Stress associated coda attenuation from ultrasonic waveform measurements

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 34, L09307, doi: /2007gl029582, 2007 Stress associated coda attenuation from ultrasonic waveform measurements Meng-Qiu Guo 1 and Li-Yun Fu 1 Received 8 February 2007; revised 29 March 2007; accepted 2 April 2007; published 5 May [1] The theoretical and practical exploration of stress changes from seismic waves has been the focus of recent debate within the scientific community because of its direct implications on earthquake forecasts and seismic hazards. Propagating in underground structures, wave velocity and attenuation contain information on stress changes of the Earth s interior as a result of changes in the physical state of materials. Seismic coda, which consists of a superposition of incoherent scattered waves, is known to reflect smallscale random heterogeneities in the earth medium. In this article, we investigate the coda attenuation under different effective stresses using laboratory measurements to increase our understanding of the dependence of acoustic-coda attenuation on stress variations in rocks. Citation: Guo M.-Q., and L.-Y. Fu (2007), Stress associated coda attenuation from ultrasonic waveform measurements, Geophys. Res. Lett., 34, L09307, doi: /2007gl Introduction [2] The stress distribution and changing rate in the Earth s crust and upper mantle has been extensively studied in geomechanics during the past several decades. Inferring stress changes from seismic waves has been explored with static and dynamic moduli but confused by the complex relationships between them [Simmons and Brace, 1965; Walsh and Brace, 1966; Cheng and Johnston, 1981]. Generally, the manner in which waves catch information on static stress is associated with variations in the physical state of materials induced by stress changes. There are two major reasons why the seismic energy decays as it propagates through the earth medium: intrinsic attenuation and scattering attenuation. A great number of studies have assessed the dependence of intrinsic attenuation on stress variations in rocks based on laboratory measurements [Khaksar et al., 1999; Mavko and Nur, 1979; Christensen and Wang, 1985]. However, compared to large-scale heterogeneous structures, the small-scale random heterogeneities, which could be measured by scattering attenuation, may be more sensitive to stress changes as a result of changes in the physical state of materials. [3] Seismic coda is composed of a superposition of incoherent scattered waves. Aki [1969] proposed it as direct evidence of random heterogeneities in the lithosphere. It has been observed that the coda spectrum of small earthquakes is independent of earthquake size, epicentral distance, and the path between station and epicenter [Sato, 1977]. This 1 Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China. Copyright 2007 by the American Geophysical Union /07/2007GL suggests that the coda part of a seismogram is due to an average scattering effect of the medium in the region near the source and station. Therefore, seismic coda monitoring could provide information about the temporal change in fractures and attenuation caused by changes in tectonic stress during the earthquake cycle [Chouet, 1979]. Coda waves with frequencies in the order of 1 Hz were thought to be a useful seismological tool to estimate the strength of random heterogeneity [Wu and Aki, 1985]. In the range of 1 to 30 Hz, the envelope of entire seismograms, including the coda portion, can be modeled to learn more about the heterogeneity of the earth s lithosphere. Therefore in the past decades, coda attenuation has been commonly measured in a frequency range between 1 to 30 Hz. There have been some attempts to reveal shorter-wavelengths using seismogram envelopes containing frequencies of more than several hundred Hz [Gibowicz and Kijko, 1994; Nishizawa et al., 1997]. The envelopes of seismograms of artificial sources have been used to study scattering processes in the frequency range in the order of khz revealing information about inhomogeneity on a scale of meters [Fehler, 1982]. However, the tail portion of ultrasonic waveform logs are often ignored, possibly because of the sample-size limitation of experiments and some unknown factors of inhomogeneity in rocks. [4] With the availability of high-precision ultrasonic techniques, it is now possible to focus on ultrasonic coda. The motivation of this study is to test the influence of stress changes on coda attenuation, and attempt to discuss the mechanism of coda attenuation at ultrasonic frequencies. Ultrasonic waveforms are measured under triaxial loading conditions with pore pressure rising incrementally from 5 to 60 MPa at a constant confining pressure of 65 MPa. The frequency dependent values of coda Q (Q c ) are calculated under different stress conditions by employing the timedomain coda-decay method of a single back-scattering model. Subsequently the intrinsic attenuation quality factors Q P and Q S are calculated from the waveform data using the spectral ratio methods of Toksöz et al. [1979]. Comparisons of the intrinsic and coda attenuations induced by stress variations show that both Q P, Q S and Q c increase with increasing effective stress, but Q c shows a greater sensitivity to pore pressure than Q P and Q S. 2. Rock Properties and Physical Setup [5] The sample used is a high porosity (19.7%), moderate permeability (43.5 md) massive sandstone. It comprises moderately sorted, sub-angular to sub-rounded quartz grains ( mm diameter) in point contact with one another. Pore size is variable, ranging from about 0.1 mm up to about 0.4 mm. The minor clays and glauconite that are L of5

2 Figure 1. Schematic of the experimental apparatus. Labels indicate: a, transmitting piezoelectric transducer; b, pore fluid inlet; c, jacketed rock core sample; d, confining pressure control; e, downstream pore fluid outlet; f, receiving piezoelectric transducer. present generally reside in pores, and most grain boundaries are direct contacts between rigid framework grains. Intragrain fractures are rare although grain boundary cracks are ubiquitous. [6] The physical experimental apparatus is shown in Figure 1. The experimental setup consists of a digital oscilloscope (Tektronix TDS 420 A) and a pulse generator (Panametrics 5077PR). Referring to the work by American Society for the Testing of Materials [2002], the length-todiameter ratio of the rock specimen is recommended between 2and2.5toavoidendconstrainteffects[Franklin and Dusseault, 1989]. In this investigation, the core is cut to diameters of 40 mm and lengths of 80 mm, and is jacketed with rubber tubing to isolate it from the confining pressure. PZT-crystals mounted on steel endplates are used to generate P and S waves. The receiving transducer is connected to the digitizing board in the PC through a signal amplifier. A pore fluid inlet in each endplate allows passage of pore fluids through the sample. Testing is performed under ambient pressure conditions along the stress path with a constant confining pressure of 65 MPa while the pore pressure increases incrementally from 5 to 60 MPa. Ultrasonic measurements comprise full waveform recordings of both transmitted P waves and S waves at nominal centre frequencies of 600 khz. Waveforms are recorded after pore pressure equilibration at each effective stress increment. 3. Data Analysis [7] The simplest model to describe the coda is the single scattering model of Aki [1969]. The latter attempts to explain the time dependence of the scattered energy density at source location in 3-D space and the relationship between scattering and coda wave amplitude for cases in which a lapse time measured from the origin time is much shorter than the mean free time. The amplitude of coda waves at a lapse time of t seconds from the origin time for band-pass filtered seismograms at the central frequency f is given by the single back-scattering model as: Aðf; tþ ¼ KðfÞt a e pft=qc where K ( f ) is the coda source factor at frequency f, independent of time and radiation pattern, Qc(f ) is the quality factor of coda waves, a is the geometrical spreading parameter having one value out of 1.0, 0.5 or 0.75 for body waves, surface waves or diffusive waves, respectively [Sato and Fehler, 1998]. As the coda wave is a backscattered body wave, put a = 1 in equation (1) and take the logarithm as follows: ln Aðf; tþ ¼ ln kðfþ lnðþ t pf ðf Þ t Q c can be determined from the slope of a least-squares-fitting straight line in the plot of ln(a( f, t)t) versus t. [8] The direct P and S waves and reflected waves are identified by their travel times. Generally, the lapse times are selected at 2ts, with ts the S wave time, to avoid data of the direct S wave and to utilize the minimum possible sampling volume for Q c values [Havskov et al., 1989]. In the present study, the time envelope for the S-coda decay observation is taken at twice the time of the S wave from the origin time of the event (Figure 2b), while P-coda is windowed as 3 times the time of direct P wave from the origin time because there is still a direct S wave carried after the direct P wave (Figure 2a). Also, the window length is made short to reduce contamination of multiple reflections from the side ends and the reverberations between the sample surfaces, which cannot be absolutely excluded from the earlier portion of waveforms. The calculation of Q c (f) from acoustic amplitudes is shown in Figures 2c and 2d along with the plot of the coda window selected. Q c ð1þ ð2þ 2of5

3 Figure 2. (a) Unfiltered P wave data trace with coda window. (b) Unfiltered S wave data trace with coda window. PP is pore pressure. (c) RMS amplitude values multiplied with lapse time along with best square fits of selected P-coda window filtered at a central frequency of 600 khz. (d) RMS amplitude values multiplied with lapse time along with best square fits of selected S-coda window filtered at a central frequency of 600 khz. The Qc is determined from the slope of best squareline. [9] For comparison purposes, intrinsic attenuation quality factors Q P and Q S are calculated using the spectral ratio method. This methodology is described in detail by Toksöz et al. [1979], but a short, qualitative review will be provided here. The method is based on a comparison between pulse shapes observed in a reference material and in the sandstone sample of the same geometry. Aluminum is chosen as a reference material in this investigation for its virtue of a very high Q, approaching 10 4, and it is a reasonable match to the average sandstone Poisson s ratio. ln A 1ðf Þ p ¼ p xf þ ln G 1 ð3þ A 2 ðf Þ Q 2 V 2 Q 1 V 1 G 2 [10] The subscripts 1 and 2 refer to rock sample and reference material respectively. A is frequency dependent amplitude, f is frequency (Hz), G(x) is a geometrical factor which includes spreading, internal reflections, etc. If the geometric factors, G, are identical in both rock and reference material and the reference material has a very high Q then: ln A 1ðf Þ ¼ p xf ðf Þ Q 1 V 1 A 2 [11] Q can subsequently be obtained from least squares fits to the slope of the natural log of the ratio of spectral amplitudes of pulse shapes in rock sample and reference material. In this paper, Q is obtained in the transducer bandwidth, 400 khz to 1 MHz. Because the sample has a relatively low clay content, the linear fits are good, with correlation coefficients R 2 larger than This implies a ð4þ constant Q-type behaviour, which is typical of grain contact friction. 4. Results and Discussion [12] The quality factor Q c, under a number of different stress conditions, is estimated to assess the effect of stress 1 changes on coda attenuation. Figure 3 shows the plot of Q c and effective stress. Coda attenuation appears sensitive to the stress change and obviously shows a strong linear correlation. Intrinsic attenuation Q 1 P and Q 1 S are also plotted in Figure 3. Since the scattered wave is a signalinduced wave, scattering redistributes wave energy within the medium. It is therefore interesting to compare the attenuation rate against the effective stress between coda waves and direct waves. Figure 3 indicates that both intrinsic attenuation and coda wave attenuation increase as effective stress decreases. When effective stress is high, Q c values are close to the intrinsic attenuation quality factors Q P and Q S, but with increasing pore pressure, effective stress decreases, and coda waves attenuate bigger and faster than direct P and S waves. [13] For local earthquakes, the Q factor increases with frequency [Mitchell, 1981] through the relation: f n Q ¼ Q 0 where Q 0 is the quality factor at the reference frequency, f 0, and n is the frequency parameter. f 0 is generally 1Hz, and n varies from region to region on the basis of heterogeneity of f 0 ð5þ 3of5

4 Figure 3. Plots of intrinsic attenuation Q 1 P, Q 1 S, and coda attenuation Q 1 C against effective stress. Q 1 CP is P-coda attenuation, and Q 1 CS is S-coda attenuation. al. [2002] evaluated the effects of short-wavelength random heterogeneity on seismic waves by using laboratory-scale physical models. In this paper we present the attenuation of coda using laboratory measurements, and correlate them with measurements of intrinsic attenuation. [16] Aki [1985] used the temporal decay of seismic coda as a measure of scattering in the Earth. He proposed to use the change of coda Q to monitor changes in stress in the subsurface [Aki and Chouet, 1975; Jin and Aki, 1986]. Attenuation inferred from the decay rate of the coda [Aki and Chouet, 1975; Singh and Herrmann, 1983] is a combination of scattering and intrinsic attenuation. As recognized in our study, scattering attenuation is more sensitive to stress changes as a result of varieties in the physical state of materials. As is shown in Figure 3, pore pressure build-up due to injection leads to a decrease in effective pressure and an increase in rock compliance. Increased pore pressure would compress the pore lining clays adjacent to the framework grain contacts [Berge et al., 1993; Wang, 2001], and hence increase both the intrinsic attenuation and scattering attenuation. However, scattering attenuation increases faster. As a means to obtain information about the medium [Aki, 1981]. This relation indicates that the attenuation of seismic waves with the passage of time (distance from source) is different for different frequencies. In the present study, the attenuation of coda waves is calculated at six central frequencies, 0.4 MHz 0.9 MHz, after being band-pass filtered. [14] However, our calculations at ultrasonic frequencies show a different result. Q c is plotted against frequency in Figure 4 to quantitatively examine the relationship between coda attenuation and frequency under different effective stresses. It is found Q c peaks at around the central frequency and decreases with both increasing and decreasing frequency. For P-coda waves, Q c slowly increases with increasing frequency below 600 khz, after which the trends changes to a decrease with increasing frequency (Figure 4a). For S- coda, this maximum value appeared at 700 khz. In addition, this maximum value increases with an increase of effective stress. Due to the shorter wavelength of the S wave in comparison with the P wave, the scattering of the S-coda was much stronger and more stable (Figure 4b). The deviation of our laboratory result and field data may due to the variation of coda attenuation in different frequency ranges [Ibanez et al., 1993]. 5. Concluding Remarks [15] Coda waves sample a volume of rock within a region, and therefore measurements of coda characteristics may be more sensitive to short-wavelength heterogeneity than measurements of velocity or attenuation using direct waves which only sample a 1-D ray path between the source and receiver [Aki, 1985]. When investigating structures of the Earth s interior by seismic methods, short-wavelength heterogeneity is often referred to as a random heterogeneity which generates incoherent scattered waves when seismic waves propagate through a heterogeneous medium. Sivaji et Figure 4. (a) Comparison of P-coda wave attenuation under different effective stress against frequency. (b) Comparison of S-coda wave attenuation under different effective stress against frequency. 4of5

5 average media properties, coda attenuation is a more precise way to assess small-scale changes in the physical state of materials induced by stress changes, which will have its application in earthquake forecasting and seismic hazard assessments. [17] Acknowledgments. This work was supported by the National Nature Science Foundation of China under project The authors would like to thank Xiang-Yang Wu (Laboratory of High Temperature and High Pressure Geodynamics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing) for his help and constructive comments. GRL anonymous reviewers are thanked for constructive comments that improved the original manuscript. References Aki K. (1969), Analysis of seismic coda of local earthquakes as scattered waves, J. Geophys. Res., 74, Aki K. (1981), Source and scattering effects on the spectra of small local earthquakes, Bull. Seismol. Soc. Am., 71, Aki K. (1985), Theory of earthquake prediction with special reference to monitoring of the quality factor of lithosphere by the coda method, Earthquake Predict. Res., 3, Aki K., and B. Chouet (1975), Origin of the coda waves: Source, attenuation, and scattering effects, J. Geophys. Res., 80, American Society for the Testing of Materials (2002), Practice for preparing rock core specimens and determining dimensional shape tolerances, ASTM Stand. 4543, Philadelphia, Pa. Berge P. A., J. G. Berryman, and B. P. Bonner (1993), Influence of microstructure on rock elastic properties, Geophys. Res. Lett., 20, Cheng C. H., and D. H. Johnston (1981), Dynamic and static moduli, Geophys. Res. Lett., 8, Chouet B. (1979), Temporal variation in the attenuation of earthquake coda near Stone Canyon, Calif., Geophys. Res. Lett., 6, Christensen N. I., and H. F. Wang (1985), The influence of pore and confining pressure on dynamic elastic properties of Berea sandstone, Geophysics, 50, Fehler M. (1982), Interaction of seismic waves with a viscous liquid layer, Bull. Seismol. Soc. Am., 72, Franklin J. A., and M. B. Dusseault (1989), Rock Engineering, McGraw- Hill, New York. Gibowicz S. J., and A. Kijko (1994), An Introduction to Mining Seismology, Elsevier, New York. Havskov J., S. Malone, D. McClurg, and R. Crosson (1989), Coda Q for the state of Washington, Bull. Seismol. Soc. Am., 79, Ibanez J. M., E. Del Pezzo, J. Morales, M. Martini, D. Patané, F. De Miguel, and F. Vidal (1993), Estimates of coda-q using anon-linear regression, J. Phys. Earth, 138, Jin A., and K. Aki (1986), Temporal change in Qc before the Tangshan earthquake of 1976 and the Haicheng earthquake of 1975, J. Geophys. Res., 91, Khaksar A., C. M. Griffiths, and C. McCann (1999), Compressional- and shear-wave velocities as a function of confining stress in dry sandstones, Geophys. Prospect., 47, Mavko G. M., and A. Nur (1979), Wave attenuation in partially saturated rocks, Geophysics, 44, Mitchell B. J. (1981), Regional variation and frequency dependence of Q b in the crust of the United States, Bull. Seismol. Soc. Am., 71, Nishizawa O., T. Satoh, X. Lei, and Y. Kuwahara (1997), Laboratory studies of seismic wave propagation in inhomogeneous media using a laser Doppler vibrometer, Bull. Seismol. Soc. Am., 87, Sato H. (1977), Energy propagation including scattering effects, single isotropic scattering approximation, J. Phys. Earth, 25, Sato H., and M. Fehler (1998), Seismic Wave Propagation and Scattering in the Heterogeneous Earth, Springer, New York. Simmons G., and W. F. Brace (1965), Comparison of static and dynamic measurements of compressibility of rocks, Geophysics, 70, Singh S., and R. B. Herrmann (1983), Regionalization of crustal coda Q in the continental United States, J. Geophys. Res., 88, Sivaji C., O. Nishizawa, G. Kitagawa, and Y. Fukushima (2002), A physicalmodel study of the statistics of seismic waveform fluctuations in random heterogeneous media, Geophys. J. Int., 148, Toksöz M. N., D. H. Johnson, and A. Timur (1979), Attenuation of seismic waves in dry and saturated rocks, I. Laboratory measurements, Geophysics, 44, Walsh J. B., and W. F. Brace (1966), Elasticity of rock: A review of some recent theoretical studies, Rock Mech. Eng. Geol., 4, Wang Z. (2001), Fundamentals of seismic rock physics, Geophysics, 66, Wu R. S., and K. Aki (1985), Scattering characteristics of elastic waves by an elastic heterogeity, Geophysics, 50, L.-Y. Fu and M.-Q. Guo, Institute of Geology and Geophysics, Chinese Academy of Sciences, P.O. Box 9825, Beijing , China. (tatilia@126.com) 5of5