# Presentation: 851306

## title

**Dynamic Rotations and Strains at UPSAR from the September 28, 2004, M6 Parkfield Earthquake and Aftershocks**** **
- Paul Spudich and Jon B. Fletcher
*U.S. Geological Survey*
*Menlo Park, CA*

## This talk is based on the paper: 

- Spudich, P. and J.B. Fletcher (2008). Observation and prediction of dynamic ground strains, tilts and torsions caused by the M6.0 2004 Parkfield, California, earthquake and aftershocks derived from UPSAR array observations, in press, *Bull. Seismol. Soc. Am. (August issue)*
*Preprint available on the web.*

## Shaded relief, upsar, and events

**Notes:**
Red shows the fault traces of the San Andreas and the Southwest Fracture Zone.  UPSAR array is located at the yellow square.  We studied four events, the main shock, with hypocenter at the red diamond and with an extent of faulting shown by the dashed yellow line (Hartzell et al. BSSA 2007).  We also studied three aftershocks shown by black diamonds. 

## UPSAR array and local topography

*Figure by Guoquan Wang*

**Notes:**
UPSAR consists of 14 triaxial accelerographs and co-located triaxial geophones.  12 of the 14 stations worked properly during the earthquake sequence.  The UPSAR stations are located at the top of ridge lines in an area of moderate topography.  Contours are in meters. The whole array is about 900 m in extent, with stations P05, P06, and P07 being separated by 25 - 40 m, and stations like P01, P02, P03, and P08, P09, P11 being separated by about 140 m.

## Mainshock displacements at UPSAR, 0.1-1.4 Hz Bandpass

## Method - 1

- Solution of the problem is done by least-squares
-  Spudich et al, JGR, 1995
-  Spudich & Fletcher, BSSA, 2008 in press

## Uniformity assumption

- We accomplish this by low-pass filtering the displacement seismograms with corner frequency *f**max*.
- The low-pass filter corner is chosen so that the longest retained wavelength is longer than 4*(array aperture).
- If we use a subarray with a smaller aperture, a higher *f**max* can satisfy our spatial uniformity criterion.

## Subarrays used and associated bandwidths

## We did the analysis for all four events.  

- For each subarray (1-3, 8-11, 5-12)
- For *f**max* = 1.4 Hz and 3.6 Hz
- Obtained time series for:
-  Torsion and torsion rate *(rotation around a vertical axis)*
-  Tilt and tilt rate *(rotation around a horizontal axis)*
-  Total dilatation and total shear strain
-  Areal dilatation and horizontal shear strain

## Main shock rotations and strains from 7-station array 5-12 in the narrower band

## For a plane harmonic wave

- rotation = particle velocity / ( 2*phase velocity)
- rotation rate = particle acceleration / ( 2*phase velocity)

## Torsion spectrum agrees with velocity spectrum using c=1.45 km/s, 7-station array, narrow band

## Parkfield broad-band peak rotations and strains observed at UPSAR

## Comparison of main shock peak dilatations

- Dilatometer
- observation
- (Johnston et al,
- BSSA, 2006)

## A simple relation to predict peak rotations and rotation rates as 

- f(M, r, site geology)
- We use the Boore-Atkinson (2007,2008) NGA relations for PGA and PGV as a reference
- peak rotation (rad) = (B&A PGV, m/s) / (2c), c = 1000 m/s
- peak rotation rate (rad/s) = (B&A PGA, m/s2) / (2c), c = 1000 m/s

## Parkfield and Chichi rotations at upsar

## Comparison with rotation-rate sensor observations

- How do Takeo’s Ito swarm measurements compare with Parkfield?

## Parkfield and Chichi rotations at upsar

## Why are Takeo’s rotations and rotation rates from Ito, Japan, dike injection events 5x to 60x higher than predictions based on Parkfield? 

- Possibilities:
-  B&A predicted pga is biased low for Ito events *(not more than factor of 2)*
-  Rotations measured at a point are higher than array measurements which average over distances of ~150 m *(but dilatations are okay to factor of 2)*
-  Non-double couple event ground motions have a higher ratio of rotation/translation than double-couple events *(maybe!?)*

## Conclusions

-  Peak rotations and rotation rates at Parkfield and Chi-Chi scale with Boore&Atkinson’s predicted PGV and PGA, respectively, using c = 1000 m/s.
-  Parkfield main shock array-derived dilatations agree to about a factor of 2.3 with dilatometer observations by Johnston et al (2006).
-  Peak rotations and rotation rates observed (Takeo, 1998, 2007) in dike-injection events from Ito, Japan, are significantly higher than Parkfield rotations and rates.
-  The Ito-Parkfield discrepancy might be related to scale-dependence of rotation, but might also result if non-double-couple events radiate more rotation per unit translation than double-couple events.

## THE END

## Fault-parallel component of main shock motion on UPSAR

- }25 m

- }25 m

- }40m

**Notes:**
There is a fair degree of difference between the  main shock ground accelerations, even between stations like P05 and P06, separated by 25 m, and P05 and P07, separated by 40 m.  These differences probably are caused by lateral variations in geology and topography between the stations. 

## Mainshock vertical velocity at UPSAR

## Mainshock velocityfault-perpendicular				fault-parallel

- Mainshock velocityfault-perpendicular				fault-parallel

## How large can array be and keep finite difference errors below 10%? 

- If h < /4, error in tangent angle is less than 10%

## Maximum frequency which satisfies the quarter-wavelength  criterion for each subarray

- We used phase velocity c = 2.0 km/s from Fletcher et al. (BSSA, 2006) analysis of main- and aftershock records

## We have estimated rotations and strains in a narrow band (0.1 - 1.4 Hz) and in a broader band (0.1 - 3.6 Hz). 

- We want to get a broad band (0.1 - 100 Hz) estimate of peak strains and rotations.
- Because rotation and strain are proportional to particle velocity, we estimate broad-band correction factors

## Misfit ratio

## Main shock rotations and strains from 3-station array 1-3 in the narrower band

## Main shock rotations and strains from 3-station array 8-11 in the narrower band

## Main shock rotations and strains from 3-station array 1-3 in the broader band

## Rotation and strain analysis for the smallest event (our lousiest result)

## Generally, main shock peak torsions from the 7-station subarray (asterisks) agree with those from the 3 station subarrays (crosses)

## Generally, main shock peak torsions in the 0.1 - 3.6 Hz band (boxes) are about twice those in the 0.1 - 1.4 Hz band (crosses)

## Torsion spectrum agrees with velocity spectrum using c=1.45 km/s, 3-station array, broader band

## Correction factors to obtain broadband estimates of peak rotation, strain

## Parkfield main shock dilatations (from Johnston et al. BSSA 2006)

## Takeo;s instrumentation

- Takeo (Rotation Workshop, Menlo Park, 2007) presented rotation measurements  of Ito swarm events made with a lower-noise 8301F sensor.
- (The 8301F measurements corroborate the Motion-Pak peak observations.)

## Maps of Ito, Japan, swarm events, by year (from Takeo, 2007)

## Location of 1997 Ito, Japan, events observed by Takeo (GRL, 1998)

## Translations and rotations of 1997 Ito, Japan, events (Takeo, GRL, 1998)

- cmt

- fnet

- fnet

## Parkfield, Chichi, and 1997 Ito rotations

- 1997 Ito
- events

- must insert new results here

## Ito 4/25/98 2237 seismograms

## Ito 4/26/98 0603 seismograms

## Parkfield, Chichi, 1997 and 1998 Ito rotations

- must insert new results here

## Scaling of peak velocity and peak rotation, 1998 Ito Japan swarm (from Takeo, 2007) 

- Scaling of peak velocity and peak rotation, 1998 Ito Japan swarm (from Takeo, 2007)

## Checking B&A pgv predictions for Ito 1998 events

- B&A predict Parkfield, Chi-Chi pgv very well
- B&A are about a factor of 2 - 2.5 low for 1998 Ito events
- Implies B&A prediction of peak rotation might be factor of 2 - 2.5 low

## Checking B&A pga predictions for Ito 1998 events

- B&A predict 3 of 4 Ito pgas very well, underpredict 4th by about factor of 2.5
- Implies B&A prediction of peak rotation rate should be ~ okay.

## B&A predictions do not seem sufficiently biased to explain the discrepancy between Ito and Parkfield rotations

## There is some weak evidence that rotations measured over a short baseline exceed those measured over a long baseline (by about 14 - 47%)

## What about looking at observed rotation / observed translation, without worrying about a bad pga or pgv model? 

- rotation = particle velocity / ( 2*phase velocity)
- phase velocity = particle velocity / ( 2* rotation)

- The Parkfield events have a systematically lower rotation per unit translation than the Ito, Japan events

## Method refs

- <date/time>

**Method described in**
- Spudich, P. , L.K. Steck, M. Hellweg, J.B. Fletcher, and L.M. Baker (1995). Transient stresses at Parkfield, California, produced by the M 7.4 Landers earthquake of June 28,1992: Observations from the UPSAR dense seismograph array, *J. Geophys. Res*., 100, 675-690.
**with further explanations in**
- Spudich, P. and J.B. Fletcher (2008). Observation and prediction of dynamic ground strains, tilts and torsions caused by the M6.0 2004 Parkfield, California, earthquake and aftershocks derived from UPSAR array observations, accepted, *Bull. Seismol. Soc. Am.*