Peak ground displacement (PGD) derived from high-rate Global Navigation Satellite System (GNSS) can be used to determine, i.e., the estimate or scale the earthquake magnitude in real time without magnitude saturation experienced by seismic sensors at large earthquakes. Compared with relative positioning or Precise Point Positioning (PPP), the variometric approach can calculate station velocity using the broadcast ephemeris and avoiding estimating phase ambiguities. By integration, velocities can be translated into displacements. However, an inaccurate broadcast ephemeris might cause integrated displacements to show nonlinear drifts. Recently developed real-time orbit and clock products used by real-time PPP have higher accuracy and can also be employed by the variometric approach. We evaluate the performance of the variometric approach on magnitude scaling using high-rate GNSS data collected during the 2019 M_w 7.1 Ridgecrest earthquake, the 2016 M_w 7.8 New Zealand earthquake, and the 2017 M_w 6.5 Jiuzhaigou earthquake. The results indicate that a spatial filter cannot correct nonlinear drifts of integrated displacements completely and scaled magnitudes are not stable when the broadcast ephemeris is used. While using the Centre National d’Etudes Spatiales (CNES) real-time ephemeris, we find both the spatial filter and linear filter can correct drifts well and scaled magnitudes have the same accuracy as those of PPP. While comparing different GNSS systems, we find that BDS is superior to GPS and GLONASS in the case of the Jiuzhaigou earthquake because BDS has a better satellite geometry in this region. Compared with single GPS, multi-GNSS can improve satellite geometry and provide more precise seismic displacements when broadcast ephemeris and low sampling precise clocks are used by the variometric method.

中文翻译：

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使用变分法从GNSS高速峰值地面位移实时缩放地震震级

从高速全球导航卫星系统（GNSS）导出的峰值地面位移（PGD）可用于确定，即实时估计或缩放地震震级，而在大地震中地震传感器不会遇到震级饱和的情况。与相对定位或精确点定位（PPP）相比，变异函数方法可以使用广播星历来计算站速，并且避免估计相位模糊度。通过积分，可以将速度转换为位移。但是，不正确的广播星历表可能会导致积分位移显示非线性漂移。实时PPP使用的最新开发的实时轨道和时钟产品具有更高的准确度，并且也可以用于可变方法。中号_W¯¯ 7.1里奇克莱斯特地震，2016年的中号_W¯¯ 7.8新西兰地震，以及2017年的中号_{w ^}6.5九寨沟地震。结果表明，当使用广播星历时，空间滤波器不能完全校正积分位移的非线性漂移，缩放幅度不稳定。在使用国家空间研究中心（CNES）实时星历时，我们发现空间滤波器和线性滤波器都可以很好地校正漂移，并且缩放的幅度具有与PPP相同的精度。在比较不同的GNSS系统时，我们发现在九寨沟地震中BDS优于GPS和GLONASS，因为BDS在该地区具有更好的卫星几何形状。与单GPS相比，多GNSS可以改善卫星几何形状，并在使用变星法使用广播星历和低采样精确时钟时提供更精确的地震位移。