**3.2. Swath profiles**

The aftershocks of the January 26, 2001 Bhuj earthquake (Mw 7.7) are still continuing [15]. Distribution of the hypocenter of these aftershocks suggests that they are distributed mainly towards NE and SW directions. It has been observed that the WH is pronounced activated after the 2001 mainshock [12, 15, 27]. It is testified by a large number of aftershocks (Mw ≥ 2.5) occurred in the WH with focal depths ≥10 km. A few moderate earthquakes also occurred along the GF. Among these earthquakes, the most recent are the February 2006 (Mw 5.0); February 2006 (Mw 4.8); March 2006 Mw 5.7 and April 2008 Mw 4.1 [27] (**Figure 1B**). In the GF zone some 30 earthquakes (Mw 3.0–5.7) have been recorded at Seismic Network of Gujarat (SesisNetG) at shallow focal depths (≤ 20 km) during the period of 2006–2013 (**Figure 1B**).

*Global mapper 18 and finally the contouring has been done in Surfer 14 software. We used excel for generation of* **D**.

**Figure 2.** (A) Geological map of Wagad area shows especial distribution of SL along various geological units. Spatial distribution of SL class contour map of northern Wagad region. The higher activity is marked by higher order color (B) especial distribution of Ks along various geological units. Distribution of Ks class contour of northern Wagad region. Fault lines are shows by solid black line; dykes are marked by green lines; and bedding slope direction is highlighted by small black arrow. (C) Spatial variation of topography and statistics estimation for values of basin-wide hypsometric integral. The hotspots of higher uplift are marked by higher color values of hypsometric integral. (D) Relationship between amounts of stream offset along the fault and upstream length from the faults (F1–F10). *For generation of* **Figure 1A** and **B** *used Arc-GIS-10.4, Global mapper 18 software's and the final editing and contouring has been done in Surfer-11 software. We used River tool 3.0 for generation of hypsometric curves. The contour values of hypsometry Integral (HI) has been generated in* 

To investigate the relationship between brittle - ductile dynamics and surface processes in northern Wagad, we focused on topographic features (filtered topography, swath profiles, local relief), and hydrography (river longitudinal profiles), We used two elevation data sources: the CARTOSAT 2.5 m resolution digital elevation data (http://bhuvan.nrsc.gov.in) for regional scale analysis and the SRTM (http://srtm.csi.cgiar.org) of 90 m resolution for detailed analysis. Seismic tomography has been used to evaluate shallower to deeper surface dynamic

**3. Data and methodology**

134 Tectonics - Problems of Regional Settings

We have considered five swath profiles across the study area to describe and quantify the topographic trend of the northern WH. The results show the trend of minimum, maximum and mean elevation into a single plot [29, 30] (**Figure 1D**). The statistical analyses such as maximum, minimum and mean elevations were calculated along each swath profile within a GIS platform. (**Figure 1D**). A rectangular swath of 300 m width was chosen to extract a series of parallel profiles that are separated by 1-cell (5 m). The width of the swath profile has been used to condense both elevated surfaces and streams. The higher elevation in swath depicts maximum elevation corresponds to the ridgelines; whereas, the lower elevation curve for the minimum elevation represents the valley floors. The Incision by river can be measured by the arithmetic difference between the maximum and minimum elevations within the longitudinal distance of the swath rectangle [31].

## **3.3. Stream length gradient index (SL)**

The SL index is one of the quantitative geomorphic parameters included in morphotectonic assessment (Hack, [34]). This index will increase in value as rivers and streams flow over active uplifts and may have lesser values when flowing parallel to structures such as valleys made by strike-slip faulting [32]. The SL index seems to be a valid tool to detect local uplift as well as the incipient local response to regional processes [33]. Conventionally the SL index shows a quantitative approach to differential geomorphic studies related to erosion and depositional processes that include the river channel, long profile, and valley morphology as well as tectonically derived features such as fault scarps. This index was defined by [32] as:


**Table 1.** Spatial distribution of SL, HI, AF, Smf, SI, Bs, RSS, RIAT classes.

$$\text{SL} = (\Delta H / \Delta \text{L})^\* \text{L} \tag{1}$$

streams flow over active uplifts and areas with high rock resistance and may decrease with low rock resistance. The integrated plot of stream longitudinal profile and SL index of all the rivers are presented graphically on the x- and y-axis of the longitudinal profile of the main

Evolution of Drainage in Response to Brittle - Ductile Dynamics and Surface Processes…

http://dx.doi.org/10.5772/intechopen.73653

137

The normalized channel steepness index could be expected to vary with rock uplift rate (relative to base level), lithology, and climate [34, 35]. The method used for evolution of steepness index in the study area is based on the empirical power law equation of [36, 37] that relates the local slope (S) to the upstream contributing drainage basin area (A) [37, 38], However in

S = *ks A*<sup>−</sup>*<sup>Ѳ</sup>* (2)

drainage area and distance downstream often described with Hack's law strongly influences the rate of change in channel gradient with distance downstream, which of course defines the concavity of river profiles. If there is no differential uplift, the value of Ks should remain constant. In the case of the river basin is undergoing differential uplift, Ks may change from

**Figure 3.** Integrated longitudinal river profiles and SL index of eight representative, rivers (Note: For details of all integrated river profiles, see **Figure 3**, SL is shown by small green line along the profile; solid thick red dots represents values of Ks along the long profile; knickpoints are marked by black star. *After collecting data in Arc GIS we used Microsoft* 

*excel for generating long river profiles and final editing has been done in golden software Surfer 14.*

is the steepness index and Ѳ is concavity. Given Flint's law, the relationship between

channel (**Figure 3**).

where *ks*

**3.4. Steepness index (Ks)**

one segment to another [38].

present paper similar methodology has been:

where *ΔH/ΔL* is the local slope of the channel segment being evaluated, and *L* is the channel length from the divide to the midpoint of the channel reach. The SL index value increases as streams flow over active uplifts and areas with high rock resistance and may decrease with low rock resistance. The integrated plot of stream longitudinal profile and SL index of all the rivers are presented graphically on the x- and y-axis of the longitudinal profile of the main channel (**Figure 3**).

#### **3.4. Steepness index (Ks)**

*SL* = (*H*/*L*)<sup>∗</sup> *L* (1)

**Table 1.** Spatial distribution of SL, HI, AF, Smf, SI, Bs, RSS, RIAT classes.

**Basins Area (km2**

136 Tectonics - Problems of Regional Settings

**) Area % AF BS SL** 

**class**

 30.759 2.05 7.70 3.4 2 2 2 2 4 2.4 3 8.962 0.60 1.90 3.2 1 1 4 1 4 2.2 2 49.538 3.31 14.21 3.4 2 2 2 2 4 2.4 3 22.855 1.53 16.59 5.3 1 2 2 3 5 2.6 3 49.991 3.34 12.06 4.8 1 2.5 1 2 5 2.3 3 17.051 1.14 5.12 3.9 2 2 3 2 4 2.6 3 20.658 1.38 15.41 5.4 2 2 2 3 5 2.8 4 7.733 0.52 13.51 3.6 1 1 4 1 4 2.2 3 56.53 3.77 3.60 3.5 2 2 1 1 4 2 3 52.989 3.54 8.07 2.8 2 2 1 2 3 2 3 40.325 2.69 1.48 3.6 1 1 2 1 4 1.8 1 20.395 1.36 8.76 1.5 1 2 3 2 2 2 2 11.269 0.75 5.24 3.2 2 2 3 2 4 2.6 3 13.33 0.89 14.92 6.2 2 2.5 2 2 5 2.7 4 16.705 1.12 35.33 1.6 1 1 2 4 2 2 2 9.342 0.62 20.88 3.4 1 2 1 3 4 2.2 3 5.188 0.35 4.82 3.7 1 3 2 1 4 2.2 3 53.91 3.60 25.82 2.3 1 2 3 4 3 2.6 3 134.73 8.99 10.92 1.6 2 1 3 1 2 1.8 1 48.422 3.23 13.31 9.4 2 2.5 3 1 5 2.7 6 209.47 13.98 8.26 1.9 2 2 2 2 2 2 2 71.57 4.78 15.51 3.7 2 2 3 1 4 2.4 3 151.26 10.10 3.18 3.9 3 3 3 1 4 2.8 5 129.46 8.64 14.02 4.9 3 2.4 4 2 5 3.28 5 96.119 6.42 4.32 2.5 2 2 3 1 3 2.2 2 64.618 4.31 31.38 1.9 1 2 4 1 2 2 2 104.85 7.00 2.10 1.5 2 2 4 1 2 2.2 3

**Ks class** **HI class** **AF class** **BS class** **RIAT value**

**RIAT class**

where *ΔH/ΔL* is the local slope of the channel segment being evaluated, and *L* is the channel length from the divide to the midpoint of the channel reach. The SL index value increases as The normalized channel steepness index could be expected to vary with rock uplift rate (relative to base level), lithology, and climate [34, 35]. The method used for evolution of steepness index in the study area is based on the empirical power law equation of [36, 37] that relates the local slope (S) to the upstream contributing drainage basin area (A) [37, 38], However in present paper similar methodology has been:

$$\mathbf{S} = k\_s A^{-\Theta} \tag{2}$$

where *ks* is the steepness index and Ѳ is concavity. Given Flint's law, the relationship between drainage area and distance downstream often described with Hack's law strongly influences the rate of change in channel gradient with distance downstream, which of course defines the concavity of river profiles. If there is no differential uplift, the value of Ks should remain constant. In the case of the river basin is undergoing differential uplift, Ks may change from one segment to another [38].

**Figure 3.** Integrated longitudinal river profiles and SL index of eight representative, rivers (Note: For details of all integrated river profiles, see **Figure 3**, SL is shown by small green line along the profile; solid thick red dots represents values of Ks along the long profile; knickpoints are marked by black star. *After collecting data in Arc GIS we used Microsoft excel for generating long river profiles and final editing has been done in golden software Surfer 14.*
