## 1 Introduction  
Interferometric Synthetic Aperture Radar (InSAR) is a geodetic technique that can identify subsidence and uplift induced by anthropogenic activities such as subsurface fluid extraction, or injection into reservoir formations. This technique has been widely used at CO\({}_{2}\) injection sites since the first application at the In Salah CO\({}_{2}\) storage project in central Algeria [1; 2; 3]. CO\({}_{2}\) injection may cause pressure buildup, depending reservoir property such as porosity and permeability, or CO\({}_{2}\) injection rate and volume. Uplift is caused by the migration to the ground surface of the expansion of the target formation due to pressure buildup. From a geomechanical point of view, challenges remain in relating uplift at ground surface to pressure buildup in deep formation. We propose the distributed optical fiber sensing technology to monitor the deformation profile along the wellbore during CO\({}_{2}\) injection. Fiber optics sensing (FOS) systems consist of a laser, optical fiber, sensing element, and detector. Optical fiber is composed of three parts: a core generally made of glass, cladding, and coating. It can be used as a sensor if properties of propagating light wave, such as intensity, phase, polarization, and frequency, are appropriately modulated to the environment parameter of interest. Light from a laser is sent through an optical fiber, which acts as an optical waveguide. The modulated light wave then travels back to the detector. FOS systems used as sensors have such advantages as being passive, immune to electromagnetic interference, working well in harsh environment, resistant to high temperature, and easily embedded or attached due to its small size. A variety of sensing technologies has been developed over the years, including distributed sensors which are capable of measuring strain and/or temperature changes along the entire fiber based on Rayleigh, Raman, and Brillouin backscattering techniques [4; 5; 6; 7; 8; 9; 10]. The Raman scattering is widely used in Distributed Temperature Sensing (DTS) application. On the other hand, the Brillouin and Rayleigh backscattering phenomena are sensitive to both temperature and strain. Brillouin scattered light is generated by acoustic vibration of glass molecules. When light enters the optical fiber, a weak acoustic lattice vibration (acoustic phonon) is generated due to the thermal oscillation of the material silicon dioxide. The interaction between this acoustic lattice vibration (acoustic phonon) and incident light produces backscattering of the light, which is down-shifted in frequency due to the Doppler effect. The resulting frequency shift is proportional to changes in local temperature and strain at a measurement point of the optical fiber. Here a measurement point refers to the place where backscattered light is generated. The Brillouin scattering can be spontaneous or stimulated. The former is referred to as Brillouin time domain reflectometry (BOTDR), while the latter as Brillouin time domain analysis (BOTDA). Figure 1 presents a typical scheme of BOTDA system. In comparison to BOTDR systems, BOTDA systems in general have higher spatial resolutions and better accuracy. However, they require double-end access (closed fiber loop) because the light is injected from both ends, as opposed to BOTDR systems where light is injected from one end only. The standard implementations of BOTDR and BOTDA are limited to the 1-m spatial resolution. The technologies of the pulse-pre-pump (PPP) BOTDA [11] and Synthetic-BOTDR [12] have reduced the spatial resolutions to 2 cm and 10 cm, respectively. Rayleigh scattered light is generated due to fluctuation in the refractive index of the glass material (random change in glass density) when light is incident on the optical fiber. The scattered light itself does not involve a frequency change.