Earthquake Research in China  2019, Vol. 33 Issue (3): 431-436     DOI: 10.19743/j.cnki.0891-4176.201903002
Monitoring Contact State of Laboratory Fault with Coda Transmission Waves
XIE Fan, REN Yaqiong, HOU Jinxin
Institute of Geophysics, China Earthquake Administration, Beijing 100081, China
Abstract: We monitored the amplitude changes of coda transmission waves around 500kHz across the frictional interface of a simulated 1.5-meter-long fault during normal stress holding test. We find that the amplitude of coda transmission waves increases with the logarithm of stationary contact time. Localized increase amounted to a level ranging from 4% to 16% along the fault is observed during the 1-hour experiment. We discuss that the frictional strength at mesoscopic scale, which is related to the amplitude of coda transmission waves, is responsible for the phenomenon. Combining the reported method with other complementary approaches will enhance the understanding of fault mechanism either at laboratory or on-site applications.
Key words: Coda transmission waves     Laboratory fault     Frictional contact area

INTRODUCTION

Due to its inaccessibility from Earth's surface, one can infer the basic mechanical behavior of tectonic faults by quantifying velocity changes from phase shift in the signal of the approximate empirical Green's functions that are estimated from seismic noise correlation at different times (Brenguier F. et al., 2008; Bouchon M. et al., 2011). Such methodology has two major advantages: it can be done passively at lowest costs, which is essential for long-term observation; it has high sensitivity to the changes at depth because the multiply scattered coda waves densely resample the microstructural changes occurring at the solid Earth.

Nevertheless, noise-based coda wave monitoring of crust faults still faces substantial challenges (Mao Shujuan et al., 2019) (e.g. increase temporal resolution, isolating tectonic changes from multiple origins etc.). Among these challenges, the most crucial one is that the magnitude of empirical Green's function which conveys information about frictional properties (e.g. real surface contact stiffness) of the fault, cannot be fully reconstructed from seismic noise correlation (Campillo M. et al., 2003).

The physical processes that dictate the earthquake occurring at the fault interface can be simulated at laboratory scale. Laboratory studies provide accumulating evidence for relating changes in direct wave speed and acoustic transmissivity associated with a range of fault slip behaviors via ultrasound techniques (Yoshioka N. et al., 2006; Knuth M. W. et al., 2013). Moreover, recent works showing clear precursors based on wave speed to earthquake-like frictional failure could provide fundamental insights into fault mechanisms that precede failure (Nagata K. et al., 2008; Scuderi M. M. et al., 2016).

Unlike the passive cross-correlation configuration, coda waves could be fully reconstructed (e.g. amplitude, phase, attenuation) in active pulse-echo configuration (Larose E. et al., 2006; Xie Fan et al., 2018) which can offer promising means to investigate frictional evolution of laboratory fault. However, compared with velocity changes of coda waves, little attention is paid for the amplitude evolution of coda waves on laboratory fault.

In this paper, by taking advantage of fully reconstructed coda waves at ultrasonic frequencies, we perform a laboratory experiment in which coda waves are transmitted across a simulated 1.5m fault. We focus on in-situ monitoring of localized contact state of the fault interface by measuring the changes in the amplitudes of coda transmission waves during normal stress holding test.

1 MATERIALS AND METHODS 1.1 Sample Preparation

We use natural granite rock with dimensions of 1.1m × 1.1m × 0.15m from the Fangshan District, Southwest Beijing, China. The basic properties of the granite sample are as follows: P-wave speed CP=4.12km/s, S-wave speed CS=2.34km/s and the mass density ρ=2.88 × 103kg/m3. A 1.5m long simulated fault is cut diagonally through the sample. The roughness is measured by a profilometer with an average peak-to-trough surface of 10μm.

1.2 Experimental Apparatus and Procedure

As illustrated in Fig. 1, the experiment is performed in a meter-scale biaxial loading apparatus which is capable to accommodate a 1.5m square and 1m thick specimen. The apparatus consists of horizontal load frames with a servo control system to generate forces of σ1 and σ2, the principle stresses on the fault surface.

 Fig. 1 Sketch map of the biaxial loading apparatus, sample geometry, and transducers setup (black transducers labeled from 2 to 16 as receivers, and one single white (label 1) transducer as a source

As illustrated in Fig. 3(a), we perform normal stress holding test with the fault placed in contact under constant normal stress of 750kN (0.5MPa) using force-feedback servo control during 3600s for σ1 and σ2 individually. Before the test, we performed a few running-in stick-slip experiments to avoid significant changes in the fault surface in a statistical sense.

 Fig. 2 (a) The coda transmission waveforms recorded from 15# receiver and (b) its measured amplitude A by deriving the envelop of energy curve using Hilbert transform. The red line indicates the arrival time of amplitude

 Fig. 3 (a) Differential stress and displacement in Fig. 2 at σ1 (σ2 respectively) as a function of loading time. The grey area covers the time for perform normal stress holding test. (b) The coda transmission waves from 10# to 16# receiver is plotted along the fault in SW-NE direction (c) the changes in amplitudes ratio of the coda transmission waves as a function of contact time
1.3 Coda Transmission Measurements

We measure coda transmission waves within the fault zone using 16 piezo-ceramic transducers (PAC R15) which are evenly distributed, 141mm apart from the interface, on both side of the fault at the top of the sample. As illustrated in Fig. 1, the 15 black transducers (labeled 2 to 15) serve as receivers, while the single white transducer (labeled 1) at the center serves as a source. The source transmitter is driven by a 90 Vpp pulse at central frequency of 500kHz once every 30s, the 5ms long received signals are simultaneously pre-amplified and recorded at a sampling frequency of 2MHz using 14-bit Verasonics data acquisition system. The source-receiver distance and the emitting central frequency, together, they ensure a strong multiple scattering diffuse field in such polycrystalline/multi-composite granite sample.

The amplitude A of coda transmission waves (c(t)) is evaluated at eight transducers (10#, 11#, 12#, 13#, 2#, 14#, 15#, 16#) in time domain by deriving the envelop of energy curve using Hilbert transform (H(·)) for which a maximum quantity of energy is transmitted:

 $\mathrm{A}=arg \max (\mathrm{H}(\sqrt{\mathrm{c}^{2}(t)}))$ (1)

where t is the propagation time of the coda transmission waves.

2 RESULTS

As an example, Fig. 2(a) shows the amplitude of the coda transmission waves from a single transducer (15#) measured by the proposed method. We measure amplitude of coda transmission waves as a function of contact time across the fault.

As illustrated in Fig. 3(b), the coda transmission waves across the fault are plotted in SW-NE direction at the start of contact time. We can see clearly that the diffuse energy distribution across the fault is not homogeneous, say specifically, the transmission energy is higher in both end of SW and NE, while weaker in the middle of the fault despite only a part of energy is transmitted, with the remaining reflected. It suggests an non uniform distribution of the contact state at the interface along the simulated fault. Fig. 3(c) shows the change in amplitude ratio which denotes the amplitude of coda transmission waves normalized by the amplitude of the first recorded wave. We see clearly that the amplitude ratio increases proportional to the logarithm of stationary contact time which is consistent with the observed results at both laboratory (Yoshioka N. et al., 2006; Knuth M. W. et al., 2013) and field (Brenguier F. et al., 2008).

It is interesting to note that the increase in amplitude varies from one receiver to another. After the contact duration of 3600s, the maximum increase in amplitude ration (~16%) is found at 13# transducer, which is located at approximately the middle of the fault, while the minimum increase in amplitude ration (~4%) is found at 10# transducer, which is located at the SW end of the fault.

This suggests that the frictional strength of real contact area where transmission energy initially weaker increases more rapid with stationary contact time, resulting in a more rapid increase in stiffness of contacting surfaces of the fault. This is consistent with the others' experimental observations (Nagata K. et al., 2008).

3 DISCUSSION

We acknowledge that the increase in amplitude of coda transmission waves is similar to the acoustic transmissivity of direct waves increases with the stiffness of the real contact area of the interface, which could quantify the frictional strength along the fault. The explanations are compatible with the widely accept theory of rate and state-dependent friction (RSF) law which states that the internal state of frictional strength is proportional to normal stress and increasing with an effective contact time (Ruina A., 1983; Nagata K. et al., 2008). The acoustic transmissivity of direct waves is related to the associated frictional strength (Yoshioka N. et al., 2006; Nagata K. et al., 2008).

Which, if any, of the possible explanation for the increase of amplitude of direct transmission waves with stationary contact time is applicable to the observations of coda transmission waves described above is not yet entirely clear. The mesoscopic physics of asperities which affect the diffuse fields seems to offer an attractive explanation of the observed results (Johnson P. A. et al., 2005). It worth to note that the changes in weak contacts of the asperities are supposed to be responsible for the main contribution, especially for such high frequency coda transmission waves. However, the exact physics of such theories at mesoscopic scales are still an ongoing project.

4 CONCLUSION

In this study, we monitor the changes of amplitude of coda transmission waves at about 500kHz across the frictional interface of simulated 1.5m long fault during normal stress holding test. The major findings obtained are:

(1) We observed that the amplitude of coda transmission waves increased with the logarithm of stationary contact time.

(2) Localized increase amounted range from 4% to 16% along the fault is observed after about 1-hour normal stress holding test.

(3) We discuss the frictional strength of asperities at mesoscopic scale which related the coda transmission waves is responsible for this phenomenon.

The highly sensitivity of amplitude of coda transmission waves is a proof of concept to investigate the frictional earthquake-like failure (e.g., stick-slip) at laboratory scale as well as large-scale seismic applications, potentially including active fault monitoring in future.

ACKNOWLEDGMENTS

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

REFERENCES
 Bouchon M., Karabulut H., Aktar M., Özalaybey S., Schmittbuhl J., Bouin M.P.Bouchon M., Karabulut H., Aktar M., Özalaybey S., Schmittbuhl J., Bouin M.P. Extended nucleation of the 1999 MW7.6 Izmit earthquake[J]. Science, 2011, 331(6019): 877-880. DOI:10.1126/science.1197341 Brenguier F., Campillo M., Hadziioannou C., Shapiro N.M., Nadeau R.M., Larose E.Brenguier F., Campillo M., Hadziioannou C., Shapiro N.M., Nadeau R.M., Larose E. Postseismic relaxation along the San Andreas fault at Parkfield from continuous seismological observations[J]. Science, 2008, 321(5895): 1478-1481. DOI:10.1126/science.1160943 Campillo M., Paul A.Campillo M., Paul A. Long-range correlations in the diffuse seismic coda[J]. Science, 2003, 299(5606): 547-549. DOI:10.1126/science.1078551 Johnson P.A., Jia XiaopingJohnson P.A., Jia Xiaoping. Nonlinear dynamics, granular media and dynamic earthquake triggering[J]. Nature, 2005, 437(7060): 871-874. DOI:10.1038/nature04015 Knuth M.W., Tobin H.J., Marone C.Knuth M.W., Tobin H.J., Marone C. Evolution of ultrasonic velocity and dynamic elastic moduli with shear strain in granular layers[J]. Granular Matter, 2013, 15(5): 499-515. DOI:10.1007/s10035-013-0420-1 Larose E., Montaldo G., Derode A., Campillo M.Larose E., Montaldo G., Derode A., Campillo M. Passive imaging of localized reflectors and interfaces in open media[J]. Applied Physics Letters, 2006, 88(10): 104103. DOI:10.1063/1.2186112 Mao Shujuan, Campillo M., van der Hilst R.D., Brenguier F., Stehly L., Hillers G.Mao Shujuan, Campillo M., van der Hilst R.D., Brenguier F., Stehly L., Hillers G. High temporal resolution monitoring of small variations in crustal strain by dense seismic arrays[J]. Geophysical Research Letters, 2019, 46(1): 128-137. DOI:10.1029/2018GL079944 Nagata K., Nakatani M., Yoshida S.Nagata K., Nakatani M., Yoshida S. Monitoring frictional strength with acoustic wave transmission[J]. Geophysical Research Letters, 2008, 35(6): L06310. Ruina A.Ruina A. Slip instability and state variable friction laws[J]. Journal of Geophysical Research: Solid Earth, 1983, 88(B12): 10359-10370. DOI:10.1029/JB088iB12p10359 Scuderi M.M., Marone C., Tinti E., Di Stefano G., Collettini C.Scuderi M.M., Marone C., Tinti E., Di Stefano G., Collettini C. Precursory changes in seismic velocity for the spectrum of earthquake failure modes[J]. Nature Geoscience, 2016, 9(9): 695-700. DOI:10.1038/ngeo2775 Xie Fan, Ren Yaqiong, Zhou Yongsheng, Larose E., Baillet L.Xie Fan, Ren Yaqiong, Zhou Yongsheng, Larose E., Baillet L. Monitoring local changes in granite rock under biaxial test: a spatiotemporal imaging application with diffuse waves[J]. Journal of Geophysical Research: Solid Earth, 2018, 123(3): 2214-2227. DOI:10.1002/2017JB014940 Yoshioka N., Iwasa K.Yoshioka N., Iwasa K. A laboratory experiment to monitor the contact state of a fault by transmission waves[J]. Tectonophysics, 2006, 413(3/4): 221-238.