evelyn roelo s u. s. geological survey earthquake science center … · 2017. 2. 25. ·...

Analyzing Borehole Strainmeter Data

Evelyn RoeloffsU. S. Geological Survey

Earthquake Science Center

March 28, 2016

Evelyn Roeloffs, USGS ESC Analyzing BSM Data March 28, 2016 1 / 26

1 Analyzing gauge elongation dataLong-term trendsAtmospheric pressureSeasonal signals

2 Non-ideal strainmetersVertical couplingNon-identical gauges

3 Calibrating BSMsCalibration matrices from coupling coefficientsOrientation corrections


Long-term gauge elongations: Examples


What causes long-term trends?

Drilling the borehole and installing the strainmeter creates a stressfield that varies around the borehole

BSM gauges measure localized formation creep caused by thesestresses


Long-term gauge elongations: Examples

During first weeks-months, trends are complex and non-monotonicas curing grout expands and gives off heatElongation time series typically approach non-zero steady ratesSeasonal signals are superimposed on long-term trends


Long-term gauge elongations: Removal

A function that can be fit to thegauge extension time series e(t)for many PBO BSMs is:e(t) = a+ bt+ c(t− t0)

p

where:t is time, t0 is a reference timea is an arbitrary reference valueb is a constant elongation ratep is an exponent with 0 < p < 1and usually 0.1 < p < 0.4

Seasonal signals remain afterremoving this function...


Atmospheric pressure response

Atmospheric pressure is a load on the earth’s surface

PBO BSMs all have some response to atmospheric pressure


PBO BSMs: Atmospheric pressure response coefficients

940 950 960 970 980 990

10/08/11 10/22/11 11/05/11 11/19/11 12/03/11 12/17/11 12/31/11

hPa

B003_PhPa_eo

0 2 4 6 8

10

milli

met

ers B003_RFmm

-0.15

0

0.15

mic

rost

rain

B003 CH3 cB003 CH3 c.tb

-0.15

0

0.2

mic

rost

rain


-0.3

0

0.5

mic

rost

rain


-0.1

0

0.1

mic

rost

rain


BSM gauges contract whenatmospheric pressure increases

Atmospheric pressure responsecoefficients differ among thefour gauges

Atmospheric pressure responsecoefficients are generally largerin the Pacific Northwest thanin California.


Atmospheric pressure time series: Examples

Check for and correct artificial offsets and/or drift

Atmospheric pressure contributes a seasonal variation


Seasonal variations in gauge data

Seasonal variations aretypically not the same onthe different gauges of aBSM

Measured parameters maycorrelate with seasonalvariations:

downhole temperatureatmospheric pressurepore pressuredepth of surface-waterbodies

Groundwater pumping thataffects strainmeters mayalso occur seasonally


Seasonal variations compared with slip-event signals

B012

B004

M6.4 Sept. 9 2011

B927

B009B010B011

B003B005B006B007

B018

B926

B928

B013B943

B017

B014?

?B001

Seasonal variations dwarf slip-event signals


Seasonal variations after removing atmospheric pressure

No pressure correction After pressure correction


Loading from individual rainfall events

940 950 960 970 980 990

10/08/11 10/22/11 11/05/11 11/19/11 12/03/11 12/17/11 12/31/11

hPa

B003_PhPa_eo

0 2 4 6 8

10

milli

met

ers B003_RFmm

-0.15

0

0.15

mic

rost

rain


-0.15

0

0.2

mic

rost

rain


-0.3

0

0.5

mic

rost

rain


-0.1

0

0.1

mic

rost

rain



Seasonal gauge elongations and GPS-derived seasonaldisplacements


Seasonal gauge elongations and downhole temperature

Peak extension on B003 CH3lags peak downholetemperature by about twomonths

Coefficient about 2.5microstrain/◦C

For comparison, coefficients ofthermal expansion:

Steel 9.9-17 microstrain/◦CConcrete 12 microstrain/◦C


Removing repeatable seasonal signals

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

10/1/10 10/1/11 10/1/12 10/1/13 10/1/14 10/1/15 10/1/16Date m/d/y

rela

tive

gaug

e ex

tens

ion

X10-6

B024 Daily averages, trend fit and subtracted

CH0 (N142E)

CH1(N82E) CH2

(N22E)

CH3(N172E)

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

10/1/10 10/1/11 10/1/12 10/1/13 10/1/14 10/1/15 10/1/16Date m/d/y

B024 Daily averages, trend fit and subtracted

rela

tive

gaug

e ex

tens

ion

X10-6

CH0 (N142E)

CH1(N82E)

CH2(N22E)

CH3(N172E)

-0.4

-0.2

0

0.2

0.4

0.6

10/1/10 10/1/11 10/1/12 10/1/13 10/1/14 10/1/15 10/1/16Date m/d/y

CH0 (N142E)

CH1(N82E)

CH2(N22E)

CH3(N172E)

rela

tive

gaug

e ex

tens

ion

X10-6


Evidence for vertical coupling: Large atmosphericpressure response

970 975 980 985 990 995

1000

02/06/16 02/13/16 02/20/16 02/27/16 03/05/16 03/12/16 03/19/16

hPa

B084_160205_160321_PhPa 0

0.5 1

1.5 2

2.5

mm B084_160205_160321_RFmm

-0.03-0.02-0.01

0 0.01 0.02 0.03 0.04 0.05

mic

rost

rain

B084 CH3 N 47.0E-0.02-0.01

0 0.01 0.02 0.03 0.04

mic

rost

rain

B084 CH2 N 77.0E-0.04-0.03-0.02-0.01

0 0.01 0.02 0.03 0.04 0.05 0.06

mic

rost

rain

B084 CH1 N137.0E-0.03-0.02-0.01

0 0.01 0.02 0.03 0.04

mic

rost

rain

B084 pinyon084bcs2006 33.6116 -116.45637B084 CH0 N 17.0E

990 995

1000 1005 1010 1015 1020

02/06/16 02/13/16 02/20/16 02/27/16 03/05/16 03/12/16 03/19/16

hPa

-1-0.5

0 0.5

1m

m B073_160205_160321_RFmm-0.06-0.04-0.02

0 0.02 0.04 0.06 0.08 0.1

0.12

mic

rost

rain

B073 CH3 N120.0E-0.06-0.04-0.02

0 0.02 0.04 0.06 0.08 0.1

0.12

mic

rost

rain

B073 CH2 N150.0E-0.1

-0.05 0

0.05 0.1

0.15

mic

rost

rain

B073 CH1 N 30.0E-0.1

-0.05 0

0.05 0.1

0.15 0.2

mic

rost

rain

B073 varian073bcs2006 35.9467 -120.4717B073 CH0 N 90.0E


More general coupling formulation

ei = Ci(εxixi + εyiyi) +Di(εxixi − εyiyi) + Fiεzz

Each gauge has its own coupling coefficientsCoupling to vertical strain is includedCoupling to 2εxiyi is probably unnecessary


Effect of the free surface

Strainmeter responds differently to a surface load than to a sourcefrom within the earth


Effect of vertical coupling on areal strain response

εzz = −ν1−ν (εxx+εyy) = −ν

1−ν (εxixi +εyiyi)

ei = [Ci − ν1−νFi](εxixi + εyiyi) +Di(εxixi − εyiyi)

Define an apparent areal strain coupling coefficient C̃i = [Ci − ν1−νFi]

ei = C̃i(εxixi + εyiyi) +Di(εxixi − εyiyi)

For sources much deeper than strainmeter:

Vertical coupling reduces apparent areal strain responseApparent areal strain response can even be negative


Coupling and calibration matrices

Coupling coefficients Ci, Di, and Fi (or C̃i) are estimated fromgauge response to ”known” strainsThe equations expressing the responses of all the gauges to strainin common (x, y) coordinates are assembled as rows of a ”couplingmatrix”, C, in which θi is angle of ei CCW from x:e0e1e2e3

=

C0 D0 cos 2θ0 D0 sin 2θ0C1 D1 cos 2θ1 D1 sin 2θ1C2 D2 cos 2θ2 D2 sin 2θ2C3 D3 cos 2θ3 D3 sin 2θ3

εxx + εyyεxx − εyy

2εxy

= C


2εxy

The ”calibration matrix”, S, ”inverts” the coupling matrix toexpress the strains in terms of the gauge elongationsεxx + εyy

εxx − εyy2εxy

= S

e0e1e2e3


Calibration matrices


2εxy

= S

e0e1e2e3

The ”calibration matrix”, S, depends on

Coordinate system (x, y)Gauge subset used (all 4, or any subset of 3)

For identical gauges, the coupling matrices for subsets of 3 gaugescan be inverted analytically to obtain calibration matrices

In general, the coupling matrices must be inverted numerically


Need for orientation corrections

-100

-50

0

50

4/13/09 5/3/09 5/23/09 6/12/09 7/2/09-150

-100

-50

0

50

100

nano

stra

in (D

=1.5

) nanostrain(D=1.14)

CH1=N118ºE

CH1=N108ºE(measured)

CH1=N98ºE

εxx−εyyDifferentialExtension

100

150

4/13/09 5/3/09 5/23/09 6/12/09 7/2/09-100

0

100

150

200

-50

0

50

nano

stra

in (D

=1.5

)

nanostrain(D=1.14)

CH1=N118ºE

CH1=N108ºE(measured)

CH1=N98ºE

2εxyEngineering

Shear

B004 shear strains for 2009Cascadia aseismic slip event

The strain tensor is afunction of π (not 2π)

Orientation error istwice as important as fordisplacement

PBO BSM measuredorientations may requirecorrection

Some orientations werenot measured atinstallation

see Hodgkinson et al.,JGR, 2012


Calibration Choices

Assume gauges are ideal and identical, but keep in mind:

areal strain may not be reliableshear strain coupling coefficient may not be knownstated orientation may not be corrected

Use tidal calibration and orientation correction that has alreadybeen done

Roeloffs JGR, 2010; Hodgkinson et al. JGR 2012not all BSMs attempted and not all of those attempted could becalibrated successfully

Use seismic calibration for Anza BSMs (Grant and Langston)

based on strains estimated from broadband seismic array

Try your own tidal or seismic calibration


Any questions?


evelyn roelo s u. s. geological survey earthquake science center … · 2017. 2. 25. ·...

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