The detection of 11th of March 2011 Tohoku's TEC seismo-ionospheric anomalies using the Singular Value Thresholding (SVT) method

The Total Electron Content (TEC) measured by the Global Positioning System (GPS) is useful for registering the pre-earthquake ionospheric anomalies appearing before a large earthquake. In this paper the TEC value was predicted using the singular value thresholding (SVT) method. Also, the anomaly is detected utilizing this predicted value and the definition of the threshold value, leading to the use of the anomaly as a precursor. The SVT is used in the matrix completion problem, namely the accurate recovery of a matrix from a nearly minimal set of entries. In this study, the SVT has been applied to the ionospheric TEC of the global ionosphere maps (GIM) data on a powerful earthquake in Tohoku on the 11th of March in 2011. In this method, the two-hour TEC observations of this region are converted into a matrix for several consecutive days before and after the occurrence of an earthquake. In this matrix the rows and the columns represent the days and the sequential hours, respectively. The prediction of the non-linear time series is formulated as a method for solving the low-rank recovery problem. Results indicate that under suitable conditions the TEC values can be estimated properly in the aforementioned days and hours by solving a simple optimization problem. In order to show the efficiency of this method in predicting the time series, the results obtained from this research were compared with those from other researches.