A spatially-VSL gravity model with 1-PN limit of GRT

A scalar gravity model is developed according the 'geometric conventionalist' approach introduced by Poincare (Einstein 1921, Poincare 1905, Reichenbach 1957, Gruenbaum1973). In principle this approach allows an alternative interpretation and formulation of General Relativity Theory (GRT), with distinct i) physical congruence standard, and ii) gravitation dynamics according Hamilton-Lagrange mechanics, while iii) retaining empirical indistinguishability with GRT. In this scalar model the congruence standards have been expressed as gravitationally modified Lorentz Transformations (Broekaert 2002). The first type of these transformations relate quantities observed by gravitationally 'affected' (natural geometry) and 'unaffected' (coordinate geometry) observers and explicitly reveal a spatially variable speed of light (VSL). The second type shunts the unaffected perspective and relates affected observers, recovering i) the invariance of the locally observed velocity of light, and ii) the local Minkowski metric (Broekaert 2003). In the case of a static gravitation field the model retrieves the phenomenology implied by the Schwarzschild metric. The case with proper source kinematics is now described by introduction of a 'sweep velocity' field w: The model then provides a hamiltonian description for particles and photons in full accordance with the first Post-Newtonian approximation of GRT (Weinberg 1972, Will 1993).Comment: v1: 11 pages, GR17 conf. paper, Dublin 2004, v2: WEP issue solved, section on acceleration transformation added, text improved, more references, same results, v3: typos removed, footnotes, added and references updated, v4: appendix added, improved tex

A Three-Part Study of NMR Longitudinal Relaxation Properties of Water-Saturated Sandstones

Borehole measurements of the nuclear magnetic resonance (NMR) properties of rocks have been of interest for many years, especially for estimating permeability. This paper presents laboratory measurements of the NMR properties of water-saturated rocks and shows that permeability can be estimated well with expressions of the form T , where T1 is the relaxation time constant of the longitudinal nuclear magnetization of hydrogen nuclei. Different methods of representing the laboratory- measured T1 curves are shown, including a new one called the stretched- exponential representation. An improved method for estimating T1 parameters from borehole measurements that can be used with either old or new representations is presented. IntroductionIn this paper, we pursue permeability estimation from borehole NMR* longitudinal relaxation (T1) measurements. Many previous workers have demonstrated the potential of NMR for this application; however, we make closer and more consistent connections between the components linking permeability and borehole NMR than have previously been published. These components are addressed in the three parts that follow, 1. Stretched-exponential representation of laboratory T1 measurements. We present the results of laboratory NMR measurement on approximately 60 water-saturated rocks. We introduce a new representation for the NMR curve, called the stretched-exponential representation, that has the practical advantage of having fewer pa-rameters than the classical two- and three-exponential representations of NMR measurements. Such representations are important in reducing the measurement to a few parameters that can be correlated to properties of practical importance. 2. Estimation of permeability from laboratory measurements. We use the data base of 60 rocks from Part 1 to find the best estimator of permeability from NMR T1 measurements. An important result is that permeability is estimated better by T1 than by Seevers classic estimator . 3. Extraction of NMR T1 parameters from borehole NMR measurements. To apply the correlations of Part 2 to borehole data, we introduce a new method of extracting the important T, parameters from downhole NMR T1 measurements: in this method, called "global fitting," a model is fitted simultaneously to the set of free induction decay (FID) waveforms collected for different polarizing times during a station measurement. We exhibit two suitable models. Both have the advantage of accommodating some complexities observed in borehole waveforms and verified in a corresponding laboratory measurement. In particular, the observed decay time of the FID waveforms decreases as the polarizing time decreases. This paper concentrates on the NMR property T1 and does not investigate the parameter called free fluid index (FFI). The reasons for this emphasis are two-fold. First, T1 is a more complete measurement, and thus gives a better picture of the potential of NMR in permeability estimation. Second, FFI is specifically a low-field measurement, which is much less convenient to measure in the laboratory. Borehole T1 data can he obtained with existing commercial nuclear magnetic log (NMLTM) equipment by making stationary measurements. A key issue in this paper is compact representation-finding ways to describe accurately the observed behavior with only a small number of parameters. Representation is an issue in Part 1, dealing with laboratory T1 measurements, because a complete curve must be described. Part 2 shows that all the representations used here allow equally good permeability estimation. In Part 3, dealing with borehole T1 data. representation is important because of the need to work around measurement dead-time, and because borehole measurements in practice have a lower signal-to-noise ratio than laboratory measurements. Throughout, compactness of a representation is weighed against its ability to fit the measurements and its appropriateness for estimating permeability. Part 1-Stretched-Exponential Representation of Laboratory T1 Measurements Laboratory Technique. We measured porosity, permeability, and NMR T1 properties on water-saturated sandstone samples from five oilfield wells in different parts of the world, plus a number of quarried sandstone samples. Samples were cut to Hassler collar size2.0 cm [0.78 in.] in diameter and approximately 4 cm [ 1.57 in.] long; the samples were cored parallel to any visible bedding planes in the original rocks. Sample porosities were determined by Archimedes' methodi.e., measuring dry sample weight. saturated weight, and buoyant weight of the water-saturated sample. Permeabilities to water were measured end-to-end on the samples encased in a Hassler collar, at room temperature, with a collar pressure in the neighborhood of 414 kPa [60 psi]. Because our measured permeabilities are thus for single-phase parallel-to-bedding flow, the final output of our permeability estimators will be for the same quantity. Laboratory NMR measurements were made using an IBM/Bruker PC10. The PC10 is a desk-top permanent magnet instrument that makes pulsed measurements of proton resonance at 10 MHz [10(6) cycles/sec). Samples for NMR measurement were surface-dried and then wrapped in Saran(TM) wrap held in place by rubber bands to reduce evaporation during measurement; these wrapping materials contributed a negligible signal for the water volumes of our samples. Before measurement, samples were allowed to equilibrate to the magnet temperature, which is thermostatically maintained at 40 degrees C [104 degrees F]. The fundamental NMR property to be measured is the time evolution of proton magnetization along the direction of the applied magnetic field. This behavior of the "longitudinal" magnetization is called T1. SPEFE P. 622