Time Dependent Estimates of the Velocity Gradient Tensor Field for Transient Detection

William Holt, Gina Shcherbenko, Eric Caruso, Yu Chen

Acknowledgements: We thank SCEC for funding support

0.1° x 0.1° Grid

Rigid Pacific Plate

Model magnitude of shear strain rates (pure SS style)(SCEC4.0 Velocity field)

Smoothing or Damping• Maximize signal associated with GPS

• Achieve Reduced Chi-Squared misfit between model displacement and observed displacement of ~1.0 for all epochs

€

χ = ( ˙ e ij )ij,kl

∑cells

∑T

Vij,kl−1( ˙ e kl )+ (vi − v i

obs )T Vi, j−1(v j − v j

obs )i, j

∑knots

∑

Haines, Jackson, Holt, Agnew [1998]

Beavan and Haines [2001]

Time Series from SCEC IVc

WNRA – Phase 4c

4th order polynomial fit with annual and semi-annual terms

Annual and semi-annual removed

Red = 15 day moving average filter

Green = 4th order polynomial

Output 2 week epoch solutions of displacement

2 Week Displacements

Subtract out ‘master solution’ to estimate signal only from transients

-For real data we used SCEC4.0 solution as a master solution-For other groups in the SCEC exercise we used time averaged solution (2007 – 2009).5 mm

Output 2 week epoch solutions of displacement

2 Week Displacements

Subtract out ‘master solution’ to estimate signal only from transients

-For real data we used SCEC4.0 solution as a master solution-For other groups in the SCEC exercise we used time averaged solution (2007 – 2009).

Residual Displacements

Phase IVa5 mm 5 mm

What Triggers Selection of Potential Transients?

• Accelerations

• Finite Strain

• Analysis of finite strain tensor and displacement vector fields

• Does signal look tectonic?

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d

dtδE( )

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δE∫

Phase IVa

Residual displacements reference solution subtracted out

Finite Displacements + Strain (principal axes) Phase IVa

Phase IVb

Residual displacements reference solution subtracted out

Phase IVb Finite Displacements + Strain (principal axes)

Phase IVc

Residual displacements reference solution subtracted out

Finite Displacements + Finite Strain (Principal Axes) Phase IVc

Summary of results from Phase IV• The modeling of displacements with

reference field removed captures spatial and temporal magnitudes of transients

• Method can be automated

Analysis of PBO Data from 2010.35 – 2011.25• El Mayor-Cucapah post-seismic

motions and strains– Non-steady state motions with periods of

apparent increasing and decreasing strain

• High frequency strain changes in LA Basin region

Finite Strain (Dilatations) + displacements: PBO Data 2010.35 – 2011.25

See poster B-143

Residual displacements show rapid spatially correlated changes in LA region

2010.35