SUPPLEMENTARY INFORMATIONDOI: 10.1038/NGEO2797

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Supplementary Information for

NGS-2015-12-02477-T Active shortening within the Himalayan orogenic wedge implied by the 2015 Gorkha earthquake

Kelin X. Whipple, Manoochehr Shirzaei, Kip V. Hodges, J. Ramon Arrowsmith

Contents

Data and Strategy Used in Resolving the Geometry of the HST Flat

Strategy for Evaluating Geometric Complexity: the Uplift Anomaly

Geophysical Constraints on the Geometry of the HST

Tables

Table S1. Interferometric data set used in this study

Figures

Figure S1. Best-fit planar fault geometry.

Figure S2. Inversion results using Sentinel-1 ascending (T085) and descending (T019)

interferograms with best-fit planar fault.

Figure S3. Slip inversion results for May 12, 2015, Mw7.3 after-shock.

Figure S4. Slip inversion results for the aftershock with imposed HST geometry matching

the commonly assumed mid-crustal ramp model.

Figure S5. Inversion results for best-fit ramp-flat geometry using ALOS-2 T048.

Figure S6. Inversion results for best-fit planar fault (flat only) with uplift anomaly masked.

Figure S7. Akaike Information Criterion (AIC) used to identify the best geometry and slip

distribution associated with the splay fault

Figure S8. Inversion results of coseismic slip distribution using a model that combines a

planar fault and a steeper structure extending toward the surface for ALOS-2 data.

Figure S9. Inversion results of coseismic slip distribution using a model that combines a

planar fault and a steeper structure extending toward the surface for Sentinel-1 data.

Figure S10. Swath profile cross-section (N18°E) of plausible structural geometries in relation

to PT2 and seismicity in the Gorkha earthquake sequence.

Active shortening within the Himalayan orogenicwedge implied by the 2015 Gorkha earthquake

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Data and Strategy Used in Resolving the Geometry of the HST Flat

Centroid moment tensor (CMT) solutions suggest the mainshock (MW 7.8) occurred on a

northwest trending fault with depth of 10 km and dip angle of 11o (USGS event us20002926).

Kinematic fault slip inversion results using InSAR and GPS data suggested a dip angle of 7o or

shallower may provide a better fit to the deformation data1. To constrain the fault geometry and

uniform slip associated with the main-shock, here, we implement a nonlinear slip inversion scheme

(Online Methods). To this end we use LOS deformation data provided by ALOS-2 (T048) and

Sentinel-1 (T085, T019) satellites (Table S1).

We initially tested the effect of including the ascending ALOS-2 track 157 on the best-fit

fault geometry. However, we found it had little influence on the best-fit fault geometry and left it out

of our final inversions because it covers only a fraction of the area affected by coseismic

displacement, in particular missing the area where the northward extent of rupture was the greatest

and some of the uplift anomaly (the areas of most interest here). Similarly, the Sentinel-1 descending

track 019 only covers part of the deformation signal. The pair of ALOS-2 descending track 048 and

Sentinel-1 ascending track 085 provides the most effective constraints on the problem of interest.

Moreover, works that have included ALOS-2 ascending track 157 (e.g. [Wang and Fialko, 2015]) find

a very similar result as obtained here for the optimal fault geometry of the main rupture. Finally, it is

worth noting that nearly identical best-fit rupture surface geometries were found in inversions of

ALOS-2 track 048 alone.

Table S1. Interferometric data set used in this study

Satellite Mater Slave Track Orbit Inc. Ang.

Main-shock

Sentinel-1 2015/04/09 2015/05/03 085 Ascending 34-44o

Sentinel-1 2015/04/17 2015/04/29 019 Descending 34-44o

ALOS-2 2015/02/22 2015/05/03 048 Descending 18–43o

After-shock ALOS-2 2015/05/03 2015/05/17 048 Descending 18–43o

The GA algorithm is characterized by population size of 400, mutation rate of 0.6, selection rate of

0.5 and 1000 iterations. Thus we examine over 400,000 possible solutions to find optimum values

and associated PDFs. We allow dip and strike to vary between 1o – 25o and 271o - 3000, respectively,

and depth to vary between 5 and 15 km at the hypocenter, to ensure the search algorithm has

enough redundancy to explore the vicinity of the optimum solution. We find that the optimal planar

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fault has a shallow depth of ~10 ± 1.5km at the hypocenter, consistent with the centroid moment

tensor derived with a 3D earth model from HiCLIMB data by Duputel et al.2. The optimum fault

dips northward at 6.2 ± 2°, consistent with prior work, including analyses that also incorporated the

ascending ALOS-2 track1,3. For the optimal depth of 10 km at the hypocenter, a planar fault with

northward dip of 4° (within uncertainty) projects to the known depth of 5 km for the HST ~10 km

north of the MFT trace4,5 (Fig. 2b). As indicated by the grey band on Figure 2b, a fault surface with

this depth but steeper than 4° over the area of rupture, would need to flatten to ~2° south of the

rupture extent to meet the observed depth near the MFT trace. The average rake angle is 88.4 ±

3.3°, with only minor variation across the fault, consistent with seismic moment tensor solutions.

Figure S1a shows the estimated PDF for dip angle following non-linear optimization. Though a

strike near 295o suggested by moment tensor solutions has been used in several analyses of this

event6-8, we note here that a strike of 282.9 ± 4.1° provides a better fit to the InSAR data,

particularly the subsidence signal in the NW quadrant (Fig. 1b), as is shown in Figure S1b.

Figure S1. Best-fit planar fault geometry. a) Probability density function of the estimated dip angle

obtained following inverting individual interferograms as well as joint inversion of all data sets. b)

Curve showing the 𝜒2 reduction versus strike of the fault plane used for kinematic slip inversion.

The least 𝜒2 = 25.4 is obtained when strike is equal to 282.9o.

Using the best-fit fault geometry we expand the dislocation laterally and along dip and

discretize it into triangles suitable for slip distribution inversion. The triangular mesh includes 1100

triangles with average side of 5 km. In addition to InSAR data, we also include observations of

coseismic displacement obtained from GPS stations. To estimate the relative weight between GPS

and 3 different interferometric data sets, we use an interactive approach detailed in Online Methods.

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As a result, we found that the relative weight of GPS data needs to be ~6 times that of the

interferometric data sets and among interferometric data sets the weight of Sentinel-1 T019 needs to

be ~0.3 times of the other tracks. This is likely due to larger phase unwrapping error that has

affected this interferogram, which makes its measurements less reliable. As for the smoothing

operator, our L-curve suggests that a value between 1 and 3 provides an adequate balance between

model roughness and fit to the data. Using a smoothing operator equal to 2, the final slip model (χ2

= 8.8, Fig. 3a) can explain the majority of the observed surface deformation observed from both

InSAR and GPS data sets very well. The geodetic moment associated with the optimum distributed

slip model is 6.05×1020 Nm. In our optimum slip model, we find slip >2m on a planar fault

extending to 110 km north of the MFT (30 km north of PT2) and slip of 1-2m extending from 110

to 125 km north of the MFT (Figs. 2, 3a and S2), consistent with prior results1,3. Excepting a focused

zone where LOS shortening is underestimated (Fig. 3a), the model misfits are very small and at the

range of observation noise for ALOS-2 T048 (χ2 = 8.8), and quite good for Sentinel-1 T085 (χ2 =

12.9), particularly considering lower signal to noise ratios for C-Band observations in the

mountainous northern part of the deformation signal. The misfit for Sentinel-1 T019 has notably

larger residuals (χ2 = 131.3), likely due to unwrapping error that leads to underestimation of the

deformation signal.

Figure S2. Inversion results using Sentinel-1 ascending (T085) and descending (T019)

interferograms with best-fit planar fault (T085 χ2 = 12.9, T019 χ2 = 131.3). The optimum slip model

is shown in Figure (3a) with details in caption.

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We follow a similar procedure to constrain the fault geometry and obtain distributed slip

associated with the May 12, 2015, 7.3 aftershock. The uniform slip inversion yields a plane with dip,

strike and depth similar to that of mainshock (strike 282° ± 5°, dip 7° ± 4°, depth ~10 km), again

consistent with the centroid moment tensor derived with a 3D Earth model2 and prior inversions of

InSAR data3. We then expand laterally and along dip the fault plane and discretize it into triangles

suitable for slip distribution inversion. The triangular mesh includes 560 triangles with average side

of 5 km. Figure S3 shows the inversion results for this geometry.

Figure S3. Slip inversion results for May 12, 2015, Mw7.3 aftershock. Dip angle is 7°, strike 282°. Fit

(χ2 = 10.3) is indistinguishable from that shown in main text rupture on surface co-planar with the

mainshock (χ2 = 10.5) shown in Figure 3d-f.

Given the uncertainty of the dip angle for both main- and after-shock it is reasonable to

assume both are on the same plane with dip angle of 6 degrees. Therefore, we repeated the slip

distribution inversion for the aftershock using a plane identical to that used for main-shock (Fig. 3d-

f). The optimum aftershock model yields an excellent fit to the surface deformation data (χ2 = 10.5,

Fig. 3d), affirming the inferred geometry of the HST and demonstrating that the flat extends at least

to the down-dip edge the 7.3 aftershock rupture. The geodetic moment associated with the

aftershock slip model is 8.6×1019 Nm. To compare our results to the slip model associated with

mid-crustal ramp model favored by Elliot et al.9, we adapt their fault geometry as detailed in the

main text and repeat the slip inversion. Figure S4 shows the corresponding results. We find that this

model provides a worse fit to the data (2 of 29.1 vs 10.5) and the residuals map includes some

systematic pattern indicating simulated observation underestimates the observed deformation to the

north. Thus our model results indicate that a geometry similar to that of main-shock, namely

extending the flat plane of 6o dip to the southeast is a better choice.

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Because these results challenge a long-standing interpretation that the HST steepens into a

mid-crustal ramp underneath the southern flank of the High Himalaya (80 km north of the MFT

trace at PT2), we evaluate the ability of slip distributed along the commonly assumed mid-crustal

ramp geometry to explain observed surface deformation. Accordingly, we invert for slip distribution

on a fault geometry prescribed to match this well-known geometry and the best-fit presented by

Elliot et al.9 (strike 288°, HST flat with 7° dip, 5 km depth near the MFT trace, 15 km depth at the

hypocenter, and a 20° ramp starting at ~80 km from the MFT (at PT2) and extending down to 25

km depth). This geometry does not provide a satisfying to the data, particularly in the zone of

subsidence (Fig. 3g, χ2 = 81.3). The associated geodetic moment is 6.41×1019 Nm.

Figure S4. Inversion results for the aftershock with imposed HST geometry matching the

commonly assumed mid-crustal ramp model (from Elliot et al.9 same as in Fig. 3g-i2 = 29.1)

Strategy for Evaluating Geometric Complexity: the Uplift Anomaly

As seen in Fig. 1b, there is an anomalous welt of uplift within the zone of subsidence NE of

Kathmandu that at first glance suggests either a complex distribution of slip on the HST or a

geometric complexity in the structural architecture. As shown in the residual map from the best-fit

planar fault (Fig. 3c), the anomaly is restricted to a concentrated welt of uplift with no apparent

paired subsidence anomaly and so cannot be explained by a complex distribution of slip on the HST

flat, leaving a large local residual misfit anomaly.

One possible explanation for this anomalous signal is the presence of a steeper fault surface

that represents slip down-dip on a mid-crustal ramp, but at a position well north of PT2. The

location of the uplift anomaly naturally tightly constrains the map-view position of the rupture patch

responsible. Exploring the northerly ramp-flat hypothesis, we find that a ramp with strike 288°, dip

20°, and up-dip edge 22 km north of PT2 provides the best fit of any model that incorporates a

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ramp. Positions closer to PT2 degrade the fit to observed subsidence in the northwest and positions

farther north of PT2 cannot help explain the uplift anomaly. The final inversion model includes 1295

triangles with average side of ~4 km. We use same smoothing operator for model roughness and

relative weight between InSAR and GPS data as was used for mainshock inversion on the HST. This

model provides the best fit of any model that incorporates a ramp (χ2 = 11.3, Fig. S5). The

associated geodetic moment is 6.19×1019 Nm. Modeling a ramp at this position improves model fit

in the vicinity of the uplift anomaly (χ2anom

= 14.2) relative to the single planar fault model (χ2anom

=

33.2). However, it cannot fully explain the sharply defined uplift anomaly and it degrades the fit to

the northwestern part of the subsiding zone and in the vicinity of the epicenter (Fig. S5), resulting in

an overall decrease in goodness of fit (χ2 = 11.3) relative to the best-fit flat-only model (χ2 = 8.8).

Figure S5. Inversion results for best-fit ramp-flat geometry using ALOS-2 T048. a) Slip

distribution (moment 6.19x1020 Nm, Mw 7.79) on fault where the flat has strike of 283° and dip of

6° and projects to a depth of 5 km just north of the MFT trace, and the up-dip edge of a ramp with

strike of 288° and dip of 20° located 102 km north of the MFT (22 km north of PT2, thin black

dash-dot line, Fig. 2), b) Modeled surface LOS deformation, c) model residuals (χ2 = 11.3). Vectors

represent misfit between model and GPS observations.

The very localized pattern of the uplift anomaly suggests that the associated source should

be shallow, and lack of complementary subsidence signal indicates that the fault plane should be

steep, suggesting the possibility that slip occurs on a shallow splay fault rising toward the surface

from the HST (Fig. 2). To investigate this possibility, we carefully isolate the uplift anomaly. To

accomplish this we must mask the uplift anomaly when inverting for slip on the HST fault, else that

inversion will place some slip underneath and down-dip of the uplift anomaly in a futile attempt to

fit the observed deformation. The mask is chosen such that only the asymmetric zone of uplift is

removed. Then the masked signal is used for slip inversion on the fault with the same geometry as

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that of mainshock (Fig. S6). The optimum slip model in this case is very similar to that of mainshock

inversion on the HST, except in the immediate vicinity of the uplift anomaly (compare Figs. 3a and

S6b), which suggests that the application of the mask did not affect significantly the slip distribution

of HST (tests exploring larger masked areas invariably resulted in notable changes to the slip

distribution on the HST flat and produced complex residual patterns not plausibly explained by slip

on a simple structure). The estimated geodetic moment of this case is 5.98×1020 Nm. Using this slip

distribution and through forward modeling as before, we calculate the observation residuals, which

mostly reflect and effectively isolate the uplift welt (Fig. S6d).

Figure S6. Inversion results for best-fit planar fault (flat only) with uplift anomaly masked. Same as

Figure 3a-c (best-fitting result for the mainshock using a single planar fault 5 km depth near MFT

trace, strike 283°, dip 6° and ALOS-2 T048), except that the uplift anomaly is masked prior to the

slip inversion (moment 5.98x1020 Nm, Mw 7.78, χ2 = 21.3). Panel a shows the LOS deformation

after masking the localized uplift signal. Residuals determined as observed - modeled LOS

displacement and vectors represent misfit between modeled horizontal motion and GPS

observations.

We then apply a uniform slip inversion scheme to invert these residuals (Fig. S6d) and thus

constrain geometry of best fitting fault plane. The inversion is done using GA and is free to place

the additional rupture on the HST flat (which would re-affirm the single planar fault model), down-

dip on a ramp (as in Fig. S5), or up-dip on a splay fault rising toward the surface. We find that the

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anomaly is best explained by slip on a shallow plane striking 288° and dipping 25°. The strike of

288° is consistent with regional geology and the dip of 25° is confirmed using Akaike Information

Criterion (AIC)10 (Fig. S7). AIC, defined as 2k−2ln(L), where k is the number of model parameters

and ln(L) is the log-likelihood of the best-fitting model. Figure S7 shows the AIC value versus dip

angle for various model runs. As seen the least AIC is obtained for dip angle of 25o. This best-fitting

rupture plane, found by unconstrained inversion of the uplift anomaly, intersects the HST flat at

about 30km north of PT2 (~110 km north of the MFT) and projects to the surface near PT2 (Fig. 2).

Figure S7. Akaike Information Criterion (AIC) used to identify the best geometry and slip

distribution associated with the splay fault (best-fit dip is 25°).

Figure S8. Inversion results of coseismic slip distribution using a model that combines a planar fault

and a steeper structure extending toward the surface for ALOS-2 data. Same as Fig. 4 except that the

HST flat extends down-dip of the intersection with the splay fault to 125km north of the MFT (45

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km north of PT2), equivalent to the northward extent of rupture on the shallow HST flat shown in

Figure 3a-c and in prior work1,3 (moment 6.19x1020 Nm, Mw 7.79, χ2 = 7.5).

Once the geometry of the steeper plane is fixed, we generate new meshes comprising the

HST and the new steeper plane. Here, we use two different meshes considering plausible alternative

relationships between the splay fault and the HST: either the steeper splay fault roots into the HST

flat which extends farther down-dip to the north (1654 triangles with average side of ~4.5 km) or

the steeper splay fault roots into a ramp-flat transition on the HST (2082 triangles with average side

of ~4.2 km) (Fig. 2). The inversion procedure for slip distribution is identical to that used for

coseismic slip modeling on the HST. The best-fitting models are shown in Fig. S8 and Fig. 4,

respectively. Figure S9 shows the fit of this model to Sentinel-1 data.

Figure S9. Inversion results of coseismic slip distribution using a model that combines a planar fault

and a steeper structure extending toward the surface for Sentinel-1 data. Same as Fig. 4 but showing

model and residual LOS for Sentinel-1 data (T085 χ2 = 10.5, T019 χ2 = 128.9). Comparison with

Figure S2c shows the improvement obtained by including the small rupture patch on the inferred

steeper splay fault for T085 (χ2 = 10.5 vs 12.9). The fit to T019 is of course not improved as this

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image pair does not include the uplift anomaly and the misfit is dominated by likely unwrapping

errors.

The fit to observed deformation in both cases is excellent. For the scenario in which the

splay fault roots into an HST flat, slip >1m occurs from 3 to 11 km depth, while for the scenario in

which the splay fault roots into a ramp-flat transition on the HST, slip > 1m extends to 14 km depth

(since the HST flat does not extend farther north in this case, any slip otherwise placed on the HST

flat more than 110 km north of the MFT is resolved onto the HST ramp down-dip of the splay

fault). The associated geodetic moments for these scenarios are 6.19x1020 Nm and 6.50 x1020 Nm,

respectively. The scenario in which the splay fault roots into an HST flat that extends down-dip to

fully 125 km north of the MFT provides a slightly worse fit to the data (χ2 = 7.5 vs. χ2 = 7.2), but

the difference is slight and at the limit of the resolving power of the InSAR data and elastic

dislocation modeling using planar fault segments.

Geophysical Constraints on the Geometry of the HST

Here we present ancillary geophysical observations that provide important constraints on the

allowable geometry of the HST in central Nepal as additional context for the geodetic constraints

emphasized in our paper (see Fig. 2). This supporting information is presented in an augmented

version of Figure 2b that includes: (1) the microseismicity11 and creeping dislocation inferred from

inversion of interseismic uplift9,12,13 that constitute the primary evidence used to infer a mid-crustal

ramp beneath the High Himalaya, the HST geometry favored by Elliot et al.9, (2) centroid moment

tensor solutions and a new interpretation of the HST/top of Indian basement based on HiCLIMB

data from Duputel et al.2, and (3) re-located aftershocks in the Gorkha earthquake sequence14

(Figure S10). Most notably the creeping dislocation and microseismicity thought to document the

presence of a mid-crustal ramp now appear to reside deep (~10 km) within the basement of the

Indian Shield, a rather problematic disagreement between different observations. This disagreement

is particularly challenging for the thermo-kinematic models used to explain geomorphic and

thermochronometric observations at the foot of the High Himalaya9,15,16 (Figs. 1 and 2a) as these

models require underplating of Lesser Himalayan Metasedimentary rocks across the mid-crustal

ramp, which would require the top of Indian basement to be some 10 km deeper than observed

(Figure S10). Duputel et al.2, re-interpreting HiCLIMB imaging of lithospheric structure17, accentuate

steepening of the HST/top of basement, but place this ramp ~20km north of the ramp position

required to explain thermochronometric and geomorphic observations9,15,16, in closer agreement with

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geodetic constraints from co-seismic deformation in the Gorkha earthquake sequence. Aftershocks

of the Gorkha earthquake, particularly those occurring north of PT2 are similarly compatible with

the geodetically-constrained northward extent of the HST flat and not suggestive of a mid-crustal

ramp between ~80 and ~110 km north of the MFT as has been inferred by many9,15,16 (Figure S10).

Figure S10. Swath profile cross-section (N18°E) of plausible structural geometries in relation to PT2

and seismicity in the Gorkha earthquake sequence showing maximum (blue), mean (black), and

minimum (blue) elevation in a 100 km-wide swath. USGS Mw 7.8 hypocenter (white star). Heavy

grey line is the top of the seismically imaged HST (top of Indian basement)17. Heavy black line is

reinterpreted HST from HiCLIMB data2. Heavy blue line is the favored HST with mid-crustal ramp

under the High Himalaya from Elliot et al.9. Heavy dashed black line is creeping dislocation inferred

from interseismic uplift patterns9,13. Our best-fit HST geometry and down-dip structural alternatives

shown as in Figure 2. Seismicity sized by moment magnitude: red dots are aftershocks re-located

using the local Nepal network14, larger beach balls are centroid moment tensor solutions determined

using a 3D Earth model2 showing uncertainty on depth (mainshock – red, aftershocks > Mw 5 –

green). Open circles are pre-event microseismicity11 (data provided by J-P Avouac).

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