holography and electronic speckle pattern interferometry in geophysics

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Optics and Lasers in Engineering 24 (1996) 145-160 0 1995 Elsevier Science Limited

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Holography and Electronic Speckle Pattern Interferometry in Geophysics

Shuzo Takemoto

Department of Geophysics, Faculty of Science, Kyoto University, Sakyo-ku, Kyoto 606-01, Japan

ABSTRACT

Geophysical applications of holography and ESPI are reviewed. First, laboratory experiments of rock deformation and failure with holographic interferometry and holographic in situ stressmeters are briefly summarized. Then, holographic measurements of tunnel deformations made in Japan are described. The holographic recording system, consisting of an He-Ne gas laser and associated optical elements, was installed in a tunnel at the Amagase Crustal Movement Observatory, Japan in 1984. Tunnel deformations caused by tidal and tectonic forces have been precisely determined using the ‘real-time’ technique of holographic interferometry. Finally, some attempts to apply ESPI to geophysical measurements are introduced.

1 INTRODUCTION

Holographic interferometry enables small deformations of a three- dimensional object to be measured quantitatively in terms of the wavelength of laser light without touching the object. Many attempts to apply holographic interferometry to precise measurements of small deformations of solid materials as well as fluid flow phenomena have been made over the last three decades since the extremely coherent light source, ‘laser’, was developed at the beginning of the 1960s.

This paper reviews applications of holographic interferometry to geophysical sciences with an emphasis on large structures, and then reports some attempts to apply Electronic Speckle Pattern Interfero- metry (ESPI) to geophysical measurements in the field.

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146 Shuto Takemoto

2 HOLOGRAPHIC MEASUREMENTS OF ROCK DEFORMATIONS

The first application of holographic interferometry to geophysical sciences was found out in literature of laboratory experiments carried out to investigate deformation and failure of metals and rocks.‘” Introduction of holographic interferometry to measure rock deformations has the following advantages compared with conventional methods using strain gauges:2

(a) Strains can be measured simultaneously in any desired direction.

(b) Strain variation over the entire sample can be observed. (c) No physical contact is required with the sample. (d) No special sample preparation is required. (e) The experimental set-up is simple.

Based on these points of view, elastic and inelastic deformations of dry and wet rock samples under mechanical loads and thermal stresses were investigated in the USA, Russia and China. Most of them used the double exposure technique of holographic interferometry, in which an interferometric image of the resulting hologram between two exposures indicates a topographic map of surface deformation during two stages of stress conditions. Various stages of deformations before the failure are visually and quantitatively represented by successive holograms. The result of these experiments reveals that localization of a failure zone in brittle and ductile rocks can occur in the early stage of deformation. The rate of loading is an important factor in the appearance of the intense deformation zone. Time-dependent processes such as stress corrosion seem to play an important role in the early localization. These findings improved understanding of the mechanism of rock failure in the field and have contributed to earthquake prediction studies.

Holography was also employed to measure small deformations of boreholes and to estimate the state of stress acting to the Earth’s crust. Two groups in the USA and Japan (California Institute of Technology7 and Nagoya University,’ respectively) introduced holographic interferometry into in situ stress measurements. The double exposure technique of holographic interferometry was used for measurements of strain-relief displacements around a small hole drilled into a rock in

situ. The regional stress acting on a rock mass is locally relieved by drilling a small hole into the rock. The change in the stress-strain field before and after drilling the hole is measured by the resultant

Holography and ESPI in geophysics 147

interference fringe pattern superimposed on the reconstructed holographic image of the object, which represents the deformation of the object during an interval between two successive exposures. The orientation of the principal stress components can be directly measured by the interference fringe pattern, and the amount of stress is also determined from the holographic data if the elastic constants of the rock are already known.

As mentioned above, holographic interferometry has been success- fully applied to geophysical experiments of rock deformations both in the laboratory and in the field. However, the object areas of holographic interferometry employed in these experiments were limited to around 2-3 cm. On the other hand, holograms of an object larger than 1 m were used for continuous monitoring of tunnel deformations. In the following section, holographic measurements of tunnel deformations carried out in Japan are reviewed.

3 HOLOGRAPHIC MEASUREMENTS OF TUNNEL DEFORMATIONS

3.1 Circumstances of holographic measurements in tunnels

A continuous monitoring of crustal deformations by extensometers and tiltmeters is considered to be the most effective measure of earthquake precursors, especially those on short time scales of hours to days. Many extensometers and tiltmeters have been installed in deep tunnels in seismically active regions and continuous observations of crustal strains have been carried out.

During the last half of this century, various types of extensometers such as rod, wire and laser extensometers have been developed. These conventional extensometers, however, can detect only one component of strain changes, i.e. a linear component between two piers fixed into the bedrock. On the other hand, a new measurement system based on holographic interferometry has been developed in Japan.%l’ As mentioned in the previous section, the holographic method can simultaneously detect two- or three-dimensional deformations in terms of the wavelength of laser light. In addition, the holographic method allows small deformations to be measured directly without touching the object. This obviates some of the problems inherent in conventional extensometers where the effects of deformations in the solid materials used (e.g. the fused-quartz tube or the super-invar bar) and the frictional effects between materials and their supports have to be considered.

148 Shuzo Takemoto

It is, however, difficult to obtain a hologram of an object larger than 1 m by using an He-Ne laser under ordinary circumstances because of environmental perturbations caused by atmospheric changes and artificial noises. This difficulty can be overcome if the holographic recording system is installed in a deep tunnel where the temperature change is negligible and artificial noise does not exist.

Moreover, to obtain a large-object hologram it is necessary that the intensity of laser emission power should be sufficiently high, i.e. 30-50mW. Another requirement is that the maximum path difference from any points on the object to the position of the recording material (the photographic plate) should be within the coherence length of the laser light. Commercially available 30-50mW He-Ne laser sources have a coherence length of 20cm at most. If the curved wall of the tunnel can be used as the holography object, it is possible to measure the maximum difference of the reflected light paths from any point on the object, i.e. a position on the tunnel wall l-2 m in diameter, to the holographic recording position within the limits of 20 cm.

For long-term strain observations with holographic interferometry, another factor should be considered, i.e. the influence of atmospheric pressure changes on the refractive index of light. A change of 4 hPa in the atmospheric pressure causes an apparent strain of 10V6. However, the relative change of atmospheric pressure between two points within a distance of several metres is considered to be negligibly small, even if their absolute values change by a large amount. Thus, the barometric effect is cancelled in the first approximation. The humidity in the tunnel is usually high, but its variation is only slight, and does not alter the refractive index of light.

In 1984, a holographic recording system consisting of a 50mW He-Ne gas laser and associated optical elements was installed in a disused race tunnel at the Amagase Crustal Movement Observatory, Kyoto, Japan, where continuous observations of crustal deformations by employing various kinds of strainmeters and tiltmeters have been carried out since 1967.

As shown in Fig. 1, the Amagase tunnel is 1830m long and has a gradient of 1: 1300. The cross-section of the tunnel is a horseshoe shape, with a diameter of about 6m. The holographic recording system was installed 320m from the entrance of the tunnel and 130m below the surface. The annual variation of temperature at the observation site is about O-2 “C and its daily variation is less than O-05 “C. The amplitude of microtremors measured in the tunnel does not exceed 2 pkine (20 run/s) at O*l-10 Hz. In such circumstances, holograms of an object

Holography and ESPI in geophysics

(4 AMAGASE OBSERVATORY m

08s. TUNNEL(L=1830m )

0 HOLOGRAPHY SYSTEM

IDE0 CAMERA

-6m---y

Fig. 1. (a) Topographic profile of the Amagase tunnel. (b) Arrangement of the laser holography system and laser strainmeters installed in the tunnel. (c) Isometric view of

the laser holography system.

larger than 1 m can be easily obtained. Therefore, we used a white- painted, highly reflective area of the tunnel wall as the object for holographic interferometry. Using this system, tunnel deformation due to tidal and tectonic forces is continuously observed in terms of the fringe displacement of the holographic interference pattern.

150 Shuzo Takemoto

3.2 Holographic measurement system

Most geophysical applications of holographic interferometry, mentioned in the previous section, have been based on the ‘double- exposure’ technique, which requires exposing the same hologram twice, before and after the stress is introduced. In these cases, the interference fringe pattern which is superimposed on the reconstructed holographic image of the object represents the deformation on the object during an interval between two successive exposures.

On the other hand, the holographic recording system described in this section is based on the ‘real-time’ technique, in which the hologram is exposed only once. The interference fringe pattern is produced by superimposing the holographic virtual image on the current (‘real-time’) scene of the object. This technique enables deformations of the object to be measured instantaneously as they occur by looking at the interference fringe pattern on the hologram, and has been used for continuous measurements of small deformations of three-dimensional objects.

The holographic recording system consists of an He-Ne gas laser operating at 0.633 pm with an emission power of 50 mW, optical mirrors and lenses, a CCD video camera and a time-lapse video- cassette recorder. Optical elements, with the exception of a reference mirror, are fixed with magnetic holders to a massive 60 kg steel plate, which is fastened to a concrete base on the floor. The reference mirror is installed on the tunnel floor apart from other optical elements in the direction along the tunnel axis at a distance nearly equal to the light path of the object wave. This is effective in reducing the change in length of the reference light path because the strain changes along the tunnel are one order smaller than those across the tunnel. The laser source is set on another concrete base and covered by polystyrene boards. The object area of the tunnel wall, which is about 2 m X 2 m in size, is painted white for improving the reflectivity of the object. Standard marks indicating an area of 1 m X 1 m are drawn with black paint on the object area.

The arrangement of the equipment is illustrated in detail in Fig. 2. A coherent light beam emitted from the laser source (A) is bent obliquely by the beam-bender (B) and then split into two beams (object beam and reference beam) at the surface of the beam-splitter (C), which transmits about 95% of the light beam and deflects the remaining portion. The object beam is spread out by the beam-expander (D) and illuminates the object wall. The reference wave travels to the reference mirror (H) through the pin-hole (E), the neutral-density filter (F) and


OBJECT WALL

Fig. 2. Illustration of holographic recording system. (A) He-Ne laser. (B) Mirror (beam-bender). (C) Beam-splitter. (D) Beam-expander. (E) Pin-hole. (F) Neutral- density filter. (G) Collimator. (H) Reference mirror. (I) Photographic-plate and

plate-holder. (J) Video camera. (K) Time-lapse video recorder. (L) Monitor TV.

the collimator (G). The two waves which are reflected from the object wall and the reference mirror, respectively, are combined and superimposed on a photographic plate which is set on the plate-holder (I).

The intensity ratio of these two waves is adjusted to be about 1:3 by rotating the neutral-density filter (F) while the hologram is being produced. After an exposure of l-3 min, the photographic plate (Agfa-Gevaert: HOLOTEST lOE75) is developed and fixed. The developed plate is used as an original hologram. The plate (original hologram) must be carefully reset in the same position at which the hologram was taken. In this procedure, the plate is slightly inclined from the original position and the intensity of the reference wave is arranged to be a maximum. A number of dark and bright lines (‘fringes’) over the image of the tunnel wall can then be seen through the plate and the direction and density of interference fringes can be varied by adjusting the position of the plate. Since the amount of tunnel deformation along the tunnel axis is negligible compared with that across the tunnel, the plate is adjusted to produce the fringe pattern parallel to the direction of the tunnel axis. Consequently, tunnel

152 Shuzo Takemoto

deformation of its cross-section can be observed in terms of fringe displacements in the upward and downward directions, together with width changes in the fringe patterns: the former corresponds to the back and forth movement of the tunnel wall and the latter corresponds to its tilting motion. The fringe patterns are stored on a video-cassette tape using a CCD video camera (J) and a time-lapse video-cassette recorder (K). L is a television monitor. Records obtained are analysed with the image-processing system at the laboratory about 5 km away from the Amagase tunnel.

Video signals stored on a video-cassette tape are first reconstructed with a re-recording video recorder. The output of the video recorder is then fed to an image-processor through a television monitor. The image-processor captures the video signal at a rate of 60 fields per second, stores the image in a 768 X 512 X eight-bit frame memory, and simultaneously displays the stored image on the second television monitor. Each of the 768 X 256 pixels per field is digitized with an eight-bit A/D converter and represents one of 256 discrete shades of grey, where 0 denotes black and 255 denotes white. Access to the image processor is controlled by a personal computer.

3.3 Analysis of interferometric fringe displacements

Figure 3(a) shows an example of a monitor picture printed out on thermal printing paper using a TV-printer. In this figure, more than 20 dark and bright fringes parallel to the horizontal direction can be seen, together with the standard mark ‘+’ which was drawn on the tunnel wall together with other standard marks indicting an area of 1 m X 1 m (see Fig. 2).

Fringe displacements were analysed along the five vertical lines (Ll-L5) parallel to the Y-axis, within the range Y = O-200, at X = 300, 350, 400, 450 and 500, respectively. As an example, the distributions of brightness value B and its derivative dB/dY along a vertical line (Ll) are shown in Fig. 3(b) and (c), respectively. The brightness value (Fig. 3(b)) is the grey shade level of each pixel and shows that the left side is black (B = 0) and the right side is white (B = 255). A fringe pattern consisting of more than 20 dark and bright lines is clearly recognized in these figures of B-value distribution. However, this is more clearly emphasized by considering the derivative of B. Thus, dBldY (Fig. 3(c)) is used instead of B for analysing the fringe displacement. As space in the storage system is limited, the distribution of dB/dY is simplified further by making it a binary image of ‘0’ and ‘1’: if

Holography and ESPI in geophysics

L2 L4

153

w Y= 0

(Ll)

Y = 200

X= 100 200 300 400 500 600

BRIGHTNESS VALUE (B)

( > C

dB/dY

0 255 -100 0 100

Fig. 3. (a) An example of interference pattern obtained at 14: 30: 01 on 5 January 1988. (b) Brightness value of the interference fringe pattern along Ll. (c) Derivatives of

B (dB/dY).

dB/dY has a negative vahre or zero, it should be ‘O’, while if it has a positive value, it should be ‘1’. These minute-by-minute data are continuously stored on a floppy disk,

Figure 4(a) shows the fringe displacement along the line Ll (X = 300, Y = O-ZOO), which was obtained by printing out data every 5 min using a dot-printer for the period from 15 h 00 m on 5 January to 13 h 00 m on 12 January 1988. In this figure, sinusoidal changes as a whole are clearly seen, but peak and trough positions in these curves are significantly different along the vertical line (Y = O-200). For example,

Shuzo Takemoto

JAN. 05-12 ‘88 Ll(X= 300)

Fig. 4. (a) Fringe displacements along the line Ll for a period of one week. (b) Displacements of the points a-i of the tunnel wall obtained from the fringe

displacements. (c) Drift-eliminated curves of b.

the first trough in the curve near the uppermost portion (Y = 0) appears at 08 h on 6 January, while that of the lower portion near Y = 200 appears at about 01 h on 6 January. The later peaks and troughs in these curves show a similar pattern. If examined along other vertical lines (L2-LS, Fig. 3(a)), similar patterns are observed.

The displacement of an arbitrary point on the object of a tunnel wall


can be determined by examining the change of the fringe patterns at the corresponding point (X, Y) on the holographic image: one cycle of dark-bright-dark change at a point (X, Y) is equivalent to a relative change of 0.32 pm between the two light paths of object- and reference-waves.

As mentioned before, the reference mirror is installed in the direction along the tunnel (see Figs 1 and 2), and the tidal strains observed in this direction are far smaller than those across the tunnel. Thus, the change in the length of the reference light path is considered to be negligible compared with that of the object light path in which the laser beam travels in the direction across the tunnel. Consequently, the change in the fringe patterns indicates the displacement of the tunnel wall relative to the position of the optical base on which the beam-splitter and the plate-holder of the holographic recording system are installed.

Figure 4b shows the tunnel wall displacements obtained from the changes of fringe patterns (Fig. 4(a)) at the nine points (a-i) from Y = 20 to Y = 180 along the line Ll. The distance between the points a (X = 300, Y = 20) and i (X = 300, Y = 180) of the holographic image corresponds to the length of 1 m of the tunnel wall. In this figure, sinusoidal changes of the order of one fringe (= 0.32 pm) can be seen. In addition, these curves contain drift terms, the source of which is not investigated and may be caused by the creep deformation of the optical base.

Figure 4(c) shows the drift-eliminated curves in which linear trends obtained from the least squares fitting were subtracted from the original curves of Fig. 4(b). We thus compared the curves of Fig. 4(c) with the linear strain change across the tunnel obtained from laser extensometers which were installed in the same tunnel.

3.4 Comparison between holographic records and linear strains observed with laser extensometers

Figure 5 shows strain changes observed with laser extensometers together with thermometric and barometric changes measured in the same tunnel for about one week from 15 h 00 m on 5 January to 13 h OOm on 12 January 1988, in which A and B are the linear strains measured by L - 1 and L - 2 laser extensometers, respectively (see Fig. l(b), 3) which consist of a frequency-stabilized laser source and two orthogonal Michelson interferometers in evacuated light paths; one is oriented along the tunnel (N 72.5 “W) and the other is across the tunnel (N 17.5 “E). The former (L - 1) has a length of 15.8 m with a resolving

156 Shuzo Takemoto

LASER EXTENSOMETERS

Fig. 5. Strain changes observed with laser extensometers [A: L - 1; B: L - 2; C: (L - 2) - (L - 1); D: LS - 1; see text], together with thermometric and barometric

changes during the period from 15 h on 5 January to 13 h on 12 January 1988.

power of 1.0 X 10P9/digit, and the latter (L - 2) is 3.17 m in length with 5.0 X lo-‘/digit resolving power. The curve C in Fig. 5 shows the differences between these two components of linear strains [(L - 2) - (L - l)]. Curve D shows the strain measured by the LS - 1 extenso- meter (see Fig. l(b), 2) which has a simple, unstabilized laser source and two light paths of equal length, and detects the differences between two axial linear strains with a resolving power of 1.7 X 10e9. Thus, the output signal of LS - 1 should be equivalent to that of (L - 2) - (L - 1). In Fig. 5, curves C and D are consistent with each other. In any case, meteorological disturbances are very small and tidal strains are clearly recorded. It can be seen, however, that the tidal strain (A) along the tunnel is far smaller than that (B) across the tunnel. This difference was predicted from the stress-strain relationship around the Amagase tunnel considering the azimuthal’dependence of tidal strains at Ama- gase and including the ‘cavity effect’. The result shows that the amplitude of B is about seven times larger than that of A. Thus, the tidal strains of C and D should be nearly equal to B.

As a result of comparison between the displacements of the tunnel wall obtained from the holography system (Fig. 4(c)) and the strain changes across the tunnel (Fig. 5, B), the displacements of the tunnel


wall at its lower portion (e.g. Fig. 4, ‘h’ and ‘i’) are fairly consistent with the strain changes across the tunnel. However, the displacements of the upper portion of the tunnel wall (e.g. ‘a’ and ‘b’) are out of phase. It is interesting that displacements at points on the tunnel wall within a distance of 1 m show such different patterns. However, this is reason- able because the phase of tidal strain component across the tunnel differs by 180” from that of the vertical component.

Consequently, detailed patterns of tunnel deformations have been precisely determined using the holography system. The fringe displacements in interference patterns are consistent with the strain changes observed with laser extensometers which have been installed in the same tunnel. These observational results substantiate the tunnel deformation predicted by finite element calculations. The effectiveness of the holographic method to investigate crustal deformations is thus ascertained.

The holography recording system, however, has a margin for improvement to measure the long-term strain accumulation because the fringe pattern observed through the photographic plate gradually blurs over the course of time. In order to overcome this difficulty, introduction of ESPI may be available. In the ESPI technique, the interference fringe pattern can be produced without using wet photographic processing but instead using electronic processing with a video camera, image processor and personal computer.

3.5 ESPI recording system for measurements of tunnel deformations

We have been constructing a new measurement system of tunnel deformations by employing the ESPI technique. Figure 6 shows the ESPI recording system to be installed in tunnels. The laser beam is supplied from a 15 mW He-Ne laser source and fed to a beam expander in the optical module through an optical fiber. The optical module consists of optical elements and a small CCD video camera which has 512 X 582 pixels. The minimum illumination required for the normal operation of the camera is 0.2 lux. The beam is then split by a beam splitter into two waves in directions toward the upper and lower portions of the tunnel wall. Two waves reflected by these object planes on the tunnel wall are superimposed on the CCD element in the camera body. Video signals are fed to an image processor and then stored in the digital frame memory one after the other. The stored data are analysed with a personal computer. By comparing these signals with the ‘reference picture’, speckle interference patterns can be produced. The

158 Shuzo Takemoto

Fig. 6. Layout of the precise measurement of tunnel deformations. Differences between out-of-plane displacements on a side wall and upside wall are measured.

tunnel deformations caused by tidal and tectonic forces can be detected in terms of the changes of interference patterns.

We have almost completed the performance test of the system in the laboratory and will soon install the system in an observation tunnel.

4 SOME APPLICATIONS OF ESPI IN GEOPHYSICS

The ESPI technique has been widely applied to non-destructive inspections for industrial purposes during the last two decades. As an example of ESPI applications in geophysical sciences, the ESPI measurement system of tunnel deformations was mentioned in the previous section. In addition, Chengyoung et al.” applied this technique to investigate the process of the fracture zone in rocks.

We are now developing the ESPI in situ stress measurement system.13 The system consists of a 25 mW He-Ne laser source, a borehole module including optical elements, an image processor and a personal computer. The borehole module is designed to be very compact (10 cm in diameter and about 35 cm in length) and can be used in a small borehole having a diameter of 10.5-11 cm. The system is designed to be used for measurements of in situ stresses by a stress-relieving method.


In the first step, a large borehole having a diameter of about 20 cm is drilled in the underground rock and a small borehole about 11 cm in diameter is then drilled at the bottom of the first borehole. After the borehole module is firmly settled at the desired depth (5-10m) by extending lock-in feet which are driven by air pressure in cylinders, the light intensity of the speckle image is sampled to yield a digital picture and stored in a digital frame memory of an image processor as a ‘reference picture.’ Next, the small borehole is overcored by using a large diameter bit. As a result of this overcoring procedure, the rock element is separated from the surrounding rock mass, and stress around the small borehole is partially relieved. The second picture obtained after the overcoring should be compared with the ‘reference picture.’ The resulting interference fringe pattern indicates the strain changes due to the overcoring. Based on these data, the initial stress acting in the rock can be determined.

5 CONCLUSIONS

Geophysical applications of holography and ESPI are reviewed. These techniques have some attractive features compared with conventional stress-strain measurement techniques in geophysics because two- and three-dimensional small strains can be measured simultaneously in terms of the wavelength of laser light without touching the object.

It is desirable to develop reliable instruments for earthquake prediction and to search for precursory stress-strain changes before the occurrences of large earthquakes. In this respect, the holography and ESPI techniques will meet the social needs of the times. Moreover, these techniques may be utilized for precise measurements of static and dynamic stress-strain changes of underground constructions such as oil storage tunnels and underground electric power stations. This approach will contribute to earthquake effect’s mitigation.

ACKNOWLEDGEMENT

Our research summarized here was partially supported by a Grant-in- Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan (Nos 62540292, 63540304 and 03554010) and the 19th Nissan Science Foundation.

160 Shuzo Takemoto

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1. Spetzler, H., Meyer, M. & Boucher, G., Thermal expansion measurements on molten levitated aluminum by holographic interferometry. High Temperatures-High Pressures, 6 (1974), 529-532.

2. Spetzler, H., Sobolev, G. & Getting, I., Holography in laboratory experiments pertinent to rock deformation and failure. In Laser Holog- raphy in Geophysics, ed. S. Takemoto, Ellis Hot-wood Series in Applied Geology. John Wiley & Sons, New York, 1989, pp. 31-105.

3. Spetzler, H., Scholz, C. H. & Chi-Ping, J. Lu, Strain and creep measurements on rocks by holographic interferometry. Pure Appl. Geophys., 112 (1974), 571-581.

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5. Spetzler, H., Sobolev, G., Sondergeld, C., Salov, B., Getting, I. & Koltsov, A., Surface deformation, crack formation, and acoustic velocity changes in pyrophyllite under polyaxial loading. J. Geophys. Res., 86 (1981), 1070- 1080.

6. Wang, R., Zhao, Y., Chen, Y., Yan, H., Yin, Y.-Q., Yao, C.-Y. & Zhang, H., Experiment and finite element simulation of X-type shear fractures from a crack in marble. Tectonophysics, 144 (1987), 141-150.

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9. Takemoto, S., Application of laser holographic techniques to investigate crustal deformations. Nature, 322 (1986), 49-51.

10. Takemoto, S., Real-time holographic measurement of crustal deformation. In Laser Holography in Geophysics, ed. S. Takemoto, Ellis Horwood Series in Applied Geology. John Wiley & Sons, New York, 1989, pp. 129-167.

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12. Chengyoung, W., Peide, L., Rongsheng, H. & Xiutang, S., Study of the fracture process zone in rocks by laser speckle pattern interferometry. Int. J. Rock Mech. Sci. Geomech., Abstr., 27 (1990), 65-69.

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