We present a class of “ellipsoidal rotation matrices” which can be used to characterize tectonic plate motion; where geocentric Cartesian coordinates travel along paths tangential to the ellipsoid. We contrast them with conventional Euler pole plate motion models which are more closely aligned with spherical coordinate systems and inherently induce a change in geodetic ellipsoidal height. We demonstrate the use of each in the Indo-Australian tectonic plate setting, which is known to move approximately 7 cm/year in a north-northeast direction. Geocentric Datum of Australia 2020 (GDA2020) coordinates are “plate-fixed” static coordinates obtained using a conventional Euler pole plate motion model to align time dependent coordinates with the 2014 realization of the International Terrestrial Reference Frame at the epoch 2020.0. We show that this Euler pole plate motion model can introduce ellipsoidal height velocities of up to −0.2 mm/year. This is small but systematic, so pertinent for consideration with high accuracy vertical land motion studies using GDA2020 coordinates and velocities. We further investigate the comparative statistical accuracy of conventional Euler pole and the ellipsoidal models with respect to characterizing plate motion captured in high quality Global Navigation Satellite System data.

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印度-澳大利亚板块的椭球板块运动模型

我们提出了一类“椭球旋转矩阵”，可用于表征构造板块运动；其中地心笛卡尔坐标沿着与椭球体相切的路径行进。我们将它们与传统的欧拉极板运动模型进行对比，传统的欧拉极板运动模型与球坐标系更紧密地对齐，并且固有地引起大地椭球高度的变化。我们演示了每种方法在印度-澳大利亚构造板块环境中的使用，已知该板块每年向北-东北方向移动约 7 厘米。澳大利亚地心基准面 2020 (GDA2020) 坐标是使用传统欧拉极板运动模型获得的“板固定”静态坐标，以将随时间变化的坐标与 2014 年在 2020.0 纪元实现的国际地球参考系对齐。我们表明，该欧拉极板运动模型可以引入高达 -0.2 毫米/年的椭球高度速度。这是小但系统的，因此与使用 GDA2020 坐标和速度的高精度垂直陆地运动研究相关。我们进一步研究了传统欧拉极和椭球模型在表征高质量全球导航卫星系统数据中捕获的板块运动方面的统计准确性。