## 1 Introduction  
The Klauea volcano, one of the youngest and most active volcanoes in the world, showed unusual activity beginning on 21 April 2015. Klauea's summit inflated at an abnormal rate, and the Halema'uma'u crater began to fill with a rising lava lake. The rising lava finally reached the floor of the Halema'uma'u crater on 28 April, and these conditions continued for approximately two weeks until 10 May 2015. After overflowing for approximately 10 days, the lava lake began to drop along with a summit deflation starting on 10 May. Seismic activity in the southern portion of Klauea's summit increased sharply on 14 May and a tiltmeter began to tilt rapidly from the static state. In other words, the slope of the ground began to change due to magma dynamics beneath the southern part of Klauea's summit. All of these activities were interpreted as an early sign of an imminent magma intrusion into the southern portion of the Klauea caldera (U.S. Geological Survey reports; [[http://hvo.wr.usgs.gov/volcanowatch](http://hvo.wr.usgs.gov/volcanowatch)]([http://hvo.wr.usgs.gov/volcanowatch](http://hvo.wr.usgs.gov/volcanowatch))). Interferometric Synthetic Aperture Radar (InSAR) is the most powerful technique for the measurement of surface displacements using imaging-based approaches. It has been used to investigate enormous volcanic activities in recent decades [1, 2, 3, 4, 5, 6, 7]. To map realistic surface motions, three-dimensional (3D) components of surface deformation have been retrieved in recent studies [6, 8, 9, 10]. Several methods have been adopted to solve the 3D measurement problem, but weak resolving power in the along-track direction is the main obstacle for retrieving precise 3D displacements in most approaches. The Multiple Aperture Interferometry (MAI) technique uses split-beam InSAR processing to provide precise measurements in the along-track direction [11, 12], and this technique has opened a new chapter in SAR interferometry. The measurement accuracy of 3D displacements has been markedly improved by the MAI method, which is approximately two- to three-fold more accurate than the offset-based approach [10, 12, 13]. Using the MAI method, 3D measurements have been made of various geologic phenomena [6, 14, 15]. Recently, 3D measurements using multi-temporal data stacking was introduced to further improve the measurement accuracy, allowing sub-centimeter accuracy in the 3D measurements to be achieved [16]. In this study, surface deformation associated with the recent volcanic activity of the Klauea volcano, Hawai'i, was explored by conventional InSAR and MAI techniques using a multi-temporal COSMO-SkyMed X-band SAR data set. The 3D components of the surface deformation were calculated by integrating the multi-stacked InSAR and MAI interferograms, obtained from ascending and descending orbits, respectively. Compared to the C- and L-band SAR system, the X-band SAR is difficult to apply in the MAI observation because the X-band system is affected by relatively large temporal decorrelation. Despite the potential risks of temporal decorrelation associated with the X-band system, the powerful capability of data acquisition from COSMO-SkyMed enables us to measure the precise MAI deformation using the multi-temporal stacking approach [17, 18]. Model parameter estimations of the magma source were performed using the 3D components of the surface deformation. Surface displacements during periods of unrest have been used to determine the geometries and volume changes of magma bodies [2, 7, 19, 20, 21]. By modeling geodetic observations, previous studies have demonstrated that there are at least three or four discrete magma reservoirs beneath Kilauea's summit. Individual sources are located beneath Keanakako'i, Halema'uma'u, and the southern caldera [7, 20, 22]. The shallow magma source below Halema'uma'u crater is at a depth of 1-2 km [7], whereas the other sources lie at depths of 2.5-4.5 km.