Hsu Hou-Tse

Accurate and rapid error estimation on global gravitational field from current GRACE and future GRACE Follow-On missions

Firstly, the new combined error model of cumulative geoid height influenced by four error sources, including the inter-satellite range-rate of an interferometric laser (K-band) ranging system, the orbital position and velocity of a global positioning system (GPS) receiver and non-conservative force of an accelerometer, is established from the perspectives of the power spectrum principle in physics using the semi-analytical approach. Secondly, the accuracy of the global gravitational field is accurately and rapidly estimated based on the combined error model; the cumulative geoid height error is 1.985 × 10−1 m at degree 120 based on GRACE Level 1B measured observation errors of the year 2007 published by the US Jet Propulsion Laboratory (JPL), and the cumulative geoid height error is 5.825 × 10−2 m at degree 360 using GRACE Follow-On orbital altitude 250 km and inter-satellite range 50 km. The matching relationship of accuracy indexes from GRACE Follow-On key payloads is brought forward, and the dependability of the combined error model is validated. Finally, the feasibility of high-accuracy and high-resolution global gravitational field estimation from GRACE Follow-On is demonstrated based on different satellite orbital altitudes.

Efficient and rapid accuracy estimation of the Earth's gravitational field from next-generation GOCE Follow-On by the analytical method

Firstly, a new analytical error model of the cumulative geoid height using the three-dimensional diagonal tensors of satellite gravity gradiometry (SGG) is introduced based on the variance-covariance matrix principle. Secondly, a study for the requirements demonstration on the next-generation GOCE Follow-On satellite gravity gradiometry system is developed using different satellite orbital altitudes and measurement accuracies of satellite gravity gradiometer by the new analytical error model of SGG. The research results show that it is preferable to design satellite orbital altitudes of 300 km–400 km and choose the measurement accuracies of 10−13/s2–10−15/s2 from satellite gravity gradiometer. Finally, the complementarity of the four-stage satellite gravity missions, including past CHAMP, current GRACE, and GOCE, and next-generation GOCE Follow-On, is contrastively demonstrated for precisely recovering the Earths full-frequency gravitational field with high spatial resolution.

Check of Earth’s free oscillations excited by Sumatra-Andaman Large Earthquake and discussions on the anisotropy of inner core

Sumatra-Andaman Large Earthquake on Dec. 26, 2004 generated not only the Indian Ocean Tsunami but also the Earth’s free oscillations (EFO). The signals of Earth’s free oscillations were perfectly recorded by the superconducting gravimeter C0-32 at Wuhan station in China. After the pre-treatment and spectral analysis on the observational data from Wuhan station, we obtained more than ninety EFO modes including 42 fundamental modes, 2 radial modes and 49 harmonic modes. On the basis of the discussions on some observed harmonic modes and abnormal splitting phenomena, we considered that the real rigidity might be lower than the theoretical prediction of PREM model in the inner core and however the anisotropy of compressive wave was brightly higher than the present estimations in the inner core. This suggested that the anisotropy of the inner core could be much more complicated than our present understanding, and there might be some new geophysical phenomena in the formation process of the inner core.

A contrastive study on the influences of radial and three-dimensional satellite gravity gradiometry on the accuracy of the Earth's gravitational field recovery

The accuracy of the Earths gravitational field measured from the gravity field and steady-state ocean circulation explorer (GOCE), up to 250 degrees, influenced by the radial gravity gradient Vzz and three-dimensional gravity gradient Vij from the satellite gravity gradiometry (SGG) are contrastively demonstrated based on the analytical error model and numerical simulation, respectively. Firstly, the new analytical error model of the cumulative geoid height, influenced by the radial gravity gradient Vzz and three-dimensional gravity gradient Vij are established, respectively. In 250 degrees, the GOCE cumulative geoid height error measured by the radial gravity gradient Vzz is about 2½ times higher than that measured by the three-dimensional gravity gradient Vij. Secondly, the Earths gravitational field from GOCE completely up to 250 degrees is recovered using the radial gravity gradient Vzz and three-dimensional gravity gradient Vij by numerical simulation, respectively. The study results show that when the measurement error of the gravity gradient is 3 × 10−12/s2, the cumulative geoid height errors using the radial gravity gradient Vzz and three-dimensional gravity gradient Vij are 12.319 cm and 9.295 cm at 250 degrees, respectively. The accuracy of the cumulative geoid height using the three-dimensional gravity gradient Vij is improved by 30%–40% on average compared with that using the radial gravity gradient Vzz in 250 degrees. Finally, by mutual verification of the analytical error model and numerical simulation, the orders of magnitude from the accuracies of the Earths gravitational field recovery make no substantial differences based on the radial and three-dimensional gravity gradients, respectively. Therefore, it is feasible to develop in advance a radial cold-atom interferometric gradiometer with a measurement accuracy of 10−13/s2−10−15/s2 for precisely producing the next-generation GOCE Follow-On Earth gravity field model with a high spatial resolution.

Physical analysis on improving the recovery accuracy of the Earth's gravity field by a combination of satellite observations in along-track and cross-track directions

The physical investigations on the accuracy improvement to the measurement of the Earths gravity field recovery are carried out based on the next-generation Pendulum-A/B out-of-plane twin-satellite formation in this paper. Firstly, the Earths gravity field complete up to degree and order 100 is, respectively, recovered by the collinear and pendulum satellite formations using the orbital parameters of the satellite and the matching accuracies of key payloads from the twin GRACE satellites. The research results show that the accuracy of the Earths gravity field model from the Pendulum-A/B satellite formation is about two times higher than from the collinear satellite formation, and the further improvement of the determination accuracy of the Earths gravity field model is feasible by the next-generation Pendulum-A/B out-of-plane twin-satellite formation. Secondly, the Earths gravity field from Pendulum-A/B complete up to degree and order 100 is accurately recovered based on the orbital parameters of the satellite (e.g., an orbital altitude of 400 km, an intersatellite range of 100 km, an orbital inclination of 89° and an orbital eccentricity of 0.001), the matching accuracies of space-borne instruments (e.g. 10−6 m in the intersatellite range, 10−3 m in the orbital position, 10−6 m/s in orbital velocity, and 10−11 m/s2 in non-conservative force), an observation time of 30 days and a sampling interval of 10 s. The measurement accuracy of the Earths gravity field from the next-generation Pendulum-A/B out-of-plane twin-satellite formation is full of promise for being improved by about 10 times compared with that from the current GRACE satellite formation. Finally, the physical requirements for the next-generation Pendulum-A/B out-of-plane twin-satellite formation are analyzed, and it is proposed that the satellite orbital altitude be preferably designed to be close to 400±50 km and the matching precision of key sensors from the Pendulum-A/B mission be about one order of magnitude higher than from the GRACE program.