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Experimental study of velocity characteristic before rock fracture
Abstract
In order to measure the small change of velocity before rock fracture, the velocity measurement precision must be improved, the methods including digital wave form, the wave stacking, cross correlation and Subsample delay time estimate were used, the precision of time and velocity reached to 0.001 micro second and 1 m/s respectively. The delay time was measured as the stress increase with the interval of 0.17 MPa, then the rule of velocity as stress increase was obtained. Experimental results showed the velocity had the maximum value at the rock strength of 0.98, after that the velocity decreased about 30 m/s to fracture. The power of wave at main frequency was calculated and had the same characteristic with velocity, it was considered the changes may be caused by rock dilation. The square error of delay time was discussed by using the fluctuation model.
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In 1997, Geller et al. wrote `Earthquakes Cannot Be Predicted' because scale invariance is ubiquitous in self-organized critical systems, and the Earth is in a state of self-organized criticality where small earthquakes have some probability of cascading into a large event. Physically however, large earthquakes can only occur if there is sufficient stress-energy available for release by the specific earthquake magnitude. This stress dependence can be exploited for stress-forecasting by using shear wave splitting to monitor stress-accumulation in the rock mass surrounding impending earthquakes. The technique is arguably successful but, because of the assumed unpredictability, requires explicit justification before it can be generally accepted. Avalanches are also phenomena with self-organized criticality. Recent experimental observations of avalanches in 2-D piles of spherical beads show that natural physical phenomena with self-organized criticality, such as avalanches, and earthquakes, can be predicted. The key to predicting both earthquakes and avalanches is monitoring the matrix material, not monitoring impending source zones.
We have conducted a series of cross-well experiments to continuously measure in situ temporal variations in seismic velocity at two test sites: building 64 (B64) and Richmond Field Station (RFS) of the Lawrence Berkeley National Laboratory in California. A piezoelectric source was used to generate highly repeat- able signals, and a string of 24 hydrophones was used to record the signals. The B64 experiment was conducted utilizing two boreholes 17 m deep and 3 m apart for � 160 h. At RFS, we collected a 36-day continuous record in a cross-borehole facility using two 70-m-deep holes separated by 30 m. With signal enhancement techniques we were able to achieve a precision of � 6.0 nsec and � 10 nsec in delay-time esti- mation from stacking of 1-hr records during the � 7- and � 35-day observation pe- riods at the B64 and RFS sites, which correspond to 3 and 0.5 ppm of their travel times, respectively. Delay time measured at B64 has a variation of � 2 lsec in the 160-hr period and shows a strong and positive correlation with the barometric pres- sure change at the site. At RFS, after removal of a linear trend, we find a delay-time variation of � 2.5 lsec, which exhibits a significant negative correlation with baro- metric pressure. We attribute the observed correlations to stress sensitivity of seismic velocity known from laboratory studies. The positive and negative sign observed in the correlation is likely related to the expected near- and far-field effects of this stress dependence in a poroelastic medium. The stress sensitivity is estimated to be � 106/ Pa and � 107/Pa at the B64 and RFS site, respectively.
Measuring stress changes within seismically active fault zones has been a long-sought goal of seismology. One approach is to exploit the stress dependence of seismic wave velocity, and we have investigated this in an active source cross-well experiment at the San Andreas Fault Observatory at Depth (SAFOD) drill site. Here we show that stress changes are indeed measurable using this technique. Over a two-month period, we observed an excellent anti-correlation between changes in the time required for a shear wave to travel through the rock along a fixed pathway (a few microseconds) and variations in barometric pressure. We also observed two large excursions in the travel-time data that are coincident with two earthquakes that are among those predicted to produce the largest coseismic stress changes at SAFOD. The two excursions started approximately 10 and 2 hours before the events, respectively, suggesting that they may be related to pre-rupture stress induced changes in crack properties, as observed in early laboratory studies.
Creep experiments with a granite sample were performed by using graded loading method. The creep curve during the gradual loading process and creep fracture curve under uniform stress were obtained. The parameters, such as Young's modulus, creep value and creep rate, were analyzed with Load/Unload response ratio (LURR) method. There are two different types of response ratio curves, but the LURR value was near 1 at low stress or in elastic deformation phase, then the LURR was increasing at high stress or in rock dilation phase. The whole creep fracture curve under uniform stress was decomposed to three phase: instantaneous, steady and accelerating creep, with the ratio of duration time of each phase over whole time being about 18%, 75% and 7% respectively. The creep rate was increasing remarkably in accelerating phase and it was a useful parameter for predicting the creep fracture.
Time delay estimation (TDE) is commonly performed in practice by crosscorrelation of digitized echo signals. Since time delays are generally not integral multiples of the sampling period, the location of the largest sample of the crosscorrelation function (ccf) is an inexact estimator of the location of the peak. Therefore, one must interpolate between the samples of the ccf to improve the estimation precision. Using theory and simulations, we review and compare the performance of several methods for interpolation of the ccf. The maximum likelihood approach to interpolation is the application of a reconstruction filter to the discrete ccf. However, this method can only be approximated in practice and can be computationally intensive. For these reasons, a simple method is widely used that involves fitting a parabola (or other curve) to samples of the ccf in the neighborhood of its peak. We describe and compare two curve-fitting methods: parabolic and cosine interpolation. Curve-fitting interpolation can yield biased time-delay estimates, which may preclude the use of these methods in some applications. The artifactual effect of these bias errors on elasticity imaging by elastography is discussed. We demonstrate that reconstructive interpolation is unbiased. An iterative implementation of the reconstruction procedure is proposed that can reduce the computation time significantly.
Correlation interpolation is introduced as a method to determine the displacement of moving biological tissue on the basis of a sequence of ultrasonic echo signals. The echo signal is sampled along the echo depth with approximately 4 samples per average high frequency period. Sampling in time occurs with the pulse repetition frequency. The necessary information is extracted from a crosscorrelation function between successive signals, which is modelled using four parameters. The parameters are estimated from five calculated correlation sums and the shift with maximum correlation is determined. In contrast to existing techniques, the performance of this method is determined mainly by the number of samples used, while the ratio of the number of samples in depth and time is irrelevant. Using 64 samples at a signal-to-noise power ratio of 10, the standard deviation of the error in the determination of the shift in depth is 0.08 sampling intervals. As in many other methods, the width of the aliasing interval equals the mean frequency period.