Crustal Deformation and Fault Mechanics

Modeling Time-Dependent Dike Propagation From Seismicity and Deformation Data

Increases in seismicity and crustal deformation are two of the most important precursors measured prior to volcanic eruptions. Despite the fact that these observations reflect the same physical processes at depth, the two data types are almost never analyzed together in a quantitative way. We focus here on dike intrusions because: a) they commonly induce propagating swarms of earthquakes, and b) the geometry of dikes is reasonably well understood. As a dike is emplaced it deforms the surrounding crust. The resulting surface deformation can be measured by continuous GPS, tilt, and strainmeters, and InSAR. Geodetic measurements are commonly used to constrain the overall geometry of dikes, however they are typically insensitive of the detailed dike shape. At the same time, stress changes caused by the intrusion can trigger seismicity that can potentially be used to produce a more detailed image of the propagating dike. We have developed a method to combine seismicity data with surface deformation in a joint inversion to model time-dependent dike propagation.

For simplicity, we model a dike as a rectangle with a constant height but varying length and excess magma pressure (magma pressure exceeding the normal stress acting perpendicular to the dike) over time. Ignoring viscous pressure losses, the excess magma pressure can be assumed to be uniform along the dike. We relate changes in seismicity rate to the stress changes due to dike opening using the seismicity-rate equations of Dieterich (1994). These equations account for time-dependent earthquake nucleation on faults with rate- and state-dependent friction. Combining this forward model for seismicity rate with geodetic Green’s functions, we use a nonlinear least squares algorithm to invert surface displacements and seismicity rate for changes in dike length and excess magma pressure as a function of time. We also constrain two of the key rate-state model parameters, the reference stressing rate and the frictional constitutive parameter as, which controls the temporal evolution of seismicity rate following a stress change.

We have tested our technique by simulating noisy seismicity and surface deformation observations for a case where a dike propagates unilaterally at a time-varying velocity, with an excess magma pressure that decreases over time (as would be expected due to draining magma reservoir). The seismicity is triggered predominantly at the edges of the dike due to the strong stress concentrations there. We find that the inversion procedure is able to recover the true length and pressure histories quite well.

We are currently applying this technique to the 2007 Father’s Day dike intrusion in the East Rift Zone of Kilauea Volcano, Hawaii, for which we have excellent seismic, GPS, tilt and InSAR data (Figure 1). The intrusion began on June 17 accompanied by an earthquake swarm and lasted almost 3 days, during which time seismicity propagated down-rift. The seismicity that occurred during the swarm is relocated and combined with GPS and tiltmeter data (Montgomery-Brown et al., 2011). Our preliminary results show that the intrusion initially propagated slowly before jumping several kilometers over a few hours, causing the sudden down-rift migration of seismicity (Fig. 2-3). The excess dike pressure initially decreased from about 4.5 MPa to about 2 MPa, before suddenly increasing at t=9 when the dike propagating rapidly down-rift. This increase in pressure appears to be robust and may indicate that the dike tapped a second magma reservoir at higher pressure, allowing the dike to extend further than it otherwise would have.

Figure 1. Time history of the Father’s Day intrusion on Kilauea Volcano, Hawaii. Top: Tilt of ERZ (ESC), summit (UWE), and Pu’u ’O’o (POC) at indicated azimuth. Distance change between GPS stations NUPM and KTPM (open symbols), processed at 4 minute intervals. Bottom: Space-time distribution of rift zone seismicity. Summit GPS displacements and tilts are scaled to aid in comparing event timings; scale factors are noted in the legend of each frame. Vertical bars indicate the following events: (T1) ESC and UWE tilt begins with onset of seismicity (T2) ESC tilt flattens, seismicity concentrates down-rift (T3) seismicity concentrates down-rift, summit tilt rate increases (T4) slight increase in tilt rate at UWE and down-rift concentration of seismicity (T5) summit tilt returns to inflation (After Poland et al, Montgomery-Brown et al, 2010).

Figure 2. Preliminary inversion results for the 2007 Kilauea dike intrusion, showing dike length and excess pressure (color) at different time steps. The black dots in indicate earthquake projected onto the plate of the dike.

Figure 3. Map view at different time steps of estimated dike length (thin black line), seismicity (blue dots), observed cumulative displacement (solid black vectors) and tilt (dashed black vector). Predicted displacement and tilt are shown in red.


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