Technology of determining the Earth’s gravitational field parameters using gradiometric measurements Part 6. Calculation the components of the gravitational potential tensor in the earth’s spatial rectangular coordinate system

This is the sixth one in a series of articles describing the technology of determining the Earth’s gravitational field parameters through gradiometric measurements performed with an onboard satellite electrostatic gradiometer. It provides formulas for calculating the components of the gravitational potential tensor in a geocentric spatial rectangular earth coordinate system in order to convert them into a gradiometric one and obtain a free term for the equations of correcting gradiometric measurements when determining the parameters of the Earth’s gravitational field. The components of the gravitational gradient tensor are functions of test masses accelerations measured by accelerometers and relate to the gradiometer coordinate system, while the desired parameters of the Earth’s gravitational field model relate to the Earth’s coordinate one. The components of the gravitational gradient tensor are the second derivatives of the gravitational potential in rectangular coordinates. The calculated values of the gravitational potential tensor components in the earth’s spatial rectangular coordinate system are obtained through double differentiation of the gravitational potential formula. Basing on the obtained formulas, an algorithm and a program in the Fortran algorithmic language were developed. Using this program, experimental calculations were performed, the results of which were compared with the data of the EGG_TRF_2 product.

Temporal gravity variations in GOCE release 6 gravitational gradients

<p>As opposed to the level 1B release 5 GOCE gravitational gradient data, the newly reprocessed release 6 gradients provide reduced noise amplitudes in the low frequency-range, leading to reduced noise amplitudes of the derived gravity field models at large spatial scales, where temporal variations of the Earth’s gravity field have their highest amplitudes. This is the motivation to test the release 6 gradients for their ability to resolve temporal gravity variations.</p><p>For the gravity field processing, we apply a conventional spherical harmonics approach using the time-wise (TIM) processing method as well as a mass concentration (mascon) approach using point masses as base elements, which are grouped to land or ocean mascons by taking into account the coastlines.</p><p>By means of a closed-loop simulation study, we find that the colored instrument noise of the GOCE gravitational gradiometer introduces noise amplitudes into the derived gravity field models that lie above the amplitude of the gravity trend signal accumulated over 5 years. This indicates that detecting gravity variations taking place during the four-year GOCE data period from GOCE gradients only is challenging.</p><p>Using real GOCE data, we test bimonthly gradiometry-only gravity field models computed by both the spherical harmonic and the mascon approach for gravity signals that are resolved by GRACE data, being the temporal signals due to the ice mass trends in Greenland and Antarctica and the 2011 earthquake in Japan. Besides, corresponding GRACE/GOCE combination models are used to test whether the incorporation of GOCE data increases the resolution of temporal gravity signals.</p><p>We found that high-amplitude long-wavelength noise prevented the detection of temporal gravity variations among the bimonthly GOCE-only models. Using the SH approach, it was possible to detect the mean trend signal contained in the data by averaging multiple bimonthly models and considering their difference to a reference model. Using the mascon approach, trend signals contained in GOCE data could be recovered by including a GRACE model truncated to d/o 45 in a GRACE/GOCE combination model and thus let the GOCE data determine the short-scale signal structures instead of GRACE.</p><p>Finally, compared to the temporal gravity signal as resolved by GRACE data, no significant benefit of using or incorporating GOCE gravitational gradient data was found. The reason are the still rather high noise amplitudes in the derived models at large spatial scales, where the considered signal is strongest.</p><p>In order to detect temporal gravity variations in satellite gravitational gradiometry data, the measurement noise amplitudes in the low-frequency range would need to be reduced.</p>

Posisi komponen GPP terhadap variasi konstituen harmonik pasang surut bulan Muharram di Stasiun Sabang

The movement of celestial bodies produces a variation of a gravitational gradient as a tidal generation force (GPP). Position Sabang Station, declination maximum and position lunar month of Muharram aka n generate harmonic constituent character identifier of GPP, where the water level is the sum of the amplitude of harmonic constituent that generated at a certain time.This research is to determine the variation of harmonic constituents and identify the character of harmonic constituents of GPP component position characterization in Muharram month. The results show Katrakteristik tidal movement beginning of the month of Muharram in Sabang Station occurred 1-2 hours after ijtimak.. Value riding dominant water derived from the value of Mean Sea Level ( 52%), and the dominant contribution hamonik constituents derived from component M 2 (28 - 33%). Harmonic constituents M 2 does not show the position of the moon in Muharram, while the position of the sun is reflected in the constituent phase harmonic S 2..

CO-SEISMIC GRAVITY GRADIENT CHANGES OF THE 2006–2007 GREAT EARTHQUAKES IN THE CENTRAL KURIL ISLANDS FROM GRACE OBSERVATIONS

GRACE satellites (the Gravity Recovery And climate Experiment) are very useful sensors to extract gravity anomalies after earthquakes. In this study, we reveal co-seismic signals of the two combined earthquakes, the 2006 Mw8.3 thrust and 2007 Mw8.1 normal fault earthquakes of the central Kuril Islands from GRACE observations. We compute monthly full gravitational gradient tensor in the local north-east-down frame for Kuril Islands earthquakes without spatial averaging and de-striping filters. Some of gravitational gradient components (e.g. ΔVxx, ΔVxz) enhance high frequency components of the earth gravity field and reveal more details in spatial and temporal domain. Therefore, co-seismic activity can be better illustrated. For the first time, we show that the positive-negative-positive co-seismic ΔVxx due to the Kuril Islands earthquakes ranges from − 0.13 to + 0.11 milli Eötvös, and ΔVxz shows a positive-negative-positive pattern ranges from − 0.16 to + 0.13 milli Eötvös, agree well with seismic model predictions.