## 3 Materials and Methods
### Well Log Data  
As a numerical simulation input, it is important to know the lithost stratigraphic unit distribution in every well and the quantitative lithological composition of unique formations [50]; thus, the integral natural gamma-ray logs have been used to identify the Late Miocene and Pliocene formations. The spontaneous potential logs were applied for a more reliable lithology evaluation, and the gamma ray or spontaneous potential logs have been combined with deep resistivity logs. The main lithost stratigraphic units have been identified within the Late Miocene and Pliocene series, but the delta front (Ujfalu Fm.) and the alluvial plan (Zagyva Fm.) sediments have not separated. The hydrostatic pressure regime is present within the delta front and alluvial sediments, which is controlled by the topography-driven flow system above the overpressured confined pressure regime [12; 51]. Shale volume has been calculated with the Larionov formula (Tertiary) that was applied to develop unique compositional lithologies as an input [52]. The filtering out of the non-shale samples to the identification of top of overpressure has been carried out based on the shale volume values. Moreover, the overpressure generation mechanisms have been identified on the physical properties of shale samples that were separated based on the shale volume values, too. Porosity values for the whole Late Miocene and Pliocene series have been calculated from bulk density logs [53]. The porosity values take part in the calibration of numerical simulation and delivered the input values to the porosity-depth relationships to describe  
Figure 4: Developed workflow with the three main phases that can deliver the stochastic pressure models to predict and evaluate the subsurface pressure regime on a basin scale. the compactional behaviour of the unique lithologies. The density porosity has been derived from a linear response function:  
\[\phi_{DEN} = \frac{\left(\rho_{matrix}-\rho_{bulk}\right)}{\left(\rho_{matrix}- \rho_{fluid}\right)},\]  
where \(\phi_{DEN}\) is density porosity, \(\rho_{matrix}\) is matrix density, \(\rho_{bulk}\) is measured density, \(\rho_{fluid}\) is pore fluid density and the fluid density derived from the measured water density values. Matrix density has been back calculated from measured core porosity data, and the calculated porosity values have been calibrated with measured data. Acoustic P-wave travel-time logs have been applied to determine the top of the overpressure; previously, the non-shale intervals have been filtered out with calculated shale volumes. The acoustic travel time values have been converted into compressional wave velocities (V\({}_{\text{p}}\)) and were visualized on V\({}_{\text{p}}\)-depth plots (Figure 5). According to the V\({}_{\text{p}}\)-depth plots, the normal compactional trend was identified, because the compressional wave velocities increase linearly with depth in case of hydrostatic pressure conditions [51]. The presence of overpressure can result in a lag between the measured and normal compactional trends, so the top of the overpressured zone is identifiable. Depth intervals have been used as an indirect calibration point to the numerical simulations. The V\({}_{\text{p}}\)-depth plots also can show information about the overpressure generation mechanisms, because the wireline log signatures are unique in case of the main overpressure generation mechanisms. The non-equilibrium compaction results in almost constant compressional wave velocities with the increase of depth and the generated overpressure increases continuously with depth, i.e., it does not show pore pressure jumps. The compressional wave velocities will not catch up to the normal compactional trend in the case of under-compaction [54]. On the contrary, the fluid expansion triggers a fast pore pressure build up that results in sharp pressure increases on the pore pressure-depth plots.