soil water content measurements can be used to convert two-way travel times to depth values.) Antenna frequency, soil moisture conditions, clay content, salinity, and the amount of iron oxide present all have a substantial influence on the distance beneath the surface to which the radar signal penetrates. Differences in the dielectric constant across a buried feature discontinuity govern the amount of radar energy that reflects off the buried feature and then returns to surface to be recorded by the receiving antenna. Previous research [5] shows that the GPR drainage pipe response (i.e., amount of radar energy reflected from a buried pipe) does not depend on the type of pipe (clay tile or CPT) but rather the difference between the dielectric constant of the soil surrounding the pipe versus the dielectric constant of the air and/or water inside the pipe. A GPR profile (i.e., cross-section) of the subsurface beneath a GPR transect is generated by sequentially combining, side-by-side, one after another, the signal traces obtained at each measurement point along the transect. The horizontal axis on a GPR profile represents distance along the transect (in meters), while the vertical axis represents two-way radar signal travel time (in nanoseconds) and/or depth (in meters). With depths of investigation of 1.5 or 2.0 m, the GPR profiles generated for this study essentially depict GPR responses only within the soil profile. Figure 5 depicts the two types of GPR profile drainage pipe responses. Where there is a somewhat modest to large angle (i.e., 15\({}^{\circ}\) < x\({}^{\circ}\) < 90\({}^{\circ}\)) between the GPR transect orientation and drain line directional trend, the GPR response is that of an upside-down U-shaped feature (i.e., reflection hyperbola), and the position for the top of the drainage pipe corresponds with the apex of the reflection hyperbola (Figure 5a). The drainage pipe reflection hyperbola is horizontally compressed if the angle is closer to 90\({}^{\circ}\), while alternatively, if the angle is closer to 15\({}^{\circ}\), then the reflection hyperbola becomes spread out horizontally. It is important to note other buried features, such as large stones can produce a reflection hyperbola, but in map view, the location of these features are isolated, while mapped locations of actual drainage pipe reflection hyperbolas form a line. Where the GPR transect is essentially over top and along trend (x\({}^{\circ}\) < 15\({}^{\circ}\)) of a drain line, the GPR response formed is that a banded linear feature, with the position for the top of the drainage pipe corresponding to the top of the banded linear feature (Figure 5b). Obtaining the banded linear GPR drainage pipe response is fairly uncommon because this response requires, without any prior knowledge of drain line locations and directional trends, that a GPR transect just happens to be oriented over the top and along the trend of a drain line. EKKO Project 5 software (Sensors & Software Inc., Mississagua, ON, Canada) was used to process and interpret the GPR-RTK/GNSS data acquired at Sites 1, 2, and 3, starting with the generation of GPR profiles from the GPR measurement transects.