HR: 17:15h
AN: G32C-06    [PDF]
TI: When is the strain in the meter the same as that in the rock?
AU: * Segall, P
EM: segall@stanford.edu
AF: Geophysics, Stanford University, Stanford, CA 94306 United States
AU: J\'{o}nsson, S
EM: sj@eps.harvard.edu
AF: EPS, Harvard Unversity, Cambridge, MA 02138 United States
AU: \'Ag\'ustsson, K
EM: kri@vedur.is
AF: Icelandic Meteorological, Office, Reykjavik, 150 Iceland
AB: Borehole strainmeters are a valuable tool for monitoring crustal deformation and an important component of the Plate Boundary Observatory (PBO). One type, the dilatometer, measures the volumetric strain; three component strainmeters measure the dilatation and two in-plane shear strains. Borehole strainmeters are emplaced in porous fluid saturated rock. Pore-fluid flow induces strain, however there is no fluid exchange with the strainmeter. Thus, the dilatation measured by the strainmeter is the same as that in the rock only when the rock remains undrained. Assuming that the rock is homogeneous and isotropic, the instrumental dilatation $\Delta^{\rm inst}$ is given by $\Delta^{\rm inst} = C_1 (\Delta^{\infty} - C_2 p^{\infty})$, where $\Delta^{\infty}$ and $p^{\infty}$ are strain and pore pressure far from the borehole, and $C_1$ and $C_2$ depend on poroelastic rock properties; $C_1 = [{1-(1+ \alpha)\nu_u}]/[{1-(1+ \alpha)\nu}]$, $C_2 = [{3(1+\alpha)(\nu_u - \nu)}]/[{2\mu B(1+\nu_u)}]$, and $\nu, \nu_u$ are the drained and undrained Poisson's ratios, $\mu$ is shear modulus, $B$ is Skempton's coefficient, and $\alpha$ measures the vertical strain sensitivity of the instrument. This predicts that increases in pore-pressure, due for example to rainfall, cause a contractional strain. A large rainfall event in south Iceland raised water levels by 1-2 meters (10 - 20 kPa). Assuming $\nu_u = 0.33, \nu = 0.25, B = 0.7, \mu = 10^{10}$ Pa we predict contractions of order 180 nanostrain, in reasonable agreement with 4 of the 5 dilatometers in the area. Postseismic strain in the rock is expected to increase as the induced pore pressure gradients relax. However, a dilatometer $\sim 3$ \ km from a $M_w$ 6.5 earthquake in the South Iceland Seismic Zone shows a postseismic strain change {\em opposite} in sign to the coseismic response. { Rice and Cleary, Rev. Geophys.,} [1976] give the solution for two-dimensional edge dislocation in a poroelastic medium. From their results and the theory described above, we predict that the dilatation recorded by a strainmeter will be time invariant! This despite the fact that the mean stress, pore pressure, and dilatational strain in the rock all are time dependent. We conclude that the effects of drainage of a homogeneous, isotropic medium gives a correction of the observed sign, but can only partly explain the observed discrepancy. Fracture dominated poroelastic response, as described in the companion study, yields a qualitatively better explanation of the strainmeter data.
DE: 5104 Fracture and flow
DE: 7209 Earthquake dynamics and mechanics
DE: 8164 Stresses--crust and lithosphere
DE: 8194 Instruments and techniques
SC: Geodesy [G]
MN: 2003 Fall Meeting