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**Κωνσταντίνος Ευταξίας**

Αναπληρωτής Καθηγητής Τμήματος Φυσικής ΕΚΠΑ Seeding light to fractures on geophysical scale (earthquakes) from nanoscale fracture findings

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**Understanding how earthquakes occur **

is one of the most challenging questions in fault and earthquake mechanics (Shimamoto and Togo, 2012). Earthquakes in the lab SCIENCE, 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.

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**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).

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**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.

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J. Phys. D: Applied Physics 42 2009

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**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.

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**But why does nature paint such a picture?**

PHYSICS REPORT 313, 1-108, 1999 Nature Vol. 397, 333, 1999

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

Physical Review E., 74, /21, 2006 Physical Review E, 77, 36101, 2008 PUZZLINGFEATURE PUZZLING FEATURE

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**Pre-seismic anomalies associated with the Kozani-Grevena EQ**

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**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.

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**OBJECTIVES In the frame of the aforementioned directions,**

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

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We base on two well established experimental results

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**the MHz radiation is observed prior to the kHz one.**

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: The kHz 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.

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**PARADOX FEATURE 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. PARADOX FEATURE

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**OUR PROPOSAL 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. OUR PROPOSAL 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.

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Rcritical LOCATION COMLEXITY Symmetry breaking Adaptability Complexity The challenge is to determine the “critical epoch” during which the “short-range” correlations evolve into “long-range” ones. CRITERION

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**Nature seems to paint the following critical picture: MHz EM PRECURSOR**

FRACTURE OF HETEROGENEOUS MEDIA NON-LINEAR NEGATIVE FEEDBACK MECHANISM If the amplitude of fluctuations increases in a time interval It is likely to continue decreasing in the interval immediately following THIS MECHANISMS KICKS THE CRACKIN RATE AWAY FOR EXTREMES Nature seems to paint the following critical picture:

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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

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**SYMMETRY BREAKING 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 symmetrical cracking distribution to a directional localized cracking zone that includes the 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.

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**Phys. Rev. Lett, 89, 035701, 2002. Contoyiannis, Y.F., et al.,**

Contoyiannis, Diakonos, Malakis: Intermittent Dynamics of Critical Fluctuations, Phys. Rev. Lett, 89, , 2002. The earth as a living planet: Human-type diseases in the earthquake preparation process. Y. F. Contoyiannis, S. M. Potirakis, and K. Eftaxias Contoyiannis, Y.F., et al., Phys. Rev. Lett, 93, , 2004. HEALTHY CRITICAL POINT SYMMETRY BREAKING NEGATIVE FEEBACK MULTIFRACTALITY PATTIENT PHYSICAL REVIEW E, 82, 2010 Ivanov, P. C., et al., Multifractality in human heartbeat dynamics, Nature, 399, , 1999. Goldberger, A.L., et al., Fractal dynamics in physiology: Alterations with disease and aging, PNAS, 99, , 2002.

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**FRACTURE OF HETEROGENEOUS NEDIA**

MHz EM PRECURSOR FRACTURE OF HETEROGENEOUS NEDIA NON-LINEAR NEGATIVE FEEDBACK MECHANISM THAT KICKS THE CRACKIN RATE AWAY FOR EXTREMES 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.

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**Satellite thermal imaging**

Nature, 321,1986, 488 Satellite thermal imaging LAI-coupling . SILENCE

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

A magnified view of fault surfaces reveals a rough looking surface with high asperities and low valleys. Two surfaces in sliding motion will contact first at these high asperities. 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. 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.

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

Physical Review E., 74, /21, 2006 Physical Review E, 77, 36101, 2008 PUZZLINGFEATURE PUZZLING FEATURE

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J. Phys. D: Applied Physics 42 2009

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SECOND PHASE: Sliding at high velocity characterized by a shear-thinning rheology. 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. Fine Grain gouge Since in a bearing, one has rolling friction but no gliding friction, two fault surfaces slide against each other with a low friction

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**PHYSICAL REVIEW LETTERS**

92, , 2004 Space-Filling Bearings in three Dimension 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 . SELF-SIMIRARITY Lubrication

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**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

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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.

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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, 2013 At 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.

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**ENIGMATIC FEATURE! 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%. ENIGMATIC FEATURE!

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**Satellite Synthetic Aperture Radar (SAR) interferometry **

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) interferometry is 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.

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**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! Geophysical Research Letters 28, , 2001

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**self-affine nature of faulting and fracture**

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

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**ΜΙΑ ΑΝΤΙ-ΔΗΜΟΚΡΑΤΙΚΗ ΚΑΤΑΝΟΜΗ**

N(>A) = A-b

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**persistent factional Brownian motion**

Fracture surfaces were found to be self-affine following the persistent factional Brownian motion model over a wide range of length scales

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**A question arises whether**

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. THIS HAPPENS.

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**when there is an intersection of the two profiles **

PHYSICAL REVIE LETTERS, 76, 2599, 1999 PHYSICAL 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. An “EM-EQ” occurs when there is an intersection of the two profiles representing the two fault faces. 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 The population of natural EQs follows the law P(E) ~ E-B, where B ~ 1.6. The population of EM-EQs follows the law P(E) ~ E-B where B =1.6.

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**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.

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**The roughness of the profile of H ~ 0.75 the observed**

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 profile of the observed KHz EM time series is H ~ 0.75 The roughness of the kHz pre-seismic EM time series is H ~ 0.75

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**Geophysical Research Letters,**

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

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**The analysis for the whole Greece seismisity **

reveals that it is characterized by H ~ 0.77

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**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. FRACTAL ELECTRODYNAMICS

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N(>A) = A-b b = 0.62 b = 0.62

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**THE ACTIVATION OF A SINGLE FAULT SHOULD BE **

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

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NONEXTENSIVE Fragment-Asperity Interaction model for Earthquakes Physical Review Letters, 92, Physical Review E, 73, , 2006

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FRACTURE !

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**PHYSICAL REVIEW LETTERS**

92, , 2004 Space-Filling Bearings in three Dimension 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 . 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. HEAT-FLOW PARADOX

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**Rock Mechanics Rock Engineering**

44, , 2011 SILENCE

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**the compressive strength, the greater the EMR energy generated, **

International Journal of Rock Mechanics 57, 57–63 , 2013. Numerical simulation of electromagnetic radiation caused by rock deformation and failure “The greater the compressive strength, the greater the EMR energy generated, especially during main failure”

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GRANULAR MATTER., 13, , 2011 Precursors of failure and weakening in a biaxial test. Numerical simulations

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**But why does nature paint such a picture? S = 103 – 106 m2 for each m2**

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?

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**PARADOX! 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. PARADOX!

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**But why does nature paint such a picture?**

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**Individually, we are one drop. Together, we are an ocean. **

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