(Table 1) Gravity and pressure within the Sleipner area relative to ones at the reference station in 2002 and 2005

At Sleipner, CO2 is being separated from natural gas and injected into an underground saline aquifer for environmental purposes. Uncertainty in the aquifer temperature leads to uncertainty in the in situ density of CO2. In this study, gravity measurements were made over the injection site in 2002 and 2005 on top of 30 concrete benchmarks on the seafloor in order to constrain the in situ CO2 density. The gravity measurements have a repeatability of 4.3 µGal for 2003 and 3.5 µGal for 2005. The resulting time-lapse uncertainty is 5.3 µGal. Unexpected benchmark motions due to local sediment scouring contribute to the uncertainty. Forward gravity models are calculated based on both 3D seismic data and reservoir simulation models. The time-lapse gravity observations best fit a high temperature forward model based on the time-lapse 3D seismics, suggesting that the average in situ CO2 density is about to 530kg/m**3. Uncertainty in determining the average density is estimated to be ±65 kg/m**3 (95% confidence), however, this does not include uncertainties in the modeling. Additional seismic surveys and future gravity measurements will put better constraints on the CO2 density and continue to map out the CO2 flow.

Sensitivity analysis of vehicle tripped rollover model. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Toy model for a relational formulation of quantum theory

In the absence of an external frame of reference-i.e., in background independent theories such as general relativity-physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is twofold. First, we demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental. Second, we describe how the original non-relational theory approximately emerges from the fully relational theory when reference systems become semi-classical. Our technique is motivated by a Bayesian approach to quantum mechanics, and relies on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, our model circumvents the problem of the collapse of the wave packet as the probability interpretation is only ever applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of spin networks introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semiclassical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.

Gravity field recovery using two low satellites in different orbital planes

This study is concerned with gravity field recovery from low-low satellite to satellite range rate data. An improvement over a coplanar mission is predicted in the errors associated with certain parts of the geopotential by the separation of the orbital planes of the two satellites. Using Hill's equations an analytical scheme to model the range rate residuals is developed. It is flexible enough to model equally well the residuals between pairs of satellites in the same orbital plane or whose planes are separated in right ascension. The possible benefits of such an orientation to gravity field recovery from range rate data can therefore be analysed, and this is done by means of an extensive error analysis. The results of this analysis show that for an optimal planar mission improvements can be made by separating the satellites in right ascension. Gravity field recoveries are performed in order to verify and gauge the limitations of the analytical model, and to support the results of the error analysis. Finally the possible problem of the differential decay rates of two satellites due to the diurnal bulge are evaluated.