Validation of calibrated GOCE gravity gradients GRD_SPW_2 by least-squares spectral weighting

<p>The Gravity field and steady-state Ocean Circulation Explorer (GOCE) was the first mission which carried a novel instrument, gradiometer, which allowed to measure the second-order directional derivatives of the gravitational potential or gravitational gradients with uniform quality and a near-global coverage. More than three years of the outstanding measurements resulted in two levels of data products (Level 1b and Level 2), six releases of global gravitational models (GGMs), and several grids of gravitational gradients (see, e.g., ESA-funded GOCE+ GeoExplore project or Space-wise GOCE products). The grids of gravitational gradients represent a step between gravitational gradients measured directly along the GOCE orbit and data directly from GGMs. One could use grids of gravitational gradients for geodetic as well as for geophysical applications. In this contribution, we are going to validate the official Level 2 product GRD_SPW_2 by terrestrial gravity disturbances and GNSS/levelling over two test areas located in Europe, namely in Norway and former Czechoslovakia (now Czechia and Slovakia). GRD_SPW_2 product contains all six gravity gradients at satellite altitude from the space-wise approach computed only from GOCE data for the available time span (r-2, r-4, and r-5) and provided on a 0.2 degree grid. A mathematical model based on a least-squares spectral weighting will be developed and the corresponding spectral weights will be presented for the validation of gravitational gradients grids. This model allows us to continue downward gravitational gradients grids to an irregular topographic surface (not to a mean sphere) and transform them into gravity disturbances and/or geoidal heights in one step. Before we compared results obtained by spectral downward continuation, we had to remove the high-frequency part of the gravitational signal from terrestrial data because in gravitational gradients measured at GOCE satellite altitude is attenuated. To do so we employ EGM2008 up to d/o 2160 and the residual terrain model correction (RTC) has been a) interpolated from ERTM2160 gravity model, b) synthesised from dV_ELL_Earth2014_5480_plusGRS80, c) calculated from a residual topographic model by forward modelling in the space domain.  </p>

An upward continuation method based on spherical harmonic analysis and its application in the calibration of satellite gravity gradiometry data

The ground gravity anomalies can be used to calibrate and validate the satellite gravity gradiometry data. In this study, an upward continuation method of ground gravity data based on spherical harmonic analysis is proposed, which can be applied to the calibration of satellite observations from the European Space Agency's Gravity Field and Steady-State Ocean Circulation Explorer (GOCE). Here, the following process was conducted to apply this method. The accuracy of the upward continuation method based on spherical harmonic analysis was verified using simulated ground gravity anomalies. The DTU13 global gravity anomaly data were used to determine the calibration parameters of the GOCE gravitational gradients based on the spherical harmonic analysis method. The trace and the tensor invariants I2, I3 of the gravitational gradients were used to verify the calibration results. The results revealed that the upward continuation errors based on spherical harmonic analysis were much smaller than the noise level in the measurement bandwidth of the GOCE gravity gradiometer. The scale factors of the Vxx, Vyy, Vzz, and Vyz components were determined at an order of magnitude of approximately 10−2, the Vxz component was approximately 10−3, and the Vxy component was approximately 10−1. The traces of gravitational gradients after calibration were improved when compared with the traces before calibration and were slightly better than the EGG_TRF_2 data released by the European Space Agency (ESA). In addition, the relative errors of the tensor invariants I2, I3 of the gravitational gradients after calibration were significantly better than those before calibration. In conclusion, the upward continuation method based on spherical harmonic analysis could meet the external calibration accuracy requirements of the gradiometer.

Daily generation of a footward fluid shift attenuates ocular changes associated with head-down tilt bed rest

Choroid measurements appear to be sensitive to changes in gravitational gradients, as well as periods of head-down tilt (HDT) bed rest, suggesting that they are potential indicators of early ocular remodeling and could serve to evaluate the efficacy of countermeasures for SANS. Eight hours of lower body negative pressure (LBNP) daily attenuates the choroid expansion associated with 3 days of strict −6° HDT bed rest, indicating that LBNP may be an effective countermeasure for SANS.

Temporal Gravity Signals in Reprocessed GOCE Gravitational Gradients

The reprocessing of the satellite gravitational gradiometry (SGG) data from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission in 2018/2019 considerably reduced the low-frequency noise in the data, leading to reduced noise amplitudes in derived gravity field models at large spatial scales, at which temporal variations of the Earth’s gravity field have their highest amplitudes. This is the motivation to test the reprocessed GOCE SGG data for their ability to resolve time-variable gravity signals. For the gravity field processing, we apply and compare a spherical harmonics (SH) approach and a mass concentration (mascon) approach. Although their global signal-to-noise ratio is <1, SH GOCE SGG-only models resolve the strong regional signals of glacier melting in Greenland and Antarctica, and the 2011 moment magnitude 9.0 earthquake in Japan, providing an estimation of gravity variations independent of Gravity Recovery and Climate Experiment (GRACE) data. The benefit of combined GRACE/GOCE SGG models is evaluated based on the ice mass trend signals in Greenland and Antarctica. While no signal contribution from GOCE SGG data additional to the GRACE models could be observed, we show that the incorporation of GOCE SGG data numerically stabilizes the related normal equation systems.

Using gravity gradients to estimate fault parameters in the Wichita Uplift region

SUMMARY The geological setting of southwestern Oklahoma and northeastern Texas is an ideal example of an aulacogen, the result of the tectonic evolution of a failed rift of the North American continent during the Palaeozoic era (540–360 Ma). The Wichita Province forms the uplifted basement portion of this Southern Oklahoma Aulacogen (SOA). The major fault zones to its north and south are clearly evident in gravity gradient maps produced by the recently constructed Earth Gravitational Model 2008 (EGM2008). Fault parameters, such as the dip angle, location and density contrasts have been estimated from profiles of seismic data and local gravimetry in the 1990s. On the other hand, gravitational gradients that are derived from EGM2008 and then combined to form the differential field curvature are particularly indicative of linear structures such as dip-slip faults. They are used here exclusively, that is, without additional geophysical constraints, in an optimal, least-squares estimation based on the Monte Carlo technique of simulated annealing to determine dip angle and location parameters of the major faults that border the Wichita Uplift region. Results show that these faults have small dip angles, in basic agreement with the low-angle faults inferred from seismic studies. The EGM2008 gradients also appear in some cases to provide an improved map of the major faults in the region, thus offering a strong constraint on their location.

Temporal gravity variations in GOCE release 6 gravitational gradients

&lt;p&gt;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&amp;#8217;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.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;

Dynamic behavior of coalbed methane flow along the annulus of single-phase production

Dynamic behavior of coalbed methane (CBM) flow will provide the theoretical basis to optimize production performance for a given well. A mathematical model is developed to simulate flowing pressures and pressure drops of CBM column from well head to bottom hole. The measured parameters and independent variables of flow rates, flowing pressures and temperatures are involved in CBM producing process along the annulus. The developed relationships are validated against full-scale measured data in single-phase CBM wellbores. The proposed methodology can analyze the dynamic behavior in CBM reservoir and process of CBM flow with an overall accuracy of 2%. The calculating process of flowing pressures involves friction factor with variable Reynolds number and CBM temperature and compressibility factor with gravitational gradients. The results showed that the effect of flowing pressure on CBM column was more obvious than that on CBM and water column accompanied by an increase of dynamic water level. The ratios of flowing pressure on increment of CBM column to the whole column increased with the declined flow rates of water column. Bottom-hole pressure declined with the decreased flowing pressure of CBM column along the annulus. It will lead to the results of the increased pressure drop of CBM column and CBM flow rate in single-phase CBM wellbores.