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The aim of this work is the evaluation of the geothermal potential of Luxembourg. The approach consists in a joint interpretation of different types of information necessary for a first rather qualitative assessment of deep geothermal reservoirs in Luxembourg and the adjoining regions in the surrounding countries of Belgium, France and Germany. For the identification of geothermal reservoirs by exploration, geological, thermal, hydrogeological and structural data are necessary. Until recently, however, reliable information about the thermal field and the regional geology, and thus about potential geothermal reservoirs, was lacking. Before a proper evaluation of the geothermal potential can be performed, a comprehensive survey of the geology and an assessment of the thermal field are required.
As a first step, the geology and basin structure of the Mesozoic Trier–Luxembourg Basin (TLB) is reviewed and updated using recently published information on the geology and structures as well as borehole data available in Luxembourg and the adjoining regions. A Bouguer map is used to get insight in the depth, morphology and structures in the Variscan basement buried beneath the Trier–Luxembourg Basin. The geological section of the old Cessange borehole is reinterpreted and provides, in combination with the available borehole data, consistent information for the production of isopach maps. The latter visualize the synsedimentary evolution of the Trier–Luxembourg Basin. Complementary, basin-wide cross sections illustrate the evolution and structure of the Trier–Luxembourg Basin. The knowledge gained does not support the old concept of the Weilerbach Mulde. The basin-wide cross sections, as well as the structural and sedimentological observations in the Trier–Luxembourg Basin suggest that the latter probably formed above a zone of weakness related to a buried Rotliegend graben. The inferred graben structure designated by SE-Luxembourg Graben (SELG) is located in direct southwestern continuation of the Wittlicher Rotliegend-Senke.
The lack of deep boreholes and subsurface temperature prognosis at depth is circumnavigated by using thermal modelling for inferring the geothermal resource at depth. For this approach, profound structural, geological and petrophysical input data are required. Conceptual geological cross sections encompassing the entire crust are constructed and further simplified and extended to lithospheric scale for their utilization as thermal models. The 2-D steady state and conductive models are parameterized by means of measured petrophysical properties including thermal conductivity, radiogenic heat production and density. A surface heat flow of 75 ∓ 7 (2δ) mW m–2 for verification of the thermal models could be determined in the area. The models are further constrained by the geophysically-estimated depth of the lithosphere–asthenosphere boundary (LAB) defined by the 1300 °C isotherm. A LAB depth of 100 km, as seismically derived for the Ardennes, provides the best fit with the measured surface heat flow. The resulting mantle heat flow amounts to ∼40 mW m–2. Modelled temperatures are in the range of 120–125 °C at 5 km depth and of 600–650 °C at the crust/mantle discontinuity (Moho). Possible thermal consequences of the 10–20 Ma old Eifel plume, which apparently caused upwelling of the asthenospheric mantle to 50–60 km depth, were modelled in a steady-state thermal scenario resulting in a surface heat flow of at least 91 mW m–2 (for the plume top at 60 km) in the Eifel region. Available surface heat-flow values are significantly lower (65–80 mW m–2) and indicate that the plume-related heating has not yet entirely reached the surface.
Once conceptual geological models are established and the thermal regime is assessed, the geothermal potential of Luxembourg and the surrounding areas is evaluated by additional consideration of the hydrogeology, the stress field and tectonically active regions. On the one hand, low-enthalpy hydrothermal reservoirs in Mesozoic reservoirs in the Trier–Luxembourg Embayment (TLE) are considered. On the other hand, petrothermal reservoirs in the Lower Devonian basement of the Ardennes and Eifel regions are considered for exploitation by Enhanced/Engineered Geothermal Systems (EGS). Among the Mesozoic aquifers, the Buntsandstein aquifer characterized by temperatures of up to 50 °C is a suitable hydrothermal reservoir that may be exploited by means of heat pumps or provide direct heat for various applications. The most promising area is the zone of the SE–Luxembourg Graben. The aquifer is warmest underneath the upper Alzette River valley and the limestone plateau in Lorraine, where the Buntsandstein aquifer lies below a thick Mesozoic cover. At the base of an inferred Rotliegend graben in the same area, temperatures of up to 75 °C are expected. However, geological and hydraulic conditions are uncertain. In the Lower Devonian basement, thick sandstone-/quartzite-rich formations with temperatures >90 °C are expected at depths >3.5 km and likely offer the possibility of direct heat use. The setting of the Südeifel (South Eifel) region, including the Müllerthal region near Echternach, as a tectonically active zone may offer the possibility of deep hydrothermal reservoirs in the fractured Lower Devonian basement. Based on the recent findings about the structure of the Trier–Luxembourg Basin, the new concept presents the Müllerthal–Südeifel Depression (MSD) as a Cenozoic structure that remains tectonically active and subsiding, and therefore is relevant for geothermal exploration. Beyond direct use of geothermal heat, the expected modest temperatures at 5 km depth (about 120 °C) and increased permeability by EGS in the quartzite-rich Lochkovian could prospectively enable combined geothermal heat production and power generation in Luxembourg and the western realm of the Eifel region.
The aim of this paper is to bring together two areas which are of great importance for the study of overdetermined boundary value problems. The first area is homological algebra which is the main tool in constructing the formal theory of overdetermined problems. And the second area is the global calculus of pseudodifferential operators which allows one to develop explicit analysis.
This article assesses the distance between the laws of stochastic differential equations with multiplicative Lévy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Lévy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate.
We elaborate a boundary Fourier method for studying an analogue of the Hilbert problem for analytic functions within the framework of generalised Cauchy-Riemann equations. The boundary value problem need not satisfy the Shapiro-Lopatinskij condition and so it fails to be Fredholm in Sobolev spaces. We show a solvability condition of the Hilbert problem, which looks like those for ill-posed
problems, and construct an explicit formula for approximate solutions.