One of the most exciting discoveries in recent decades has been the recognition that many subduction zones undergo transient slip events at depths below the locked mega-thrust zone. These slow slip events, or silent earthquakes, have been detected by GPS networks in Cascadia, southwest Japan, Mexico, New Zealand, and Alaska. We have also discovered slow slip events beneath Kilauea volcano in Hawaii.
Understanding the physics of slow slip events and how they differ from normal, fast earthquakes is one of the most pressing current challenges in seismology. Understanding what causes some events to slip slowly compared to others that slip rapidly, radiating damaging seismic waves would provide a fundamental insight into how earthquakes work. The societal importance is that every slow slip event adds stress to the adjacent locked megathrust zone bringing it closer to failure.
We have been exploring the possibility that dilatant strengthening may provide a reasonable explanation for slow slip events. Dilatancy is the tendency for the pore space in granular materials to expand during shear. The increased pore-space decreases the fluid pressure within the fault zone, increasing fault strength according to the effective stress principal, unless pore-fluid can flow into the fault zone fast enough to keep up with the rate of dilatancy. Our hypothesis is that frictional weakening allows slip to nucleate, but that as the slip-rate increases fluid flow becomes increasingly unable to keep up with the rate of dilatancy. Depending on the constitutive parameters and the ambient effective normal stress, dilatancy can quench the instability resulting in a slow slip event.
Our approach has been to use numerical modeling to understand the conditions when dilatancy stabilizes fault slip. This involves coupling the equations of elasticity, rate-and state dependent friction laws, to fluid transport equations, generating a large system of coupled partial differential equations. We take depth-variable frictional properties, based in part on lab experiments, and assume low effective stress, presumed to be driven by dehydration reactions, in the depth range of slow slip events. Simulations reveal generic behavior: dynamic events (DE) repeat every few hundred years, and between each DE is a quiescent period and then a long sequence of SSE. During this period, the SSE moment rates generally (but not monotonically) increase with time. Eventually slip speeds become high enough to induce thermal pressurization, which nucleates a DE. The predicted behavior, in terms of SSE slip, stress drop, and repeat time bear many similarities to SSE in Cascadia.
Figure 1 shows slip rate from a simulation. The along-fault direction is the x axis; time increases nonlinearly along the y axis. Time progression is indicated on the right side. Friction properties a and b and bacground effective normal stress are shown at the bottom of the figure. Three excerpts from the simulation are shown, each excerpt separated from the others by a black horizontal line. In the first excerpt, an earthquake nucleates at the transition between the locked and ETS zones. A quiescent period follows. Then a long sequence of slow-slip events occur. These gradually increase in size. Two periods are shown in the next two excerpts. Not shown is the the next earthquake, which starts the cycle again.
To test model predictions against GPS data, we develop a pseudo-3D method that accounts for the markedly non-2D geometry of the plate interface. The approach employs 3D elastic Green's functions but assumes that slip rate is a function of depth only, as computed in the physics based model. Figure 2, shows the average slip distribution for one case, with slip tapered along strike to match a typical SSE (contours at 20, 30, 40, 50 km depth). Figure 3, shows the predicted displacements compared to the mean SSE displacement over the past decade. The good agreement strongly suggests that the depth distribution of physical properties is reasonable.
Our focus now is on understanding several correlated questions related to Cascadia: whether there is creep updip of the ETS transition; whether dynamic ruptures indeed propagate into and through the ETS zone as our models to date predict; and the extent of the slip deficit in the ETS zone.
Meanwhile, we are developing algorithms and software for fully 3D simulations. The final figure (movie) is a very preliminary and under-resolved example of a simulation of the ETS zone with small randomly distributed regions that represent tremor sources. Color is slip-rate and the down-dip direction is to the bottom. Note the coherent slip-rate fronts that propagate backward into the previously slipped region.