Data

GPS velocitiesUplift ratesTilt rates

Slip vectors

Transform azimuths

Spreading rates

Fault slip rates

Strain rates

Parameters

Block rotations Reference frame

Fault locking

Uniform strain rates

OutputText files GMT mappable filesUncertainties (linearized)Solution

Grid search Downhill simplex

Velocity field for Pacific Northwest derived from campaign and continuous sites.

Reference frame is North America and ellipses are 1

Region is divided into ‘blocks’, contiguous areas that are thought to rotate rigidly.

Each block rotates about a pole.

The rotating blocks are separated by dipping faults.

Velocities due to fault locking are added to rotations to get full

velocity field.

The relative long-term slip vectors on the faults

are determined from rotation poles.

Back-slip is applied at each fault to get surface

velocities due to locking.

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.

X is the position of the surface observation point,k represents the velocity component (x, y, or z),

RB is the angular velocity of the block containing the observation point relative to the

reference frame,

RG is the angular velocity of the GPS velocity solution containing the observation point

relative to the reference frame,is the horizontal strain rate tensor (X is the offset from strain rate origin)

HF 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)

GPS velocity vectors and uplift rates

Vk(X) = [ RG X ]k + [ RB X ]k + kkXk+klXl +

j=1,2 i=1,N [- HF Qi ]j i Gjk (X, Xi)

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{[( HR - FR ) X]x / [( HR - FR ) X]y }

 

Geologically estimated fault slip rates or spreading rates:

  R(X) = | ( HR - FR ) X |

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

Representation of fault slip

• Nodes are specified along depth contours of fault

• Slip at each node is V, where ranges fromto 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

= 1

Pacific – Juan de Fuca spreading rates

Pacific – North America slip vectors

Degrees North

Degrees North

Azi

mut

hm

m/y

ear

Block boundaries placed alongmajor fault systems.

Baja

Ventura

No. America

Salinian

Sierra Nevada

E B&R

Salton

S. Mojave

Mojave

Pacific

W B&R

Rotational part of velocity field relative to North America

Locking on the Cascadia thrust

Top image from http://www.pgc.nrcan.gc.ca/geodyn/docs/cascadia/content.html

Slip deficit rate and surface velocities from fault locking

Locking fraction Uncertainty in locking fraction

Applied to North Island, NZ