## 2 Notes on the Theory, Method and Data  
### Theory: Theoretical Preliminaries about the Strike Angles  
The strike angle \(\theta\) (strike directions) is one of the gravity aspects (descriptors) and is defined as follows (see [1,3] and references therein):  
\[\tan 2\theta=2\ \frac{T_{xy}\Big{(}T_{xx}+T_{yy}\Big{)}+T_{xz}T_{yz}}{T_{ xx}^{2}-T_{yy}^{2}+T_{xz}^{2}-T_{yz}^{2}}=2\frac{-T_{xy}T_{zz}+T_{xz}T_{yz}}{T_{ xx}^{2}-T_{yz}^{2}+T_{ZZ}(T_{XX}-T_{YY})} \tag{1}\]  
(unambiguity within a multiple of \(\pi\)/2); \(T_{\bar{\jmath}}\) are the components of the Marussi tensor (e.g., [7]), i.e., the tensor of gravity gradients or second derivatives of the disturbing potential. These are non-linear combinations of the harmonic geopotential coefficients (Stokes parameters), and these are (in the form of a gravity field model) the input data for all our analyses. The full Marussi tensor is a convenient source of information about the density anomalies of the causative bodies, providing useful details about the underground objects located close to the Earth'ssurface and their shape and orientation. It was tested for local features (economic minerals, oil and gas deposits, faults, etc. ), e.g., [8; 9; 10]. Mathematically, the strike angle \(\theta\) is the main direction of the tensor \(\Gamma\); geophysically, it may indicate areas with lower porosity and/or stress anisotropy. For example, we observed that the strike angles are combed inside and within a certain distance from the impact craters, owing to the impact event [11]. Strike angle values contain information about the anisotropy, specifically about the target material and, in some cases, about the impactor direction (they are combed perpendicular to the impactor direction). The strike angles seem to be parallel to the weakness in the strength of the rock, e.g., schistosity and/or presence of micro-faults. The liberation of the energy of the impactor releases the stress of the rock along the cleavage planes, while the stress perpendicular to these planes is maintained. This anisotropy is what is being detected by the strike angles. The usual situation is that the strike angle \(\theta\) has diverse, random directions, as projected on the Earth's surface. The combed strike angles are the strike angles oriented roughly in one and the same direction in the given area (tutorial Figure 1), or creating a \"halo\" around the objects (e.g., around the impact crater) (tutorial Figure 2). It is not so important in which direction combed strike angles are, but the unidirectionality (or shaping a halo) is important. A theory for the \"combed\" strike angles was explained, together with relevant empirical statistics and examples, in [12]. Under any coordinate transformation, the Marussi tensor \(\Gamma\) preserves just three invariant parameters (\(I_{0}\), \(I_{1}\), \(I_{2}\)), known as gravity invariants:  
\[I_{0}=\textit{trace}\left(\Gamma\right)=T_{\text{xx}}+T_{\text{yy}}+T_{\text{ zz}}=\ 0\]  
\[I1\ =\left(T_{\text{xx}}T_{yy}+T_{yy}T_{zz}+T_{xx}T_{zz}\right)-\left(T_{xy}{}^ {2}+T_{yz}{}^{2}+T_{xz}{}^{2}\right)=\frac{1}{2}\sum_{\{i,j\}\in[x,y,z]}\left( T_{ii}T_{jj}-T_{ij}^{2}\right)\]  
\[I_{2}=\textit{det}\left(\Gamma\right)=\left(T_{xx}(T_{yy}T_{zz}-T_{yz}{}^{2} \right)+T_{xy}(T_{yz}T_{xz}-T_{xy}T_{zz})+T_{xz}\left(T_{xy}T_{yz}-T_{xz}T_{ yy}\right).\]  
The ratio \(I\) of the two gravitational gradients \(I_{1}\) and \(I_{2}\)  
\[0\leq I=-\frac{\left(I_{2}/2\right)^{2}}{\left(I_{1}/3\right)^{3}}\leq 1 \tag{2}\]  
Figure 1: Tutorial: the strike angles \(\theta\) [deg] combed (**a**) and chaotic (**b**); red color indicates their direction to the west and blue to the east of the local meridian, respectively. is always between zero and unity [7]. If the causative body is strictly 2D, then \(I\) equals zero; the higher \(I\), the \"more 3D\" the causative object. For oil and gas deposits, we rather expect flat (like 2D) than 3D objects, i.e., rather smaller than higher values in the interval \(I<\)0, 1\(>\).