# Seismic Identification and Characterization of Deep Strike-Slip Faults in the Tarim Craton Basin
## 4 Seismic Attribute Generation
### Gradient Attributes  
The amplitude spectrum gradient of the seismic dataset refers to the change rate of the seismic reflected wave amplitude with frequency in the effective frequency band, which highlights the variation characteristics of the seismic dataset amplitude at different frequencies. The strike-slip fault will lead to the wrong movement of strata on both sides, which makes the original uniform physical properties discontinuous. The gradient-like attribute body can sensitively capture the seismic waveform changes caused by discontinuities. (1) Amplitude variance  
The seismic variance body attribute is based on error analysis, which describes the geological structure data mainly through the similarity attribute of adjacent seismic signals [55]. Based on the seismic variance body attribute, the discontinuous fault and fold relationship between geological structures can be expressed. The specific steps for calculating the amplitude variance of this point are as follows [56]: (1) take the upper and lower half of the sampling points in the window, and first calculate the average amplitude value of all sampling points in each line of \(n\) channels of the seismic dataset in the window; (2) calculate the sum of the variance in the amplitude value and the mean value of the amplitude of each sampling point and the \(n\)-channel data at the same time; and (3) multiply the weighting coefficient and normalize to obtain the variance value of this point, move by the window and iterate steps 1, 2, and 3 to obtain the variance value of each sampling point of the whole data body of the work area, and then obtain the variance body. According to the identification results of strike-slip faults in the craton basin with amplitude variance attributes, the main and branch faults are relatively clear, but the whole area is disturbed by a large number of noise points, which makes the attribute body as a whole appear chaotic and not suitable for the fine characterization of strike-slip faults (Figure 7a). (2) Amplitude gradient  
The core idea of the fault prediction method based on amplitude gradient vector disorder detection is to assume that a fault plane is a plane in the local area. By searching the disorder of the seismic amplitude gradient vector in each azimuth and dip angle in 3D space, the most disordered surface is found to be the fault location [57]. The messiness of the amplitude vector needs to be searched along a certain direction of a seismic sample point, and the gradient construction tensor field expression is constructed as shown in Equation (23):  
\[(s,v)= \begin{bmatrix}\int D_{x}^{2}SW_{N}(s,v)&\int D_{x}D_{y}SW_{N}(s,v)&\int D _{x}D_{l}SW_{N}(s,v)\\ \int D_{x}D_{l}SW_{N}(s,v)&\int D_{y}^{2}SW_{N}(s,v)&\int D_{y}D_{l}SW_{N}(s,v) \end{bmatrix}  \tag{23}\]  
where \(D_{x}\), \(D_{y}\), and \(D_{z}\) are the rates of change in the seismic amplitude along \(x\), \(y\), and z with time \(t\), respectively; \(SW_{N}(s,v)\) is the smoothing factor along the direction \(v\); and the smoothing function is the multi-point Gaussian function. After establishing the matrix in direction \(s\), Equation (24) is used to obtain the disorder property of the amplitude vector:  
\[F(s,v)=\frac{3}{2}\frac{\lambda_{2}(s,v)+\lambda_{3}(s,v)}{\lambda_{1}(s,v)+ \lambda_{2}(s,v)+\lambda_{3}(s,v)} \tag{24}\]  
\(\lambda_{1}\), \(\lambda_{2}\), and \(\lambda_{3}\) are the first, second, and third eigenvalues of \(T\), respectively. Based on the seismic amplitude data, this method can directly search the distribution law of faults, and it is simple and efficient. The results show that the fault can be interpreted well both in the horizontal section and vertical section, and it is a good 3D automatic fault tracking scheme. According to the identification results of strike-slip faults in the craton basin with amplitude gradient attributes, both main and branch faults can be clearly shown (Figure 7b). At the same time, many details in the main fault can be detected with minimal interference from non-breaks.