Earthquake slip estimation from the scarp geometry of Himalayan Frontal Thrust, western Himalaya: implications for seismic hazard assessment

Abstract

Geometric and kinematic analyses of minor thrusts and folds, which record earthquakes between 1200 AD and 1700 AD, were performed for two trench sites (Rampur Ghanda and Ramnagar) located across the Himalayan Frontal Thrust (HFT) in the western Indian Himalaya. The present study aims to re-evaluate the slip estimate of these two trench sites by establishing a link between scarp geometry, displacements observed very close to the surface and slip at deeper levels. As geometry of the active thrust beneath the scarp is unknown, we develop a parametric study to understand the origin of the scarp surface and to estimate the influence of ramp dip. The shortening estimates of Rampur Ghanda trench by line length budget and distance–displacement (D–d) method show values of 23 and 10–15 %, respectively. The estimate inferred from the later method is less than the line length budget suggesting a small internal deformation. Ramnagar trench shows 12 % shortening by line length budget and 10–25 % by the D–d method suggesting a large internal deformation. A parametric study at the trenched fault zone of Rampur Ghanda shows a slip of 16 m beneath the trailing edge of the scarp, and it is sufficient to raise a 8-m-high scarp. This implies that the Rampur Ghanda scarp is balanced with a single event with 7.8-m-coseismic slip in the trenched fault zone at the toe of the scarp, 8–15 % mean deformation within the scarp and 16-m slip at depth along a 30° ramp for a pre-1400 earthquake event. A 16-m slip is the most robust estimate of the maximum slip for a single event reported previously by trench studies along the HFT in the western Indian Himalaya that occurred between 1200 AD and 1700 AD. However, the Ramnagar trenched fault zone shows a slip of 23 m, which is larger than both line length and D–d methods. It implies that a 13-m-high scarp and 23-m slip beneath the rigid block may be ascribed to multiple events. It is for the first time we report that in the south-eastern extent of the western Indian Himalaya, Ramnagar scarp consists of minimum two events (i) pre-1400 AD and (ii) unknown old events of different lateral extents with overlapping ruptures. If the more optimistic two seismic events scenario is followed, the rupture length would be at least 260 km and would lead to an earthquake greater than Mw 8.5.

Appendix

X axis is parallel to top of the uplifted terrace and perpendicular to strike of the scarp. To apply the Suppe (1983) approach to the scarp geometry, we assume that the hanging wall is divided in 4 domains (see Fig. 14): (1) a rigid one, (2) a blind triangle, (3) a homogeneously deformed zone and (4) a toe of the scarp affected by several thrusts and where the trenches are usually performed. The blind triangle zone is a simple geometric solution allowing a folding without fault at the transition between the rigid uplifted hanging wall and the tilted beds of the scarp. This blind triangle is bounded by fix and mobile axial planes generated by change of slope of the fault. These two axial planes are not parallel due to thickening of the beds between domains (2) and (3): Initial thickness of a bed, T0, becomes T1 in domain (3).

Fig. 14

a Area balancing: green is excess area beneath the scarp (Sx); red is excess area between the change of ramp dip and the scarp (Se1); gray is excess area of the scarp (Se2). b Domains and parameter definitions; c Triangles resolution (see text), blue area (Sb) is the initial location of the tilted hanging wall between mobile and fixed axial surfaces; A, B, C, D, G, F, K and L refer to dots defining geometry in the calculation. The color version of this figure is available only in the electronic edition

The measured parameters are excess area of the scarp (Se2), slope of upper part of the scarp (α), final length of the scarp (Lf), uplift of the scarp (Ur) and sum of the displacement (Dt) along the faults at the toe of the scarp (deduced from line length balancing in the trench).

We explore the influence of the ramp dip (βr) and depth of the leading edge of the ramp (H).

From the calculation, we successively deduced the values of the 3 summit angles of the triangles at the scarp break (dot A) that delineate the domains (1), (2) and (3) (Φ0, Φt and Φ1), the mean dip of the thrust beneath the scarp (β), the respective thickening of the beds in the domains (2) and (3) (ε et εat) and the attenuation ratio (R) linked to the change of slope of the thrust.

The surface displaced above the ramp at the trailing edge of the model (Sx) is:

$${\text{Sx}}: = \left( {{\text{H}} + \frac{\text{Ur}}{ 2}} \right) \cdot \frac{\text{Ur}}{{{\text{tan(}}\beta {\text{r)}}}} $$

(7)

Excess area balance (Goguel 1948) during deformation:

$${\text{Sx}} = \left( {{\text{Se1}} + {\text{Se2}}} \right) $$

(8)

where Se1 is transferred area located between the lines at the vertical scarp break (“A” on Fig. 14c) and of the fault break (“C” on Fig. 14c). Se2 is excess area of the scarp:

$${\text{Sel}} = \frac{{{\text{Ur}} \cdot ({\text{Ur + H)}}}}{{{\text{tan(}}\phi 0 )}} $$

(9)

By substituting the Sx value deduced from (7) and the Se1 value deduced from (9) in (8):

$$\Upphi 0: = { \arctan }\left[ {\frac{{{\text{Ur}} \cdot ({\text{Ur}} + {\text{H}})}}{{\left( {{\text{H}} + \frac{\text{Ur}}{ 2}} \right) \cdot \frac{\text{Ur}}{{{\text{tan(}}\beta {\text{r)}}}} - {\text{Se2}}}}} \right] $$

(10)

The mean dip of the thrust beneath the scarp (β) is found in the triangle BCE by calculating successively the length DA and BE:

$$\beta : = { \arctan }\left[ {\frac{\text{H}}{{{\text{Lf}} + \frac{{ ( {\text{Ur + H)}}}}{{{\text{tan(}}\Upphi 0 )}}}}} \right] $$

(11)

By substituting the Φ0 value deduced from (10) in (11):

$$\beta : = { \arctan }\left[ {\frac{\text{H}}{{{\text{Lf}} + \frac{{ ( {\text{Ur + H)}}}}{{{ \tan }\left[ {{ \arctan }\left[ {\frac{{{\text{Ur}} \cdot ({\text{Ur}} + {\text{H}})}}{{\left( {{\text{H}} + \frac{\text{Ur}}{ 2}} \right) \cdot \frac{\text{Ur}}{{{\text{tan(}}\beta {\text{r)}}}} - {\text{Se2}}}}} \right]} \right]}}}}} \right] $$

(12)

The summit angle Φt of triangle CAF is also the summit angle of the triangle KAF, where FK is the median of triangle CFG.

The surface of CFG is

$${\text{Sb:}} = \frac{{{\text{FK}} \cdot {\text{Ur}}}}{{ 2\cdot {\text{sin(}}\Upphi 0 )}} $$

(13)

The area of triangle CFG is preserved during deformation and is calculated before tilting (light blue on (Fig. 14):

$${\text{Sb:}} = \frac{\text{Ur}}{ 2} \cdot \left( {\frac{\text{Ur}}{{{\text{tan(}}\beta {\text{r)}}}} + \frac{\text{Ur}}{{{\text{tan(}}\Upphi 0 )}}} \right) $$

(14)

From (13) and (14), it is found

$${\text{FK}}: = {\text{Ur}} \cdot \sin (\Upphi 0) \cdot \left( {\frac{ 1}{{\tan (\beta {\text{r}})}} + \frac{ 1}{\tan (\Upphi 0)}} \right) $$

(15)

And by solving Фt in the triangle KAF:

$$\Upphi {\text{t}} = {\text{arctan(FK/(AC}} - {\text{CK))}} $$

(16)

AC and CK are calculated in triangles CFK and CDA and FK are deduced from (15):

$$\Upphi {\text{t}}: = { \arctan }\left[ {\frac{{{\text{Ur}} \cdot {\text{sin(}}\Upphi 0 )\cdot \left( {\frac{ 1}{{{\text{tan(}}\beta {\text{r)}}}} - \frac{ 1}{{{\text{tan(}}\Upphi 0 )}}} \right)}}{{\frac{{\left( {\text{H + Ur}} \right)}}{{{\text{sin(}}\Upphi 0 )}} - \frac{{{\text{Ur}} \cdot {\text{sin(}}\Upphi 0 )\cdot \left( {\frac{ 1}{{{\text{tan(}}\beta {\text{r)}}}} - \frac{ 1}{{{\text{tan(}}\Upphi 0 )}}} \right)}}{{{\text{tan(}}\Upphi 0- \beta )}}}}} \right] $$

(17)

To calculate the change of bed thickness T1/T0 (εat) between domains (1) and (3), we solve the triangle AFL where FL is the final thickness of the all the beds of domain (3):

$${\text{AF:}} = \frac{\text{FK}}{{{\text{sin(}}\Upphi {\text{t)}}}} $$

(18)

and

$${\text{FL: = AF}} \cdot \sin ( 1 8 0^{ \circ } - \alpha - \Upphi 0- \Upphi {\text{t}}) $$

(19)

The initial thickness of the beds in the scarp was H and

$$\varepsilon {\text{at: = }}\frac{\text{FL}}{\text{H}} $$

(20)

By a succession of substitution in 15, 18, 19 and 20:

$$\varepsilon {\text{at:}} = \frac{{{\text{sin(}}\Upphi 0 )\cdot \left( {\frac{ 1}{{{\text{tan(}}\beta {\text{r)}}}} + \frac{ 1}{{{\text{tan(}}\Upphi 0 )}}} \right)}}{{{\text{sin(}}\Upphi {\text{t)}}}} \cdot \frac{\text{Ur}}{\text{H}} \cdot \sin ( 1 8 0^{ \circ } - \alpha - \Upphi 0- \Upphi {\text{t}}) $$

(21)

The transition between the homogeneously deformed domain (3) and the domain (4) affected by faults is not detailed. Nonetheless, Eq. (8) implicitly incorporates the deformation of the toes, whatever the geometry of the small faults. Furthermore, another condition has to be checked. The displacement that remains along the basal thrust at the transition between domain (4) and (3) (after attenuation due to the R ratio and the thickening of the beds) has to be equal to the total displacement along the faults located at the toes of the scarp (Dt).