## 1 Introduction  
The 'inverse problem', i.e., finding the driving best-fit stress tensor of a given fault population, has been central to the geological community for at least 40 years. Only four parameters, i.e., the orientations of the three principal stress axes (\(\sigma_{1}\), \(\sigma_{2}\), and \(\sigma_{3}\)) and the stress ellipsoid shape ratio \(\mathrm{R}=(\sigma_{2}-\sigma_{3})/(\sigma_{1}-\sigma_{3})\) with \(0\leq\mathrm{R}\leq 1\)[1; 2] are needed to obtain the driving stress tensor. Using numerous stress inversion algorithms with the aid of available software can quickly solve the inverse problem, e.g., [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12]. Despite the debate on whether the determined principal stress axes represent strain (kinematics) or stress (dynamics) (cf. [13]), there is an increasing number of methods for interpreting fault-slip data and calculating the driving stress tensors. The solutions are mathematically robust and not time-consuming for best-fit stress inversion methods, since they require at least four differently oriented fault planes with slickenlines [1; 14]. Nonetheless, they are geologically admissible only if the following fundamental assumptions are satisfied, e.g., [2; 3]: (1) The fault-slip data are homogeneous, i.e., they have been activated simultaneously under the same regional stress regime, (2) the orientation of the fault planes is random, (3) displacements on the fault planes are small concerning their lengths, (4) there are no rotations of the fault planes, and (5) slips on the fault planes are independent, and therefore, there is no fault interaction. Best-fit stress inversion algorithms, e.g., [3; 5], were deployed to define the four parameters of the driving stress tensor without having any limitation in the orientation of the stress axes. However, they have been based on the analysis of [15], which is carried out with a stress tensor, having one of its principal stress axes in a vertical position, like the Andersonian model [16]. More precisely, [15] evidenced that any fault slip, even an oblique-slip one, coinciding with the maximum shear stress, i.e., the Wallace-Bott hypothesis [15; 17], can be driven by a stress state with a vertical principal stress axis depending only on the stress ratio \(\mathrm{R}\). Despite some arguments about the validity of the Wallace-Bott hypothesis (e.g., [18; 19; 20; 21], the 'enhanced' Andersonian model with the addition of the stress ratio succeeds in describing any fault activation, even those driven by transpresional (TRP) or transtransional (TRN) stress regimes, without the need for the principal stress directions to rotate away from the recommended positions of [16; 22; 23]. Moreover, [24; 25; 26] presented a theoretical analysis, i.e., the Slip Preference Analysis (SPA), which indicates the geometry and kinematics of all possible optimal fault planes and their activations under the different enhanced Andersonian states of stress, i.e., extension, compression, and strike-slip, enhanced with the stress ratio values. The importance of the Slip Preference Analysis is that it provides additional compatibility criteria for the simultaneously activated faults under the enhanced Andersonian stress regimes, and therefore, the homogeneity of the fault-slip data. Geoscientists have tried to unravel the paleotress history of many regions by defining the'mean' or 'average' stress tensors that can better describe and represent the different tectonic events and concomitant fault reactivations over the rock volume investigated (e.g., [27; 28]). They use fault-slip data with various orientations recorded at different sites by applying several best-fit stress inversion methods [29; 30; 31; 32; 33]. The best-fit stress methods define stress tensors based only on the Misfit Angle (MA) minimization criterion between the observed fault slickenline and slip preference (SP) [24].