Current Reference Frame Treatment and Future Needs:

Regional Arrays

SNARF Workshop 27 January 2004

Rick BennettHarvard-Smithsonian CfA

…from the southwestern US perspective

North America plate frame realization for southwestern US

Choose RF rotation rate so as to minimize velocities at sites in North America interior:

I used ALGO, DRAO, NLIB, STJO, MDO1, PIE1, HEBE, PRDS, CAST, FRED, FERN

Southwestern US North America plate frame statistics

SITE R.R. Sigma (all values in mm/yr)--------- ------ --------ALGO 1.1 0.03NLIB 0.4 0.04DRAO 2.8 0.03STJO 3.3 0.04MDO1 0.3 0.03PIE1 0.8 0.03HEBE 0.4 0.03PRDS 2.5 0.04 CAST 0.4 0.03FRED 0.8 0.07FERN 1.0 0.07

Number of sites = 11Number sites with R.R. < 1 mm/yr = 6Percentage with < 1 mm/yr = 55The rate NRMS is 48The rate WRMS is 1.6 mm/yrThe component NRMS is 34The component WRMS is 1.1 mm/yr

R.R. = rate residual to realization of the plate frame.

Some southwestern US North America plate frame caveats

1) Data used to define the frame is evolving

• New NA stations

• Changing equipment

• Always more data

2) Inconvenient to compute geophysical models in the geodetically determined frame.

Example 1

Estimate relative motions of fault-bounded blocks accounting for elastic strain associated with locked faults.

Half-space fault models do not accurately represent far-field plate rates.

Observed velocities

Example 1 continuedOne solution is to define local no-net translation reference frame:

Residual velocities

Example 2

Determine the relative motions between the Colorado Plateau (CP), central Great Basin (CGB), and Sierra Nevada-Great Valley (SNGV) regions.

Example 2 continuedSNGV-CGB SNGV-CP

Bennett et al., 2003

Motion of a deforming body in space

Deformation term depends on reference frame selection.

Simple 2D Cartesian deformation analysis problem:

Choose coordinate axes such that:

Then the information matrix looks like this:

Note the trade-off depending on network and/or model geometry.

Motion Cont…

Summary

• BARGEN North America plate frame determined by minimizing velocities at 11 NA interior sites.

• Should distinguish between geodetic and geophysical reference frame issues– Geodesist

• Frame definition• Frame realization

– Geophysicist• Account for differences between model and data frames,

regardless of errors.