## 1. Introduction

[2] Understanding the behavior of ionospheric electron densities has recently become important for both academic purposes and practical applications. For investigation of the dynamics of ionospheric phenomena, three-dimensional ionospheric tomography is effective. The ionospheric total electron content (TEC) observed by a ground-based receiver is an integrated value of the ionospheric electron density along the raypath between the satellite and the receiver. The electron density distribution can be reconstructed based on a number of TEC data points. However, it is an ill-posed problem, and accurate reconstruction is difficult because of the small number of data points and the lack of a horizontal raypath. Especially, the lack of a horizontal raypath made reconstruction of vertical electron density distribution extremely difficult. Previous studies have proposed various algorithms for ionospheric tomography.

[3] Two-dimensional tomography was proposed by *Austen et al.* [1988], who applied the algebraic reconstruction technique (ART) to reconstruct simulated data. Two-dimensional tomography has since been studied by several researchers [*Raymund et al.*, 1990; *Kunitake et al.*, 1995; *Mitchell et al.*, 1997]. However, these approaches can only obtain two-dimensional ionospheric distributions within a cross-section defined by the satellite orbit and the receivers on the ground. Therefore, the reconstruction area and time interval are limited.

[4] To obtain the vertical electron density profile, radio occultation observations have been performed using GPS satellites and a low-Earth-orbit (LEO) satellite. In essence, the vertical electron density profile is estimated using the Abel inversion technique based on the assumption of a spherically symmetric electron density distribution around the Earth [*Hajj et al.*, 1994; *Hajj and Romans*, 1998; *Tsai et al.*, 2001; *Liu et al.*, 2010]. Although this technique is useful in investigating the comprehensive altitudinal electron density distribution, the assumption is not always accurate for the actual ionosphere, because the actual ionospheric electron density distribution varies both vertically and horizontally. To overcome this problem, *Garcia-Fernandez et al.* [2003] proposed a method that considers the horizontal gradient in the Abel inversion by reference to the International Reference Ionosphere (IRI) model. Recently, many researchers have investigated the vertical profile and the global ionospheric electron density distribution using occultation observations by FORMOSAT-3/COSMIC [*Lei et al.*, 2007; *Hsiao et al.*, 2009, 2010]. However, these radio occultation observations are difficult to use for investigations of fine structure in the ionosphere. Therefore, in addition to occultation observations, three-dimensional tomography, based on data from ground-based receivers, is required to understand the detailed dynamics of the ionosphere. *Saito et al.* [2007] and *Lee et al.* [2008] proposed ground GPS-receiver-based three-dimensional tomography, and they showed the significant promise of the technique for reconstruction of local ionospheric distributions with large data set from GEONET (Japan). Similarly, *Mitchell and Spencer* [2003] demonstrated the ground-based tomography for European region.

[5] The methods discussed above require an initial ionospheric model and/or a large amount of data for computation, but model-free reconstruction is essential for investigations of the disturbed ionosphere. In fact, our analysis is focused on the disturbed and/or irregular ionospheric electron distribution. Moreover, for applications in regions where only small numbers of ground-based GPS receivers are available, satisfactory reconstruction based on sparse data is a necessity. At tropical latitudes, equatorial plasma depletions and traveling ionospheric disturbances have been observed by ground-based instruments such as GPS receivers, radars, and airglow cameras. In addition, many anomalous ionospheric phenomena, possibly associated with large earthquakes, have been reported [*Calais et al.*, 2003; *Heki et al.*, 2006; *Liu et al.*, 2006, 2009; *Otsuka et al.*, 2006]. For instance, Sumatra island (Indonesia) is one of the most seismically active regions in the world, where large earthquakes occur frequently. However, at these low-latitude regions the number of available GPS receivers is insufficient for application of these reconstruction techniques using only ground-based receivers.

[6] In this paper, the Residual Minimization Training Neural Network (RMTNN) tomographic approach is selected [*Ma et al.*, 2005a; *Takeda and Ma*, 2007], using TEC data, including location and altitude, derived by ground-based GPS receivers and ionosondes. This approach can be applied to reconstruction based on sparse data and a multilayer neural network. They proposed the new ionospheric tomography method and demonstrated the effectiveness of the resulting reconstruction using GEONET data from Japan under a quiet ionosphere. Although they found that the RMTNN method is promising, they did not consider reconstruction in practical situations where ionospheric disturbances are present, and/or when the region of interest is sampled by a small number of ground-based GPS receivers. We validate the performance of RMTNN tomography under both disturbed and sparse data conditions.