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This report constitutes Deliverables 9.8 for Work Package 9 of the InGRID-2 project. Small area estimation (SAE) has received considerable attention in the recent decades and is becoming increasingly important for a variety of socio-economic and policy purposes (Ghosh and Rao, 1994; Rao, 2003; Pfeffermann, 2013). As remarked by Tzavidis et al. (2018), SAE is a 'simultaneous' rather than a 'point' estimation problem. Both area-specific and ensemble properties of a set of small area estimates, such as their dispersion, rank and order statistics, are undoubtedly of interest. This is a distinctive feature of small area statistics in comparison with the national estimate that is a single number. As we shall explain, to accommodate multiple purposes, the set of small area estimates need to be derived in a constrained fashion, hence the term constrained SAE. This methodological report consists of two parts. In the first part, we review and explore the central ideas relevant to constrained SAE, as well as the most common model-based approaches. Formulating a constrained optimisation problem appears to be a more practical approach. In particular, we shall develop an analytic solution, when the constraints include three first- and second-order empirical moments of the small area estimates. The existing approaches in the literature accommodate only one or two of these constraints. However, even this approach may lack compatibility to the reality of survey sampling, where the national and major domain estimates are derived under the inference framework that is not model-based but design-based. In the second part, we develop a new design-based model-assisted approach to SAE, where we extend generalised regression (e.g. Särndal et al., 1992) from direct estimation for the whole population to indirect estimation of all the area populations. This enables a practical methodology for estimation, which is coherent numerically between the different aggregation levels, as well as conceptually in terms of the inference outlook.

The role of lateral variations of crustal rheology and surface heat flow in the Northern Apennines is explored in order to investigate the geodynamic conditions correlated with the formation of a new E-dipping normal faults in the belt. The sharp variation of the heat flow at the surface along SW-NE profiles marks the transition from a western or Tyrrhenian domain, where extensional deformation has destroyed the preexisting compressional belt, and an eastern or Adriatic domain, where the compressional structures are preserved. The present extension-compression boundary approximately coincides with the youngest and easternmost expression of extension of the Northern Apennines: the Alto Tiberina E-dipping normal fault and associated antithetic faults (cf. e.g Barchi et al., 1999; Boncio e Lavecchia 2000; Collettini and Barchi, 2002; Piccinini et al., 2003; Chiaraluce et al., 2007; Mirabella et al., 2011). The transition between the two domains is approximately marked by the zero gravimetric anomaly (Marson et al., 1998) and by an increase in the depth of the Moho towards the east (from about 20 km to about 40 km, cf. e.g. De Franco et al., 1998). In the transition area, a decrease of surface heat flow is observed, from values of 150 mW/m2 or higher in the Tyrrhenian domain to 70-40 mW/m2 in the Adriatic domain However, the change in surface heat flow occurs in an area where the measuring points are very few (CNR, 1994). To reconstruct the thermal state of the subsurface, we review and analyze the available geothermal measurements from 192 deep boreholes present in this sector of the Northern Apennines and drilled for geothermal and oil exploration purposes, available from the Istituto di Geoscienze e Georisorse (IGG) of the Italian National Research council (CNR) which, has updated the Italian National Geothermal Database (Trumpy and Manzella, 2017). The borehole temperatures have been corrected for drilling, inclination, and topographic effects. The corrected temperature data, combined with petrophysical parameters for each individual formation, have been used to derive shallow geotherms (down to a maximum depth of 8 km), which have yielded site-specific heat flow values. These values, once corrected for palaeoclimatic and erosion/ sedimentation effects, have been contoured by a kriging procedure to obtain the heat flow map. The heat flow map shows clearly two areas, a western one characterized by high and spatially inhomogeneous heat flow, and an eastern one characterized by lower and spatially more homogeneous heat flow (extending approximately to the Adriatic coast). The surface heat flow isoline of 70 mW/m2 separates these two areas, and correlates well with a significant tectonic transition, separating a rheologically weak, hot lithosphere in the western sector and a stronger, cooler lithosphere in the eastern sector, as shown by rheological profiles. Surface heat flow increases (to values larger than 100 mW m2) approaching the Adriatic coast and especially offshore; the latter part was not covered in previous maps. The temperature distribution thus obtained was used to estimate the rheological characteristics of the subsurface. Two-dimensional rheological profiles across the ATF show that lateral rheological crustal variations have played an important role in the formation of the ATF and similar previously active extensional faults to the west. Lithospheric delamination and mantle degassing in the Tyrrhenian domain resulted in an easterly-migrating extension-compression boundary, characterized by the following properties: (i) the thickness of the upper crust brittle layer reaches a maximum; (ii) the critical stress difference required to initiate faulting at the base of the brittle layer is at a minimum; and (iii) the total strengths of both the brittle layer and the whole lithosphere are at a minimum. Our conclusions are independent of any specific geodynamic models, and their reliability is a function only of the estimated crustal temperature distribution and rheological parameters.With respect to the latter, we have explored a range of values in the brittle and ductile fields, and the results are not critically parameter-dependent.

Rifting processes result from the application of extensional stresses to a pre-deformed, and thus already structured, anisotropic lithosphere; consequently, the pre-rift lithospheric rheological structure and its along-axis variations play a major role in controlling the evolution and architecture of continental rifts. The East African Rift is a classic example of this process. The rift system developed within a region that has experienced several deformation events, which have given rise to significant variations in the rheological structure of the lithosphere. These variations -in turn- have played a major role on rift evolution, as clearly testified by the localisation and propagation of major rift segments within weak Proterozoic mobile belts surrounding cratonic areas. Linkage and mechanical interaction between adjacent rift segments typically occurred in correspondence to transverse pre-existing fabrics, where structurally complex areas (transfer zones) allowed significant along-axis variations in subsidence of grabens and elevation of uplifted flanks. One of these complex areas is the Turkana depression where the Ethiopian and Kenyan rifts interact. The region is characterised by anomalous morphology and distribution of deformation with respect to the rift valleys in Kenya and Ethiopia. In this work we investigate whether these anomalies result from the presence of a pre-existing Mesozoic graben, transverse to the trend of the rift valleys and characterized by thin crust and lithosphere. To this aim, we integrate crustal-scale, isothermal analog experiments with lithospheric-scale, thermo-mechanical numerical models. The two different methodologies generate very similar results, reproducing the along-axis transition from narrow rift valleys in Ethiopia/Kenya to a distributed deformation within the Turkana depression. Modeling results indicate that this variation results from the inherited distribution of lithospheric strength and -in particular- from the presence of a NW-SE trending region of thinned crust generated during the Mesozoic rifting event. Similarly to what observed in nature, our models show that the rift valleys propagated away from each other within the Turkana depression, thus avoiding a direct link to form a throughgoing N-S structure. Our models indicate that local-scale characteristics of the fault pattern (such as the occurrence of horse-tail splays at fault terminations or the presence of faults with zig-zag plan-view geometry giving rise to basins with a ’staircase’ pattern as in the case of Lake Turkana) may result from a minor component of strike-slip motion controlled by relative orientation between the NW-SE oriented domain of thinned crust and roughly E-W direction of Extension.

Inherited rheological structures in the lithosphere are expected to have large impact on the architecture of continental rifts. The Turkana depression in the East African Rift connects the Main Ethiopian Rift to the north with the Kenya rift in the south. This region is characterized by a NW-SE trending band of thinned crust inherited from a Mesozoic rifting event, which is cutting the present-day N-S rift trend at high angle. In striking contrast to the narrow rifts in Ethiopia and Kenya, extension in the Turkana region is accommodated in subparallel deformation domains that are laterally distributed over several hundred kilometers. We present both analog experiments and numerical models that reproduce the along-axis transition from narrow rifting in Ethiopia and Kenya to a distributed deformation within the Turkana depression. Similarly to natural observations, our models show that the Ethiopian and Kenyan rifts bend away from each other within the Turkana region, thus forming a right-lateral step over and avoiding a direct link to form a continuous N-S depression. The models reveal five potential types of rift linkage across the preexisting basin: three types where rifts bend away from the inherited structure connecting via a (1) wide or (2) narrow rift or by (3) forming a rotating microplate, (4) a type where rifts bend towards it, and (5) straight rift linkage. The fact that linkage type 1 is realized in the Turkana region provides new insights on the rheological configuration of the Mesozoic rift system at the onset of the recent rift episode.

The East Tenda Shear Zone (ETSZ) is themajor Alpine tectonic boundary marking the overthrusting of the ocean-derived Schistes Lustrés nappe onto the Variscan crystalline basement of Corsica. New structural, mineralogical, and geochemical investigations along a transect ranging from the Variscan basement to the contact with the Schistes Lustrés are used to construct a rheological model for the ETSZ during its polyphase deformation history. The progressive transformation of the isotropic granitoid protolith into gneisses, shear zones, and, locally, phyllonites is described. The textural/mineralogical change suggests a concurrent increasing metasomatism associated with structurally controlled fluid flow. The effect of such textural/mineralogical evolution on the bulk rheology of the ETSZ is estimated. Rheological flow laws are obtained using an averaging procedure based on the integration of single-phase rheological behavior. The flow laws are used to infer strain rates and construct strength envelopes for each structural domain during progressive deformation, which highlight the relative rheological differences of the main textural components of the ETSZ and the variations in their brittle/ductile transition depths. Two competing processes are inferred. On the one hand, the combined effects of the feldspar-to-mica reaction and the development of a strong planar fabric induce weakening and strain localization along shear zones. On the other hand, fluid channeling along these shear zones enhances alkali feldspar neoblastesis, inducing strain hardening. Among the possible consequences of such feedback processes between strain localization andfluid-rock interaction are episodes of rheological transitions fromductile to brittle behavior during the polyphase tectonic evolution of the ETSZ.

Analogue models are used to investigate extension of a continental lithosphere weakened by asthenospheric melts percolating through the upper mantle, a process that has been hypothesised to control the opening of the Ligurian Tethys. Models were performed in a centrifuge apparatus and reproduced, by using materials such as sand and viscous mixtures, extension of ∼60-km thick, three-layer continental lithosphere floating above the asthenosphere. The percolated lithospheric mantle was assumed to be characterised by a rheological behaviour similar to that of the asthenosphere. Two sets of experiments investigated the influence on deformation of (1) the thickness of the percolated mantle and the associated strength contrast between the normal and weakened lithosphere, and (2) the lateral width of the weakened zone. Model results suggest that mantle percolation by asthenospheric melts is able to promote strong localised thinning of the continental lithosphere, provided that a significant thickness of the lithospheric mantle is weakened by migrating melts within a narrow region. Strain localisation is maximised for percolation of the whole lithospheric mantle and strong strength contrast between the normal and weakened lithosphere. Under these conditions, the thickness of the lithosphere may be reduced to less than ∼12 km in ∼3 Ma of extension. Conversely, localised thinning is strongly reduced if the thickness of the percolated zone is ≤1/3 of the thickness of the whole lithospheric mantle and/or the lithosphere is weakened over wide regions. Overall, model results support the working hypothesis that mantle percolation by asthenospheric melts is a controlling factor in the transition from distributed continental deformation to localised oceanic spreading.

The beneficial effects of biochar, obtained from the carbonization of orchard pruning residues were analyzed on lettuce (Lactuca sativa L.) and tomato (Solanum lycopersicum Mil.) in a pot experiment with four substrates. Lettuce plants were grown in poor soil (PS), poor soil plus biochar (PSB), poor soil plus compost (PSC) and poor soil ((in term of carbon content and nitrogen content) plus compost and biochar (PSCB). Tomato plants were grown in poor soil (PS), poor soil plus biochar (PSB), rich soil (in term of carbon content and nitrogen content) (RS) and rich soil plus biochar (RSB). The effects of different substrates were assessed by chemical, physical and microbiological analysis of soil. Additionally, a first screening was done on the potential toxicity of biochar on plant seeds, using Lepidium sativum as model species, and earthworm (Lombricus terrestris) as bioindicator of the soil quality (Standard methods: ISO 17512-1:2008). To accomplish this aim, the main chemical parameters of the substrates were analyzed: moisture, pH, electrical conductivity (EC), ash, organic matter (OM), cation exchange capacity (CEC), total nitrogen (N), total and available phosphorus (P) and organic carbon (Corg). The main nutritional traits (free sugar, phenols, protein content, etc) were determined in plants. The amounts of toxic elements were assessed in plants and substrates. In detail, sixteen polycyclic aromatic hydrocarbons and main polychlorinated biphenyls were analyzed after automated Soxhlet extraction using 1:1 (v/v) acetone/hexane (EPA methods 3541) and quantified by GC-MS. The heavy metal concentrations were analyzed by using atomic absorption spectrophotometer (ISO 11466). For microbiological analysis, the activity of 19 hydrolytic enzymes was assessed by API-ZYM system together with the analysis of total aerobic viable, cellulolytic and spore-forming bacteria. Experimental results showed that biochar was not toxic to biotic soil communities (seeds and earthworms). The chemical analysis of PS lettuce plants indicated that biochar increased EC, OM, total N, Corg, total and available P in PSB and PSCB. However, the highest increments were obtained in PSBC. The chemical analysis of soil growing tomato plants demonstrated that the biochar addition increased EC, OM, Corg, total N and moisture in PSB and RSB; whereas total and available P increased in PSB and RSB, respectively. Again, the highest increments were obtained in RSB. No variations were recorded in Cd, Cr, Co and Pb content between the different treatments. Microbiological analysis confirmed that biochar increased the microbe biomass and the enzymatic activities. Analyses of substrate-microbe-plant system provide an experimental framework that help defining the benefit and toxicity of biochar addition on physical and chemical properties of PS and RS, as well as the interactions with microbial communities.

The East Tenda Shear Zone (ETSZ) is the major Alpine tectonic boundary marking the overthrusting of the oceanicderived Schistes Lustrés nappe onto the Hercynian crystalline basement of western Corsica. In this work we present new structural and geochemical investigations along a transect ranging from the undeformed protolith (PR) to the contact with the Schistes Lustrés. The results are used to construct a rheological model for the ETSZ. Shear deformation within the ETSZ is heterogeneously distributed with high-strain domains (shear zones, SZ) wrapping sigmoid shaped low-strain domains (massive lenses, ML). Locally, mica-rich mylonites occur (phyllonites). The main foliation is concordant with that in the overlying Schistes Lustrés, strikes NW-SE, and is dominantly shallow-dipping to NE. The ML mineralogy consists of an assemblage made of quartz, phengite and (relict) feldspar (epidote, Fe-oxides, zircon and allanite as accessory phases). The SZ mineralogy is invariably dominated by highly celadonitic (Si4+= 3.5-3.7 a.p.f.u.) phengite (40 ± 10 vol%) and modally abundant quartz (35 ± 5 vol%), albite (15 ± 5 vol%) epidote (