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Crustal Deformation and Fault Mechanics

 
    Crustal Deformation and Fault Mechanics

 

 

 

Seismicity Associated With Dike Intrusion

 

Dike intrusions, as well as industrial hydraulic fractures, are commonly associated with propagating swarms of earthquakes.  Some large basaltic dike intrusions have generated tens of thousands of seismic events and propagated tens of kilometers.  Dikes have also been imaged by ground deformation measurements including GPS, tiltmeters, and InSAR.  Deformation measurements are only weakly sensitive to the detailed geometry of the dike, but can be used to determine the overall dike size and volume.   Seismicity, on the other hand, is triggered by stress changes associated with the growing crack and are therefore sensitive to the detailed shape of the dike.

We are investigating a method for joint inversion of deformation and seismicity data in both volcanic and hydraulic fracturing settings.  A dike is taken to be an opening mode fracture with uniform internal pressure, but unknown shape. We model the dike with elements that either open, and are subject to the pressure boundary condition, or remain closed.  The surface deformation is computed from the amount of opening in each of the elements, as is the stress change in the rock surrounding the fracture.  We relate the changes in stress to predicted changes in the rate of seismicity using Deiterich (1994) seismicity rate theory. The binary inversion to determine whether an element opens or not is determined by a simulated annealing procedure, that optimizes the fit to both the deformation and seismicity data (see movie).  In simulations we have found that joint inversion of deformation and seismicity does a better job of recovering the input dike model than simply inverting the deformation data alone (figure 1).


Figure 1.  Invesion of geodetic data only, compared to a joint inversion of geodetic data and seismicity data.

The space-time evolution of stress near a propagating dike or facture can lead to important differences in the predicted seismicity. We model an arbitrary stress history with a sum of piece-wise constant stress-rate segments.  Consider a two points, labeled 1 and 2 in Figure 2.  Point 1 is in front of the propagating dike, point 2 is below the bottom edge of the dike.  Point 1 undergoes a dramatic increase in stress as the dike tip passes, leading to a sharp increase in the rate of earthquakes followed by a slow (aftershock-like) decay.  Point 2 on the other hand experiences a rapid stress increase followed by a sharp stress drop as the crack tip passes and the volume falls into a “stress shadow”.  In this case there is a brief spurt of seismicity that stops as soon as the crack tip passes.


Figure 2.  Point 1 (red) is offset perpendicular to the final state of the dike, and sees a stress increase as the dike approaches followed by a stress shadow after the dike has passed.  Point 2 (blue) is below the final dike position.  It sees only a stress increase during dike propagation. 

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