### O pewnym zastosowaniu metody analizy trendu powierzchni w badaniach hydrogeologicznych

#### Abstract

Certain application of trend surfaces analysis to geohydrology

The object of author’s investigations was the .confined aquifer of Triassic period. The authors had at one’s disposal the dense but irregularly distributed piezometric hydraulic head measurement system on an average one observation well per 1 km2. It was possible to suppose that in the measurements taken in observation wells could appear some faults of unknown but different quantity. In the farther investigations, .which had to be conducted by means of the electric analog simulation method, the knowledge of local ground water flow pattern was indispensable. In order to attain it, they had to prepare, on the ground of measurement data, the maps of the piezometric surface in the considered aquifer. It was indispensable to determine the average values of local subpopulations of information regarding to hydraulic head, which corresponded with particular fragments of investigated surface, that is to say, the computing blocks of analog model. With the aim of attaining it the authors applied statistical method of trend surface analysis. In this paper the authors describe the chief point of the matter and they give the reasons for bringing this method into practice in the particular case. They accepted that the local hydraulic head distribution background results of the groundwater flow within confined aquifer from recharge zone to discharge zone. This background could be described by means of the coordinate functions of points (x, y ) in which the observations take place (Fig. 1). The polynomial of the first, the second or the third degree has to represent the assumed function because it renders possible the description of direction changes of the trend value. The polynomials of higher degrees often reveal the local periodic trend change, which in fact, doesn’t exist. Therefore, they are less serviceable for direction description of trend differentiation, which are expectable in case of local changes in piezometric hydraulic head. In their investigations, the authors realized an approximation of the observation data with polynomials of the degree from the first to the sixth. The testing of these functions was realized through determination coefficient and trend significance level calculation (Table 2). On the hydrogeological interpretation the graphic form of the trend function, the distribution and deviation values from this surface are more than mathematical form of polynomial. This interpretation is represented as a map in which the trend surface arrangement in space is illustrated with isolines (Fig. 2) and as a contour map of trend deviations (Fig. 3 ). For calculation of approximation function trends and for contour maps printing the authors used Leary, Lippert and Spitz program (1966) adapted for EMC ODRA 1305 computer. The authors realized the hydrogeological analysis and interpretation of these maps and they had motivated that the third degree trend surface represents the best way the local accordance of piezometric hydraulic differentiation. When there in the map the deviations from the trend surface appear and their location indicates that the accidental measurement errors can’t cause them, there are the other factors that cause them. After discussing the theoretical reason the authors submit a proposition that the positive „anomalies” in the map of piezometric pressure correspond with hidden recharge zones, while the negative anomalies correspond with discharge zones of this confined aquifer. On this ground, it was possible to note that the field of positive deviations in the eastern part of the area under consideration (Fig. 3) corresponds with the Triassic aquifer ascending recharge zone through Devonian limestones and dolomites forming its besement (Fig. 4). Their outcrops are situated hypsometrically higher. The field of positive deviations in the western part of the considered area corresponds with an isolated hydrostructure with the free water table which creates a morphological rise. The fields of negative deviations correspond with this part of surface, where there is a developed hydrographic system — or there is no impermeable cover. In both cases the Triassic aquifer is drained directly or indirectly. In conclusion, the authors note that the application of the trend surfaces analysis method for the ground — water flow pattern description of confined aquifers is justifiable everywhere where the large number of observation points are at one’s disposal. This method permits to decrease, in comparison with the visual method, measurement error consequences in the maps of the piezometric surface elaboration and it renders possible the detection and location of covered recharging and discharging zones of investigated confined aquifer.

The object of author’s investigations was the .confined aquifer of Triassic period. The authors had at one’s disposal the dense but irregularly distributed piezometric hydraulic head measurement system on an average one observation well per 1 km2. It was possible to suppose that in the measurements taken in observation wells could appear some faults of unknown but different quantity. In the farther investigations, .which had to be conducted by means of the electric analog simulation method, the knowledge of local ground water flow pattern was indispensable. In order to attain it, they had to prepare, on the ground of measurement data, the maps of the piezometric surface in the considered aquifer. It was indispensable to determine the average values of local subpopulations of information regarding to hydraulic head, which corresponded with particular fragments of investigated surface, that is to say, the computing blocks of analog model. With the aim of attaining it the authors applied statistical method of trend surface analysis. In this paper the authors describe the chief point of the matter and they give the reasons for bringing this method into practice in the particular case. They accepted that the local hydraulic head distribution background results of the groundwater flow within confined aquifer from recharge zone to discharge zone. This background could be described by means of the coordinate functions of points (x, y ) in which the observations take place (Fig. 1). The polynomial of the first, the second or the third degree has to represent the assumed function because it renders possible the description of direction changes of the trend value. The polynomials of higher degrees often reveal the local periodic trend change, which in fact, doesn’t exist. Therefore, they are less serviceable for direction description of trend differentiation, which are expectable in case of local changes in piezometric hydraulic head. In their investigations, the authors realized an approximation of the observation data with polynomials of the degree from the first to the sixth. The testing of these functions was realized through determination coefficient and trend significance level calculation (Table 2). On the hydrogeological interpretation the graphic form of the trend function, the distribution and deviation values from this surface are more than mathematical form of polynomial. This interpretation is represented as a map in which the trend surface arrangement in space is illustrated with isolines (Fig. 2) and as a contour map of trend deviations (Fig. 3 ). For calculation of approximation function trends and for contour maps printing the authors used Leary, Lippert and Spitz program (1966) adapted for EMC ODRA 1305 computer. The authors realized the hydrogeological analysis and interpretation of these maps and they had motivated that the third degree trend surface represents the best way the local accordance of piezometric hydraulic differentiation. When there in the map the deviations from the trend surface appear and their location indicates that the accidental measurement errors can’t cause them, there are the other factors that cause them. After discussing the theoretical reason the authors submit a proposition that the positive „anomalies” in the map of piezometric pressure correspond with hidden recharge zones, while the negative anomalies correspond with discharge zones of this confined aquifer. On this ground, it was possible to note that the field of positive deviations in the eastern part of the area under consideration (Fig. 3) corresponds with the Triassic aquifer ascending recharge zone through Devonian limestones and dolomites forming its besement (Fig. 4). Their outcrops are situated hypsometrically higher. The field of positive deviations in the western part of the considered area corresponds with an isolated hydrostructure with the free water table which creates a morphological rise. The fields of negative deviations correspond with this part of surface, where there is a developed hydrographic system — or there is no impermeable cover. In both cases the Triassic aquifer is drained directly or indirectly. In conclusion, the authors note that the application of the trend surfaces analysis method for the ground — water flow pattern description of confined aquifers is justifiable everywhere where the large number of observation points are at one’s disposal. This method permits to decrease, in comparison with the visual method, measurement error consequences in the maps of the piezometric surface elaboration and it renders possible the detection and location of covered recharging and discharging zones of investigated confined aquifer.