An algorithm and software are developed for fast and accurate evaluation of the elements of the geomagnetic field represented in high degree (>720) solid spherical harmonics at many scattered points in the space above the surface of the Earth. The algorithm is based on representation of the geomagnetic field elements in solid ellipsoidal harmonics and application of tensor product needlets. Open source FORTRAN and MATLAB realizations of this algorithm that rely on data from the Enhanced Magnetic Models 2015, 2017 (EMM2015, EMM2017) have been developed and extensively tested. The capabilities of the software are demonstrated on the example of the north, east, and down components of the geomagnetic field as well as the derived horizontal intensity, total intensity, inclination and declination. For the range from −417 meters under the Earth reference ellipsoid up to 1,000 kilometers above it the FORTRAN and MATLAB versions of the software run 465 and 189 times faster than the respective FORTRAN and MATLAB versions of the software using the standard spherical harmonic series method, while the accuracy is less than 1 nanoTesla and the memory (RAM) usage is 9 GB.

中文翻译：

---

快速准确地评估空间中任意点的地磁场元素

开发了一种算法和软件，用于快速，准确地评估在地球表面上方空间中许多分散点处以高度（> 720）固体球形谐波表示的地磁场元素。该算法基于固体椭圆谐波中地磁场元素的表示以及张量积小针的应用。该算法的开源FORTRAN和MATLAB实现依赖于增强型电磁模型2015、2017（EMM2015，EMM2017）中的数据进行了开发和广泛测试。该软件的功能在地磁场的北，东和向下分量以及导出的水平强度，总强度，倾角和磁偏角的示例中得到了证明。