DEFNODE: Fault Coupling and Block Motion inversion

1. DEFNODE: Fault Coupling and Block Motion inversion R. McCaffrey

3. Parameters Data Block rotations Reference frame Fault locking Uniform strain rates GPS velocities Uplift rates Tilt rates Slip vectors Transform azimuths Spreading rates Fault slip rates Strain rates Output Text files GMT mappable files Uncertainties (linearized) Solution Grid search Downhill simplex

4. Velocity field for Pacific Northwest derived from campaign and continuous sites. Reference frame is North America and ellipses are 1s.

5. Region is divided into ‘blocks’, contiguous areas that are thought to rotate rigidly. The relative long-term slip vectors on the faults are determined from rotation poles. Each block rotates about a pole. Back-slip is applied at each fault to get surface velocities due to locking. Velocities due to fault locking are added to rotations to get full velocity field. The rotating blocks are separated by dipping faults.

6. The strain rate tensor near a locked fault represents a spatial transition from the velocity of one block to the velocity of the other. In other words, a locked fault allows one block to communicate information about its motion into an adjacent block. For example, strain rates at the Oregon coast tell us about Juan de Fuca motion even though no GPS sites are on the JdF plate.

7. GPS velocity vectors and uplift ratesVk(X) = [RGX]k+ [ RBX ]k + ekk DXk+ ekl DXl+ • j=1,2i=1,N [- HFQi ]jiGjk (X, Xi) X is the position of the surface observation point,k represents the velocity component (x, y, or z),RB is the angular velocity of the block containing the observation point relative to the reference frame,RG is the angular velocity of the GPS velocity solution containing the observation point relative to the reference frame,e is the horizontal strain rate tensor (DX is the offset from strain rate origin) HF is the Euler pole of the footwall block of fault relative to the hangingwall block,N is the number of nodes along the fault,Qi is the position of node i, i is the coupling fraction at node i, Gjk (X, Qi) is the kth component of the response function giving the velocity at X due to a unit velocity along fault at Qi in the jth direction on fault plane (downdip or along strike)

8. Other data types Tilt rates: T(X) = [ Vz(X+X) - Vz(X - X) ] / (2 X ) (X is at the mid-point of the leveling line and X is the offset from the mid-point to the ends) Slip vector and transform fault azimuths: A(X) = arctan{[( HR - FR ) X]x / [( HR - FR ) X]y } Geologically estimated fault slip rates or spreading rates:   R(X) = | ( HR - FR ) X |

9. Half-space dislocation model (HSDM) to calculate surface deformation due to fault

11. Representation of fault slip • Nodes are specified along depth contours of fault • Slip at each node is jV, where j ranges from 0 to 1 and V is taken from poles • Area between nodes is broken into small patches • Surface deformation for each patch is determined and summed Response functions are determined by putting unit velocity at one node and zero at all other nodes, then calculating the surface velocities by integration. Pyramidical Bilinear

12. F = 0 F = 1

13. Pacific – North America slip vectors Azimuth Degrees North mm/year Pacific – Juan de Fuca spreading rates Degrees North

14. W B&R E B&R Sierra Nevada Salinian Mojave S. Mojave Ventura Salton No. America Pacific Baja Block boundaries placed along major fault systems.

17. Rotational part of velocity field relative to North America

18. Locking on the Cascadia thrust Slip deficit rate and surface velocities from fault locking Locking fraction Uncertainty in locking fraction Top image from http://www.pgc.nrcan.gc.ca/geodyn/docs/cascadia/content.html

19. Applied to North Island, NZ