acoustic emission(발표할 때 유용할것)

7/31/2019 acoustic emission( )

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Physical Properties during rock deformation

1. Testing machine stiffness

2. Pre- and post-peak behaviour3. Volume changes (volumetric strain)

4. Elastic wave speeds

5. Acoustic emission

Tuesday, April 19, 2011



1. Testing machine stiffness (and other corrections)

Low machine stiffness -k High machine stiffness -k

k

The first important correction is for the deformation of the loading machine itself:

- sample is usually much more compressible (less still) so dominates- but even so, for frame of low stiffness, an apparent lower modulus will be measured




Complete force-displacement curves

Especially important when comparing deformation of rocks of widely differingstiffnesses...




axial

Volume

Dilatancy, rupture and compaction

lateral

I – phase of compaction of pores and cracks (stiffening = increase in E)

II – linear elastic phase (no change in stiffness; E = constant)

III – non-linear phase – growth of new cracks – dilatancy (E decreases)

IV – strain softening phase – cracks link up to form the shear fault

V - dynamic instability and failure – equivalent to an earthquake in the crust

VI – stable frictional sliding on the fault plane

Reminder...

This time w.r.t.lateral and

volumetric strains




Sample shortening (Vp/Vs/AE)

Another calibration is the natural ‘shortening’ of the sample. This will lead toelastic wave velocities higher than they should be. Measure via LVDT vs. pressure




2. Pre- and Post-peak behaviour

Pre-peak behaviour veryhard to measure!

- fast loading leads tohigher peak stresses

- ‘roll-over’ and failuretakes longer at slow rates

- b-value can be used toasses the size distribution

of fracture

- at very slow rates, weenter the creep regime




Increasingconfinement increasesstrength, as well as thepost peak behaviour:

brittle -> cataclasis

Another example of

increasing strain rateincreasing the

apparent strength of the rock...

Pre- and Post-peak behaviour




Use AE as a feedback... slow the process

Solution championed by lockner (USGS) was to slow the process by using afeedback from the AE itself, converted to a voltage. This way, strain is variable.




Post-peak behaviour is investigated through

‘cyclic’ means to keep the sample intact...




...Both axial and radial cycles show the same

effect of decreasing stiffness with time




Anisotropy

Normal to bed parallel to bed

Deformation of Takidani granite (Japan Alps) normal and parallel to jointing




3. Volumetric strain

Volumetric strain,

unlike axial orradial, can give a

sense of the

changing volume of

the sample,

including thecontribution of the

cracks and pores as

they deform. In this

case, measured via

strain gauges




Alternatives, use

the servo-

controlled pore

pressure system

to receive the

pore fluid atconstant

pressure, thus

measuring

volumetric strain

vie the volume of water expelled

from the cracks

Volumetric strain




Volume change

AxialMean

Radial

A

B

C D i f f e r e n t i a l S t r

e s s ( M P a )

Axial Strain (fractional)

Time from start (s)

P - w a v e

V e l o c i t y ( m / s )

V o l u m

e c h a n g e ( ml )

C u m

u l a t i v e A E ( h i t s )

AE Hit rate

0

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400

-1

-0.5

0

0.5

1

0

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200

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3500

4000

4500

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6000

-0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025

0

100

200

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1000

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2000

0 1800 3600 5400

This measure

is very

sensitive to:

- pores vs.

cracks

- anisotropy

and loading

direction

- the crack

aspect ratio...

Etna basalt

(cracked)




• We have just seen the effect of micro-cracks have upon deformation via

volumetric strain...• Other methods are also available that give more detailed data, including

tomography.• Relies on a active system of sending a mechanical pulse through the sample

and receiving it at the other end. Typically a piezoelectric transducer is

used that converts voltage to mechanical pulses directly and vice versa.

P-wave ‘sender’

Cracked medium

P-wave ‘receiver’

Mechanical pulse in:

Traveling parallel to

cracks

Mechanical pulse in:

Traveling normal to

cracks

Mechanical pulse out:

Time taken to cross sample

Gives a velocity.

Mechanical pulse out:

This time, the pulse

takes longer to be

received (Tn>Tp), and

has loweramplitude….

T0 Tp

T0 Tn

4. Elastic wave speeds

Anisotropy and wave speed...




Measurement of Vp/Vs and AE: Piezoelectric

Crystals and Transducers

ValpeyFisher Crystals ValpeyFisher Transducers

P-Wave crystal signal output S-Wave crystal signal output

Relatively new (~25 years) development...




Measurement of Vp/Vs and AE: set-up

- A pulse generator sends volt spikes (usually square waves of short

duration) to the transducer, and simultaneously a ‘trigger is sent to therecording device to tell it when the pulse was sent

- The transducer active element is excited and sends a mechanical pulseacross a specimen, where it is received by a second identical sensor

- The mechanical signal is converted into electrical voltage.-The voltage is first amplified, by 20/40/40 dB (x10/100/1000) depending on

the rock material, distance, etc.-The oscilloscope records the received pulse, as well as the start time from

the trigger.




Picking the arrival time:

P-wave




Picking the arrival time:

S-wave

S-wave is challenging, as a certain amount of conversion (P-S) can take

place, especially with inclined surfaces




Applications:

P-wave and S-wave anisotropy

In this example, the P-wave velocity wasmeasured as a functionof radial angle aroundthe edge of a cylindrical

core

For visible layering in asedimentary rock type(shown here) there is apronounced anisotropy

Important for manyareas of Geoscience...oil, gas exploration,seismic tomography,exploration...

Bentheimsandstone,

porosity ~23%




Same rock type, but thistime water saturated.

As water has a higherP-wave velocity that air,the bulk velocity is

higher

Applications:

P-wave and S-wave anisotropy




Applications:

P-wave and S-wave variation with isostatic pressure

Another important

application

Crucial for

interpreting seismicdata where we wishto know the velocityof the propagating

medium at differentburial depths, e.g.

deep subductionzones, exploration,etc.




Applications:


Another importantapplication.

Different rock type...

‘Crab orchard

sandstone’ withporosity of only 4%




Applications:


Takidanigranite,porosity ~1%


A l



Applications:

P-wave and S-wave anisotropy with isostatic pressure

By measuring the fabric of the rocks, and examining the fast and slow velocity

planes, we can establish the degree of anisotropy (more on Thursday)


A l



Applications:





A li i



Applications:







Influence of crack shape

Vp : Influence shape of porosity

What causes anisotropybesides the sedimentary

fabric?

- Cracks

- Pores

- Crystallographicpreferred orientation

- Lattice preferredorientation


fl f





What causes anisotropybesides the sedimentary

fabric?

- Cracks

- Pores

- Crystallographicpreferred orientation

- Lattice preferredorientation

Closing a ‘crack’ requiresless pressure than a

‘pore’. Key parameter:

aspect ratio


I fl f k h





By considering the degree, alignment, and density of ‘penny shaped’ cracks, atheoretical framework can be derived, allowing a comparison to the laboratorydata to be made in terms of the degree of contribution to the anisotropy

Schubnel, Benson et al., 2006


V f k d d



Variation of crack density and

aspect ratio with pressure

Schubnel, Benson et al., 2006

Using those Vp and Vs data, which can be linked theoretically to the crack network via a non-interactive effective medium model (Kachanov, 1994), one can, forexample, invert the velocity for the changing microstructural parameters:




Examination of the microstructure reveals

the classic ‘pores vs. cracks’ argument!




Examination of the microstructure reveals

the classic ‘pores vs. cracks’ argument!

Somewhat off-topic... Mercury injection porosimetry alsogenerates data to support this hypothesis:


C bi V k



In all cases:

- Velocity increases withPressure

- Crack density decreaseswith pressure

- aspect ratio increases

But with very different

relative responses withrespect to the balancebetween ‘pores’ and ‘cracks’as well as the anisotropy of the rock

Combine Vp, crack

density, and aspect ratio


Influence of fluid bulk modulus



Influence of fluid bulk modulus

We have seen the effect of ‘dry’ vs. ‘water saturated’ rocks. But actually this issimply two end members. The compressibility of the ‘fluid’ in the pore space alsohas a significant effect on the seismic velocities:


S k di t ib ti l ti l iti



Summary: crack distributions vs. elastic wave velocities(also see Zimmerman ‘Compressibility of sandstones’ for a good review)


5 Acoustic emissions



5. Acoustic emissions

- One of the most usefulinnovations in the last ~20 yearsor so

- Essentially, the ‘wave’ received isanalogous to tectonic earthquakes

- BUT still a caveats: they are notcalibrated like a seismometer (i.e.acceleration/velocity per mV isnot known)

- Only work a low temperatures(~200C for PZT). although someexotic materials have been usedto ~600C (but with lowerresponse)


Acoustic Emission



• Acoustic emissions (AEs) are high frequency (100 kHz – 5 MHz) strain waves.

• Emitted by rapid strain events: cracking, phase transformations, etc.

• They are the laboratory analogue for seismic events in the crust.

• Schematic of a received AEwaveform (known as a hit ).

• We measure specificparameters of each AE hit:• Amplitude threshold• Onset time• Rise time• Duration• Peak amplitude• Energy

• We also measure the hitrate and cumulative hits.

• We look at hit statistics.• We use multiple

transducers to locate thesources of AE events in 3D.

Acoustic Emission


Acoustic Emission location



We can alreadyfail samples inthe laboratory,and use acoustic

emission (AE) tolocate the faultproduced usingminiature piezo-electric sensors

Lab setup

Schematic

‘Microseismic’

(AE) event

‘Fault’

LOAD

To measurement and dataanalysis equipment…

Miniature

‘Sensor’







First pioneered by Lockner, Byerlee, and others at the USGS in the 80’s and

90’s (during the last bug Rock physic ‘push into understanding earthquakes






Once the first arrivals

are known (time), these

data can then be

inverted to calculate the

event location that

produced the radiation

seen on that sensorarray.

Depends on accurate

picking of waveform

times, as well aknowledge of the velocity

and velocity anisotropy of

the sample! (which

changes with stress!)





0

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16:18:00 16:18:30 16:19:00 16:19:30

S t r e s s ,

M P a

Hi t r a t e ,1 / s

Time, H:M:S






0

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600

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18:51:30 18:52:00 18:52:30 18:53:00

S t r e s s ,

M P a

Hi t R a t e ,1 / s

Time, H:M:S






0

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200

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400

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600

0

100

200

300

400

500

600

17:06:00 17:07:00 17:08:00 17:09:00

S t r e s s , M

P a A

E Hi t s / s

Time, H:M:S






Pick the data



Pick the data...


Pick the data



Pick the data...

Window

‘Pick’

Function


Source location methods and accuracy




Everyone expects good accuracy (they believe what theysee!). But...

Main factors:

• Picked arrival times (random error)• Velocity model (systematic error)

Also:

• Sensor array is important (3D distribution, and surveyedlocations

• Source location method

Main criteria... time residuals






• Direct Grid Search methods

• Standard iterative methods

• Simplex

• Geiger

• Other methods:

• Joint hypocentre

• Relative location

• Genetic algorithms

Some of these better than others... usuallyinvolving analytical vs. computational (iterativeapproaches). Computing is cheaper these days so...







Simplex and Geiger methods



Simplex and Geiger methods

Solving for:

θ=(t0, x0, y 0, zo )

with residual:ri=ti-to-Ti(x0, y 0, z0 )

where: ti = measured arrival time; Ti = calculated time

Minimizing a misfit function:

Φ(r)

The function relating the arrival times and the locationis nonlinear since there is no single step approach to

find the best event location.Tuesday, April 19, 2011

Geiger method



Geiger method

Linearize the problem by saying:

θ = θ* + Δθ& Solve:

Α Δθ = r

Where A = matrix (n x 4) of partial derivatives (e.g. δTi/δx0)Matrix inversion problem, via SVD (singular valued decomposition).

Important parameters:

• ‘Tolerance’ - Repeat until Δθ < tolerance• ‘Max iterations’ - Stop if exceeded

• ‘Condition # limit’ - Stop if exceeded. SVD condition condition #is inversely proportional to the stability of the inversion

•‘Step size’ - starting step size for partial derivative calculation.


Simplex method



Simplex method

A simplex is a shape having one more vertex than the

number of dimensions for which it is defined (figureshows a 2D example)

A misfit function Φ(r) is calculated at each vertex.

The vertex with the highest misfit, can then reflect,

expand or contract in order to search for a lower misfitposition.

Important parameters:

• ‘Tolerance’ - continue until value of misfit function falls

below this• ‘LPNorm’ = (1 or 2) power to raise the travel time

residuals (r) in he misfit function

• Use of an ‘outlier’ or not

• ‘Arrival error factor’ (e.g. x3). If yes, drop an arrival timefrom a sensor that is larger than the time multiplied by

this factor (i.e. assumes it is bad)Tuesday, April 19, 2011

Common parameters



Common parameters

• ‘Phases’: P-wave and/or S-wave

• ‘Velocity structure’: Isotropic,transversely isotropic, etc

• ‘Maximum residual’: if a sensor

residual is greater than a certainvalue, drop the arrival time, and re-locate

• ‘Starting position’: Can and issue if the

sensor array is sub planar, or has aarrangement with a high degree of symmetry, or a complex velocitymodel


Geiger (G) vs. Simplex (S)...



g ( ) p ( )

G is generally more efficient and faster than S (but not such anissue with todays faster computing)

Occasionally G can become unstable (e.g. ill-conditioned inversematrix problem, problems with partial derivative calculation,etc.). In this case solution will not converge, or will have a largecondition #. Reduction of the condition # will occur through:

• Increased number of arrival times

• Improved 3D coverage

• Use of more than one seismic phase

G allows the calculation of a 3D error ellipsoid, which is usefulfor analysis, clustering techniques, etc.

In many software packages, ‘Simplex into Geiger’ is used tocombine the best of both methods.


Magnitude



g

The traditional measurement of earthquake size/strength is ‘magnitude’,which is a number based on the measurement of the maximum motion

recorded by a seismic instrument, corrected for distance and instrumentresponse.

Earthquake magnitude (ML) was first introduced by Charles Richter in 1935.Determined from the log of the peak amplitude of displacement on a Wood-Anderson seismograph

Most common magnitude calculations:

• ML: local or richter magnitude

• MS: surface wave magnitude

• Mb: body wave magnitude

•Mw: moment magnitude

All magnitude scales should yield approximately the same value for anyparticular earthquake

mw is considered appropriate over the largest range


Magnitude



g

mw - moment magnitude

mw = C . log Mo + D

where Mo: seismic moment; C,D: user defined variables [C=2/3, D=6 fromHanks and Kanamori 1979]

Seismic moment has become the most universal measure the size of a seismic

eventSeismic moment can be physically realized for a shear displacement:

M0 = μ . u . A

where,μ: shear modulus and, u: slip displacement, A: fault area.

• Seismic moment can also be directly calculated from the far field displacementspectra (FFT) of P- and/or S-waves, or from time domain waveforms.

• Seismic moment (aka scalar moment) is also directly estimated from the scalarpart of a moment tensor solution

• BUT requires a triaxial sensor... which is not avail in the lab (yet)Tuesday, April 19, 2011

Magnitude



g

Mw = -4 Mw = 8

URL AE

(Mw~-7 to -5)

URL MS

(Mw~-4 to -1)

(from McGarr, 1999)

S t r e s s D r o p

Moment Magnitude

Stress Drop / Scaling relationship: AE/MS to natural EQ

McGarr, JGR, 1999


Example: U.R.L.



**

AE events before first MS event

AE events after first MS event

~50cm

Note: Higher sourcelocation accuracy of AE

events compared to MS

events.

AE Clusters are Associated with large MS events

Cluster of 86 AE events; associated with2 MS events in the same space/time

AE migrates

with time


Moment tensor inversion



P T

P T

Fault Plane

Solution...





N

P T

P T

Fault Plane

Solution...





(tremor model)


Seismic b-value



• N(m) = number of EQs or AEs withmagnitude ≥ m

• a = proportionality constant

• b = the seismic b-value

• Related to scale of cracking:

• high b = distributed small-scalecracking.

• low b = localization and larger-scale

cracking.

Note: magnitude and amplitude (dB) are

both logarithmic measurement scales.

• A simpler way to utilise AE... as many systems (including the patersonrig!) can only accept 2 external sensors and thus no location is possible...

• Slope of the relationship between the amplitude (magnitude) andfrequency of occurrence of AE hits or seismic events.

• Laboratory AE data provide an exact analogy for the Gutenberg-Richtermagnitude-frequency relation for crustal earthquakes:


AE during deformation of Darley Dalesandstone #1



• Sample: dry• Pc = 50 MPa

• Strain rate = 10-5 s-1

• Measurement of AE rate

and seismic b-value• AE rate increases with

crack growth up to pointof dynamic failure(past peak stress).

• b-value decreases frombackground value to aminimum around dynamicfailure.

sandstone #1





• Sample: water saturated

• Pc(eff) = 50 MPa

• Pf = 7 MPa (constant)

• Drained conditions


• Again, AE rate increases withcrack growth up to point of dynamic failure.

• Again, b-value decreases from

background value to aminimum around failure.

• Sample is weaker.

• More pronounced strainsoftening phase.

sandstone #2





• Sample: water saturated

• Initial Pc(eff) = 50 MPa

• Initial Pf = 20 MPa

• Un-drained conditions


• Pf increases during compaction,

then decreases during dilatancy.• AE increases very rapidly due to

decreasing Pc(eff).

• Cracking causes Pf to fall and Pc(eff)

to increase – so AE rate stopsaccelerating.

• Temporary strengthening duringextended strain softening phase.

• Sample fails later.

• AE shows double b-value minimumwith a recovery in between.

• This behaviour is often observed in

seismic zones prior to EQs.

sandstone #3




End of Lecture 2, part 3.

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acoustic emission(발표할 때 유용할것)

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