# The Impact of Gravity on Different Height Systems: A Case Study on Mt. Medvednica
## 4 Gravity Measurements
### Corrections of Gravity Measurements
#### 4.1.1 Corrections Related to the Measuring Instrument
To obtain the gravity value at the Earth's surface, it is necessary to determine how gravity changes with height variation and to measure the distance between the instrument's sensor and the physical surface of the Earth at the time of measurement. The change in gravity with height variation is called the vertical gradient, and the value used in practice is 0.3086 mGal/m. The height of the measurement sensor relative to the physical surface of the Earth cannot be directly determined, as the sensor is enclosed within the instrument's housing. For this reason, the manufacturer specifies in the user manual the distance between the measuring sensor and the lower edge of the instrument. The user must then measure the distance from the Earth's surface to the lower edge of the instrument in the field, based on which the correction for the sensor height in mGal can be calculated using the following equation [4; 28; 29]:  
\[g_{tms}=0.3086(h_{m}+h_{0}), \tag{38}\]  
where \(h_{m}\) is the height from the Earth's surface to the lower edge of the instrument measured in the field and \(h_{0}\) the height between the measuring sensor and the lower edge of the instrument given by the manufacturer (for _Scintrex CG-6_, \(h_{0}=0.066\) m [33]). For the gravimeter to accurately determine the gravity value, the equipotential surface on which the measuring sensor is located must be parallel to the equipotential surface at the point of interest. If these two surfaces are not parallel, the measurement will not be entirely correct. The tilt of the gravimeter relative to its ideal position can be considered in relation to two axes (\(x\) and \(y\)) and can be denoted as \(\theta_{x}\) and \(\theta_{y}\). The correction for the tilt of the measuring sensor can then be calculated using the following equation [34]:  
\[g_{tms}=g_{m}\big{(}1-\cos\theta_{x}\cos\theta_{y}\big{)}, \tag{39}\]  
where \(g_{m}\) is the measured gravity value at the point. Since the gravimeter must be precisely leveled before measurement, the \(\theta_{x}\) and \(\theta_{y}\) values are always very small, expressed in arcseconds. As a result, this correction will always be very minor and practically negligible. Due to the imperfections of the measurement system during field surveys, the gravimeter's spring undergoes a time-dependent variation from its initial equilibrium position. This variation is called gravimeter drift, and to obtain a correct gravity value, it must be eliminated. While the order of other corrections is not crucial, the gravimeter drift correction must always be applied last to ensure that only the time-dependent changes in the spring's zero position are modeled. A necessary condition for drift elimination is that at least one point is observed at least twice within a single day [28]. If this condition is met, the drift correction can be calculated in three steps (Figure 12):From the measurement day, the gravity values of the point that was observed multiple times that day (in this case, point AGT03-E3) need to be extracted, with all the previously mentioned corrections already applied (black circles);
2. A gravimeter drift model is created based on the extracted gravity values and their corresponding measurement times. In this article, the method of linear regression is used for this purpose, resulting in a drift model, i.e., the coefficients of the equation of the line that best approximates all the measurements (red line);
3. Based on the drift model, it is necessary to calculate the gravimeter drift value for each point in a day and correct the gravity measurements accordingly (blue circles). In Table 4, the procedure for the numerical correction of the gravimeter drift is presented. The first column shows the difference between the first and last gravity acceleration values of a repeatedly observed point in a day. The second column contains the gravimeter drift model, i.e., the equation of the trendline that best describes the measurements.