Empirical 3D basis for the internal density of a planet

International audienceVarious papers have discussed the forward relationships between internal density anomalies of a planet and its external gravity field. The inverse modeling, i.e. finding the internal density anomalies from the external potential is known to be highly non unique. In this research note, we explain how a 3D basis can be built to represent the internal density variations which includes a subset that explicitly spans the kernel of the forward gravity operator. This representation clarifies the origin of the non-uniqueness of the gravity sources and implies the existence of a natural minimal-norm inverse for the internal density. We illustrate these ideas by comparing a tomographic model of the mantle to the minimal norm density

Slightly more births at full moon

A popular belief holds that the number of births highly increases when the moon is full. To test this belief, we use a 50-year data set of 38.7 million births in France. The signal includes quasi-periodic and discrete components that need to be subtracted. This is done using a non-linear Gaussian least-squares method. It results in residuals with very good statistical properties. A likelihood ratio test is used to reject that the residual means for the 30 days of the lunar month all equal 0 (p-value = $5 \times 10^{-5}$): the residuals show very small but highly significant variations in the lunar month due to an increase of births at full moon and the day after. The reason for the very small increase of birth at full moon is not investigated but can be suspected to result from a self-fulfilling prophecy

Slightly more births at full moon

A popular belief holds that the number of births highly increases when the moon is full. To test this belief, we use a 50-year data set of 38.7 million births in France. The signal includes quasi-periodic and discrete components that need to be subtracted. This is done using a non-linear Gaussian least-squares method. It results in residuals with very good statistical properties. A likelihood ratio test is used to reject that the residual means for the 30 days of the lunar month all equal 0 (p-value = $5 \times 10^{-5}$): the residuals show very small but highly significant variations in the lunar month due to an increase of births at full moon and the day after. The reason for the very small increase of birth at full moon is not investigated but can be suspected to result from a self-fulfilling prophecy

Présentation et annotations du mémoire 8

International audienc

Earth gravity up to second order in topography and density

International audiencehe gravity potential of a planet is usually expanded up to first order only as a linear function of topography and lateral variations of density. In this article, we extend these expressions up to second order and we estimate the magnitude of the new non-linear terms. We find that they are not negligible when compared to observed values: tens of metres for height anomalies and tens of milligals for gravity anomalies. Therefore, second-order expressions should be taken into account when inverting global gravity data

Mean radius, mass, and inertia for reference Earth models

International audienceThis paper focuses on the global quantities, radius, mass, and inertia that are needed for the construction of reference Earth density models. We recall how these quantities b, M, and I are measured and we give realistic estimates and uncertainties. Since a reference model corresponds to a spherical average of the real Earth, we detail how these estimates need to be corrected in order to be used as input data for such a mean model. The main independent data to be used for reference models are: b=6 371 230±10 m, M0=(5.9733±0.0090)×10 24 kg, I0/ M0=(1.342 354±0.000 031)×10 13 m 2

Faut-il faire une description bibliographique des Principes mathématiques ?

International audienc

A stress interpretation scheme applied to lunar gravity and topography data

International audienceWe present an approach of the inverse gravimetric problem that allows the gravity to be directly related to the deviatoric stresses without any rheological assumptions. In this approach a new set of parameters is considered: (1) the density variations over equipotential surfaces and the height of interfaces above the corresponding equipotential surfaces and (2) the stress difference. The method is applied to lunar topographic and gravimetric data that are interpreted in term of transversally isotropic deviatoric stress within the Moon. It also provides inference on density and crustal thickness variations. The estimated lateral variation in deviatoric stress is about 500 bars within the crust and upper mantle. In the crust, because of topography, the strongest stress differences take place on the far side, with large lateral compressions beneath the south pole–Aitken basin. Vertical compression under the mascons of the nearside is the main feature within the upper mantle

Seismic attenuation in a phase change coexistence loop

International audienc

Constraining the kinetics of mantle phase changes with seismic data

International audienceIn a system where two phases coexist, a seismic wave can disrupt the pre-existing equilibrium and induce a re-equilibration process. Because the kinetics of the phase change is not instantaneous, the transformation induces an attenuation of the wave that can be quantified using an appropriate physical theory. Kinetics of Earths phase transitions are not well known: in this paper we show that they can be constrained by seismic attenuation data. We quantify the influence of a phase transition upon seismic mode attenuation and body wave reflexion coefficient. We perform a numerical application for the olivine to wadsleyite transition at 410 km depth, assuming a phase loop thickness of 10 km. We show that the relaxation time that controls the frequency band of attenuation and the velocity at which the interface evolves when submitted to a pressure disequilibrium, is likely larger than 7000 s. For this kinetics slower than typical seismic waves periods, the transformation loop does not affect S waves attenuation but potentially that of P waves and normal mode