SRL 88:3, Electronic Supplement to Wang et al.

Electronic Supplement to
Induced Seismicity in Oklahoma Affects Shallow Groundwater

by Chi-Yuen Wang, Michael Manga, Manoochehr Shirzaei, Matthew Weingarten, and Lee-Ping Wang

This electronic supplement consists of three subsections with a supporting figure and a table: (1) barometric pressure and water level in wells; (2) coseimic static strain and water-level change; and (3) derivation of equation (3) in the main article.

Barometric Pressure and Water Level in Wells

Because barometric measurement is not available at the wells, we make qualitative comparisons between water level and the barometric pressure at the Cherokee Airport, Oklahoma, ~40 km southwest of the two U.S. Geological Survey (USGS) wells. Figure S1 shows the corresponding changes of opposite signs in water level and the barometric pressure, as expected, and that the barometric pressure was stable at the time of the earthquake (indicated by red vertical line).

Coseimic Static Strain and Water-Level Change

Coseismic strain is calculated using a square dislocation model buried in an elastic half-space. We choose a shear modulus of 30 GPa and a Poisson ratio of 0.25. We also consider a stress drop of 30 bars and compute the slip on the fault using an empirical relationship by Kanamori and Anderson (1975). Table S1 lists the calculated volumetric strains at the four wells of this study produced by fault ruptures during the three earthquakes.

The decrease of 5 cm of water level at the Oklahoma Water Resource Board (OWRB) well 171706 at the 13 February M_w 5.1 earthquake occurred within an hour (Fig. 2d in the main article). If this decrease is due to diffusion into a dilated aquifer, the time constant of the diffusive process is H²/D ~ 1 hr, in which H is the thickness of the aquifer. Given D = 0.05 m²/s from well test (see the main article), we have H ~ 10 m. The volumetric strain of the aquifer would have to be ~10⁻³ to cause a decrease of 5 cm of water level, assuming reasonable porosity, which is 5 orders of magnitude greater than the calculated volumetric strain (Table S1). Thus, the static strain hypothesis cannot explain the coseismic decrease of water level in this well.

Derivation of Equation (3) in the Main Article

Appendix B in Wang and Manga (2010) showed that the differential equation (1) in the main article with the boundary condition (2) in the main article has the following solution:

$h (x, t) = \frac{1}{L} \sum_{n = 1}^{\infty} \cos (\frac{n π x}{2 L}) e^{- \frac{n^{2} π^{2} D}{{4 L}^{2}} t} \int_{- L}^{L} W_{o} (x^{'}) \cos \frac{n π x'}{2 L} d x' .$

Assuming W_o is constant between L₁ and L₂, but zero elsewhere, integration of the above equation leads to equation (3) in the main article.

Table

Table S1. Calculated coseismic volumetric strains at the well sites based on the half-space dislocation model and focal plane solutions of the three 2016 M_w ≥5 Oklahoma earthquakes.

Figure

Figure S1. Barometric pressure at the Cherokee Airport before and after the 6 November Cushing earthquake plotted together with water level in wells 36492109 and 36483109 during the same time period.

References

Kanamori, H., and D. L. Anderson (1975). Theoretical basis of some empirical relations in seismology, Bull. Seismol. Soc. Am. 65, 1073–1096.

Wang, C.-Y., and M. Manga (2010). Earthquakes and Water, in Lecture Notes in Earth Science, Vol. 114, Springer, Berlin, Germany, 249 pp.

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