## 2 Materials and Methods  
### Experimental Data Acquisition  
In the summer of 2019, soil sampling was conducted in the Olesnica district, Lower Silesia province of Poland, on a 12.86 ha field (Figure 1). After the combined harvestingof winter oilseed rape grown in the 2018-2019 growing season, a universal cultivator, Horsh Terrano, was used to cultivate the field at a depth of 0.01 m. This was preceded by measurement procedures in accordance with the Polish Soil Classification System [50] and USDA Soil Taxonomy [51], which classified the soil as sandy clay loam (sand 57.3%, clay 24.3%, and silt 18.4%).  
The Geonics EM38 conductivity meter [52] is a movable field instrument designed to approximate soil ECa and MS in the rooting zone (depth of 1.5 m). Its high speed and accuracy support broadscale soil conductivity measurements. EM38 sets up a primary electromagnetic field; small horizontal electrical currents in the soil are induced, and as a result, a subsequent electromagnetic field is generated. It has a built-in receiver coil that detects both fields, and the proportion of these is the measurement of ECa displayed in units of ms\(\cdot\)m\({}^{-1}\). EM38 measures electrical conductivity either vertically (EM38V), with a theoretical depth response curve of 0 to 1.5 m, or horizontally (EM38H), with a theoretical depth response curve of 0 to 1 m [53], and allows for a faster method of determining if conductivities increase or decrease with depth. Soil moisture equaled 30% measured over a short interval after the EM38 survey; temperature was equal to 15 \({}^{\circ}\)C.  
Using the cone penetrometer (Eijkelkamp Soil & Water, Giesbeek, The Netherlands) with GPS, soil compaction was measured for a soil layer between 0-0.5m. A cone with a base of 0.0001 m\({}^{2}\) and an angle of 60\({}^{\circ}\) was used during field measurements with a penetration speed of 0.03 m\(\cdot\)s\({}^{-1}\). After measuring electrical parameters and analyzing the results, a total of five management zones were mapped. In a 30 m grid, soil compaction measurements were conducted, and coordinates were assigned to each measured point based on the GPS position of the Eijkelkamp Penetrologger. The nearest point of soil electrical conductivity and magnetic susceptibility measurements were linked to each spot of soil compaction measurement using the least-squares method. Based on previous research [54], soil compaction was estimated at a depth of 0-0.5 m, and between 0.4 and 0.5 m was chosen for further analysis.  
For shear stress measurement, the field inspection tester VANE-H60 (Eijkelkamp Soil & Water, The Netherlands) was used. This tool allows for a swift determination of soil shear stress. It comprises exchangeable vanes of different dimensions (16 \(\times\) 32, 20 \(\times\) 40, 25.4 \(\times\) 50.8 mm (extended)) and many 0.5-m rods. This equipment makes it possible, depending on the vane used, to measure shear stress between 0 and 260 kPa. The peak value is determined using a scale ring, which must be turned back to the zero position before and after every measurement. The extension rods are specially designed to provide the connection maximum with bending resistance. It has a maximum measuring depth of 3 m (reasonable correlation to full-scale field vane tests), shear stress of 260 kPa, measuring accuracy of \(<\)\(\pm\)10%, and reading accuracy of 1%. Dummy tests were performed with rods only to perfect the skin friction of the extension rods. The measurement of shear stress was conducted at the depth of 0.25 m. The measurement points (GPS positions) for shear stress  
Figure 1: The location of the study area (\(\bullet\)) on a map of Europe, Poland, and Lower Silesia province.  
and the method for linking ECa and MS measurements were the same as in the case of soil compaction.