J Geod (2016) 90:741–755 DOI 10.1007/s00190-016-0906-9 ORIGINAL ARTICLE A new computerized ionosphere tomography model using the mapping function and an application to the study of seismic-ionosphere disturbance Jian Kong 1 · Yibin Yao 2 · Lei Liu 2 · Changzhi Zhai 2 · Zemin Wang 1 Received: 23 October 2015 / Accepted: 13 April 2016 / Published online: 4 May 2016 © Springer-Verlag Berlin Heidelberg 2016 Abstract A new algorithm for ionosphere tomography using the mapping function is proposed in this paper. First, the new solution splits the integration process into four layers along the observation ray, and then, the single-layer model (SLM) is applied to each integration part using a mapping function. Next, the model parameters are estimated layer by layer with the Kalman filtering method by introducing the scale factor (SF) γ to solve the ill-posed problem. Finally, the inversed images of different layers are combined into the final CIT image. We utilized simulated data from 23 IGS GPS sta- tions around Europe to verify the estimation accuracy of the new algorithm; the results show that the new CIT model has better accuracy than the SLM in dense data areas and the CIT residuals are more closely grouped. The stability of the new algorithm is discussed by analyzing model accuracy under different error levels (the max errors are 5TECU, 10TECU, 15TECU, respectively). In addition, the key preset para- meter, SFγ , which is given by the International Reference Ionosphere model (IRI2012). The experiment is designed to test the sensitivity of the new algorithm to SF variations. The results show that the IRI2012 is capable of providing initial SF values. Also in this paper, the seismic-ionosphere distur- bance (SID) of the 2011 Japan earthquake is studied using the new CIT algorithm. Combined with the TEC time sequence of Sat.15, we find that the SID occurrence time and reaction area are highly related to the main shock time and epicenter. According to CIT images, there is a clear vertical electron density upward movement (from the 150-km layer to the B Yibin Yao ybyao@whu.edu.cn 1 Chinese Antarctic Center of Surveying and Mapping, Wuhan University, Wuhan 430079, China 2 School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China 450-km layer) during this SID event; however, the peak value areas in the different layers were different, which means that the horizontal movement velocity is not consistent among the layers. The potential physical triggering mechanism is also discussed in this paper. Compared with the SLM, the RMS of the new CIT model is improved by 16.78%, while the CIT model could provide the three-dimensional variation in the ionosphere. Keywords Mapping function · Computerized ionosphere tomography · Kalman filtering · Seismic-ionosphere disturbance · TEC variation sequence · Electric field effect 1 Introduction Multi-dimensional ionosphere monitoring greatly improves the study of the ionosphere, as the multi-dimensional ionosphere models can reflect the horizontal variation of mul- tiple layers and effect of electron coupling in the vertical direction. This is helpful in improving our understanding of ionosphere properties and in providing more extensive infor- mation for study of disaster ionospheric disturbances (Hajj et al. 1994; Hernandez-Pajares et al. 1999). Hajj et al. intro- duced computerized ionosphere tomography (CIT) in 1994. But until to 1997, the CIT algorithm realized by Rius with the Kalman filtering for the first time when GPS/MET occulta- tion data from 28 stations and 160 IGS stations are combined to successfully invert three-dimensional ionosphere images (Rius et al. 1997). Due to poorly sampled observations at the edge of the inversion region and the near-vertical signals observed from GNSS satellites containing little horizontal information, CIT is a typical ill-posed problem; in the presence of measure- ment errors, the estimated solution is extremely unstable. 123