Method Of Spherical Cap Harmonic Analysis Research Articles

Spherical cap harmonic analysis of the Arctic ionospheric TEC for one solar cycle

AbstractPrecise knowledge of the Arctic ionosphere total electron content (TEC) and its variations has scientific relevance due to the unique characteristics of the polar ionosphere. Understanding the Arctic TEC is also important for precise positioning and navigation in the Arctic. This study utilized the spherical cap harmonic analysis (SCHA) method to map the Arctic TEC for the most recent solar cycle from 2000 to 2013 and analyzed the distributions and variations of the Arctic TEC at different temporal and spatial scales. Even with different ionosphere conditions during the solar cycle, the results showed that the existing International Global Navigation Satellite Systems Service stations are sufficient for mapping the Arctic TEC. The SCHA method provides adequate accuracy and resolution to analyze the spatiotemporal distributions and variations of the Arctic TEC under different ionosphere conditions and to track ionization patches in this polar region (e.g., the ionization event of 26 September 2011). The results derived from the SCHA model were compared to direct observations using the Super Dual Auroral Radar Network radar. The SCHA method is able to predict the TEC in the long and short terms. This paper presented a long‐term prediction with a relative uncertainty of 75% for a latency of one solar cycle and a short‐term prediction with errors of ±2.2 total electron content units (TECUs, 1 TECU = 1016 el m−2), ±3.8 TECU, and ±4.8 TECU for a latency of 1, 2, and 3 days, respectively. The SCHA is an effective method for mapping, predicting, and analyzing the Arctic TEC.

Modeling the lithospheric magnetic field over France by means of revised spherical cap harmonic analysis (R‐SCHA)

We have recently proposed the revised spherical cap harmonic analysis (R‐SCHA) modeling technique. The new mathematical functions represent faithfully the spatial variations of potential fields in a restricted area. In this paper, we tackle the inverse problem and outline the efficiency of the new basis functions with respect to real magnetic data. Processing simultaneously repeat stations, observatory, aeromagnetic, and CHAMP satellite data provides our first vector lithospheric field model over France, which extends from surface to 500 km of altitude. The magnetic field is represented with a minimum horizontal spatial representation of 40 km at the mean Earth radius. The magnetic lithospheric map consistency is confirmed with a comparison to known geological features. The model variation with altitude also suggests that the major French magnetic anomaly, the Paris basin anomaly, is produced by a deep‐rooted geological structure. These results demonstrate the superiority of regional modeling over global modeling for delineating small‐scale details in the lithospheric field. In view of forthcoming satellite missions, like Swarm, the revised spherical cap harmonic analysis method will help to accurately represent the lithospheric field for more detailed geological interpretations.

Selection of the Geomagnetic Normal Field and Calculation of Geomagnetic Anomalous Field

According to the geomagnetic observation data in China for 2003 from 135 geomagnetic stations and 35 geomagnetic observatories, and the geomagnetic data of 38 IGRF calculated points in China's adjacent regions, the distribution of the geomagnetic anomalous field in China was calculated. Two kinds of geomagnetic models are selected as the geomagnetic normal field: one is the spherical harmonic model of the international geomagnetic reference field, and the other is the Taylor polynomial model of the geomagnetic field in China. Based on the geomagnetic anomaly values (the observed value minus the calculated value of the model) at various stations, the spherical cap harmonic model of the geomagnetic anomalous field was calculated by using the spherical cap harmonic analysis method. The geomagnetic anomaly charts (∆D, ∆I, ∆F, ∆X, ∆Y and ∆Z) in China for 2003 are drawn. The geomagnetic anomalous field in China is analyzed and discussed.

Study of Geomagnetic Field Models of the Qinghai‐Xizang (Tibetan) Plateau

AbstractBased on three‐component absolute geomagnetic survey data and by use of the Taylor polynomial method and the spherical cap harmonic analysis method, the Taylor polynomial models of the geomagnetic field (X, Y and Z) and spherical cap harmonic models of the geomagnetic residual field (∆X,∆Y and ∆Z) over the Qinghai‐Xizang plateau are calculated, and corresponding theoretical geomagnetic maps are also constructed. The effects of geomagnetic anomalous stations on the geomagnetic field model are analysed, a comparison between the polynomial model and the spherical cap harmonic model of the geomagnetic field is carried out, and the boundary effects of the geomagnetic field model are discussed, too.