Interrelationship between seismicity and seismic velocity during compression rock failure
TITLE: Spatial and temporal correlation between seismicity and
seismic velocity during compression rock failure
ABSTRACT: We propose to examine the
propagation of fracture and seismic wave
during the development of a fault or
subcritical growth under tensile and
compressing loading. The parameters
related to the propagation of fracture and
seismic wave in the earth have been cited
to have potential at least sensitive short-
term predictors of major earthquakes: (I)
Spatial and temporal variations in wave
propagation parameters such as seismic
velocity ratios, scattering attenuation
and coda Q 1
[Aggarwal, 1973, Scholz et
al., 1973, Rikitake, 1976; Rikitake,
1987;Jin, 1986; Jin, and Aki, 1989]. (II)
variations in seismicity statistics such as
event rates [Smith, 1981., Wyss, 1985,
Wyss, 1997 #800 ; Wyss et al., 1984;
Wyss et al., 1998; Wyss and Martyrosian,
1998 ; Wyss and Wiemer, 1997 ] and
seismic b- values [Jin, 1986, Smith, 1981
#1232; Smith, 1986]
The differential stress , crack density changes from Acoustic Emission (AE) and
seismic waveforms will be determined through successive stages of: (I) fault nucleation;
(II) frictional sliding; (III) strengthening (Figure 2). For each individual phases, crack
density changes from AE will be interpreted using Mean Field Theory (MFT) for
subcritical crack growth based on a modified Griffith criterion (Main, 1991; Main et al.,
1993, Liakopoulou-Morris, 1994). Damage evolution is going to be determined from a
mean seismogenic crack length <c> from seismic b-value and seismic event rate and a
mean energy release rate <G> from <c> and . Seismic waveforms will be measured of
compressional waves (P) and two shear waves (S) or examine waveform (P or S) patterns
for the same phases during the rock experiments as that performed (Satoh et al., 1987;
Oda 1990 #1222).
We believe that investigation on spatial and temporal correlation between the
parameters of crack propagation such as <c>, <G> and seismic wave propagation such
as seismic velocity of P-wave will contribute to ongoing research in relation to the
preparation process for natural earthquakes and rock fracture in the laboratory. Also,
granites of different grain sizes will be used to correlate fracture and seismic wave
propagation. Also, we propose to estimate the fractal distribution of cracks and
determine its relationship to the seismic b values as a function of time and space in the
rock specimens. By examining of the spatial and temporal correlation between the
METHODS of INVESTIGATION
Mean Energy release rate <G>
Mean crack length <c>
Seismic event rates
Seismic b value
Fractal dimension D
parameters of seismicity and seismic wave, we hope to develop a model for the observed
changes of those parameters prior to dynamic failure of laboratory rock samples or the
Meredith and Atkinson (1983) showed that the event rate N was also non-linearly
related to the stress intensity consistent with Charles' power low for stress corrosion
crack as :
KKVV )/( 00 (1)
where V is the average velocity of crack tiop extension and the exponent n is known as
the stress corrosion index, and is respectively greater at low stress intensities for poly
minerallic rocks, and a single crystal slicates (Atkinson and Meredith, 1987). In general,
for polycrystalline rocks under tension 20 <n<60, so the process of accelerating crack
growth is in fact non-linear. n '
is referred as an 'effective' stress corrosion index, since
the exponents n and n '
are found to be equal within a few percent: n=29.0 (0.990),
=29.1 (0.977), with correlation coefficients in brackets (Main and Meridedith, 1991).
The general form and physical significance of spatial and temporal fluctuations in
seismic b value has been discussed by many authors (e.g., Gibovicz, 1973; Smith, 1986;
Main et al., 1990., Oncel et al., 1996 a,b). The general observation is that (1) the b value
usually increases to a peak value usually after a major earthquake or dynamic rupture,
and (2) the b value usually increases to a peak value and then decreases to a minimum at
the time of occurrence of the next event. Similar variations are seen in laboratory
experiments and have been attributed to rock heterogeneity (Mogi, 1962) or stress
(Scholz, 1968). The most recent studies (Meredith et al., 1990) have extended and unified
these observations into a single negative correlation between b and the degree of stress
concentration measured relative stress intensity factor K/K c , where K c is the fracture
)]/())[(( 0000 KKKKbbbb cc (3)
K 0 is a threshold stress intensity for subcritical crack growth, below which no crack
healing takes place.
The first geophysical precursor is the velocity of the P-wave changes. The change in the
velocity of the P-wave is measured by measuring the change in the ratio of the P- wave
velocity to the S- wave velocity (Vp/Vs). The Vp/Vs ratio is obtained from an analysis of
the travel times of P- and S- waves [Rikitake, 1976].
OBJECTIVES: The main objective of this study is to analyze the data of Acoustic Emission
(AE) in time and space domains by a modified Griffith criterion to detect the evolution of fractal
damage during compressional deformation (Main, 1991). Spatial and temporal variations of mean
crack length <c> from the seismic event rate N and the seismic b value and mean energy release
rate per unit crack surface area <G> from differential stress and <c> will be computed. <c>
and <G> characterizes both the non-linear nature of fracture growth and the fractal nature of
damage, and associated with large fluctuations in the scaling exponent b (Main et al., 1993). A
statistical comparison of these different measures will provide a more sensitive interpretation of
fault development or fracture growth with long-range interactions. A secondary objective is
to evaluate possible interrelationships between parameters of fracture and seismic wave
propagation. Seismic waveforms will be measured automatically of compressional waves
(P) and two shear waves (S) for the same phases during compressional deformation on the
basis of the computer software developed by Satoh et al., .
IMPORTANCE: The prime importance of the present project is to relate the temporal
changes of fracture propagation such as mean seismogenic crack length <c> and mean
seismic energy rate <G> as much as the seimic wave propogation. The second
importance is to compare these quantitative parameters related to the propogation of
fracture and seismic wave with the synoptic model of Figure 2. The comprehensive
evaluation of both the temporal and spatial attributes of the propagation of fracture and
seismic wave during compression rock failure will define the evolution of fractal damage
in both time and space and provide basic information relevant to earthquake prediction.
EXPERIMENTAL PROCEDURE: Cylindrical granites (Westerly, Oshima and Inada
of Figure 1) will be examined under conditions of constant strain rate loading (1.6x10 5
) at three different confining pressure (Table 1). Specimens with 50 mm in diameter
by 100 mm in length will be deformed either air-dried or water-saturated. Figure 2
shows a schematic illustration of the test conditions through successive stages of fractal
damage during compressional deformation (Liakopoulou-Morris et al.,1994).
METHODS of INVESTIGATION:
Mean energy release rate <G>: Mean Field Theory based on a modified Griffith
criterion for a fractal ensemble of cracks (Main,1991) is used to monitor the evolution of
damage for due to an array of tensile (Main et al., 1993). A mean potential strain
energy release rate <G> (per unit crack surface area A) is defined by
where U is the elastic strain energy, is the stress applied to the boundary of each
element containing a crack, assumed uniform, and c is the crack semi-length in a volume
element. For different loading configurations, the combined geometric and scaling
constant may be different from tensile case, where EB /2
, and E is Young’s modules.
Mean crack length <c>: By assuming that the damage had the form of a fractal array of
cracks within specific upper and lower bounds ( minc , maxc ) with a probability density
distribution p(c) ~ )1( D
c , Main (1991) showed that
The minimum condition for subcritical crack growth K>K 0 implies the inequality
)/( 0min YKc , so that 0min c , where K 0 is threshold intensity for subcritical crack
growth and Y is a dimensionless constant depending on the loading configuration. This
is also a necessary condition for defining a finite mean crack length from a fractal
distribution. A finite upper bound maxc is required so that the strain energy stored in the
body (U 2
c for Griffith cracks) remains finite. The upper bound c max (Main, 1991):
may be calculated by assuming that there is only one crack of this size, where fractal
dimension D=2b, NT is the number of cracks.
Seismic event rates: Meredith and Atkinson (1983) showed that acoustic emissions from
tensile subcritical growth experiments exhibited the same frequency-magnitude
distribution as earthquakes, which is expressed in the form:
)(log cc mmbaN (8)
Where N c is the number of magnitudes greater than or equal to m in a unit time interval,
cc mNN 10)( (9)
the event rate for occurrence above a threshold magnitude m c and b is the seismic b
value. Main and Meridedith (1991) explained the proportionality between N and
NT and briefly given in the following form:
Where constant is constant. Seismic event rate of fracture density N T is easily
determined from the N when =1 is assumed.
Seismic b value : The b- value is estimated by using the maximum likelihood method
and standart deviation of the calculated b-value
Nbs / (12)
Where b is the AE b-value, iM is the sum of all event amplitudes in dB and M c is the
lower amplitude cut-off used in the calculation and must be slightly greater then the
threshold amplitude set during the experiment, since electronic threshold represents a
gradual rather than a sudden cut-off in reality (Hatton et al., 1993). N is the total
number of events in the time considered. (Meredith et al., 1990).
Fractal dimension (Dc ) : The fractal dimension of earthquake hypocentres is estimated
using the correlation dimension, D c (Hirata et al., 1987):
Where C(r)=N/n is the correlation integral, N is the number of points in the particular
analysis window separated by a distance less than r, and n is the total number of points
analysed. Here we also estimate the standard error found by linear regression of logC
against log r.
1. We will examine mean energy release rate <G> per unit crack surface area,
seismogenic crack length <c> for the evolution of fractal damage in laboratory rock
fractures as a function of space and time.
2. We will examine seismic wave velocity in laboratory rock fractures as a function of
space and time.
3. We will correlate the parameters of fracture propagation <G>, <c> and seismic
wave velocity of rock samples, of sub-volumes and of selected periods with the known
stress levels in these volumes and these times qualitatively.
4. We will correlate the parameters of fracture propagation and seismic wave velocity
in rocks of different grain sizes since the changes of seismic event rate as much as
and seismic waveforms are suggested to be related with grain sizes (Ksunuse et al.,
1991; Nishizawa et al., 1997).
5. We will estimate the fractal dimension, D, for sub-volumes and for periods with uniform
b-values and compare the b values with the fractal dimension, to determine if the
relationship of D=2b, proposed by Turcotte (1992) for earthquakes, is also valid for AE
in rock samples.
6. Finally, we will attempt to construct models, based on the inferring results during this
project, that may explain spatial and temporal correlation between seismicity and
Geological Survey of Japan Ali Osman Oncel
Edinburgh University Dr.Ian Main
Aggarwal, P.Y., Sykes, L.R.,Armbruster, J.,Sbar, M.L., 1973. Premonitory Changes in
Seismic Velocities and Prediction of Earthquakes, Nature, 241, 101-105.
Jin, A., Aki, K, 1986. Temporal change in coda Q before the Tangshan earthquake of
1976 and Haicheng earthquake 1975, J.Geophys. Res., 91, 665-673.
Jin, A., Aki, K, 1989. Spatial and temporal correlation between coda Q and seismicity
and its physical mechanism, J.Geophys.Res., 94, 14041-14059.
Kusunose, K., X. Lei., O. Nishizawa, and T. Satoh, 1991. Effect of grain size on fractal
structure of acoustic emission hypocenter distribution in granitic rock,
Phy.Eart.Plan.Sci., 67, 194-199.
Liakopoulou-Morris, F., I.G. Main, B.R., Crawford.,B.G.D. Smart, 1994. Microseismic
properties of a homogeneous sandstone duringfault development and frictional
sliding, Geophys. J. Int., 119, 219-230.
Main, I.G., 1991. A modified Griffith criterion for the evolutionof damage with a fractal
distribution of crack lengths: application to seismic event rates and b-values,
Geophys. J. Int., 107, 353-362.
Main, I.G., P.R. Sammonds, and P.G. Meredithi, 1993. Application of a modified Griffith
criterion to the evolution of fractal damage during compressional rock failure,
Geophys. J. Int., 115, 367-380.
Nishizawa, O., Satoh, T., Lei., Kuwahara,Y, 1997. Laboratory studies of seismic wave
propogation in inhomogenous media using a laser doppler vibrometer, Bull.
Seism. Soc. Am., 87, 809-823.
Rikitake, K., Earthquake Prediction, Elsevier, Amsterdam, 1976.
Rikitake, K., 1987. Earthquake precursors in Japan:precursor time and detectability,
Tectonophys., 136, 265-282.
Satoh, T., Kusunose, K, and O. Nishizawa, 1987. A minicomputer system for measuring
and processing AE waveforms-high speed digital recording and automatic
hypocenter determination, Bull. Geol. Surv. Japan, 38, 295-303.
Scholz, C.M., L.R. Sykes, and Y.P. Aggarwal, 1973. Earthquake prediction: a physical
basis, Science, 181, 803-810.
Smith, W.D., 1981. The b-value as an earthquake precursor, Nature, 289, 136-139.
Smith, W.D., 1986. Evidence for precursory changes in the frequency-magnitude b-value,
Geophys.J.R.Astron.Soc., 86, 815-838.
Wyss, M., 1985. Precursors to large earthquakes, Earthquake Prediction Research, 3,
Wyss, M., R.E. Habermann, and J.C. Griesser, 1984. Precursory Seismicity quiescence in
the Tonga-Kermadec arc, J. Geophys. Res., 89, 9293-9304.
Wyss, M., A. Hasegawa, S. Wiemer, and N. Umino, 1998. Quantitavive mapping of
precursory puiescence before the 1989, M7,1 off-Sanriku earthquake, Japan.,
Annali Geophysicae, submitted.
Wyss, M., and A.H. Martyrosian, 1998. Seismic quiescence before the M7, 1988, Spitak
earthquake, Armenia, Geophys. J. Int., 102, submitted.
Wyss, M., and S. Wiemer, 1997. Two current seismic quiescences within 40 km of
Tokyo, Geophys. J. Int., 128, 459-473.
Westerly granite Oshima granite Inada granite
Figure 1. Three types of granites will be used during the rock experiments and their grain size informations
are described as [Nishizawa, 1997]: (a) a fine-grained Westerly granite, grain sizes mostly 1 mm or less; (b)
medium-grained Oshima granite, grain size is distributed mostly in a range from 1 to 5 mm; and (c) coarse-
grained Inada granite, where grain size sometimes exceeds 10mmThree types of granites.
Figure 2. A Schematic load-displacement curve for (0) initial hydrostatic loading and elastic pore closure;
(I) fault nucleation; (II) frictional sliding; and (III) sliding at increased confining pressure. Phase I may be
further split into (a) a quasi-linear elastic phase; (b) a strain-hardening phase; (c) a phase of stable strain
softening and (d) dynamic failure of the specimen (modified after Liakopoulou-Morris, 1994 #1223]
Hydrostatic Post-Fracture Post-Sliding Sliding Under Increased
I II III
AE to fracture
AE for sliding
AE for re-sliding
X :discreate permability &
P-, S1- and S2- velocity
Table 1. Initial confining pressures for dynamic failure and frictional sliding and final
confining pressures for re-sharing for all test specimens.
Confining pressure in Phases
I & II
Confining pressure in
1 3000 [20.7] 4000 [27.6]
2 5000 [34.5] 6000 [41.4]
3 7000 [48.3] 8000 [55.2]