Κωνσταντίνος Ευταξίας

Αναπληρωτής Καθηγητής Τμήματος Φυσικής ΕΚΠΑ

http://users.uoa.gr/~ceftax/

Seeding light to fractures on geophysical scale (earthquakes)

from nanoscale fracture findings 

Understanding how earthquakes occur is one of the most challenging questions in fault and earthquake

mechanics (Shimamoto and Togo, 2012).

Earthquakes in the labSCIENCE, 54, 2012

In this direction, a main effort has been devoted in the study of earthquakes on laboratory scale via

different methods.

It has been found that opening cracks are accompanied by

electromagnetic emission (EME) and acoustic emissions (AE)

ranging in a wide frequency spectrum, from kHz to MHz (laboratory seismicity)

It is considered that the laboratory seismicity

mimics the natural seismicity.

Recent studies by means of MHz-kHz EME have permitted

a real-time-like monitoring of fracture / failure process.

A major difference between the laboratory and natural processes is the order of magnitude differences

in scale in space and time.

This allows the possibility of observation of a range of physical

processes not observable on a laboratory scale. (Main, 2012).

On the laboratory scale the fault growth process is normally

occurs violently in a fraction of a second

(Lockner et al., 1999).

If this concept is correct the

expectation that fracture induced MHz-

kHz EM fields would allow the clear

monitoring in real-time and step-by-step

of the gradual damage of stressed

materials during earthquake

preparation process, is not groundless.

J. Phys. D:Applied Physics

422009

Based on the above mentioned idea

we have installed a field experimental network

using the same instrumentation as in laboratory experiments

for the recording fractured/failure induced kHz

and MHZ magnetic and electric correspondingly on geophysical

scale.

PHYSICS REPORT313, 1-108, 1999

NatureVol. 397, 333, 1999

But why does

But why does

nature paint such

nature paint such

a picture?

a picture?

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PUZZLING

FEATURE

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Physical Review Letters, 92(6), 065702, 2004

Physical Review E., 74, 016104-1/21, 2006

Physical Review E, 77, 36101, 2008

Pre-seismic anomalies associated with the

Kozani-Grevena EQ

Because an earthquake is mainly a large-scale dynamic failure

process, we attempt

to formulate the observed EMEs though a shift in thinking

towards basic science

of fracture and failure mechanics.

Such a study had not previously attempted.

In the frame of the aforementioned directions, our effort is focusing, on asking three questions:

(i) How can we recognize a MHz or kHz EME as a pre-seismic one?

(ii) How can we link an individual MHz or kHz EM precursor with a distinctive stage of the earthquake preparation?

(iii) How can we identify precursory symptoms in EM observations which signify that the occurrence of the prepared EQ is unavoidable?

The comprehensive understanding of EM precursors in terms of basic science

is a path to achieve more sufficient knowledge of the last stages of the EQ preparation process

and strict definitions of EM precursors.

OBJECTIVES

We base on two

well established

experimental results

An important feature, observed both at laboratory and geophysical scale,is that

the MHz radiation is observed prior to the kHz one.

On the laboratory scale:

ThekHz EM emission is launched in the tail of pre-fracture EM emission

from 97% up to 100% of the corresponding failure strength.

On the geophysical scale:

The MHz EM precursors are emerged during

the last week before the EQ occurrence.

The kHz EM precursors are launched from

a half of hour up to a few decades of hours before the EQ.

EM silence in all frequency bands appears before the main seismic shock occurrence,

as well as during the aftershock period.

The appears of the above mentioned EM silence

is one of the most fundamental questions presently

in EM precursors research.

The view that

«acceptance of “precursive” EM signals without co-seismic signals should not be expected»

seems to be reasonable.

Asignificant EQ is what happens when two surfaces of a major fault slip past one

another under the stresses rooted in the motion of tectonic

plates.

However large stresses siege the major fault after the gradual occurrence of a population of smaller

EQs in the strongly heterogeneous region that surrounds the

main fault.

After a seismic event occurrence the stress are redistributed.

The cracking events are correlated. A higher spatial correlation is emerged with the time

between the cracking areas. Finally, the released stresses siege the main fault.

www.nature.com/nature/debate/earthquake/equake_frameset.html

RcriticalLOCATION

COMLEXITY

The challenge is to determine the “critical epoch” during which

the “short-range” correlations evolve into “long-range”

ones.

Symmetry breakingAdaptabilityComplexity

CRITERION

Nature seems to paint

the following critical picture:

NON-LINEAR NEGATIVE FEEDBACK MECHANISM

MHz EM PRECURSOR

FRACTURE OF HETEROGENEOUS MEDIA

If the amplitude of fluctuations increases in a time intervalIt is likely to continue decreasing in the interval immediately

following

THIS MECHANISMS KICKS THE CRACKIN RATE AWAY FOR EXTREMES

1. First, a population of single isolated cracking-events emerge in the system which, subsequently, grow and multiply.

2. This leads to cooperative effects. The released stresses during the damage of material siege / produce other sub-regions / cracking events.

3. Long-range correlations build up through local interactions until they extend throughout the entire system.

4. Right at the “critical point” the subunits are well correlated even at arbitrarily large separation, namely, the probability that a subunit is well correlated with a subunit at distance away is unity and the correlation function follows long-range power-law decay.

5. At the critical state appear self-similar structures both in time and space. This fact is mathematically expressed through power law expressions for the distributions of spatial or temporal quantities associated with the aforementioned self-similar structures.

6. Below and above of the critical point a dramatic breakdown of critical characteristics, in particular long-range correlations, appears; the correlation function turns into a rapid exponential decay

The challenge is to determine the

“critical epoch”

during which the “short-range” correlations evolve into “long-range” ones.

SYMMETRY BREAKING

From the phase of non-directional almost

symmetricalcracking distribution

to a directional localized cracking zone that includesthe backbone of strong asperities

The siege of strong asperities begins.

The prepared EQ will occur if and when the local stress exceeds fracture stresses of

asperities.

The earth as a living planet: Human-type diseases in the

earthquake preparation process.Y. F. Contoyiannis, S. M. Potirakis, and K. Eftaxias

PHYSICAL REVIEW E, 82, 2010

Ivanov, P. C., et al., Multifractality in

human heartbeat dynamics, Nature, 399, 461-465, 1999.

Contoyiannis, Y.F., et al., Phys. Rev. Lett, 93, 098101, 2004.

Contoyiannis, Diakonos, Malakis: Intermittent Dynamics of Critical

Fluctuations, Phys. Rev. Lett, 89, 035701,

2002.

Goldberger, A.L., et al., Fractal dynamics in

physiology: Alterations with disease and

aging, PNAS, 99, 2466-2472, 2002.

HEALTHYCRITICAL

POINTSYMMETRY BREAKINGNEGATIVE FEEBACK

MULTIFRACTALITY

PATTIENT

NON-LINEAR NEGATIVE FEEDBACK MECHANISMTHAT KICKS THE CRACKIN RATE AWAY FOR EXTREMES

MHz EM PRECURSOR

FRACTURE OF HETEROGENEOUS NEDIA

Right at the “critical point”

the subunits are well correlated even at arbitrarily large separation

The aforementioned crucial features characterize a healthy state, since such a mechanism provides adaptability,

the ability to respond to various stresses and stimuli of everyday challenges. FRE RISCK FRACTURES

“Injury” states include characteristic features of the state which is away from the critical point

The earth as a living planet: Human-type diseases in the earthquake preparation process.

HEART INFRACTION.

Nature, 321,1986, 488

Satellite thermal imaging

. 0 2f F

LAI-coupling

SILENCE

A magnified view of fault surfaces reveals a rough looking surface

with high asperities and low valleys.

If the external stress raises the local stress around of an asperity, the asperity drops, the slip instantaneously accelerates and in the following decelerates and stop. In this way, the frictional fault surfaces suddenly slip, lock and then slip again in a repetitive manner “stick-slip” state.

The population of asperities distributed along the two fault surfaces hinders their relative motion. The initial phase of slip process refer to the cumulative damage of a critical number of asperities.

FIRST PHASE:Stick-slip-like sliding at low velocity

Two surfaces in sliding motion will contact first at these high asperities.

PUZZLING

FEATURE

PUZZLINGFEATURE

Physical Review Letters, 92(6), 065702, 2004

Physical Review E., 74, 016104-1/21, 2006

Physical Review E, 77, 36101, 2008

J. Phys. D:Applied Physics

422009

The repetition of such local damage-slip events intensifies fault wear and dynamic weakening. Material between the fault surfaces, which is called ‘’gouge’’, is produced and organized itself such away that it acts like a bearing.

Since in a bearing, one has rolling friction but no gliding friction, two fault surfaces slide against each other

with a low friction

SECOND PHASE: Sliding at high velocity characterized by a shear-thinning rheology.

FineGrain

gouge

Space-filling bearings

have been introduced to explain the fact that

two faces of fault slide against each other with a friction much less

than the expected one, without production

of any significant heat .

PHYSICAL REVIEW LETTERS92, 044301, 2004

Space-Filling Bearings in three Dimension

Lubrication

SELF-SIMIRARITY

During the local damage of a strong asperity an

‘’electromagnetic earthquake’’ is emerged.

The population of ‘’electromagnetic earthquakes’’

included in the abruptly emerged intermittent avalanche-like strong EM emission may mirrors the fracture of a corresponding population of asperities

The fracture of a strong contact is associated with a corresponding sharp stress drop. Laboratory experiments should reveal that the EM signals are emitted only during sharp drops in stress. Recent laboratory studies verify that this really happens, while the amplitude of the emitted EM fields is proportional to the stress rate.

Numerical method for the determination of contac areas

of a rock joint under normal and shear loads

International Journal of Rock Mechanics,

58, 8–22, 2013At the peak stage, the normal dilation was initiated, which led to a sharp drop in the contact area. Approximately 53% of the surface area remained in contact, supporting the normal and shear loads. After the peak stage, the contact area ratio decreased rapidly with increasing shear displacement, and few inactive elements came into contact until the residual stage. At the residual stage, only small fractions, 0.3%, were involved in contact.

Two strong avalanche-like kHz EM anomalies have been detected before the Athens surface

earthquake. The larger anomaly, the second one, contains

approximately 80% of the total EM energy released;

The second anomaly contains the remaining 20%.

Vertical displacements of rock surface are associated with each slip event. On the geophysical scale

such vertical displacements cause deformations on the earth’s surface.

Satellite Synthetic Aperture Radar (SAR) interferometryis an imaging technique for measuring the topography of a earth’s surface,

its changes over time, and other changes in the detailed characteristic of the surface.

Geophysical Research Letters

28, 3321-3324, 2001

Satellite ERS2 SAR images leads

to the fault model of the Athens earthquake This model predicts the activation of two

faults. The main fault segment is responsible for the ~80% of

the total seismic energy released,

while the secondary fault segment for the remaining

20%.

A UNIQUE EXPERIMENTAL

RESULT!

The Earth's crust is extremely complex.

However, despite its complexity,

there are several universally holding scaling relations.

Such universal structural patterns of fracture and faulting process

should be included into an EM precursor which is rooted in the activation of a single fault.

From the early work of Mandelbrot

the aspect of

self-affine nature

of faulting and fracture

is well documented

from field observations,

laboratory experiments,

theoretical and numerical studies

ΜΙΑ ΑΝΤΙ-ΔΗΜΟΚΡΑΤΙΚΗ ΚΑΤΑΝΟΜΗ

N(>A) = A-b

Fracture surfaces were found to be

self-affine

following the

persistent factional Brownian motion

model

over a wide range of length scales

the sequence of precursory kHz EM pulses

(“EM-earthquakes”)

is induced by the slipping of two

rough and rigid

Brownian profiles one over the other.

A question arises whether

THIS HAPPENS.

The population of EM-EQs

follows the lawP(E) ~ E-B where B

=1.6.

The population of natural EQs follows the law

P(E) ~ E-B, where B ~ 1.6.

The model predicts that a seismic event releases energy

in the interval [E, E+dE] with a probability

P(E)dE, P(E) ~ E-B

An “EM-EQ” occurs when there is an intersection of the two profiles

representing the two fault faces.

PHYSICAL REVIE LETTERS, 76, 2599, 1999PHYSICAL REVIEW E, %^, 1346, 1997

Self-Affine Asperity Model

A model for fault dynamics consisting of two rough and rigid

Brownian profiles that slides one over the other is

introduced.

Τhe Hurst-exponent

indicates the “roughness”

of the individual fault .

• Decreasing H increases the “sharpness” of the surface topography.

• The standard random walk profile corresponds to H = 1/2.

• The value H = 1 is an upper bound reached when the “roughness” of the fault is minimum, in other words a differentiable profile corresponds to H = 1.

• Finally the value H = 0 is a lower bound; as H tends towards 0 trends are more rapidly reversed giving a very irregular look.

The roughness

was found to be

H ~ 0.75

weakly dependent on the

nature of the material and on

the failure mode.

This quantity was then

conjectured to

be universal

The roughness

of the

kHz pre-seismic

EM time series is

H ~ 0.75

The roughness

of the profile of

the observed

KHz EM time series

is

H ~ 0.75

The surface roughness of a recently studied strike-

slip fault plane has been measured by

laser scanners . The fault surface exhibits

self-affine scaling invariance with a

directional morphological anisotropy that can be

described by two scaling roughness exponents,

H = 0.7 in the direction of slip and

H = 0.8 perpendicular to the

direction of slip.

Geophysical Research Letters, 33, 04305, 2006

The analysis for the whole Greece seismisity

reveals that it is characterized by

H ~ 0.77

Analysis in terms of fractal dimension D

The fractal dimension D also specifies the strength of the irregularity

of the fBm surface topography.

Measurements as well as theoretical studies suggest that a surface trace of a single fault

is characterized by D ~ 1.2.

FRACTALELECTRODYNAMICS

N(>A) = A-b

b = 0.62 b = 0.62

SELF-SIMIRARITY

THE ACTIVATION OF A SINGLE FAULT

SHOULD BE

A MAGNIFIED IMAGE OF THE REGIONAL SEISMICITY

and

A REDUCED IMAGE OF THE LABORATORY SEISMICITY

NONEXTENSIVEFragment-Asperity Interaction model for

EarthquakesPhysical Review Letters, 92, 2004

Physical Review E, 73, 026102, 2006

FRA

CTU

RE !

The observed spontaneous formation of vorticity cells and clusters of rotating bearings may provide an explanation for the long standing

heat flow paradox of earthquake dynamics.

PHYSICAL REVIEW LETTERS92, 044301, 2004

Space-Filling Bearings in three DimensionSpace-filling bearings have been introduced to explain the fact that

two faces of fault slide against each

other with a friction much less

than the expected one, without production

of any significant heat .HEAT-FLOW PARADOX

Rock Mechanics Rock Engineering

44, 269-280, 2011

SILENCE

“The greater the compressive strength,

the greater the EMR energy generated,

especially during main

failure”

International Journal of Rock Mechanics

57, 57–63 , 2013.

Numerical simulation of electromagnetic radiation

caused by rock deformation and failure

GRANULAR MATTER., 13, 93-105, 2011

Precursors of failure and weakening in a biaxial test.Numerical simulations

Experimental results lead to the conclusion:

The new surface areas

generated during an EQ is

S = 103 – 106 m2 for each m2

of fault area.

But why does nature paint such a picture?

Scale-free intermittent plastic flow from nanoscale up to geophysical scale

That avalanche strains decease in inverse proportion to sample size explains why it is difficult to observe strain bursts in macroscopic samples. The energy release by contrast may be assumed to be proportional to the dissipated energy e, which is related to the strain by e = σsV, where σ is the stress and V is the volume. Hence, the cutoff of the energy released distribution is expected to increase with sample size as

e ~ L2.

But why does

But why does

nature paint such

nature paint such

a picture?

a picture?

Individually, we are one drop.

Together, we are an ocean.

 Ryunosuke Satoro

Japanese Poetry