DEFNODE: Fault Coupling and Block Motion inversion
description
Transcript of DEFNODE: Fault Coupling and Block Motion inversion
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