# Seismic Identification and Characterization of Deep Strike-Slip Faults in the Tarim Craton Basin
## 4 Seismic Attribute Generation
### Curvature Attributes  
The curvature attributes of the seismic dataset reflect the degree of plane bending when the stratum is compressed by tectonic stress. The characteristics of small disturbances, folds, bulges, and differential compaction are identified from the curvature attributes [47]. The large faults show an obvious stagger of the in-phase axis in the conventional seismic profile, while the faults with small displacements show slight stagger, distortion, and sudden weakening of the amplitude in the seismic profile. Figure 4: Attributes of seismic energy. Most areas are significantly disturbed by “non-fault” areas, and a small number of branch faults can be shown but are not obvious. (**a**) Map of the RMS amplitude attribute. It has a good correlation with the rock density and is often used in lithologic phase transition analysis. (**b**) Plane graph of the low-frequency energy attribute. (**c**) Map of the high-frequency attenuation attribute. Due to the seismic response characteristic of high-frequency absorption shown by the faults, characteristics similar to “low-frequency enhancements” appear, and the waveform characteristics show little variation with depth. The maximum positive curvature and minimum negative curvature attributes are 3D plane attributes used to quantify the degree of layer interface deviation from the plane. The largest positive curvature in the normal curvature is called the maximum positive curvature. This curvature can amplify the fault information and some small linear structures in the plane [48; 49]. This curvature property is very useful for defining faults and their geometries. Faults represented by this attribute exhibit positive curvature values (high values). The minimum negative curvature in the normal curvature is called the minimum negative curvature, and its function is similar to that of the maximum positive curvature [50]. Combined with the maximum positive curvature, the characteristics of the surface can also be determined. The rate of change in the reflecting surface along different directions is reflected by the gradient \(grad(u)\):  
\[grad(u)=\frac{\partial u}{\partial x}\overset{\rightarrow}{i}+\frac{ \partial u}{\partial y}\overset{\rightarrow}{j}+\frac{\partial u}{\partial t }\overset{\rightarrow}{k}=p\overset{\rightarrow}{i}+q\overset{\rightarrow} {j}+r\overset{\rightarrow}{k} \tag{15}\]  
where \(p\), \(q\), and \(r\) are the components of apparent inclination along the \(x\), \(y\), and \(t\) directions, respectively. By substituting the apparent inclinations \(p\) and \(q\) into the equation, the curvature components along the \(x\) and \(y\) directions can be written as follows:  
\[ \begin{cases}\kappa_{x}=\frac{\frac{\partial^{2}u(x,y)}{\partial x}}{\left[1 +\left[\frac{\partial u(x,y)}{\partial x}\right]\right]^{\frac{3}{2}}}=\frac{ \frac{\partial p}{\partial x}}{\left[1+p^{2}\right]^{\frac{3}{2}}}\\ \kappa_{y}=\frac{\frac{\partial^{2}u(x,y)}{\partial x}}{\left[1+\left[\frac{ \partial u(x,y)}{\partial x}\right]\right]^{\frac{3}{2}}}=\frac{\frac{\partial u }{\partial x}}{\left[1+q^{2}\right]^{\frac{3}{2}}}\end{cases}  \tag{16}\]  
According to the identification results of the strike-slip faults of the cratonic basin with the maximum positive curvature and the minimum negative curvature attributes, the general trend of the main fault can be seen, but the internal details of the branch fault and the main fault cannot be identified and are significantly disturbed by the non-fault areas (Figure 5a,b). Dip  
The dip attribute reflects the change in the dip angle, and it is effective in depicting the dominant section with a large fault distance but is insensitive to small faults, which are affected by the data quality [51]. To calculate the inclination property, the instantaneous wavenumbers of the horizontal direction and the depth direction, \(L_{x}(x,y)\) and \(L_{y}(x,y)\), are first calculated:  
\[