Subsections

Weak Mantle in NW India Probed by Postseismic GPS Measurements Following the 2001 Bhuj Earthquake

D. V. Chandrasekhar and Roland Bürgmann

Introduction

Transient crustal deformations induced by large earthquakes are used to infer the rheology of the continental crust and the upper mantle. Generally, these studies find that the elastically strong part of the continental crust is 15-30 km thick, that the lower crust has a higher viscosity than the uppermost mantle, and that the mantle asthenosphere has a low viscosity ( $<5 \times 10^{19}$ Pa s) (Bürgmann and Dresden, 2008). However, all of the postseismic deformation transients considered to date are from active plate boundary zones with strongly thinned lithosphere ($<$60 km), and relatively hot and hydrated mantle asthenosphere. In contrast, studies of postglacial rebound in stable shield areas (Fennoscandia, North America) indicate an elastic plate thickness of $\sim$100 km overlying a high viscosity substratum ($>10^{20}$ Pa s) (Milne et al., 2001). The Bhuj earthquake of January 26, 2001 in Kachchh, India is the largest event ($M_{w}$ 7.6) in the last 50 years to strike the Indian shield in its recorded history, lies $>$ 300 km from the nearest active Plate boundary and provides a unique opportunity to probe the rheology of the deep lithosphere in an intraplate region. We use GPS displacements to models of postseismic deformation caused by the earthquake to assess the viscous strength of the lower crust and upper mantle.

Postseismic GPS Observations

Time series of GPS-measured surface displacements document transient deformation during 6 years following the Bhuj earthquake. We update and expand on initial results from this network published by Reddy and Sunil, 2007 who provide further detail on the GPS observations and analysis. Sites are labeled in the maps of Figure 2.55. Time series of positions of each site in the well-determined ITRF 2000 are obtained from the combined quasi-observations and provide relative position time series from February 2001 to January 2007 of each site with respect to a station at Ahmedabad (AHMD). The time series show the decaying nature of the postseismic motions and are well represented by a log function a' $+$ b' log (t), where t is the time (yr) and a' and b' are constants to fit the displacement time series. We used the logarithmic curve-fit values to estimate total displacements at each site with respect to AHMD for 6 months, 1 year, 2 years and 6 years after the Bhuj earthquake.

Viscoelastic models and results

The broadly distributed nature of the postseismic deformation field suggests a deeply buried source of transient deformation and thus we primarily consider models of viscous relaxation in our investigation. To calculate the viscoelastic postseismic deformation we adopt the earthquake source parameterization of Antolik and Dreger (2003), which is also consistent with geodetic constraints on the rupture (Chandrasekhar et al., 2004; Schmidt and Bürgmann, 2006). The location of the rupture is shown in the maps in Figure 2.55. Strike, dip, rake, and seismic moment are 82$^{\circ}$, 51$^{\circ}$, 77$^{\circ}$, and $1.6 \cdot 10^{20}$ Nm, respectively. The model rupture is 40 km long and 10$-$32 km deep. The slip distribution of Antolik and Dreger (2003) is simplified with a larger amount of slip (8.2 m) confined to the center ( $25 \times 15 km^2$) and less slip (1.7 m) on the surrounding part. We calculate postseismic deformation using VISCO1D (Pollitz, 1997), for a simple layered Earth model consisting of an elastic plate overlying a viscoelastic substrate. The free model parameters are the thickness Hp of the elastic plate and the viscosity $\eta_a$ of the viscoelastic material below. The minimum root mean-square error (RMS) between the observed and predicted motions is found at Hp= $\sim$34 km for all time periods considered (Figure 2.55), which is close to the local crustal thickness inferred from seismic data (Sarkar et al., 2001). Optimal effective mantle viscosities increase with time from $\eta_a$= $3 \times 10^{18}$ Pa s for the first 6 month period to $2 \times 10^{19}$ Pa s for the full 6 years displacements, which is consistent with a stress dependent rheology of the upper mantle (Freed and Bürgmann, 2004). An increase of the coseismic moment of the rupture by 1 $\frac{1}{2}$ times raises the effective viscosity estimates by 30-50% for the different time intervals considered, given that some teleseismic moment estimates are as high as $3.6 \times 10^{20}$ Nm (Wesnousky et al., 2001). We also estimate the viscosity of a 15-km-thick lower crustal layer separate from the upper mantle. The misfit suggests that the observed data do not require relaxation of the lower crust and indicate a lower bound of $10^{20}$ Pa s on its effective viscosity. We find very small contribution of mainshock induced pore-pressure changes to the near-field horizontal deformation and subsidence of as much as 65 mm localized over the buried coseismic rupture. None of the afterslip models demonstrate the observed pattern or magnitude of motions of the GPS network, suggesting that viscous relaxation and afterslip are distinctly different.

Discussion and Conclusions

The estimated first-order viscoelastic structure deduced consists of an elastic plate whose thickness is $\sim$ 34 km and an underlying viscoelastic asthenosphere whose effective viscosity is $2 \times 10^{19}$ Pa s, during the 6-year observation period. Estimated effective viscosities increase with time suggesting power-law rheology due to dislocation creep. Modest, shallow afterslip may have contributed to the near-field GPS. The inferred viscosity of the upper mantle below the Bhuj region is closer to that found for thermally weakened and hydrated mantle below western North America and other back-arc or former back-arc regions (viscosity estimates generally range from 0.1 $- 1 \times 10^{19}$ Pa s below 40-60 km depth) than that found from ice-unloading studies over the North American and Fennoscandian cratons (ranging from 0.5 $- 1 \times 10^{21}$ Pa s below a $>$100 km thick elastic lithosphere). The low mantle viscosity deduced may be the result of thermal weakening due to the late Cretaceous Reunion (Deccan) plume, which is indicated by a  200-km-wide seismic wave speed anomaly in the uppermost mantle beneath the region (Kennett and Widiyantoro, 1999). In contrast, the apparent strength of the lower crust is consistent with a mafic and dry composition indicated by unusually high seismic velocities at lower crustal depths (Mandal and Pujol, 2006), which may have developed in association with intrusive activity during an early Jurassic period of rifting (Chandrasekhar and Mishra, 2002). The mantle lithosphere in the Gujarat region in NW India appears to be weaker than fully intact continental shields. Relaxation of remote stresses in such a weak zone can concentrate stress in the overlying crust and lead to the observed intraplate seismicity in this region.

Acknowledgements

This study was accomplished while DC was visiting researcher at the University of California, Berkeley, USA, funded by the DST, New Delhi through a BOYSCAST fellowship. RB acknowledges support by NSF grant EAR-0738298.

References

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Figure 2.55: Model results. The RMS misfit between the calculated and observed horizontal displacements as a function of elastic plate thickness (Hp) and asthenosphere viscosity ($\eta_a$) for the two layer Earth model as a function of time since the earthquake. The star marks the best-fit displacement model with the least RMS error value, whose best-fit horizontal displacements are plotted adjacent to the misfit plot. Vectors in black denote the observed displacement tipped with 95% confidence ellipses and yellow arrows are the calculated model displacements. (See color version of this figure at the front of the research chapter)
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