Figure 2.6 shows surface displacement rates as a function of distance from the San
Andreas Fault in California.
(a) Consider this as a 2-D problem with the x-axis perpendicular to the fault and
the y-axis parallel to the fault. From these data, estimate the yearly strain (e)
and rotation () tensors for a point on the fault. Express your answers as
2 × 2 matrices.
(b) Assuming the crustal shear modulus is 27 GPa, compute the yearly change
in the stress tensor. Express your answer as a 2 × 2 matrix with appropriate
units.
(c) If the crustal shear modulus is 27 GPa, what is the shear stress across the fault
after 200 years, assuming zero initial shear stress?
(d) If large earthquakes occur every 200 years and release all of the accumulated
strain by movement along the fault, what, if anything, can be inferred about
the absolute level of shear stress?
(e) What, if anything, can be learned about the fault from the observation that
most of the deformation occurs within a zone less than 50 km wide?
(f) Note: The asymmetry in the deformation pattern is a long-standing puzzle.
To learn more, see Schmalzle et al. (2006).