**3.5. Hypsometric integral (HI)**

The hypsometric integral is an index that describes the distribution of elevation of a given area of a landscape [39]. The integral is generally derived for a particular drainage basin and is an index that is independent of basin area. The index is defined as the area below the hypsometric curve and thus expresses the volume of a basin that has not been eroded. The simple equation that may be used to calculate the index [32, 40] is:

*HI* = (*average elevation* − *minimum elevation*)/(*maximum elevation* − *minimum elevation*) (3)

The hypsometric curve indicates degree of dissection of the basin, i.e., erosional stage of the basin. Concave profiles represent long-term equilibrium between uplift and erosion rates. Concave – convex profiles with erosion steps in the middle reaches indicate long-term predominance of erosional processes. Convex profiles are characteristic of areas where uplift (active tectonics) is dominant [41] The area below the hypsometric curve is known as the hypsometric integral (HI). The value of HI varies from 0 to 1 [41–43]. These profiles are drawn by projecting rivers onto a theoretical pre-incision surface that is obtained by interpolating the altitudes from present-day lateral divides of the basins (**Figure 4**). The values of elevation necessary for the calculation are obtained from a digital elevation mode.

#### **3.6. Basin asymmetry (AF)**

The asymmetric factor (AF) is a way to evaluate the existence of tectonic tilting at the scale of a drainage basin. The method may be applied over a relatively large area [32, 41] AF is defined by:

$$\text{AF} = 100 \,\text{(Ar/At)}\tag{4}$$

where Ar is the area of the basin to the right (facing downstream) of the trunk stream and At is the total area of the drainage basin. If a basin has developed under stable conditions with little or no tilting, the Af factor is close to 50. The index is sensitive to change in inclination perpendicular to the channel direction. An AF factor above or below 50 may result from basin tilting, resulting either from active tectonics or lithologic, structural control, differential erosion. The AF value ranges from 18 to 85. The absolute difference (AF-50) has been calculated and the obtained values are grouped into four classes: class-1 (AF ≤ 5; symmetric basins), class-2 (6 ≤ AF ≤ 15; gently asymmetric basins), class-3 (16 ≤ AF ≤ 25; moderately asymmetric basins), and class-4 (AF ≥ 26; strongly asymmetric basins) (**Table 1**). The area of these drainage basins corresponding to asymmetric values is shown on the map (**Figure 5A**).

#### **3.7. Basin shape (Bs)**

The horizontal projection of a basin may be described by the basin shape index or the elongation ratio, Bs [43]:

$$Bs \quad = Bl \quad = Bw \tag{5}$$

**Figure 4.** Hypsometry curves of all river basins integrated with youth (brown color), mature (cyan color), and old stages (green color) of river basin. *The hypsometric curves has been generated using River Tool 3.0 software and final editing has been* 

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*done in golden software Surfer 14.*

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**3.5. Hypsometric integral (HI)**

138 Tectonics - Problems of Regional Settings

elevation mode.

by:

(**Figure 5A**).

**3.7. Basin shape (Bs)**

tion ratio, Bs [43]:

**3.6. Basin asymmetry (AF)**

equation that may be used to calculate the index [32, 40] is:

The hypsometric integral is an index that describes the distribution of elevation of a given area of a landscape [39]. The integral is generally derived for a particular drainage basin and is an index that is independent of basin area. The index is defined as the area below the hypsometric curve and thus expresses the volume of a basin that has not been eroded. The simple

*HI* = (*average elevation* − *minimum elevation*)/(*maximum elevation* − *minimum elevation*) (3)

The hypsometric curve indicates degree of dissection of the basin, i.e., erosional stage of the basin. Concave profiles represent long-term equilibrium between uplift and erosion rates. Concave – convex profiles with erosion steps in the middle reaches indicate long-term predominance of erosional processes. Convex profiles are characteristic of areas where uplift (active tectonics) is dominant [41] The area below the hypsometric curve is known as the hypsometric integral (HI). The value of HI varies from 0 to 1 [41–43]. These profiles are drawn by projecting rivers onto a theoretical pre-incision surface that is obtained by interpolating the altitudes from present-day lateral divides of the basins (**Figure 4**). The values of elevation necessary for the calculation are obtained from a digital

The asymmetric factor (AF) is a way to evaluate the existence of tectonic tilting at the scale of a drainage basin. The method may be applied over a relatively large area [32, 41] AF is defined

AF = 100 (Ar/At) (4)

where Ar is the area of the basin to the right (facing downstream) of the trunk stream and At is the total area of the drainage basin. If a basin has developed under stable conditions with little or no tilting, the Af factor is close to 50. The index is sensitive to change in inclination perpendicular to the channel direction. An AF factor above or below 50 may result from basin tilting, resulting either from active tectonics or lithologic, structural control, differential erosion. The AF value ranges from 18 to 85. The absolute difference (AF-50) has been calculated and the obtained values are grouped into four classes: class-1 (AF ≤ 5; symmetric basins), class-2 (6 ≤ AF ≤ 15; gently asymmetric basins), class-3 (16 ≤ AF ≤ 25; moderately asymmetric basins), and class-4 (AF ≥ 26; strongly asymmetric basins) (**Table 1**). The area of these drainage basins corresponding to asymmetric values is shown on the map

The horizontal projection of a basin may be described by the basin shape index or the elonga-

*Bs* = *Bl* = *Bw* (5)

**Figure 4.** Hypsometry curves of all river basins integrated with youth (brown color), mature (cyan color), and old stages (green color) of river basin. *The hypsometric curves has been generated using River Tool 3.0 software and final editing has been done in golden software Surfer 14.*

**4. Relationship between fault displacements and drainage offset**

Conventionally, quantitative displacement in a fault zone has been demonstrated by an offset of the river channel [25, 44, 45]. Usually, it has been widely observed that the maximum displacement occurred in the central part of the fault zone [46] and that the displacement decreases with increasing length. Decrease of river offset towards the west is possibly, westward propagation of the faults. These streams were taken into account to calculate offset ratio:

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*a* = *D*/*L* (6)

where *D* is the amount of stream offset along fault and *L* is upstream length of the displaced stream [47]. A relationship between long-term slip rate (S) along the lateral slip of a fault and offset ratio (*a* = *D/L*) has been roughly calculated as S (m/1000 years), *i.e.,* 10 *a* [25, 44, 45].

We investigated the major to north flowing rivers such as the Suvai, Bhimguda, Narelawali, Dhadawali, Karaswali, Malan, Baniyo, and Dabhodanwari rivers and adjoining streams to estimate river offset along the E-W faults F1–F4 (GF). However, 17 south flowing rivers such as 1–8, Khalwa River (9), 10, 11, Sharan Nadi (12), and rivers 13–17 have been analyzed to estimate offset along faults F6–F8. Based on offset of river channel we estimated net displacement

Several remote sensing studies have used the geomorphic indices to obtain index of relative tectonic activity [48–50]. To understand the RIAT of the fault segments, the results of all calculated geomorphic indices were synthesized. In this study we used geomorphic indices of active tectonics to obtained RIAT for the (NWF) North Wagad Fault, (GF) Gedi Fault, Bharudia Fault and (IBF) Island Belt Fault. Based on these classes we have considered each basin class average and combined to obtain the RIAT. The values of RIAT is assigned into five classes as Class- VI (RIAT >4), Class V: (> 3.5 RIAT <4), Class IV: (>3 RIAT <3.5), Class III: (>2.5 RIAT <3), Class II (>2 RIAT <2.5), and Class I (RIAT <2), (Supplementary Table 1; **Figure 5B**). Depending on the relative index of active tectonics classes, Western part of Wagad uplift covering basin 11, and Easterly covering 15 and 16 comes in highly active zone and shows offsetting drainage pattern (Class 5). Basin 1, 3, 4, 7 and 10 in Bela island, basin 13 and 18 in Wagad uplift are tectonically active and comes in (Class 4) zone and also delimiting by transverse fault between Basin 5, 6 and 9 in Bela Island 12, 14 and 17 in Wagad uplift are moderately active zones (Class 3) (**Figure 5B**). Basin 2 is intermediately active and comes in (Class 4) and Basin 8 is low active region.

The evidences of geomorphological in the Kachchh Rift Basin (KRB) is also supported by available high resolution seismic structures, fault plane solutions and recorded seismicity at

along F2–F10 respectively.

**6. Seismological approaches**

**5. Relative index of active tectonics (RIAT)**

**Figure 5.** A spatial distribution of basin asymmetry along the northern Wagad area. (B) Estimated relative index of active tectonics (RIAT) distribution pattern of the area. A *and* B *have been generated using Global mapper 18 software and the final editing has been done in surfer 14 software.*

where *Bl* is the length of a basin measured from the highest point, and *Bw* is the width of a basin measured at its widest point. Relatively young drainage basins in tectonically active areas tend to be elongated in shape, normal to the topographic slope of a mountain [41, 43]. Therefore*, Bs* may reflect the rate of active tectonics.
