Evidence for anthropogenic surface loading as trigger mechanism of the 2008 Wenchuan earthquake

Abstract

Two and a half years prior to China’s M7.9 Wenchuan earthquake of May 2008, at least 300 million metric tons of water accumulated with additional seasonal water level changes in the Minjiang River Valley at the eastern margin of the Longmen Shan. This article shows that static surface loading in the Zipingpu water reservoir induced Coulomb failure stresses on the nearby Beichuan thrust fault system at <17 km depth. Triggering stresses exceeded levels of daily lunar and solar tides and perturbed a fault area measuring 416 ± 96 km². These stress perturbations, in turn, likely advanced the clock of the mainshock and directed the initial rupture propagation upward towards the reservoir on the "Coulomb-like" Beichuan fault with rate- and state-dependent frictional behavior. Static triggering perturbations produced up to 60 years (0.6%) of equivalent tectonic loading, and show strong correlations to the coseismic slip. Moreover, correlations between clock advancement and coseismic slip, observed during the mainshock beneath the reservoir, are strongest for a longer seismic cycle (10kyr) of M > 7 earthquakes. Finally, the daily event rate of the micro-seismicity (M ≥ 0.5) correlates well with the static stress perturbations, indicating destabilization.

Appendix

Everyday, the moon and sun cause tidal elongations on earth (Bartels 1985). These daily pull/push effects, in turn, induce stabilizing and destabilizing stresses on preexisting fault zones in the earth’s crust and are independent from any geological forces on earth, including endogenous forces (e.g., volcanism, tectonics) and exogenous forces (e.g., erosion, sedimentation). Moreover, it has been shown that tidal stress changes have weak effects on triggering medium- to large-size earthquakes (Beeler and Lockner 2003a). Thus, it can be anticipated that any triggering stress perturbation on the earth’s crust must exceed at least stress levels resulting from the tidal elongation of the earth. Analytically, it can be shown how high these tidal stress changes are.

Let’s assume, F ₀ is the earth’s gravitational potential, which results from both attraction force and centrifugal force of the earth and moon/sun. Tidal forces V, however, deform F ₀:

$$ F = F_0 - V $$

(10)

This results in a vertical surface displacement ξ with respect to the average value of the gravitation acceleration on earth g = 9.798 ms⁻¹.

$$ \xi = \frac{F_0 - F}{g} = \frac{V}{g}. $$

(11)

Tidal forces change with geocentric zenith distance θ from the moon/sun (Bartels 1985), whereas the main term of the tidal potential is

$$ V \approx \left(\frac{G}{\overline r_{\rm E}^2} \right) r_{\rm E}^2 \left( \cos 2\theta + \frac{1}{3} \right) $$

(12)

with the lunar tidal constant G _l  = 2.6206 m² s⁻² and the solar tidal constant G _s  = 1.2068 m² s⁻², the radius of the earth r _E and the mean radius of the earth $\overline r_{\rm E} = 6371.221$ km. Assuming the earth is a sphere $(r_{\rm E} = \overline r_{\rm E})$, the general form of vertical surface displacement is

$$ \xi = \frac{G}{g} \left(\cos 2\theta + \frac{1}{3}\right). $$

(13)

The displacement due to the moon and sun is

$$ \xi_l = 0.267\;\hbox{m} \left( \cos 2\theta + \frac{1}{3} \right), \;\;\; \xi_s = 0.123\;\hbox{m} \left( \cos 2\theta + \frac{1}{3} \right). $$

(14)

Thus, the ξ _l and ξ _s are amplified at the zenith (θ = 0°) by 0.356 m and 0.164 m. On the other hand, they are depressed at the nadir (θ = 90°) by 0.178 m and 0.082 m. The peak-trough difference for the moon is 0.534 m and 0.246 m for the sun.

Both vertical displacements induce maximal shear stresses τ and normal stresses σ _n on preexisting faults (e.g., dipping 45°) in the earth’s crust with an average shear modulus of about G = 30 GPa and friction angle of, let’s assume, ϕ of 29°:

$$ \tau = \frac{\xi}{\overline r_{\rm E}} 2G, $$

(15)

$$ \sigma_n = \frac{\tau}{\tan\phi}, $$

(16)

Thus, maximum induced stresses that need to be exceeded by any additional triggering stress (e.g., due to surface loading) are:

• by the moon τ _l  = 5.03 kPa and σ _n,l  = 9.07 kPa,

• by the sun τ _s  = 2.32 kPa and σ _n,s  = 4.18 kPa.