Shallow Domain Research Articles

Rigidity of a Thin Domain Depends on the Curvature, Width, and Boundary Conditions

This paper is concerned with the study of linear geometric rigidity of shallow thin domains under zero Dirichlet boundary conditions on the displacement field on the thin edge of the domain. A ribbon is a thin domain that has in-plane dimensions of order O(1) and \(\epsilon ,\) where \(\epsilon \in (h,1)\) is a parameter (here h is the thickness of the domains). The problem has been solved by Grabovsky and the second author in (Ann de l’Inst Henri Poincare (C) An Non Lin 2018 35(1):267–282, 2018) and by the second author in (Arch Ration Mech Anal 226(2):743–766, 2017) for the case \(\epsilon =1,\) with the outcome of the optimal constant \(C\sim h^{-3/2},\) \(C\sim h^{-4/3},\) and \(C\sim h^{-1}\) for parabolic, hyperbolic, and elliptic thin domains respectively. We prove in the present work that in fact there are two distinctive scaling regimes \(\epsilon \in (h,\sqrt{h}]\) and \(\epsilon \in (\sqrt{h},1),\) such that in each of which the thin domain rigidity is given by a certain formula in h and \(\epsilon .\) An interesting new phenomenon is that in the first (small parameter) regime \(\epsilon \in (h,\sqrt{h}]\), the rigidity does not depend on the curvature of the thin domain mid-surface.

Liberating microfossils from indurated carbonates: comparison of three disaggregation methods

Abstract. Three disaggregation methods, i.e. Calgon, acetic acid and electric pulse fragmentation (EPF), have been applied to a range of heavily lithified, carbonate-rich sedimentary rock samples of Paleogene age. Samples are predominantly from the carbonate-rich, shallow water domain (<250 m palaeo-water depth) of Tanzania, Malta and the United Arab Emirates (Paleogene Tethys Ocean). The effectiveness and efficiency of each method has been compared, in addition to the preservation of the resultant liberated microfossil material (primarily larger foraminifera; LF). Of the three methods, the most efficient and effective was EPF, which liberated the largest number of LF in a very short processing time and resulted in the best preservation. Samples with calcitic, silicic, and clay matrices and cements were successfully disaggregated using EPF. In this study, recovered microfossils were largely >500 µm, suggesting this technique may be more appropriate for liberating larger microfossils (e.g. LFs); however, we discuss nuances to the method that would allow for more effective recovery of smaller microfossil specimens. The more traditional acetic acid method was also able to disaggregate a number of the samples; however, preservation of the LF was compromised. We suggest a best-practice methodology for implementing EPF in micropalaeontological studies.

Weak solution of the merged mathematical equations of the polluted atmosphere

Considered as a geophysical fluid, the polluted atmosphere shares the shallow domain characteristics with other natural large‐scale fluids such as seas and oceans. This means that its domain is excessively greater horizontally than in the vertical dimension, leading to the classic hydrostatic approximation of the Navier–Stokes equations. In the past there has been proved a convergence theorem for this model with respect to the ocean, without considering pollution effects. The novelty of this present work is to provide a generalization of their result translated to the atmosphere, extending the fluid velocity equations with an additional convection–diffusion equation representing pollutants in the atmosphere.

Characterizing hydrological processes within kettle holes using stable water isotopes in the Uckermark of northern Brandenburg, Germany

AbstractUnderstanding the hydrologic connectivity between kettle holes and shallow groundwater, particularly in reaction to the highly variable local meteorological conditions, is of paramount importance for tracing water in a hydro(geo)logically complex landscape and thus for integrated water resource management. This article is aimed at identifying the dominant hydrological processes affecting the kettle holes' water balance and their interactions with the shallow groundwater domain in the Uckermark region, located in the north‐east of Germany. For this reason, based on the stable isotopes of oxygen (δ18O) and hydrogen (δ2H), an isotopic mass balance model was employed to compute the evaporative loss of water from the kettle holes from February to August 2017. Results demonstrated that shallow groundwater inflow may play the pivotal role in the processes taking part in the hydrology of the kettle holes in the Uckermark region. Based on the calculated evaporation/inflow (E/I) ratios, most of the kettle holes (86.7%) were ascertained to have a partially open, flow‐through‐dominated system. Moreover, we identified an inverse correlation between E/I ratios and the altitudes of the kettle holes. The same holds for electrical conductivity (EC) and the altitudes of the kettle holes. In accordance with the findings obtained from this study, a conceptual model explaining the interaction between the shallow groundwater and the kettle holes of Uckermark was developed. The model exhibited that across the highest altitudes, the recharge kettle holes are dominant, where a lower ratio of E/I and a lower EC was detected. By contrast, the lowest topographical depressions represent the discharge kettle holes, where a higher ratio of E/I and EC could be identified. The kettle holes existing in between were categorized as flow‐through kettle holes through which the recharge takes place from one side and discharge from the other side.

Sensitivity of a 3D Shelf Sea Ecosystem Model to Parameterizations of the Underwater Light Field

The inherent optical properties of water over the North Sea vary widely in space and time. Their impact on the performance of 3D-ecosystem-model of the North Sea needs to be critically evaluated, which is the major research issue in the present paper. We have performed a sensitivity analysis to a modification of a common approach of light treatment that is both valid for the North Sea, as well as computationally efficient to implement and run within a 3D-ecosystem-model. Using a coupled hydrodynamical model (Regional Ocean Modelling System, ROMS) and biological model (Carbon Silicate and Nitrogen Ecosystem model, CoSiNE), we found that simple changes to the original parameterization can yield significant improvements. ROMS is shown to be suitable for application in the North Sea. The model accurately reproduces the seasonal cycle of primary production in terms of timing and magnitude, while still being more affordable in comparison to full hyperspectral treatment or solving the radiative transfer equation. The modification introduces vertically increasing attenuation that is stronger in shallow domains, in a way that is similar to attenuation due to sediment. The resulting reduction of light availability leads to strongly reduced phytoplankton growth in shallow areas with high turbidity. Areas of depths between $50m$ and $100m$ show greatest relative change with respect to their total ranges, while the deepest areas remain largely unchanged. We found that the consideration of spacial varibility of light attenuation is necessary when modelling a heterogeneous domain, such as the North Sea.

Oncoid distribution in the shallow domains of a Kimmeridgian carbonate ramp (Late Jurassic, NE Spain)

The distribution and abundance of oncoids in the shallow domains of a latest Kimmeridgian carbonate ramp was accomplished on the basis of a detailed sedimentological and petrographic analysis of the lower part of the Higueruelas Formation (Iberian Basin, northeastern Spain). Six types of oncoids are recognized based on the internal structure of the cortex, and show a preferential distribution on the carbonate ramp, which record from intertidal, lagoon, backshoal, shoal-sand blanket, foreshoal to offshore domains. Spherical type I oncoids, composed of continuous micritic laminae, occur in all the subenvironments in low proportions. Sub-spherical type II oncoids, constituted by micritic laminae and discontinuous organism-bearing laminae of mostly Bacinella irregularis, dominate in the higher-energy shoal-sand blanket domain. Type III oncoids, with alternating micritic and organism-bearing laminae of mostly Bacinella irregularis-Lithocodium aggregatum association, include two varieties: type IIIa oncoids, with micritic and organism-bearing laminae of similar thickness, preferentially formed in the foreshoal domain; and type IIIb oncoids, with thinner micritic laminae, formed in a low-energy sheltered lagoon. Irregular type IV oncoids characterize the low-energy settings, and include two varieties: type IVa oncoids, mainly consisting of a Bacinella-Lithocodium meshwork, which occur abundantly in the lagoon; and less abundant type IVb oncoids, composed of a continuous organism-bearing laminae of Lithocodium, which are found in the offshore domain. Water energy and platform morphology played an important role in formation and distribution of the oncoids in these shallow domains, where normal-marine water and oligotrophic conditions are highlighted by the high-diversity of light-dependant micro-encrusters in type III and IV oncoids. Comparable oncoid distribution patterns of diverse Late Jurassic shallow carbonate platforms enhance their potential use as reliable palaeoenvironmental proxies.

Application of SWAN model for storm generated wave simulation in the Canadian Beaufort Sea

The wave model SWAN (Simulating WAves Nearshore) is implemented for the Canadian Beaufort Sea and storm generated waves are investigated through comparisons between in situ buoy observations and numerical simulations. Simulations are performed for four storms using the SWAN wave model. We specifically use SWAN's non-stationary and two-dimensional modes in a fine resolution nested domain within a coarse resolution domain. Two established whitecapping formulations in SWAN are examined; one is dependent on mean spectral wave steepness and the other is on local spectral steepness. Model simulations in the shallow fine resolution domain also consider the effects of bottom friction and nonlinear triad interactions. For the Beaufort Sea study area, wave simulations in which the white capping formulation is dependent on local spectral steepness are better than those where the dependency is on mean spectral steepness; however implementation of bottom friction term and triad mechanisms in the present study does not lead to any notable enhancement in the simulations.

Carbonate production, accumulation and sea-level change in fault-block platform setting: a case study on the Albian sequences in Central Tunisia

The Albian series have been deposited on both sides of a major E–W paleogeographic fault, which was inherited in the early stages of the Tethyan-rifting phase. To the south of this fault, a shallow platform domain (footwall block or horst) occurred and is relayed northward by a slope-deep shelf setting (hanging wall block or graben). The platform to basin transition was analyzed northward of this fault nearby M’rhila Mountains. A detailed sedimentological study, coupled with a tectonic analysis, indicates that the Albian sedimentary deposits consist of four third-order depositional sequences. The three lower ones are only present in the deep-shelf setting and include substantial carbonate accumulations. The latter deposits are generally arranged into alternating mud-rich-bedded limestone and conglomeratic levels. Most of this material was exported from the adjacent shallow platform by mass flow and suspension transport processes. In the studied series, the maximum carbonate accumulation is recorded in the deep shelf during the moderate transgressive increasing and the late highstand decreasing rates of sea-level rise. However, the minimum carbonate sedimentation is thought to be linked to both the minimum lowstand and the maximum transgressive sea-level rise. The uppermost depositional sequence—which occurs on both sides of the major fault, is different from the three lower ones as it includes only scarce thin re-sedimented limestone beds. The youngest sequence is related to an important interplay between a pulse of tectonic subsidence and the major see level rise that happened during the upper Albian (100–98.9 Ma), resulting in a regional collapse of the substratum and the drowning of the carbonate factory situated southward. Therefore, the uppermost sequence is considered as a tectonically originated depositional sequence rather than a “pure” eustatic one. The organic-rich deposits associated to this sequence south and north of the major fault correlate well with the global anoxic events. The present study case represents a good example illustrating the role of local tectonics and global eustatic fluctuations in controlling not only the facies and thickness distribution but also the carbonate production and accumulation.

Deep visual domain adaptation: A survey

Deep domain adaption has emerged as a new learning technique to address the lack of massive amounts of labeled data. Compared to conventional methods, which learn shared feature subspaces or reuse important source instances with shallow representations, deep domain adaption methods leverage deep networks to learn more transferable representations by embedding domain adaptation in the pipeline of deep learning. There have been comprehensive surveys for shallow domain adaption, but few timely reviews the emerging deep learning based methods. In this paper, we provide a comprehensive survey of deep domain adaptation methods for computer vision applications with four major contributions. First, we present a taxonomy of different deep domain adaption scenarios according to the properties of data that define how two domains are diverged. Second, we summarize deep domain adaption approaches into several categories based on training loss, and analyze and compare briefly the state-of-the-art methods under these categories. Third, we overview the computer vision applications that go beyond image classification, such as face recognition, semantic segmentation and object detection. Fourth, some potential deficiencies of current methods and several future directions are highlighted.

The Fe–C–O–H–N system at 6.3–7.8 GPa and 1200–1400 °C: implications for deep carbon and nitrogen cycles

Interactions in a Fe–C–O–H–N system that controls the mobility of siderophile nitrogen and carbon in the Fe0-saturated upper mantle are investigated in experiments at 6.3–7.8 GPa and 1200–1400 °C. The results show that the γ-Fe and metal melt phases equilibrated with the fluid in a system unsaturated with carbon and nitrogen are stable at 1300 °C. The interactions of Fe3C with an N-rich fluid in a graphite-saturated system produce the e-Fe3N phase (space group P63/mmc or P6322) at subsolidus conditions of 1200–1300 °C, while N-rich melts form at 1400 °C. At IW- and MMO-buffered hydrogen fugacity (fH2), fluids vary from NH3- to H2O-rich compositions (NH3/N2 > 1 in all cases) with relatively high contents of alkanes. The fluid derived from N-poor samples contains less H2O and more carbon which mainly reside in oxygenated hydrocarbons, i.e., alcohols and esters at MMO-buffered fH2 and carboxylic acids at unbuffered fH2 conditions. In unbuffered conditions, N2 is the principal nitrogen host (NH3/N2 ≤ 0.1) in the fluid equilibrated with the metal phase. Relatively C- and N-rich fluids in equilibrium with the metal phase (γ-Fe, melt, or Fe3N) are stable at the upper mantle pressures and temperatures. According to our estimates, the metal/fluid partition coefficient of nitrogen is higher than that of carbon. Thus, nitrogen has a greater affinity for iron than carbon. The general inference is that reduced fluids can successfully transport volatiles from the metal-saturated mantle to metal-free shallow mantle domains. However, nitrogen has a higher affinity for iron and selectively accumulates in the metal phase, while highly mobile carbon resides in the fluid phase. This may be a controlling mechanism of the deep carbon and nitrogen cycles.

Effect of free surface on submerged stratified shear instabilities

In this paper, we have considered the effects of the shallowness of the domain as well as the air–water free surface on the stratified shear instabilities of the fluid underneath. First, we numerically solve the non-Boussinesq Taylor–Goldstein equation for smooth velocity and density profiles of a model shear layer with a free surface. When the depth of the fluid is relatively shallow compared to the shear layer thickness, the surface gravity waves existing at the free surface come closer to the waves existing in the shear layer. This can lead to resonant wave interactions, making the flow unstable to more varieties of modal instabilities. In order to obtain a deeper understanding of the instability mechanisms, we have performed analytical studies with broken-line profiles (profiles for which vorticity and density are piecewise constant). Furthermore, reduced-order broken-line profiles have also been developed, based on which dispersion diagrams are constructed. Through these diagrams we have underpinned the resonantly interacting waves leading to each type of instability. Two new instabilities have been found; one of them, referred to as the ‘surface gravity – interfacial gravity (SG-IG) mode’, arises due to the interaction between a surface gravity wave and an interfacial gravity wave, and would therefore be absent if there is no internal density stratification. The other one – the ‘surface gravity – lower vorticity (SG-LV) mode’, which arises due to the interaction between a surface gravity wave and the lower vorticity wave, surpasses Kelvin–Helmholtz (KH) instability to become the most unstable mode, provided the system is significantly shallow. Stability boundary of the SG-LV mode is found to be quite different from that of KH. In fact, KH becomes negligible for relatively shallow flows, while SG-LV’s growth rate is significant – comparable to the growth rate of KH for unbounded domains (${\approx}0.18$). Moreover, the SG-LV mode is found to be analogous to the barotropic mode observed in two-layer quiescent flows. We have found that the effect of a free surface on the Holmboe instability is not appreciable. Holmboe in the presence of a free surface is found to be analogous to the baroclinic mode observed in two-layer quiescent flows. Except for the Holmboe instability, remarkable differences are observed in all other instabilities occurring in shallow domains when the air–water interface is replaced by a rigid lid. We infer that the rigid-lid approximation is valid for large vertical domains and should be applied with caution otherwise. Furthermore, we have also shown that if shear is absent at the free surface, our problem can be modelled using Boussinesq approximation, that is, $O(1)$ density variations in the inertial terms can still be neglected.

The architecture and associated fauna of Perouvianella peruviana, an endemic larger benthic foraminifera from the Cenomanian–Turonian transition interval of central Peru

During the Cenomanian–Turonian transition interval, larger benthic foraminifera became extinct or suffered decreases in terms of their diversity. Anoxic/dysoxic conditions of oceanic bottom water masses and potentially seawater acidification during this pivotal time also affected ecological niches in the shallow epeiric domain and resulted in the demise of many taxa of benthic foraminifera worldwide. Nevertheless, exceptions to this pattern have been reported too. Here, evidence is presented for mass occurrences of larger benthic foraminifera (Perouvianella peruviana) from the Western Platform in Peru that were not affected by environmental conditions related to the Cenomanian–Turonian transition. A new architectural analysis of P. peruviana tests found in abundance in central Peru has permitted a detailed update on its systematic and functional morphology. The paleoenvironment associated with the P. peruviana mass occurrence was characterized by mesotrophic conditions, perhaps in one way or another similar to the environmental parameters that lead to Aptian and Albian larger benthic foraminifera mass occurrences at the southern Tethyan margin (‘Orbitolina levels’). Algae and small, cosmopolitan r-strategist foraminifera coexisted with P. peruviana. Moreover, a first description of the soritid taxa Pseudopeneroplis oyonensis n. gen., n. sp. is provided. Interestingly, the superposition of local and global environmental patterns onto the Western Peruvian shelf water masses triggered a mass development of the Perouvianella population coincident with Oceanic Anoxic Event 2. Conversely, the migration of foreign complex-shelled K-strategist larger benthic foraminifera from neighboring realms was inhibited.

Vortex merger near a topographic slope in a homogeneous rotating fluid

The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two-dimensional, quasi-geostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This alongshelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclones and near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.

Numerical investigation of shallow water effect on a barge ship resistance

The inland waterway cargo transport has extended over the decades, bringing up specific technical issues. From the hydrodynamics point of view, for the inland ships one of the most challenging issue is the effect of shallow water on the ship resistance. In the present study, there are developed numerical analyses for the viscous flow around a barge hull in the case of the shallow water fluid domain. The barge hull has prismatic shapes, in the cargo holds areas, with vertical sides, and geometric non-linear shapes more significant at the fore part. The hull shape CAD model is developed by Rhinoceros software. The numerical analyses are performed by CFD RANS-VOF method, with free surface and shallow-water, using the NUMECA / FineMarine software, having free sinkage and trim conditions. The shallow-water flow induces significant hydrodynamic non-linearities in compare to the deep-water flows. Several ship speeds and water depths are considered. We have focused on the identification of the ship’s induced waves system and the resulting barge resistance. The conclusions of this study are stressing out the significant influence of the shallow-water conditions on the barge resistance, making possible to draw up practical technical information’s for the barge hull design.

Early dolomitisation of the Lower-Middle Ordovician cyclic carbonates in northern Tarim Basin, NW China

High-frequency metre-scale cycles are present within the Lower-Middle Ordovician carbonate successions in northern Tarim Basin, NW China. These metre-scale cycles were variably dolomitised from top to bottom. Three types of replacive dolomites were recognised, including dololaminite (very finely to finely crystalline, planar-s to nonplanar-a dolomite; type-1), patterned dolomite (finely crystalline, planar-s dolomite; type-2), and mottled dolomite (finely to medium crystalline, nonplanar-a(s) dolomite; type-3). Petrographic evidence indicate these dolomites were primarily deposited in supratidal to restricted subtidal environments, and formed in near-surface to shallow burial realms. Geochemically, all types of dolomites have similar δ 13C and 87Sr/86Sr ratios comparable to calcite precipitated in equilibrium with the Early-Middle Ordovician seawater. These geochemical attributes indicate that these dolomites were genetically associated and likely formed from connate seawater-derived brines. Of these, type-1 dolomite has δ 18O values (‒4.97‰ to‒4.04‰ VPDB) slightly higher than those of normal seawater dolomite of the Early-Middle Ordovician age. Considering the absence of associated evaporites within type-1 dolomite, its parental fluids were likely represented by slightly evaporated (i.e., mesosaline to penesaline) seawater with salinity below that of gypsum precipitation. More depleted δ 18O values (‒7.74‰ to‒5.20‰ VPDB) of type-2 dolomite and its stratigraphic position below type-1 dolomite indicate the generation of this dolomite from mesosaline to penesaline brines at higher temperatures in near-surface to shallow burial domains. Type-3 dolomite yields the most depleted δ 18O values (–9.30‰ to–7.28‰ VPDB), pointing to that it was most likely formed from coeval seawater-derived brines at highest temperatures in a shallow burial setting. There is a downward decreasing trend in δ 18O values from type-1 through type-2 to type-3 dolomites, and in abundance of dolomites, indicating that the dolomitising fluids probably migrated downward from above and persisted into shallow burial conditions.

Occurrence of high-diversity metazoan- to microbial-dominated bioconstructions in a shallow Kimmeridgian carbonate ramp (Jabaloyas, Spain)

The horizontal and vertical transitions of a wide range of bioconstructions are documented from the shallow domains of a Kimmeridgian carbonate ramp (Upper Jurassic) in the Jabaloyas area of NE Spain. The bioconstructions include microbial buildups, coral-bearing thrombolite buildups, coral-microbial buildups, branching coral patches, oyster patches, and stromatoporoid carpets. Buildups form stacked pinnacles up to 19 m thick, within a broad spectrum of coeval inter-buildup carbonate facies. Coral-bearing thrombolites are coincident with shallow-marine oolitic sands, indicating development during the initial platform flooding (unit 1). During the continued sea-level rise (units 2 and 3), coral-microbial buildups [encrusted by Crescentiella (Tubiphytes) and serpulids] were established from proximal to distal mid-ramp domains, and these showed an increasing proportion of microbial crust in distal domains. Inter-buildup oolitic facies sharply grade down-dip to hummocky cross-stratified intraclastic, peloidal, and skeletal deposits, mostly sourced from the coral-microbial buildups. The lower part of unit 4 was dominated by microbialites in the proximal areas, related to local fresh-water input causing seawater stratification and oxygen depletion. The upper part of unit 4 indicates an initial recovery of metazoan frame builders, with abundant branching corals. During the late regression (units 5 and 6), Marinella lugeoni red algae, oyster patches, and stromatoporoid boulders developed close to the shoreline in well-oxygenated waters with high nutrient content. The reported data contribute to the discussion of the optimal environmental conditions for each “bioconstruction window” in Jabaloyas, namely sediment and nutrient supply, water depth, water oxygenation, wave energy and light availability.

Compositional layering within the large low shear‐wave velocity provinces in the lower mantle

AbstractThe large low shear‐wave velocity provinces (LLSVP) are thermochemical anomalies in the deep Earth's mantle, thousands of km wide and ∼1800 km high. This study explores the hypothesis that the LLSVPs are compositionally subdivided into two domains: a primordial bottom domain near the core‐mantle boundary and a basaltic shallow domain that extends from 1100 to 2300 km depth. This hypothesis reconciles published observations in that it predicts that the two domains have different physical properties (bulk‐sound versus shear‐wave speed versus density anomalies), the transition in seismic velocities separating them is abrupt, and both domains remain seismically distinct from the ambient mantle. We here report underside reflections from the top of the LLSVP shallow domain, supporting a compositional origin. By exploring a suite of two‐dimensional geodynamic models, we constrain the conditions under which well‐separated “double‐layered” piles with realistic geometry can persist for billions of years. Results show that long‐term separation requires density differences of ∼100 kg/m3 between LLSVP materials, providing a constraint for origin and composition. The models further predict short‐lived “secondary” plumelets to rise from LLSVP roofs and to entrain basaltic material that has evolved in the lower mantle. Long‐lived, vigorous “primary” plumes instead rise from LLSVP margins and entrain a mix of materials, including small fractions of primordial material. These predictions are consistent with the locations of hot spots relative to LLSVPs, and address the geochemical and geochronological record of (oceanic) hot spot volcanism. The study of large‐scale heterogeneity within LLSVPs has important implications for our understanding of the evolution and composition of the mantle.

Uncertainty quantification in littoral erosion

We aim at quantifying the impact of flow state uncertainties in littoral erosion to provide confidence bounds on deterministic predictions of bottom morphodynamics. Two constructions of the bathymetry standard deviation are discussed. The first construction involves directional quantile-based extreme scenarios using what is known on the flow state Probability Density Function (PDF) from on site observations. We compare this construction to a second cumulative one using the gradient by adjoint of a functional involving the energy of the system. These ingredients are illustrated for two models for the interaction between a soft bed and a flow in a shallow domain. Our aim is to keep the computational complexity comparable to the deterministic simulations taking advantage of what already available in our simulation toolbox.

Oscillatory convection and limitations of the Boussinesq approximation

We determine the asymptotic conditions under which the Boussinesq approximation is valid for oscillatory convection in a rapidly rotating fluid. In the astrophysically relevant parameter regime of small Prandtl number, we show that the Boussinesq prediction for the onset of convection is valid only under much more restrictive conditions than those that are usually assumed. In the case of an ideal gas, we recover the Boussinesq results only if the ratio of the domain height to a typical scale height is much smaller than the Prandtl number. This requires an extremely shallow domain in the astrophysical parameter regime. Other commonly used ‘sound-proof’ approximations generally perform no better than the Boussinesq approximation. The exception is a particular implementation of the pseudo-incompressible approximation, which predicts the correct instability threshold beyond the range of validity of the Boussinesq approximation.

A Magnetotelluric survey of the North Perth Basin: A technical case study

SUMMARY Original motivation of this study was to understand important structures with a proven geothermal signature associated with high temperatures in the shallower basin and high flow rates in the aquifers. Anomalous temperatures are recorded around the Beagle Ridge and significant flow rates observed near the Urella Fault, factors important to unconventional geothermal prospects. The focus of this study was therefore a detailed geophysical investigation of several Geothermal Exploration Permits (GEPs) in the North Perth Basin. Two Magnetotelluric (MT) surveys are conducted over target areas in the North Perth Basin and adjoining tectonic domains to provide information about the electrical conductivity regime of the basin and western margin of the Yilgarn Craton. Existing geophysical data in this part of the basin are sparse and electrical data for the basin in general is limited to shallow Time Domain Electromagnetic (TDEM) data targeting superficial aquifers. High-resolution MT data, acquired between 2011 and 2013, provide information on mid-deep crustal rocks. In addition, new gravity data and joint interpretation of these data sets are undertaken to improve the geological model of the North Perth Basin and test some existing hypotheses. We present a best practice case study and workflow for data acquisition and filtering, robust dimensionality analysis and removal of distortion effects from impedance tensor estimates. 1D and 2D inversions are found to be largely sufficient for the majority of these data while 3D modelling provides an additional tool to verify results. Finally, modelling of gravity data and integrated interpretation ensures robust geological models for the area are consistent with all data available. We conclude with several inferences about the geology in this area. 1) Electromagnetic (EM) and gravity data does not seem to support significant crustal thinning beneath the basin. 2) The Dandaragan Trough appears deeper than generally modelled and 3) extremely high conductivities persist to depth in the basin.