Dislocation in Elastic Halfspace Model of the Earthquake Cycle

Lecture Notes 16 Dislocation in Elastic Halfspace Model of the Earthquake Cycle Interseismic: Slip below depth D �xy 5 10 15 X/D -15 -10 -5 y Displacement -3 0 3 X/D Strain Figure 16.1 Coseismic: Region above D “catches up” �xy 5 -15 -10 -5 y -3 0 X/D Figure 16.2 3 10 15 X/D Displacements from Earthquakes, Fault Slip, etc Consider a strike-slip fault with displacement S, independent of depth – A screw “dislocation” – i.e., a slip discontinuity. Original ring (dashed) becomes helix (solid). 2 x3 ce rfa t u S aul f Fault displacement S 1 x2 on ati c o sl s Di axi D S/2 S/2 x1 Figure 16.3. Section across a mathematical model of a transcurrent fault. “Dislocations” are used to describe defects in crystals, as well as fault motions. A crystal disrupted by a screw dislocation is shown in the figure below. 7 8 9 10 6 b* 5 1 4 3 2 Figure 16.4. A screw dislocation in a cubic lattice constitutes a deformation that is out of the plane of atoms illustrated. The two atoms denotes by solid circles are essentially part of a second plane. The Burgers circuit indicated by the numbered steps naturally moves into this second plane. Therefore in order to close the circuit the Burgers vector b* must be perpendicular to the plane of atoms shown. Types: Edge Screw Figure 16.5 b* 1 2 3 10 4 9 5 8 7 6 1 2 3 10 4 9 5 8 7 6 Figure 16.6 Side view of an edge dislocation in a cubic lattice. Dislocation motion helps crystals deform (don’t all have to slip at one time). Also helps Earth deform! C B D S E A Figure 16.7 A dislocation. b C B C A A E E E E b S S B S S Figure 16.8 Upper group: Slip by propagation of an edge dislocation EE. Lower group: Slip by propagation of a screw dislocation SS. Displacement (meters) 2 1 0 0 2 4 6 8 10 Distance from fault (km) NE Figure 16.9 Displacement as a function of distance from a transcurrent fault.