Inelastic Caterpillar-like Deformational Wave as a Trigger of Tremors, Very-low-frequency Earthquakes and Slow Slip Events

Deep low-frequency tremors, very-low-frequency earthquakes (VLFE), short-term slow slip events (SSE), and step-like tilt changes are different manifestations of plate motion along faults. It has been observed [Shelly et al, 2007; Ito et al, 2007; Shelly et al, 2009; Obara, 2009] that: 1) tremor sources migrate with speeds from about 1km per minute to 10 km per day - a few orders of magnitude less than the speed of elastic waves (c); 2) the direction of a tremor source in some cases changes periodically in sign; 3) periodic step-like tilt changes coincide with the tremor bursts (the duration of tilt changes is much smaller than the time interval between them). It can be shown that the Frenkel-Kontorova (FK) model, well known from the theory of dislocations in crystalline materials, intrinsically explains these features [Gershenzon et al, 2009]. Remarkably, the FK model predicts that: 1) the steady state shear stress can generate an inelastic caterpillar-like deformational wave along a plate boundary, i.e. the migration of one or more periodic deformational pulse(s)/dislocation(s); 2) a pulse/dislocation has a short spatial extent in the direction of the shear stress (in comparison with the distance between dislocations) and a long extent in the perpendicular direction; 3) there is a strong local positive or negative stress/strain anomaly inside of the dislocation area; 4) dislocations are able to move along a fault with migration velocity v ranging from -c to +c or can even be stationary (v = 0); 5) the magnitude of the migration velocity is a strong, almost exponential function of the averaged accumulated shear stress. In the case of slow slip events, the migration velocity is usually much smaller than the seismic velocity (v << c); 6) under external shear stress, positive and negative dislocations move in opposite directions, resulting in sliding of the plates relative to each other with average plate slip velocity of a few cm/year; 7) measurable parameters such as plate slip velocity and migration velocity are connected to the parameters of average and local accumulated stress, stress drop, and density of dislocations; 8) plate boundary dynamics (spatiotemporal distribution of stress and strain) can be quantitatively described. In the FK model, the passage of a dislocation through a monitored area appears as a step-like tilt change, since passage of a dislocation actually causes displacement of the plate boundary. In this respect, the detection of periodic step-like tilt changes (Obara, 2009) could be considered as a direct observation of a caterpillar-like deformational wave. One would also anticipate a burst of tremors, VLFE, and/or SSE from the passing dislocation, since it is accompanied by large local stress/strain changes. Migration of tremor sources with particularly small velocities (compared with c), as well as changes in migration direction, could be explained by the migration of positive and negative dislocations.