PS-INSAR MONITORING AND FINITE ELEMENT ...

PS-INSAR MONITORING AND FINITE ELEMENT SIMULATION OF GEOMECHANICAL AND HYDROGEOLOGICAL RESPONSES IN SEDIMENTARY FORMATIONS Qi Li State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics (IRSM), Chinese Academy of Sciences, Wuhan, China Kazumasa Ito Geological Survey of Japan, AIST Tsukuba, Japan Yanfang Dong Institute of Earthquake Science, China Earthquake Administration, Beijing, China Isao Sato, Yoji Seki, Yasuo Tomishima Geological Survey of Japan, AIST Tsukuba, Japan Satoshi Okuyama Institute of Seismology and Volcanology, Hokkaido University, Japan ABSTRACT With the first use of the corner reflector based permanent scatterer interferometric synthetic aperture radar (CR-PSInSAR) technology, the earth’s surface deformation, strongly associated with subsurface flow, of Horonobe underground research laboratory (URL) is successfully monitored during its construction. The temporal and spatial characteristics of interferometric signatures collected from CR point targets are exploited to accurately map surface deformation histories and terrain heights of the URL site, especially around the monitoring boreholes. By developing a hydromechanical poroelastic model, satellite monitoring is linked to characterization of deep groundwater flow. The geomechanical and hydrogeological responses of sedimentary formations to the drilling of the shaft was modeled using a two-dimensional finite element model. A good correlation between measured and modeled responses indicated that both the boundary conditions and rock properties are well understood by the proposed coupled inversion methodology. Index Terms— Coupled inversion, Corner reflector, PS-InSAR, Sedimentary formation, Underground research laboratory. 1. INTRODUCTION

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With the advancement of satellite and radar technologies, the satellite InSAR (Interferometric Synthetic Aperture Radar) was recognized as a powerful technique for indirect measurement of earth’s surface changes since the early 1990s [1, 2]. The multi-image Permanent Scatterer (PS) technique was introduced in an innovative way to deal with the temporal and geometrical decorrelation problems, which usually lead to the misinterpreted surface change from the corresponding phase changes, encountered in traditional InSAR processing in the late 1990s [3]. Up to now, many successful applications of SAR technologies have been achieved in different research fields, e.g. [4-6]. Associated with other geophysical methods and numerical analysis tools, many more research fields are investigated by SAR technologies, e.g. [7, 8]. Recently, PS-InSAR technologies get the great developments in geosciences, e.g. [9-12]. In this paper, the CR-PS-InSAR technology is firstly used to monitor the earth’s surface deformation, strongly associated with subsurface flow, of an URL during its construction. The JAEA’s Horonobe URL in sedimentary zone is considered as an experimental site (Fig. 1) [13], and the detailed introduction of Horonobe URL project can be accessed in the publication, e.g. [14]. The most motivation of this study is to try to identify the hydrogeological characteristics of site sedimentary formations during the construction of the Horonobe URL with the aid of high precision surface mapping by CR-PS-InSAR technology [15]. The temporal and spatial characteristics of interferometric signatures collected from CR point targets

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are exploited to accurately map surface deformation histories and terrain heights of the URL site, especially around the monitoring boreholes. By developing a hydromechanical poroelastic model, satellite monitoring is linked to characterization of deep groundwater flow [16, 17]. The geomechanical and hydrogeological responses of sedimentary formations to the drilling of the shaft were modeled using a two-dimensional axisymmetrical finite element model [18]. 2. METHODOLOGY In this paper, we used a CR-PS-InSAR based coupled inverse modeling to study the subsurface flow related with surface deformation [18]. The starting point is Biot’s equations [19], which well established the relationship between surface deformations and subsurface flow changes in porous media as follows: 3( u  )  (1) 2G ij   ij  p  kk  ij  1 B (1 )(1 u ) ij 3  0 ( u  ) 3 (2) m  m0    p 2GB (1 )(1 u ) kk B where four elastic constants, i.e., G (shear modulus), 





B (Skemptons coefficient), and  u (undrained Poisson ratio) are involved. p is the pore pressure.  ij is the total stress.  ij is the strain. m is the

(Poisson ratio),

pore fluid mass per unit volume.

0

is the fluid density.

In this study, we are interested in quasi-static deformation in which we may neglect inertial terms in the equation of equilibrium. Then, a partial differential equation for the displacements is obtained as follows [20]:    ui u j G  x j   x j xi 



   uk    x j  u x   ij  k     x j

where

 BKu    m   ij  0 

(3)

m = m  m0 ; u indicates displacement; u is the

undrained Lame constant, and

K u is the undrained bulk

modulus. By Eq. (2) and Eq. (3), we can estimate m , the change in fluid mass per unit volume in the subsurface. Then, by solving (2) for the pore pressure, we can map our estimated m into subsurface pressure. Because m enters Eq. (3) on the right-hand-side as a source term, the inverse problem is linear. The solution of the inverse problem for m can be described as follows: B (4) ui ( x , t )   g ( x,y )m ( y , t ) dV 0 V i

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where

g i ( x, y ) is the Green’s function solution of Eq. (3).

Furthermore, the basic datum in InSAR is the change in range over some time interval. If the earth’s surface deforms during this period, the accumulated displacements of the imaging elements are projected onto the range vector which points toward the satellite. Thus, the change in distance to the satellite,  , that we seek can be written as [20]:  ( x )  ui  li (5) in which li is a unit range vector. With the numerical processing, we can get the Green’s function solution of  as follows: (6)  ( x )   r ( x,y ) ( y ) dy V

r ( x, y )  li g i ( x, y ) is the projection of the displacement Green’s functions onto the range vector. The components of the range vector are known from the geometry of the satellite orbit.  (y ) is stress-free volume strain. The detailed solution of this optimization problem will be discussed elsewhere. 3. EXPERIMENTS To improve the radar signal return to the satellite SAR sensors, corner reflectors are installed in this study. The reflectors are trihedral shaped and made of aluminum. The trihedral design ensures that the radar signal is returned exactly in the incident direction and with the same polarity. The size of the corer reflector is proportional with the quality of the signal strength and implicitly with the quality of the measurement. The minimum size of the reflectors is a function of the SAR sensor wave-length and of the expected strength of the natural radar targets. The corner reflector signal should dominate all the other reflections located in the immediate vicinity. The orientation of the corner reflector is perpendicular to the radar line of sight. This needs a very delicate design and installation [18]. The total five corner reflectors installed in the Horonobe URL site were designed to properly work with Canada RADARSAT-2 by Japan ImageONE Co., Ltd. The C-band RADARSAT-2 data are collected for the Horonobe URL since June 2009. The whole PS-InSAR processing is conducted on the platform of Gamma (GAMMA Remote Sensing AG, Switzerland). The preregistration of satellite images is processed for highprecision matching [21]. The hydromechanical coupled model is developed by finite element method to investigate the geomechanical and hydrogeological responses of the sedimentary formation to the drilling of the shaft. The forward and inverse analyses are encoded by different programming languages with focus on the development of cost-effective simulators to this over-determined system. Even when the system is formally over-determined, trade-

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offs between parameters may render the system effectively underdetermined [22]. Because of the limited space, the regularization process to stabilize the aforementioned inverse problem is not addressed herein. The detail will be discussed elsewhere, or referred to [20, 22]. 4. RESULTS AND DISCUSSION Fig. 2 depicts the identification of CR point targets between optical and RADARSAT-2 images. HDB-X, X=3, 5, 8, 9, 11, indicates the installed position of CR point targets near the boreholes. The CR point targets are verified to be well installed after the identification experiment. Fig. 3 shows the InSAR deformation results from RADARSAT-2 data collected during the year of 2009. The relative vertical deformations of HDB-3, 5 8, 9 are plotted with the reference of HDB-11. In general, all the decrease trends are depicted, and about several millimeters of the largest vertical deformation are observed. Fig. 4 presents the vertical deformations of earth surface around the excavated shaft in the Horonobe URL site at different times in the year of 2009. It should be noted that this simulation is conducted on the case of high permeability between Koetoi and Wakkanai formations [23]. The magnitude of finite element computed deformation basically agrees with the one of InSAR results. The reason of low-order deformation of HDB-3 is investigated as the part of future work.

Fig. 3 CR-PS-InSAR inferred relative vertical deformations of corner reflectors (HDB-3, 5, 8, 9) with reference to HDB11.

Fig. 4 Vertical surface deformations around the excavated shaft by coupled poroelastic analysis for high-permeability case. 5. CONCLUSIONS Fig. 1 Location map of Horonobe URL, Hokkaido, Japan.

The temporal and spatial characteristics of interferometric signatures collected from CR point targets are exploited to accurately map surface deformation histories and terrain heights of the Horonobe URL site. The proposed methodology is promising to link satellite monitoring to characterization of deep groundwater flow in sedimentary formations. 6. ACKNOWLEDGEMENTS

Fig. 2 Identification of CR point targets (HDB-X) between optical and RADARSAT-2 images.

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Q.L. thanks the support of the BaiRenJiHua (Hundred Talent) program of the Chinese Academy of Sciences. DONG gratefully acknowledges the fund from State Basic Research Development Program of China (Grant No. 2008CB425703). Funding acknowledgements for other aspects of the work are given to NISA of Japan.

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7. REFERENCES [1] Q. Li, B.-H. Fu, and Y. Dong, "Registration of Radar and Optical Satellite Images Using Multiscale Filter Technique and Information Measure," in Geoscience and Remote Sensing New Achievements, P. Imperatore and D. Riccio, Eds. In-Tech, Vienna, pp. 457-476, 2010. [2] D. Massonnet and K.L. Feigl, "Radar Interferometry and Its Application to Changes in the Earth's Surface," Rev. Geophys., vol. 36, issue 4, pp. 441-500, 1998. [3] A. Ferretti, C. Prati, and F. Rocca, "Nonlinear Subsidence Rate Estimation Using Permanent Scatterers in Differential SAR Interferometry," in International Geoscience and Remote Sensing Symposium (IGARSS 99), Hamburg, Germany, pp. 2202-2212, 1999. [4] E.J. Fielding, R.G. Blom, and R.M. Goldstein, "Rapid Subsidence over Oil Fields Measured by SAR Interferometry," Geophys. Res. Lett., vol. 25, issue 17, pp. 3215-3218, 1998. [5] D.L. Galloway and J. Hoffmann, "The Application of Satellite Differential SAR Interferometry-Derived Ground Displacements in Hydrogeology," Hydrogeol. J., vol. 15, issue 1, pp. 133-154, 2007. [6] Y. Dong, Q. Li, A. Dou, and X. Wang, "Extracting Earthquake Damages Due to Wenchuan Ms 8.0 Earthquake, China from Satellite SAR Intensity Image," J. Asian. Earth. Sci., vol. 40, issue 4, pp. 907-914, 2011. [7] T. Masterlark, Z. Lu, and R. Rykhus, "Thickness Distribution of a Cooling Pyroclastic Flow Deposit on Augustine Volcano, Alaska: Optimization Using InSAR, FEMs, and an Adaptive Mesh Algorithm," J. Volcanol. Geoth. Res, vol. 150, issue 1-3, pp. 186201, 2006. [8] D.W. Vasco, A. Ferretti, and F. Novali, "Reservoir Monitoring and Characterization Using Satellite Geodetic Data: Interferometric Synthetic Aperture Radar Observations from the Krechba field, Algeria," Geophysics, vol. 73, issue 6, pp. WA113-WA122, 2008. [9] A. Hooper, P. Segall, and H. Zebker, "Persistent Scatterer Interferometric Synthetic Aperture Radar for Crustal Deformation Analysis, with Application to Volcan Alcedo, Galapagos," J. Geophys. Res., vol. 112, issue B07407 2007. [10] C. Meisina, F. Zucca, F. Conconi, F. Verri, D. Fossati, M. Ceriani, and J. Allievi, "Use of Permanent Scatterers Technique for Large-Scale Mass Movement Investigation," Quatern. Int., vol. 171-172, pp. 90-107, 2007. [11] C.R. Froese, V. Poncos, R. Skirrow, M. Mansour, and D. Martin, "Characterizing Complex Deep-Seated Landslide Deformation Using Corner Reflector InSAR (CR-InSAR): Little Smoky Landslide, Alberta," in Proceedings of the 4th Canadian Conference on Geohazards: From Causes to Management, Quebec City, Canada, pp. 287-294, 2008.

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[12] J. Wasowski, F. Bovenga, N. Florio, and G. Gigante, "PSInSAR for the Investigating of Unstable Slopes and Landslides," in The First World Landslide Forum, N. Casagli, R. Fanti, and V. Tofani, Eds. ICL and ISDR, Tokyo, Japan, pp. 34-36, 2008. [13] N. Shigeta, S. Takeda, H. Matsui, and S. Yamasaki, "Underground Research Laboratories for Crystalline Rock and Sedimentary Rock in Japan," in Waste Management 2003 Symposium, Tucson, AZ, USA, pp. 1-13, 2003. [14] Q. Li and K. Ito, "Analytical and Numerical Solutions on the Response of Pore Pressure to Cyclic Atmospheric Loading: With Application to Horonobe Underground Research Laboratory, Japan," Environ. Earth Sci., DOI: 10.1007/s12665-011-1058-0, 2011. [15] B.M. Kampes, Radar Interferometry: Persistent Scatterer Technique. Springer, Dordrecht, The Netherlands, 2006. [16] Q. Li, K. Ito, B.-H. Fu, I. Sato, X.-L. Lei, S. Okuyama, T. Sasai, Z.S. Wu, K. Kazahaya, and B. Shi, "Coupling and Fusion in Modern Geosciences," Data Sci. J., vol. 8, pp. S45-S50, 2009. [17] K. Ito, K. Karasaki, K.-I. Hatanaka, and M. Uchida, "Hydrogeological Characterization of Sedimentary Rocks with Numerical Inversion Using Vertical Hydraulic Head Distribution: An Application to Horonobe Site," J. Japan Society Eng. Geol., vol. 45, issue 3, pp. 125-134, 2004. [18] Q. Li, K. Ito, Y. Tomishima, and Y. Seki, "Bridging Satellite Monitoring and Characterization of Subsurface Flow: With a Case of Horonobe Underground Research Laboratory," in Prediction and Simulation Methods for Geohazard Mitigation, F. Oka, A. Murakami, and S. Kimoto, Eds. CRC Press, New York, pp. 519524, 2009. [19] H.F. Wang, Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology. Princeton University Press, Princeton, NJ, USA, 2000. [20] D.W. Vasco, C. Wicks, K. Karasaki, and O. Marques, "Geodetic Imaging: Reservoir Monitoring Using Satellite Interferometry," Geophys. J. Int., vol. 149, issue 3, pp. 555-571, 2002. [21] Q. Li, I. Sato, and Y. Murakami, "Simultaneous Perturbation Stochastic Approximation Algorithm for Automated Image Registration Optimization," in 2006 IEEE International Geoscience and Remote Sensing Symposium - Remote Sensing: A Natural Global Partnership (IGARSS 2006), Denver, CO, USA, pp. 184-187, 2006. [22] W. Menke, Geophysical Data Analysis: Discrete Inverse Theory. Academic Press, New York, 1984. [23] Research Core for Deep Geological Environments, Validation Study on the Groundwater Flow Model Using Comprehensive Approaches (Observation Survey of Horonobe URL). Geological Survey of Japan, Tsukuba, 2010.

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