Introduction to the modelling of GPS results

• GPS provides

• Surface crustal velocities in a global reference frame, or with respect to a block, realized through a set of stations (globk ‘plate’ command)

• Time dependent deformation (mainly CGPS & time series from glred)

What can be asked of geodetic results ?

What can be asked of geodetic results ?

Time dependent deformation

• co-seismic displacement: location, slip distribution, moment

• post-seismic deformation: afterslip, visco-elastic processes

• detection and quantification of slow slip events

Modelling velocities for tectonics

In actively deforming zones, the velocities are the sum of several contributions:

• global plate motion – estimated & removed during Globk analysis to obtained velocities with respect to stable plate interiors

• long-term tectonic motion – modeled using either blocks or distributed deformation

• because most faults are locked during the period separating two earthquakes (inter-seismic phase), they induce surface elastic deformation

Rigid blocks approach

Assumptions

• deformation is localized along major faults

• small internal deformation (<< deformation across major boundaries)

• blocks defined by closed boundaries

Methods solve for rigid rotation rates (Euler poles)

Exemple: Nazca/South America convergence

Villegas, 2009

Refinement: elastic blocks approach

Same assumptions as for the blocks

But, interseismic elastic deformation accounted for

Results slip rates along major faults locking depth, coupling coefficient large faults like subduction interface: spatial distribution of coupling

Figure from Z.-K. Shen, in Stein and Wysession, 2006

Strain rate• We now consider the local change of velocity

• the velocity gradient tensor is defined by the derivative of the velocity components wrt to the coordinates

• It can be divided into:

• A local rotation

• A strain rate tensor (symetric)

Example of strain rate analysis using polygons

Aktug et al., 2009

Strain rate analysis using a regular grid

Kreemer et al., 2003

Thin viscous sheet approach

Assumptions

• deformation at scale (>>100 km) is driven by the balance of stress distribution induced by boundary conditions and stress arising from crustal thickness lateral variations

• Lithosphere modeled as fluid

• thin sheet approximation: all quantities are averaged over lithosphere thickness

Example: large scale velocity field in Asia

Vergnolle et al., 2006Using SHELLS,

http://peterbird.name

Example: large scale velocity field in Asia

Vergnolle et al., 2006Using SHELLS,

http://peterbird.name

Elastic Block Models as a Tool for GPS Analysis

• Account for surface deformation from fully or partially locked faults

• Provide secular constraints in estimating time- dependent motion

• Create a kinematically consistent model for large-scale motions

There are (at least) two well-developed, documented

software packages freely available:

DEFNODE / TDEFNODE

Rob McCaffrey, Portland State University (formerly at RPI)

http://web.pdx.edu/~mccaf/www/defnode/

BLOCKS

Brendon Meade, Harvard University (formerly at MIT)

http://summit.fas.harvard.edu/~meade/meade/Software.html

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.

Courtesy Rob McCaffrey

Okada model applied at boundaries

Model velocities same for any path integral

Meade et al., [2002]

DataGPS velocities

InSAR line-of-site rates

Uplift rates

Tilt rates

Slip vectors

Transform azimuths

Spreading rates

Fault slip rates

Strain rates

ParametersBlock rotations Reference frame

Fault locking

Uniform strain rates

OutputText files GMT mappable filesUncertainties (linearized)

SolutionGrid search Downhill simplex

McCaffrey [1995; 2007]

Program Flow for DEFNODE

Example from the eastern Mediterranean

Seismicity and earthquake focal mechanisms provide a first-cut for block boundaries

GPS velocities refine the boundaries

GPS velocities

observed modeled

block motion

Residuals

GMT representation of DEFNODE output

Large-scale rotation with subduction locking superimposedExample from the western Mediterranean :

GPS velocities from 10

years of CGPS and

SGPS measurements

Note rigid rotation of

Africa with respect to

Iberia and independent

motion of the Rif

(Morocco) and Betic

(Spain) mountains

Koulali et al. (2011)

Velocity residuals from a 3-block model

Error elliipses are 70% confidence

Large-scale rotation with subduction locking superimposed

McCaffrey et al. [2007]

Example from Cascadia: Large-scale rotation with subduction locking superimposed

McCaffrey et al. [2007]

Example from Cascadia: Large-scale rotation with subduction locking superimposed

GPS velocities from continuous (red) and survey-mode (blue) sites. Insert shows depth of the subducting slap and fault nodes used in the inversion. Triangles are volcanoes.

Surface velocities from subduction aloneDeep red is fully locked; deep blue freely slipping

A block model can be used in non-steady state settings to separate kinemtics from transients

Example: Spatially propagating slow slip events (SSEs) in Cascadia

Time series data from PANGAModel showing rotating blocks, subduction

locking, and rates of uniform strain