Generation of 3D Spatially Variable Anisotropy for Groundwater Flow Simulations

Sedimentary units generally present anisotropy in their hydraulic properties, with higher hydraulic conductivity along bedding planes, rather than perpendicular to them. This common property leads to a modeling challenge if the sedimentary structure is folded. In this paper, we show that the gradient of the geological potential used by implicit geological modeling techniques can be used to compute full hydraulic conductivity tensors varying in space according to the geological orientation. For that purpose, the gradient of the potential, a vector normal to the bedding, is used to construct a rotation matrix that allows the estimation of the 3D hydraulic conductivity tensor in a single matrix operation. A synthetic 2D cross section example is used to illustrate the method and show that flow simulations performed in such a folded environment are highly influenced by this rotating anisotropy. When using the proposed method, the streamlines follow very closely the folded formation. This is not the case with an isotropic model.     

Identification of Groundwater Parameters Using an Adaptative Multiscale Method

The identification of groundwater parameters in heterogeneous systems is a major challenge in groundwater modeling. Flexible parameterization methods are needed to assess the complexity of the spatial distributions of these parameters in real aquifers. In this article, we introduce an adaptative parameterization to identify the distribution of hydraulic conductivity within the large‐scale (4400 km²) Upper Rhine aquifer. The method is based on adaptative multiscale triangulation (AMT) coupled with an inverse problem procedure that identifies the parameters' distributions by reducing the error between measured and simulated heads. The AMT method has the advantage of combining both zonation and interpolation approaches. The AMT method uses area‐based interpolation rather than an interpolation based on stochastic features. The method is applied to a standard 2D groundwater model that takes into account the interactions between the aquifer and surface water bodies, groundwater recharge, and pumping wells. The simulation period covers 204 months, from January 1986 to December 2002. Recordings at 109 piezometers are used for model calibration. The simulated heads are globally quite accurate and reproduce the main dynamics of the system. The local hydraulic conductivities resulting from the AMT method agree qualitatively with existing local experimental observations across the Rhine aquifer.     

Active spreading and hydrothermalism in North Fiji Basin (SW Pacific). Results of Japanese French Cruise Kaiyo 87

The aim of the Japanese-French Kaiyo 87 cruise was the study of the spreading axis in the North Fiji Basin (SW Pacific). A Seabeam and geophysical survey allowed us to define the detailed structure of the active NS spreading axis between 16° and 22° S and its relationships with the left lateral motion of the North Fiji Fracture Zone. Between 21° S and 18°10′ S, the spreading axis trends NS. From 18°10 S to 16°40 S the orientation of the spreading axis changes from NS to 015°. North of 16°40′ S the spreading axis trends 160°. These two 015° and 160° branches converge with the left lateral North Fiji fracture zone around 16°40′ S to define an RRFZ triple junction. Water sampling, dredging and photo TV deep towing give new information concerning the hydrothermal activity along the spreading axis. The discovery of hydrothermal deposits associated with living communities confirms this activity.     

Structural controls on the formation of BSR over a diapiric anticline from a dense MCS survey offshore southwestern Taiwan

A dense seismic reflection survey with up to 250-m line-spacing has been conducted in a 15 × 15 km wide area offshore southwestern Taiwan where Bottom Simulating Reflector is highly concentrated and geochemical signals for the presence of gas hydrate are strong. A complex interplay between north–south trending thrust faults and northwest–southeast oblique ramps exists in this region, leading to the formation of 3 plunging anticlines arranged in a relay pattern. Landward in the slope basin, a north–south trending diapiric fold, accompanied by bright reflections and numerous diffractions on the seismic profiles, extends across the entire survey area. This fold is bounded to the west by a minor east-verging back-thrust and assumes a symmetric shape, except at the northern and southern edges of this area, where it actively overrides the anticlines along a west-verging thrust, forming a duplex structure. A clear BSR is observed along 67% of the acquired profiles. The BSR is almost continuous in the slope basin but poorly imaged near the crest of the anticlines. Local geothermal gradient values estimated from BSR sub-bottom depths are low along the western limb and crest of the anticlines ranging from 40 to 50 °C/km, increase toward 50–60 °C/km in the slope basin and 55–65 °C/km along the diapiric fold, and reach maximum values of 70 °C/km at the southern tip of the Good Weather Ridge. Furthermore, the local dips of BSR and sedimentary strata that crosscut the BSR at intersections of any 2 seismic profiles have been computed. The stratigraphic dips indicated a dominant east–west shortening in the study area, but strata near the crest of the plunging anticlines generally strike to southwest almost perpendicular to the direction of plate convergence. The intensity of the estimated bedding-guided fluid and gas flux into the hydrate stability zone is weaker than 2 in the slope basin and the south-central half of the diapiric fold, increases to 7 in the northern half of the diapiric fold and plunging anticlines, and reaches a maximum of 16 at the western frontal thrust system. Rapid sedimentation, active tectonics and fluid migration paths with significant dissolved gas content impact on the mechanism for BSR formation and gas hydrate accumulation. As we begin to integrate the results from these studies, we are able to outline the regional variations, and discuss the importance of structural controls in the mechanisms leading to the gas hydrate emplacements.     

On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited

In the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance with the planet, characterized by a nonzero eccentricity and a resonant angle that librates around zero. Likewise, in the rotating frame with the planet, it describes the same trajectory as the one of a retrograde satellite even though the planet acts as a perturbator. In the last few years, the discoveries of asteroids in this type of motion made the term “quasi-satellite” more and more present in the literature. However, some authors rather use the term “retrograde satellite” when referring to this kind of motion in the studies of the restricted problem in the rotating frame. In this paper, we intend to clarify the terminology to use, in order to bridge the gap between the perturbative co-orbital point of view and the more general approach in the rotating frame. Through a numerical exploration of the co-orbital phase space, we describe the quasi-satellite domain and highlight that it is not reachable by low eccentricities by averaging process. We will show that the quasi-satellite domain is effectively included in the domain of the retrograde satellites and neatly defined in terms of frequencies. Eventually, we highlight a remarkable high eccentric quasi-satellite orbit corresponding to a frozen ellipse in the heliocentric frame. We extend this result to the eccentric case (planet on an eccentric motion) and show that two families of frozen ellipses originate from this remarkable orbit.     

On the co-orbital motion of two planets in quasi-circular orbits

We develop an analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. The Hamiltonian, averaged over one of the planetary mean longitudes, is expanded in power series of eccentricities and inclinations. The model, which is valid in the entire co-orbital region, possesses an integrable approximation modeling the planar and quasi-circular motions. First, focusing on the fixed points of this approximation, we highlight relations linking the eigenvectors of the associated linearized differential system and the existence of certain remarkable orbits like the elliptic Eulerian Lagrangian configurations, the anti-Lagrange (Giuppone et al. in MNRAS 407:390–398, 2010) orbits and some second sort orbits discovered by Poincaré. Then, the variational equation is studied in the vicinity of any quasi-circular periodic solution. The fundamental frequencies of the trajectory are deduced and possible occurrence of low order resonances are discussed. Finally, with the help of the construction of a Birkhoff normal form, we prove that the elliptic Lagrangian equilateral configurations and the anti-Lagrange orbits bifurcate from the same fixed point $L_4$ L 4 .