The horizontal velocities are decomposed into the fault-parallel and fault-perpendicular components to characterize the movement behaviors of the fault zone by following equations.
sin 90°) (6‐1) cos 90° (6‐2) where is the velocity vector, is the fault-perpendicular component, is the fault-parallel component, is the azimuth of fault strike, is the azimuth of velocity vector. For the fault-perpendicular component, it could indicate the contraction or extension movement across the fault. For the fault-parallel component, right-lateral or left-lateral strike-slip components can be detected across the fault. The positive fault-perpendicular component means the east-northeast direction and the negative means west-southwest direction. The positive fault-parallel component means the north-northwest direction and the negative means south-southeast direction.
In this study, three velocity profiles (Fig. 6-1) across the northern, middle and southern part of the fault zone are selected. The fault parallel components in three velocity profiles have significant velocity gradient across the fault zone. It has about 1.6 mm/yr in 4 km across the northern part of the fault zone (Fig. 6-2). The middle part of the fault zone has about 20.9 mm/y across the fault (Fig. 6-3) and the southern part of the fault zone has about 23.4 mm/y in 8 km (Fig. 6-4). The fault normal component also has about 1.9 mm/yr contraction in 4 km across the northern part of the fault zone (Fig. 6-2). Besides, the middle part of the fault zone has about 1.0 mm/y extension across the fault (Fig. 6-3) and the southern part of the fault zone has about 4.5 mm/y extension in 8 km (Fig. 6-4). However, the vertical velocities have no significant difference across the fault zone in three velocity profiles. In the northern and the southern profile, velocity gradient is also observed in the fault parallel component and the fault perpendicular component near the fault zone.
Fig. 6-1: Velocity profile maps of northern, middle and southern part of fault zone. Blue arrows are the fault perpendicular components, red arrows are the fault parallel component. Red dash lines are active fault. HCLF: the Houchiali fault, CCUF: the Chaochou fault, FTFZ: the Fengshan transfer fault zone.
Fig. 6-2: The velocity profile of the Fengshan transfer fault zone (northern part). Upper panel shows the fault parallel component. Middle panel shows the fault perpendicular component. Lower panel shows vertical velocity.
Fig. 6-3: The velocity profile of the Fengshan transfer fault zone (middle part). Upper panel shows the fault parallel component. Middle panel shows the fault perpendicular component. Lower panel shows vertical velocity.
Fig. 6-4: The velocity profile of the Fengshan transfer fault zone (southern part). Upper panel shows the fault parallel component. Middle panel shows the fault perpendicular component. Lower panel shows vertical velocity.
7. 2D Fault Model
7.1 2D dislocation model
The 2-D dislocation fault mode is used to invert the horizontal velocities for estimating slip rates and fault parameters in this study. Base on the analysis of velocity profiles, the fault behavior of the northern, middle, southern segment of the fault zone are different. Therefore the northern is assumed as a left lateral strike-slip fault with contraction component and it is locked at surface. The middle segment is assumed as a creeping left lateral strike slip fault with extension component. Finally, the southern segment is assumed as a left lateral strike-slip fault with extension component and locked at surface. And the patch number of northern and southern profiles is 15 and the middle profile is 10. Following equations shows the basic relation between surface displacements and slip rate on the fault of dislocation model
d s ε (7‐1) where G is a Green function contains dislocation model parameters (strike, dip angle, length, width, depth, horizontal position) and is computed in elastic half-space [Okada, 1985], d is surface displacement, s is slip rate and ε means error. The best-fit solution is approximated by dividing the fault into small rectangular patches of uniform dislocation and minimizing the data misfit and the model roughness by minimizing the functional
, || || || || (7-2) The smoothing operator is the finite difference approximation of the Laplacian operator and is a measure of roughness of the slip distribution. In equation (7-2), the first term on the right side compute the model misfit and the second term compute the roughness [Johnson et al., 2001].
Due to lack of seismicity or other data to provide the information of fault geometry, hence the estimation of the fault parameters (dip angle, depth, locations of fault planes) is using the Monte Carlo inversion to search the optimal parameter set. One million parameter sets are used to search the optimized fault parameters for each model.
The searching boundary for dip angle, depth, location (position on the velocity profile) and searching steps of each model are listed in Table 2. The dislocation model inverts the horizontal velocity to infer the long-term and the back-slip rate than estimate the interseismic slip by subtracting the back-slip rate from the long-term velocity.
Table 2: Searching boundaries and searching steps of 2D dislocation models.
Northern segment Middle segment Southern segment
Location 5~8 (km) 11~13 (km) 13~15 (km)
Searching step 0.1 (km) 0.1 (km) 0.1 (km)
Dip angle 40∘~60∘ 40∘~60∘ 40∘~60∘
Searching step 1∘ 1∘ 1∘
Depth 6~10 (km) 10~15 (km) 6~10 (km)
Searching step 0.1 (km) 0.1 (km) 0.1 (km)
7.2 Modeling result of the Northern segment
The modeling result of the northern profile is shown in Fig. 7-1A, basically the modeling result correspond with observations in both fault normal and fault parallel components. And the simulated result of fault parallel component has about 4.1 mm/yr velocity difference across the fault zone whereas the fault normal component has about 1.7 mm/yr velocity difference across the fault zone. The searching result of fault geometry (Fig. 7-1 B) indicates the top position of the fault zone is at 7.1 km and extends to 13.6 km on the profile, the dip angle is 50° and the depth is about 7.9 km.
The probability distribution of searching result shows a concentrated trend along the fault hence the searching result is statistically acceptable.
The slip rate distribution (Fig. 7-1 C) shows the long-term slip rate of the fault parallel component is 17.7 mm/yr and the fault normal component is 14.6 mm/yr. The back-slip rate of the fault parallel component is 2.3 mm/yr at the depth of 7.1 km whereas the back-slip of the fault normal component is 2.0 mm/yr at the depth of 7.1 km. Hence the maximum interseismic slip rate of strike slip component is about 15.4 mm/yr and the maximum interseismic slip rate of dip slip component is about 12.6 mm/yr.
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7.3 Modeling result of the Middle segment
The simulated result (Fig. 7-2 A) of fault parallel component shows a velocity discontinuity across the fault zone which is same as the observations. And fault normal component of simulations also shows a velocity discontinuity across the fault zone though observations are dispersive compare to the observations of fault parallel component. The velocity difference of simulated result in fault parallel component is about 11.2 mm/yr and the fault normal component has about 1.8 mm/yr velocity difference. The searching result of fault geometry (Fig. 7-2 B) indicates the top position of the fault zone is at 11.5 km and extends to 23.3 km on the profile, the dip angle is 48°
and the depth is about 13.2 km. The probability distribution of searching result only shows a concentrated trend above the depth of about 9 km. Below 9 km of the fault, the probability distribution is more and more scattered with depth.
The slip rate distribution (Fig. 7-2 C) shows the long-term slip rate of the strike slip component is 25.8 mm/yr and the dip slip component is 2.7 mm/yr. The back-slip rate of the strike slip component is 2.5 mm/yr at the depth of 13.2 km whereas the back-slip of the dip slip component is 0.0 mm/yr at the depth of 13.2 km. Hence the maximum interseismic slip rate of strike slip component is about 23.3 mm/yr and the maximum interseismic slip rate of dip slip component is about 2.7 mm/yr.
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7.4 Modeling result of the Southern segment
The simulated result (Fig. 7-3 A) of fault parallel component and fault normal component also show a velocity discontinuity across the fault zone. And the velocity difference of simulated result in fault parallel component is about 22.9 mm/yr and the fault normal component has about 4.67 mm/yr velocity difference. The searching result of fault geometry (Fig. 7-3 B) indicates the top position of the fault zone is at 14.1 km and extends to 20.6 km on the profile, the dip angle is 50° and the depth is about 7.8 km.
The probability distribution of searching result shows a concentrated trend along the fault. Even for deeper part of the fault, the probability distribution is still concentrated.
The slip rate distribution (Fig. 7-3 C) shows the long-term slip rate of the strike slip component is 26.2 mm/yr and the dip slip component is 9.7 mm/yr. The back-slip rate of the strike slip component is 0.8 mm/yr at the depth of 7.8 km whereas the back-slip of the dip slip component is 0.6 mm/yr at the depth of 7.8 km. Hence the maximum interseismic slip rate of strike slip component is about 25.4 mm/yr and the maximum interseismic slip rate of dip slip component is about 9.2 mm/yr.
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