Interrelationship between seismicity and seismic velocity during compression rock failure

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I have just found a research proposal which I had prepared for a research support in 1999, but it did not come out with any result.

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Interrelationship between seismicity and seismic velocity during compression rock failure

  1. 1. 1 RESEARCH PROPOSAL 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 Contents ABSTRACT BACKGROUND Fracture growth Seismicity changes Seismic Waves OBJECTIVES IMPORTANCE EXPERIMENTAL PROCEDURE METHODS of INVESTIGATION Mean Energy release rate <G> Mean crack length <c> Seismic event rates Seismic b value Fractal dimension D EXPECTED RESULTS PROJECT PERSONEL REFERENCES FIGURES
  2. 2. 2 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 Earth. BACKGROUND: Fracture growth 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 : n KKVV )/( 00 (1) ' )/(/ 000 n KKNNN  (2) 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), n ' =29.1 (0.977), with correlation coefficients in brackets (Main and Meridedith, 1991). Seismicity Changes 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
  3. 3. 3 concentration measured relative stress intensity factor K/K c , where K c is the fracture thoughness as: )]/())[(( 0000 KKKKbbbb cc  (3) K 0 is a threshold stress intensity for subcritical crack growth, below which no crack healing takes place. Seismic Waves 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., [1987]. 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
  4. 4. 4 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 s 1 ) 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  cBAUG 22 /  (4) 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                   D D cc cc D D cc )/(1 )/(1 1 minmax 1 minmax min (5)
  5. 5. 5 or         D cc cc cc )/(1 )/ln( minmax minmax min (6) 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): )1/(1 minmax )(   D TDNcc (7) 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, a 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: N=NT (10)
  6. 6. 6 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 (Aki, 1965):  ci 10 NMM eN =b  log (11) 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): c r D = C(r) r lim log log0 (13) 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. EXPECTED RESULTS: 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.
  7. 7. 7 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 seismic wave. PROJECT PERSONEL Geological Survey of Japan Ali Osman Oncel Osamu Nishizawa Xinglin Lei Edinburgh University Dr.Ian Main REFERENCES: 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.
  8. 8. 8 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, 519-543.
  9. 9. 9 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.
  10. 10. 10 FIGURES: 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 Confining Pressure AXIALLOAD I II III AE to fracture AE for sliding AE for re-sliding 0 a b c d  AE :acoustic emission logging interval X :discreate permability & P-, S1- and S2- velocity measurements AXIAL DISPLACEMENT
  11. 11. 11 Table 1. Initial confining pressures for dynamic failure and frictional sliding and final confining pressures for re-sharing for all test specimens. Specimen (Test) Number Confining pressure in Phases I & II (psi) [Mpa] Confining pressure in Phase III (psi) [Mpa] 1 3000 [20.7] 4000 [27.6] 2 5000 [34.5] 6000 [41.4] 3 7000 [48.3] 8000 [55.2]

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