The Rupture Process of the August 23, 2011 Virginia Earthquake

Martin ChapmanVirginia Tech

Circles show mainshock and early (August 24-26) aftershock epicenters from a 7 stationtemporary deployment of instruments by VPI &SU. The beachball diagram indicates the mainshock focal mechanism (USGS/SLU). Colors show major geologic units.

North AnnaPower Station

21 km

AAftershocks between

August 24 and September 22011

Looking approximately N29E

Aftershock hypocenters, Aug. 24 - Sept. 2, 2011

Looking broadside at thefault plane (strike N29E, dip 51 deg)

Strong motion recordingson the foundation base matof the unit 1 containment structureat North Anna.

The records are remarkable for thevery short duration, and pulse-likecharacter of the largest motion---the S wave(s).

Note the modulated character ofthe Fourier amplitude spectra.

Recordings from Unit 1, Dominion, Inc., North Anna power station 23 km from epicenter

A weak initiation phase and two strong pulses are apparent on the transverse component

Observed Transverse

Full wave-field syntheticChapman and Godbee,BSSA 2012.

17 stations at distances beyond 20 degrees showed clearsub-event arrivals

Observed data (transverse)

0.25 x 1024 dyne-cm50 bars

2.25 x 1024 dyne-cm300 bars

1.22 x 1024 dyne-cm300 bars

North Anna Transverse Record And Source function used toModel the teleseismic data

Broadband velocity recordings atSelected Teleseismic Stations

We wish to determine the actual locations and origin times of the 3 principle subeventscomprising the major moment release. The process used is as follows:

1) determine arrival times of the two later subevents relative to the initial (small) subevent at local and teleseismic receiver locations.

2) Assume that all subevents occur on the same fault plane, strike N29oE, dip 51o, and solve for the locations of the two later events relative to the initial subevent.

3) Locate the epicenter of the mainshock initial subevent relative to the well-determined epicenters of the best recorded aftershocks, using the handful of local stations that recorded the mainshock as well as the aftershocks.

4) Determine the focal depth of the mainshock by comparing actual teleseismic waveforms with synthetics.

(all of this requires an accurate velocity model of the shallow crust)

Steps

1) Assume a half-space structure with an initial estimate of P and S wave velocities.

2) Get initial estimates of 36 aftershock hypocenter locations using the initial velocity model and P and S arrival time data.

3) Determine joint estimates of aftershock origin times and P/S velocity ratio, following the Wadati approach.

4) Use the initial epicenter locations and the joint estimates of the origin times from step (3) to obtain joint estimates of the P wave velocity and the focal depths of the aftershocks.

5) Update the velocity model using the estimate of P-wave velocity from 4), and velocity ratio from step 3), fix the aftershock origin times using the results of step 3) and repeat the process from step 2).

After a few iterations, the process converged to an estimate of P-wave velocity (the values of the parameter estimates of subsequent iterations stopped changing).

Determination of P and S wave Velocities in the Aftershock Zone

Joint Wadati-type inversion for origin times and P/S velocity ratio

solve for slope and intercept terms for i = 1 to 36 aftershocks using least squares.

Joint T2 versus X2 inversion for P-wave velocity and focal depth

solve for the slope and intercept terms for i =1 to 36 aftershocks

Plot of S-P arrival time intervalsversus P arrival time for 36aftershocks

Vp/Vs= 1.69Joint estimate of

Plot of residuals from the Joint estimate of P-wavevelocity and focal depth.

P-wave velocity = 5.96 km/s

s = striked = dipa = epicenter - station azimuth = P-wave velocity, P = ray parameter

Vop = position vector of subevent w/r to origin at location of initial subevent.

Vr = unit vector in direction of ray.

p - o = difference in origin times of later subevent and initial subevent.

tp-o = observed arrival time of later subevent - observed arrival time of initial subevent.

The unknowns are p - o , I, and J, defining the origin time difference and the location ofthe later subevent relative to the initial subevent in the fault plane. With observations oftp-o at 4 or more stations, the unknowns can be determined by the method of least squares.

Results of 500 solutions using 1/2 the total data set, randomly sampledwith substitution (bootstrap)

location of initialsubevent, at origin

location of 2nd subevent X = 0.98 +/0.12 km, Y = 0.85 +/- 0.17 kmorigin time difference: 0.75 +/- 0.01 sec.

location of 3rd subevent X = 1.48 +/- 0.27 km, Y = 1.33 +/- 0.39 kmorigin time difference: 1.57 +/- 0.03 sec.

strike direction

up-d

ip d

irecti

on

Locations constrained to lie on a fault plane striking N29oE, dip 51o

Permanent Local Stations that Recorded the Mainshockand Larger Aftershocks

• Assume Vp = 5.96 km/sec Vs = 3.52 km/sec, a focal depth and focal mechanism strike, dip and rake. (N29E, 51 deg to the southeast, 113 deg.

• Determine Ray Parameter P for surface focus, at given epicentral distance

• For given focal depth, determine the time intervals between the direct P and the surface reflections TsP - TP and TpP - TP, assuming constant ray parameter. • Generate a source pulse for a given subevent in the frequency domain , S(). • Use a causal attenuation operator in the frequency domain... A()

Signal () = S() A() [Rp + RsP SP exp(i(Tsp-TP) + RpP PPexp(i(TpP-TP)] (Geometrical Spreading)

Where PP and SP are the free surface reflection coefficients, and Rp, RsP and RpPare the radiation pattern values for direct P, sP and pP.

The process is repeated for each subevent, with time shifts accounting for therelative locations and origin times of the subevents, and the results are summed.

Transform to time domain and compare with data

Calculation of Synthetics

Velocity and Acceleration waveforms at Eskdalemuir, Scotland, compared withsynthetics for 3 different depths.

Eskdalemuir, Scotland, NE az

Alert, Canadian Arctic, due North az

Yellowknife, Northwest Territory, NW az

Early aftershock locations using data from 7 VPI&SU stations: (August 26 - September 2, 2011)

Looking N29oE, in strike direction

Looking N61oW, normal to strike

mainshock initiation 1

subevent 2subevent 3

12

3

Conclusions

• Most of the moment release occurred in 3 distinct slip events.

• The mainshock occurred on the southwestern end of the early aftershock zone. The aftershocks define a tabular zone with orientation in good agreement with the mainshock focal mechanism.

• Most of the mainshock moment release is from two sub-events in the depth range 7.0 to 7.5 km, deeper than most of the early aftershocks which lie in the range from near-surface to 7 km, averaging about 4 km. These aftershocks appear to occur in a part of the planar zone that lies in the direction of mainshock rupture propagation.

• The rupture sequence initiated at approximately 8 km, and proceeded up-dip and and to the northeast along strike with a velocity of less than 2.0 km/sec, based on the estimates of origin time and location of the subevents.

• The implied fault rupture area is small (approximately 2.0 km between subevent 1 and subevent 3), but the total rise time (based on the North Anna recording) is about 3.0 seconds.

Preliminary Results Concerning High-Frequency Ground MotionFrom the Aftershock Sequence

Vertical component (acceleration) recordings of the 16:54, Sept. 5, 2011 UTC aftershock recorded by the AIDA profile stations

(Left) Acceleration recorded at AIDA profile station 3120 at 3.8 km from the epicenter of the 16:54, Sept. 5, 2011 UTC aftershock. (Right) Acceleration recorded at station 3510, 42.6 km from the epicenter.

3.8 km 42.6 km

(Left) Fourier amplitude spectra of the S wave and pre-P wave noise at AIDA profile station 3120. (Right) station 3510.

AIDA Profile: Blue trianglesYC network (IRIS Ramp Stations): SquaresXY network (VT stations): Triangles

The profile data are important because they provide a substantial amount ofcontrol in regard to source radiation pattern effects.

• Geometrical spreading near the source• Kappa• Q

The aftershocks are less than magnitude 3.0, and the spectra are very rich inhigh-frequency information.

AIDA Profile: BlackYC network: GreenXY network: Red

Band-Pass Filtered Max. Amplitudes of the 16:54, Sept. 5, 2011 UTC

aftershock

PGA, geometric mean of the horizontal comp. 8 -16 Hz pass-band,

Geometric mean horizonal

Band-Pass Filtered Max. Amplitudes recordings of the 16:54, Sept. 5, 2011 UTC aftershock

AIDA Profile: BlackYC network: GreenXY network: Red

bogus bogus

4 - 8 Hz pass-band,Geometric mean horizontal

2 - 4 Hz pass-band,Geometric mean horizontal

r-1r-1.1 r-1r-1.1

4 Hz Fourier Amp.2 Hz Fourier Amp.

Red symbols are Q correctedUsing Q=893f0.32 (A&B 2006)

Fourier Amplitude of the E-W component S wave along50 km profile from near the 2011 epicenter to Corbin, VA

Red symbols are Q correctedUsing Q=893f0.32 (A&B 2006)

r-1.0

r-1.0

r-1.6r-1.8

8 Hz Fourier Amp. 16 Hz Fourier Amp.

Theoretical Geometrical Spreading, from Chapman and Godbee (2012) BSSA, in press

Theoretical Geometrical Spreading, from Chapman and Godbee (2012) BSSA, in press

The modeling results indicatethat geometrical spreadingaround 1 Hz is approximatelyr-1.0, whereas it is approximatelyr-1.6 at higher frequencies for“rock” velocity models.

This appears to be consistentwith the VA aftershock data.

S wave window as recorded

Pre- P noise window

S-wave window correctedfor r-1.6 geometrical spreading

20110903_2110

E-W comp.

20110903_2110

N-S comp.Pre- P noise window

S-wave window correctedfor r-1.6 geometrical spreading

S wave window as recorded

20110903_2110

Vertical comp.Pre- P noise window

S-wave window correctedfor r-1.6 geometrical spreading

S wave window as recorded

Preliminary analysis suggests:

1) Geometrical spreading from shallow (e.g., 5-6 km) focal depth aftershocks appears to be frequency dependent: r -1.0 for < 4 Hz, r -1.6 for > 4 Hz

2) The high-frequency acceleration spectra appear flat to 40Hz. Apparent Kappa is very small, Q is apparently very high*

*These results are preliminary and conditional on spectral ratio analysis for confirmation.

Thank You!