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Slip pulse and resonance of the Kathmandu basin during the 2015 Gorkha earthquake, Nepal

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Science  04 Sep 2015:
Vol. 349, Issue 6252, pp. 1091-1095
DOI: 10.1126/science.aac6383

The bigger they are, the harder they fall

The magnitude 7.8 Gorkha earthquake hit Nepal on 25 April 2015. The earthquake killed thousands and caused great damage. Galetzka et al. determined how the fault that caused this earthquake ruptured. The rupture showed a smooth slip pulse 20 km wide that moved eastward along the fault over about 6 s. The nature of the rupture limited damage to regular dwellings but generated shaking that collapsed taller structures.

Science, this issue p. 1091

Abstract

Detailed geodetic imaging of earthquake ruptures enhances our understanding of earthquake physics and associated ground shaking. The 25 April 2015 moment magnitude 7.8 earthquake in Gorkha, Nepal was the first large continental megathrust rupture to have occurred beneath a high-rate (5-hertz) Global Positioning System (GPS) network. We used GPS and interferometric synthetic aperture radar data to model the earthquake rupture as a slip pulse ~20 kilometers in width, ~6 seconds in duration, and with a peak sliding velocity of 1.1 meters per second, which propagated toward the Kathmandu basin at ~3.3 kilometers per second over ~140 kilometers. The smooth slip onset, indicating a large (~5-meter) slip-weakening distance, caused moderate ground shaking at high frequencies (>1 hertz; peak ground acceleration, ~16% of Earth’s gravity) and minimized damage to vernacular dwellings. Whole-basin resonance at a period of 4 to 5 seconds caused the collapse of tall structures, including cultural artifacts.

The shape of the slip-rate time function (STF) during a seismic rupture provides critical insight into the constitutive fault properties. The abruptness of the slip onset determines the high-frequency content of the STF, and hence the intensity of the near-field ground motion (1) whereas the tail, which discriminates pulse-like and crack-like ruptures (2), has a low-frequency signature. Therefore, resolving the STF with band-limited strong-motion records is difficult. Combining high-rate Global Positioning System (GPS) waveforms (3, 4), which capture both dynamic and permanent deformation, overcomes this limitation.

The 25 April 2015 moment magnitude (Mw) 7.8 earthquake in Gorkha, Nepal resulted from the unzipping of the lower edge of the locked portion of the Main Himalayan Thrust (MHT) fault, along which the Himalayan wedge is thrust over India (5). The earthquake nucleated ~80 km northwest of Kathmandu and ruptured a 140-km-long segment of the fault (Fig. 1A), with a hypocentral depth of ~15 km and a dip angle of 7° to 12° (5, 6). The MHT accommodates most of the convergence between India and southern Tibet, with a convergence rate between 17 and 21 mm/year (7). For the 2015 event, which resulted in over 8000 deaths (mostly in Kathmandu and adjacent districts), modified Mercalli intensities (MMIs) reported by the National Society for Earthquake Technology–Nepal (NSET) (8) reached up to IX (violent shaking) and exceeded VI (strong shaking) over an area 170 km by 40 km. Kathmandu has been struck by repeated earthquakes in the past, with major destruction [MMI > X (extreme shaking)] in the years 1255, 1344, 1408, 1681, 1833, and 1934 (911). These earthquakes all occurred close to Kathmandu and have been assigned magnitudes between Mw 7.5 and 8.4. During the Gorkha earthquake, damages in the Kathmandu basin were probably amplified by site effects, as has happened in past events (12, 13). The basin is filled with 500 to 600 m of fluviolacustrine sediments resting on a metamorphic basement (14).

Fig. 1 Cumulative slip distribution of and static stress drop due to the Gorkha earthquake.

(A) Slip inversion results for the Mw 7.8 Gorkha event. The red star is the hypocenter. Dashed contours are depths to the fault. Orange diamonds are 5-Hz cGPS stations, and white diamonds are low-rate (1/30-Hz) stations. The green triangle is the strong-motion station. Kathmandu is represented by the blue square. The black arrows indicate the coseismic offsets measured at the sites (the values and uncertainties are given in table S1). Vectors with less than 10 cm of displacement are not shown. (B) Static stress drop predicted by the model of Fig. 1A. Green circles are aftershocks with local magnitudes greater than four, recorded and located by the Nepal National Seismic Center. Focal mechanisms (yellow and white circles) represent the global centroid-moment tensor solutions for aftershocks with magnitudes greater than six.

The damage to the most vulnerable vernacular dwellings in Kathmandu, which rarely exceed four stories, was much less than expected in view of the 2015 earthquake’s magnitude and its proximity to Kathmandu. In contrast, some taller structures were more severely affected, such as the 60-m-tall Dharahara tower, which collapsed even though it had partially survived an Mw 8.1 to 8.4 earthquake in 1934. The 1934 event caused much more extensive destruction to vernacular dwellings in Kathmandu than the 2015 event did: 20% of the buildings in Kathmandu were destroyed in 1934 versus less than 1% in 2015 (15). These observations reflect the combined effects of the earthquake source characteristics and local geological conditions, in addition to the evolution of building practices.

The 2015 Gorkha earthquake ruptured a subhorizontal portion of the MHT that lies directly beneath a network (16) of continuous GPS (cGPS) stations, which record data at a high rate of five samples per second, and one accelerometer station (17) (Fig. 1A). In addition, surface displacements were measured with interferometric synthetic aperture radar [InSAR (18, 19)] (fig. S1). Although a number of recent earthquakes have been documented with similar techniques (20, 21), the Gorkha event is the first occurrence of a large continental thrust earthquake to be recorded by high-rate cGPS stations very close to and completely encompassing the rupture area. The combination of these measurements provides the opportunity to image the kinematics of the source process and the strong ground motion that led to the particular pattern of structural damage observed during this earthquake.

The records of seismic displacements and accelerations (Fig. 2 and fig. S2) show southward motion of up to 2 m, with a rise time on the order of 6 s. The pulse is particularly clear at cGPS station KKN4, located on bedrock just north of Kathmandu and only ~13 km above the fault. The displacement at this station started about 25 s after the onset of the rupture, corresponding to 15 s after the P-wave arrival (Fig. 2); it reached its final static value by about 32 s, based on the origin time of 06:11:26.270 UTC determined by the U.S. Geological Survey (USGS) from the arrival of radiated direct P waves (6). The records indicate a pulse-like rupture (22), with slip on any given portion of the fault occurring over a short fraction of the total ~70-s earthquake source duration (5). Given the ~78-km distance of KKN4 from the epicenter, the pulse must have propagated at ~3 km/s, a value consistent with waveform modeling and back projection of high-frequency seismic waves recorded at teleseismic distances (5). Surface velocities reached values of ~0.7 m/s. In addition to the pulse recorded at KKN4, the cGPS station NAST within the Kathmandu basin detected strong oscillations of about 3- to 4-s periods lasting for ~20 s (Fig. 2 and Fig. 3A). The Gorkha earthquake must have excited a resonance of the Kathmandu basin as a whole. The resonance is evident in the response spectra from these stations and in data from the accelerometer station, KATNP (Fig. 3, G to I).

Fig. 2 Records of ground displacements and accelerations during the Gorkha earthquake.

Shown are displacement waveforms at cGPS stations KKN4 and NAST (five samples per second) and acceleration waveforms at strong-motion station KATNP (Fig. 1).

Fig. 3 Evidence for resonance of the Kathmandu basin.

(A to C) Three components of ground velocity observed at two high-rate GPS stations (KKN4 and NAST) and one strong-motion station (KATNP) in the Kathmandu region. KKN4 is located on hard rock northwest of Kathmandu, whereas the other two stations are located on soft sediment in the basin. The GPS is differentiated to velocity, and the strong-motion data are integrated after high-pass filtering at 0.02 Hz. (D to F) Ground-motion amplification observed at the two basin stations. Plotted is the ratio of the amplitude spectra of the basin stations to the amplitude spectra of the reference bedrock station, KKN4. (G to I) Five-percent damped velocity response spectra for all three stations. (J) Close-up map showing the location of the basin and bedrock stations.

To determine the kinematics of the seismic rupture, we carried out a formal inversion of time-dependent slip on the fault (23, 24) and compared the recorded waveforms with forward predictions, assuming a propagating slip pulse with varied characteristics. We assumed a planar fault geometry with a strike of 295° and a dip of 11°, in accordance with the teleseismic W-phase moment tensor solution calculated by the USGS (6). We tested shallower dips up to 7° but found that 11° provided a better fit to the data. The fault was discretized into 10 km by 10 km subfault segments. We jointly inverted the three-component 5-Hz GPS–derived velocity waveforms, the GPS static offsets, and the InSAR line of sight (LOS) static displacements measured between 22 February and 3 May (fig. S1). The GPS displacement time series shows large postseismic motion at only one station (CHLM), with a magnitude of less than 2 cm in both the horizontal and vertical directions over the week after the earthquake. Therefore, we neglected the contribution of postseismic deformation to the LOS displacements. The model fits both data sets closely (Fig. 1A), with an 86% reduction in variance for the InSAR and GPS coseismic displacements and a 74% reduction in variance for the GPS velocity waveforms (figs. S2 and S4). The model indicates a predominantly unilateral rupture to the southeast, with a peak slip of ~6.5 m on a large asperity to the north of Kathmandu. The event duration was 65 s (fig. S4), with the peak moment release at 23 s when the slip pulse was less than 10 km north of Kathmandu (movie S1); the peak slip rate was 1.1 m/s. Most of the slip was concentrated within a narrow region between the 10- and 20-km fault-depth contours. We found a large asperity with 3.0 m of slip, located east of the main asperity and between 20 and 23 km below the surface. The rupture velocity of the propagating slip pulse, indicated by the onset of slip in our best-fitting model, was ~3.2 km/s and had a maximum allowed velocity of 3.3 km/s (fig. S4). This velocity corresponds to ~95% of the shear wave speed at the depth where the majority of the slip occurred (15 km), according to the local velocity model used to calculate the Green’s functions (table S2), which indicates a very fast rupture propagation. The slip tapered at 17 to 20 km depth along the edge of the locked zone of the MHT.

Fig. 4 Slip-pulse kinematics during the Gorkha earthquake.

(A) Snapshot of the slip rate on the MTH at 27 s after the origin time, during propagation of the seismic rupture from the model in Fig. 1. The red star is the hypocenter, and dashed contours represent the depth to the fault. The white circles are the centers of five subfaults used to compare against theoretical regularized Yoffe source time functions (28). (B) STFs at the five locations from (A). Plotted are the inverted slip rates and the regularized Yoffe functions measured from the vertical velocity at KKN4, scaled to the maximum observed slip rate at each point, which is indicated numerically. Time is relative to the hypocentral origin (28.147°N, 84.708°E; 25 April 2015, 06:11:26.270 UTC).

The inversion that we performed includes a large number of parameters, which would allow for a relatively complex rupture history. However, the resulting model is simple, with essentially a single propagating slip pulse. The spatiotemporal evolution of the slip pulse matches well with the location of the sources of high-frequency seismic waves (0.5 to 2 Hz) derived from back projection of the teleseismic waveforms (5) (movie S1).

We calculated the static stress change on the fault plane due to the earthquake (Fig. 1B). This calculation showed loading of the fault around the main asperity where most of the aftershocks occurred, including the Mw 7.3 aftershock of 12 May, as expected for aftershocks triggered by coseismic stress transfer (25). The model predicted a pattern of uplift in the Kathmandu basin and subsidence at the front of the high range (fig. S4), approximately opposite to the pattern observed in the interseismic period, as expected from simple models of the seismic cycle on the MHT (26, 27).

The record at station KKN4 should be a close representation of the STF, as it lies only about 13 km above the propagating slip pulse and is not affected by the site effects observed at the stations in the Kathmandu basin. We conducted synthetic tests with the same Earth structure model used in the inversion (table S1) to assess the distortion and smoothing introduced by the elastic half-space response (fig. S5). We found a vertical velocity amplitude of about 70% of the peak slip rate on the fault directly beneath the station, along with a well-preserved temporal shape. Furthermore, the tests demonstrated that the smooth onset of slip is not an artifact of the transfer through the elastic medium, represented by the elastodynamic Green’s functions. The shape of the slip pulse can also be retrieved from the GPS records at NAST and the strong-motion vertical records at KATNP, which are less affected by site effects than the horizontal records (Fig. 1). All three records indicate a pulse ~6 s in duration. The shape of the pulse fits the regularized Yoffe function (28), yielding a smooth rise, with an acceleration time to the peak slip rate of τs = 1.7 s, a rise time of τR = 3.3 s, and a total effective duration of τeff = 6.7 s. The slip-rate pulse derived from the inversion also fits well, using the same values of τs and τR and peak slip-rate of ~0.9 m/s (Fig. 4). We compared the recorded waveforms with predictions from a suite of forward models to test the robustness of our results. We used the static slip model in these tests, deduced from the inversion of the GPS static and InSAR measurements (fig. S7). We assumed a propagating slip pulse and a regularized Yoffe STF with varying characteristics. We varied the rupture velocity between 2.8 and 3.6 km/s and the rise time between 2 and 10 s (fig. S8). By inverting synthetics calculated from forward modeling, we also tested the resolution power of the inversion and the limited bias introduced by the regularization applied to the inversion (24) (figs. S10 and S11). Together, these tests demonstrated that the duration of the slip pulse was probably less than 10 s, the time to the peak slip rate could not have been shorter than 1 s (we would otherwise have observed a much larger amplitude at high frequencies), and the average propagation rate of the slip pulse was not less than ~3.0 km/s over the first 30 s (until KKN4, NAST, and KATNP recorded a pulse signal).

Tinti et al. (28) analyzed how the shape of the STF relates to the characteristics of the friction law that governs the dynamics of the rupture. Based on this rationale (their equations 6 and 11), we estimated the slip-weakening distance to be ~5 m (for a peak slip of 6.5 m). This distance is large compared with those estimated from kinematic and dynamic modeling of seismic ruptures (29, 30), which tend to be overestimated (1) and are typically on the order of 0.5 to 1 m. The large value we obtained is possibly related to the earthquake’s having occurred close to the brittle-ductile transition at the lower edge of the locked portion of the MHT. The modeled smooth onset of the STF and the related large slip-weakening distance provide an explanation of the relatively low amplitude of shaking at frequencies above 1 Hz. The observed slip-weakening behavior does not require the slip-weakening friction law to be in effect: A fault obeying the rate-and-state friction law can show an apparent slip-weakening behavior with an effective critical distance that is several orders of magnitude larger than the critical distance entering the friction law (31). Aspects of the rupture kinematics and ground strong motion observed during the Gorkha event may also be due to hanging wall effects, the importance of which could be assessed through dynamic modeling of the rupture (32, 33).

Our study provides insight into the main factors that determined the damage sustained during the Gorkha earthquake. Although the hypocenter was ~80 km away from the city, the main asperity that radiated most of the energy was much closer, just north of the basin and at a relatively shallow depth. Comparison of the waveforms recorded within the sedimentary basin at NAST and KATNP (Fig. 3) with the bedrock records at KKN4 shows prominent differences, even though the stations are less than 13 km apart. The waveforms recorded at the bedrock station KKN4 were simple, mostly dominated by the single pulse, whereas within the basin, peak horizontal ground velocities of 0.5 to 0.8 m/s [considered severe to violent (34)] were sustained for 20 s at KATNP and 40 s at NAST. The ratio of the amplitude spectra of the basin waveforms to those recorded at the bedrock station (Fig. 3, D to F) indicates an amplification of long-period energy between 1 and 9 s, with horizontal-direction amplitudes in the basin six to seven times as large as those at the bedrock station. The response spectra (Fig. 3, G to I) show that, within this amplified period band, the 4-s-period shaking was the strongest at the basin stations.

The 4-s peak in the response spectra agrees with the observation that the source time function beneath Kathmandu had a duration of ~6 to 7 s. The net effect of this long source duration with a slow onset time was to produce radiated energy depleted in the high-frequency component (fig. S11). This explains why vernacular dwellings with only a few stories were not severely affected, despite the anticipated short-period site effects from microzoning (13). Furthermore, high-frequency intensity measures such as peak ground accelerations (Fig. 2) were modest (~1.6 m/s2, MMI = VI), whereas longer-period intensity measures such as peak ground velocity (Fig. 3) were very large (80 cm/s, MMI = IX). Kathmandu was faced with a combination of source and site effects. The rupture directivity focused radiated seismic energy toward the city; the smooth onset and 6- to 7-s duration of the pulse excited a resonance of the Kathmandu basin, producing a protracted duration of violent shaking at a period of around 4 s.

Supplementary Materials

www.sciencemag.org/content/349/6252/1091/suppl/DC1

Materials and Methods

Figs. S1 to S11

Tables S1 and S2

Movie S1

References (3545)

  • * Present address: UNAVCO, Boulder, CO 80301, USA.

References and Notes

  1. The Nepal Geodetic Array (www.tectonics.caltech.edu/resources/kmlnepal.html) was deployed through a collaboration between the Caltech Tectonics Observatory (USA), the Department of Mines and Geology (Nepal), and the Department Analyse et Surveillance de l’Environnement (CEA, France).
  2. Materials and methods are available as supplementary materials on Science Online.
  3. Acknowledgments: The GPS data are available from the UNAVCO website. The InSAR data are available at http://topex.ucsd.edu/nepal/. The Nepal Geodetic Array was funded by Caltech and DASE (to J.-P.A.) and by the Gordon and Betty Moore Foundation, through grant GBMF 423.01 to the Caltech Tectonics Observatory; support was maintained by NSF grant EAR-1345136. A. Miner and the Pacific Northwest Geodetic Array (PANGA) at CWU are thanked for technical assistance with the construction and operation of the Tribhuvan University (TU)–CWU network. Additional funding for the TU-CWU network came from the United Nations Development Programme and the Nepal Academy for Science and Technology. The high-rate data were recovered thanks to (i) a rapid intervention funded by NASA (USA) and the Department of Foreign International Development (UK) and (ii) engineering services provided by UNAVCO via the GAGE (Geodesy Advancing Geosciences and EarthScope) Facility, with support from NSF and NASA under NSF Cooperative Agreement no. EAR-1261833. We also thank Trimble Navigation and the Vaidya family for supporting the rapid response. The accelerometer record at KATNP was provided by USGS. We thank A. Nathan (U.S. Embassy in Kathmandu), S. Hough, D. Given, I. Flores, and J. Luetgert for contributions to the installation of this station. Research at UC–Berkeley was funded by the Gordon and Betty Moore Foundation through grant GBMF 3024. A portion of this work was carried out at JPL under a contract with the NASA. The GPS data were processed by the Advanced Rapid Imaging and Analysis Center for Natural Hazards (JPL) and the Scripps Orbit and Permanent Array Center. The effort at the Scripps Institution of Oceanography was funded by NASA grants NNX14AQ53G and NNX14AT33G. Advanced Land Observing Satellite–2 data were provided by the Japan Aerospace Exploration Agency under investigations 1148 and 1413. J.-P.A. thanks the Royal Society for support. We thank D. Dreger for discussion and W. Mooney for comments. J.-P.A led the study and wrote the article. D.M. performed the kinematic modeling and wrote the article. Y.B. supervised the high-rate data processing and wrote the article. J.Ga. led the field operations. J.Ge. conducted the high-rate data processing. S.O., A.M., W.S., and J.F.G. conducted the low-rate data analysis to estimate coseismic offsets. E.O.L. and X.X. conducted the InSAR data processing. L.B. helped to organize the field operations. All other authors contributed to building and servicing the GPS stations and to the post-earthquake data recovery. All authors edited the article.
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