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In this paper, we introduce some known map projections from a model of the Earth to a flat sheet of paper or map and derive the plotting equations for these projections. The first fundamental form and the Gaussian fundamental quantities are defined and applied to obtain the plotting equations and distortions in length, shape and size for some of these map projections.
Recent advances in large ring laser gyroscopes (RLG) technologies opened the possibility to observe rotations of the ground with sensitivities up to $10^{-11}$ $\frac{rad}{s}$ over the frequency band of seismological interest (0.01-1Hz), thus opening the way to a new geophysical discipline, i.e. rotational seismology. A measure of rotations in seismology is of fundamental interest for (a) the determination of all the six degrees of freedom that characterize a rigid body motion, and (b) the quantitative estimate of the rotational motions contaminating ground translation measurements obtained from standard seismometers. Within this framework, this paper presents and describes GINGERino, a new large observatory-class RLG located in Gran Sasso underground laboratory (LNGS), one national laboratories of the INFN (Istituto Nazionale di Fisica Nucleare). We also report unprecedented observations and analyses of the roto-translational signals from a tele-seismic event observed in such a deep underground environment.
A first principle micromagnetic and statistical calculation of viscous remanent magnetization (VRM) in an ensemble of cubic magnetite pseudo single-domain particles is presented. This is achieved by developing a fast relaxation algorithm for finding optimal transition paths between micromagnetic local energy minima. It combines a nudged elastic band technique with action minimization. Initial paths are obtained by repetitive minimizations of modified energy functions. For a cubic pseudo-single domain particle, 60 different local energy minima are identified and all optimal energy barriers between them are numerically calculated for zero external field. The results allow to estimate also the energy barriers in in weak external fields which are necessary to construct the time dependent transition matrices which describe the continuous homogeneous Markov processes of VRM acquisition and decay. By spherical averaging the remanence acquisition in an isotropic PSD ensemble was calculated over all time scales. The modelled particle ensemble shows a physically meaningful overshooting during VRM acquisition. The results also explain why VRM acquisition in PSD particles can occur much faster than VRM decay and therefore can explain for findings of extremely stable VRM in some paleomagnetic studies.
Inversion of potential field data is a central technique of remote sensing in physics, geophysics, neuroscience and medical imaging. In spite of intense research, uniqueness theorems for potential-field inversion are scarce. Applied studies successfully improve potential-field inversion results by including constraints from independent measurements, but so far no mathematical theorem guarantees that source localization improves the inversion in terms of uniqueness of the achieved assignment. Empirical inversion techniques therefore use numerical and statistical approaches to assess the reliability of their results. Especially when inverting magnetic field surface measurements, even seemingly advanced mathematical approaches require substantial additional assumptions about the source magnetization to achieve a useful reconstruction. Here, standard potential field theory is used to prove a uniqueness theorem which completely characterizes the mathematical background of source-localized inversion. It guarantees for an astonishingly large class of source localizations that it is possible by potential field measurements on a surface to differentiate between signals from different source regions. Non-uniqueness of potential field inversion only prevents that the source distribution within the individual regions can be uniquely recovered.
Landscapes evolve toward surfaces with complex networks of channels and ridges in response to climatic and tectonic forcing. Here we analyze variational principles giving rise to minimalist models of landscape evolution as a system of partial differential equations that capture the essential dynamics of sediment and water balances. Our results show that in the absence of diffusive soil transport, the steady-state surface extremizes the average domain elevation. Depending on the exponent m of specific drainage area in the erosion term, the critical surfaces are either minima (0<m<1) or maxima (m>1), with m=1 corresponding to a saddle point. Our results establish a connection between Landscape Evolution Models (LEMs) and Optimal Channel Networks (OCNs) and elucidate the role of diffusion in the governing variational principles.
Quasi-2D experiments of a submerged sediment layer creeping downward were performed, varying the channel tilt and a porous flow under the respective thresholds for yielding. Logarithmic decay rates of the deformation are observed, with the rate increasing with both control parameters. A new dimensionless parameter, $P^*$, accounting for both mean porous flow and gravity force effects on particle motion, allows a collapse of all the deformation results on a single curve. Two distinct creep regimes are identified, and correspond to a systematic change of the void size distribution as $P^*$ increases.
Convection and magnetic field generation in the Earth and planetary interiors are driven by both thermal and compositional gradients. In this work numerical simulations of finite-amplitude double-diffusive convection and dynamo action in rapidly rotating spherical shells full of incompressible two-component electrically-conducting fluid are reported. Four distinct regimes of rotating double-diffusive convection identified in a recent linear analysis (Silva et al., 2019, Geophys. Astrophys. Fluid Dyn., doi:10.1080/03091929.2019.1640875) are found to persist significantly beyond the onset of instability while their regime transitions remain abrupt. In the semi-convecting and the fingering regimes characteristic flow velocities are small compared to those in the thermally- and compositionally-dominated overturning regimes, while zonal flows remain weak in all regimes apart from the thermally-dominated one. Compositionally-dominated overturning convection exhibits significantly narrower azimuthal structures compared to all other regimes while differential rotation becomes the dominant flow component in the thermally-dominated case as driving is increased. Dynamo action occurs in all regimes apart from the regime of fingering convection. While dynamos persist in the semi-convective regime they are very much impaired by small flow intensities and very weak differential rotation in this regime which makes poloidal to toroidal field conversion problematic. The dynamos in the thermally-dominated regime include oscillating dipolar, quadrupolar and multipolar cases similar to the ones known from earlier parameter studies. Dynamos in the compositionally-dominated regime exhibit subdued temporal variation and remain predominantly dipolar due to weak zonal flow in this regime. These results significantly enhance our understanding of the primary drivers of planetary core flows and magnetic fields.
The transverse coherence functions (TCFs) of phase and amplitude fluctuations of a seismic wave are powerful to estimate the spatial distribution, length scales, and strength of random heterogeneities. However, TCFs have been formulated for transmitted waves only, not for reflected waves. In this paper, we derive reflection TCFs for Gaussian random media. Furthermore, we propose to invert for Gaussian random media using the reflection TCFs based on the grid search. We validate the new reflection TCF formulas using 2D finite-difference numerical experiments. The numerical example also illustrates the feasibility and efficiency of the inversion. The stochastic inversion using reflected waves can be used in both exploration and global seismology.
Earthquake early warning systems are required to report earthquake locations and magnitudes as quickly as possible before the damaging S wave arrival to mitigate seismic hazards. Deep learning techniques provide potential for extracting earthquake source information from full seismic waveforms instead of seismic phase picks. We developed a novel deep learning earthquake early warning system that utilizes fully convolutional networks to simultaneously detect earthquakes and estimate their source parameters from continuous seismic waveform streams. The system determines earthquake location and magnitude as soon as one station receives earthquake signals and evolutionarily improves the solutions by receiving continuous data. We apply the system to the 2016 Mw 6.0 earthquake in Central Apennines, Italy and its subsequent sequence. Earthquake locations and magnitudes can be reliably determined as early as four seconds after the earliest P phase, with mean error ranges of 6.8-3.7 km and 0.31-0.23, respectively.
Chondrites are the likely building blocks of Earth, and identifying the group of chondrite that best represents Earth is a key to resolving the state of the early Earth. The origin of chondrites, however, remains controversial partly because of their puzzling major element compositions, some exhibiting depletion in Al, Ca, and Mg. Based on a new thermochemical evolution model of protoplanetary disks, we show that planetesimals with depletion patterns similar to ordinary and enstatite chondrites can originate at 1-2 AU just outside where enstatite evaporates. Around the "evaporation front" of enstatite, the large inward flow of refractory minerals, including forsterite, takes place with a high pebble concentration, and the loss of those minerals result in depletion in Al, Ca, and Mg. When evaporated solid grains re-condense onto pebbles, the concentration of pebbles is further enhanced, potentially triggering the streaming instability. Planetesimals with the composition of ordinary and enstatite chondrites can thus be naturally created in the terrestrial region. The preferential loss of forsterite also creates an enhancement of Mg/Si and heavy Si isotopes just inside the potential source region for ordinary and enstatite chondrites. Earth, which shows both features, may originate just inside where ordinary and enstatite chondrites were born.
Fault-zone fluids control effective normal stress and fault strength. While most earthquake models assume a fixed pore fluid pressure distribution, geologists have documented fault valving behavior, that is, cyclic changes in pressure and unsteady fluid migration along faults. Here we quantify fault valving through 2-D antiplane shear simulations of earthquake sequences on a strike-slip fault with rate-and-state friction, upward Darcy flow along a permeable fault zone, and permeability evolution. Fluid overpressure develops during the interseismic period, when healing/sealing reduces fault permeability, and is released after earthquakes enhance permeability. Coupling between fluid flow, permeability and pressure evolution, and slip produces fluid-driven aseismic slip near the base of the seismogenic zone and earthquake swarms within the seismogenic zone, as ascending fluids pressurize and weaken the fault. This model might help explain observations of late interseismic fault unlocking, slow slip and creep transients, swarm seismicity, and rapid pressure/stress transmission in induced seismicity sequences.
Future changes in the location of the intertropical convergence zone (ITCZ) due to climate change are of high interest since they could substantially alter precipitation patterns in the tropics and subtropics. Although models predict a future narrowing of the ITCZ during the 21st century in response to climate warming, uncertainties remain large regarding its future position, with most past work focusing on the zonal-mean ITCZ shifts. Here we use projections from 27 state-of-the-art climate models (CMIP6) to investigate future changes in ITCZ location as a function of longitude and season, in response to climate warming. We document a robust zonally opposing response of the ITCZ, with a northward shift over eastern Africa and the Indian Ocean, and a southward shift in the eastern Pacific and Atlantic Ocean by 2100, for the SSP3-7.0 scenario. Using a two-dimensional energetics framework, we find that the revealed ITCZ response is consistent with future changes in the divergent atmospheric energy transport over the tropics, and sector-mean shifts of the energy flux equator (EFE). The changes in the EFE appear to be the result of zonally opposing imbalances in the hemispheric atmospheric heating over the two sectors, consisting of increases in atmospheric heating over Eurasia and cooling over the Southern Ocean, which contrast with atmospheric cooling over the North Atlantic Ocean due to a model-projected weakening of the Atlantic meridional overturning circulation.
We show the capabilities of a downhole Distributed Acoustic Sensing (DAS) array in detecting, locating and characterizing low-magnitude earthquakes occurring in the vicinity of the Frontier Observatory for Research in Geothermal Energy (FORGE) site in Utah. 10.5 days of continuous data were acquired in a monitoring well at the FORGE geothermal site during the initial stimulation of an Enhanced Geothermal System in April-May 2019. Earthquake activity beneath Mineral Mountains, Utah also occurred within 10 km of the FORGE monitoring well. During the experiment, four events from those areas were cataloged by the University of Utah Seismograph Stations. Our processing of DAS data, including template matching, finds 82 earthquakes during that period, of which 16 are visible on the regional network. The magnitude of completeness obtained by DAS processing is better by at least M=0.5 than the dense surface array around the FORGE site. While a single vertical DAS array is limited in terms of event location due to its azimuthal ambiguity, multiple DAS wells or a combination of a downhole array with surface stations or near-surface horizontal DAS could jointly resolve locations. All detected events probably originated from the two active source areas and can be clustered into several distinct families.
Frequency-domain wavefield solutions corresponding to the anisotropic acoustic wave equations can be used to describe the anisotropic nature of the earth. To solve a frequency-domain wave equation, we often need to invert the impedance matrix. This results in a dramatic increase in computational cost as the model size increases. It is even a bigger challenge for anisotropic media, where the impedance matrix is far more complex. To address this issue, we use the emerging paradigm of physics-informed neural networks (PINNs) to obtain wavefield solutions for an acoustic wave equation for transversely isotropic (TI) media with a vertical axis of symmetry (VTI). PINNs utilize the concept of automatic differentiation to calculate its partial derivatives. Thus, we use the wave equation as a loss function to train a neural network to provide functional solutions to form of the acoustic VTI wave equation. Instead of predicting the pressure wavefields directly, we solve for the scattered pressure wavefields to avoid dealing with the point source singularity. We use the spatial coordinates as input data to the network, which outputs the real and imaginary parts of the scattered wavefields and auxiliary function. After training a deep neural network (NN), we can evaluate the wavefield at any point in space instantly using this trained NN. We demonstrate these features on a simple anomaly model and a layered model. Additional tests on a modified 3D Overthrust model and a model with irregular topography also show the effectiveness of the proposed method.
Pluto has a heterogeneous surface, despite a global haze deposition rate of ~1 micrometer per orbit (Cheng et al., 2017; Grundy et al., 2018). While there could be spatial variation in the deposition rate, this has not yet been rigorously quantified, and naively the haze should coat the surface more uniformly than was observed. One way (among many) to explain this contradiction is for atmospheric pressure at the surface to drop low enough to interrupt haze production and stop the deposition of particles onto part of the surface, driving heterogeneity. If the surface pressure drops to less than 10^-3 - 10^-4 microbar and the CH4 mixing ratio remains nearly constant at the observed 2015 value, the atmosphere becomes transparent to ultraviolet radiation (Young et al., 2018), which would shut off haze production at its source. If the surface pressure falls below 0.06 microbar, the atmosphere ceases to be global, and instead is localized over only the warmest part of the surface, restricting the location of deposition (Spencer et al., 1997). In Pluto's current atmosphere, haze monomers collect together into aggregate particles at beginning at 0.5 microbar; if the surface pressure falls below this limit, the appearance of particles deposited at different times of year and in different locations could be different. We use VT3D, an energy balance model (Young, 2017), to model the surface pressure on Pluto in current and past orbital configurations for four possible static N2 ice distributions: the observed northern hemisphere distribution with (1) a bare southern hemisphere, (2) a south polar cap, (3) a southern zonal band, and finally (4) a distribution that is bare everywhere except inside the boundary of Sputnik Planitia. We also present a sensitivity study showing the effect of mobile N2 ice...(cont.)
The dynamics, structure and stability of zonal jets in planetary flows are still poorly understood, especially in terms of coupling with the small-scale turbulent flow. Here, we use an experimental approach to address the questions of zonal jets formation and long-term evolution. A strong and uniform topographic $β$-effect is obtained inside a water-filled rotating tank thanks to the paraboloidal fluid free upper surface combined with a specifically designed bottom plate. A small-scale turbulent forcing is performed by circulating water through the base of the tank. Time-resolving PIV measurements reveal the self-organization of the flow into multiple zonal jets with strong instantaneous signature. We identify a subcritical bifurcation between two regimes of jets depending on the forcing intensity. In the first regime, the jets are steady, weak in amplitude, and directly forced by the local Reynolds stresses due to our forcing. In the second one, we observe highly energetic and dynamic jets of width larger than the forcing scale. An analytical modeling based on the quasi-geostrophic approximation reveals that this subcritical bifurcation results from the resonance between the directly forced Rossby waves and the background zonal flow.
The prediction of the first fluidized path of a yield-stress fluid in complex porous media is a challenging yet an important task to understand the fundamentals of fluid flow in several industrial and biological processes. In most cases, the conditions that open this first path are known either through experiments or expensive computations. Here, we present a simple network model to predict the first open channel for a yield-stress fluid in a complex porous medium. For porous media made of non-overlapping disks, we find that the pressure drop required to open the first channel for given yield stress depends on both the relative disks size to the macroscopic length of the system and the packing fraction. We also report the statistics on the arc-length of the first open path. Finally, we discuss the implication of our results on the design of porous media used in energy storage applications.
Global climate change, extreme climate events, earthquakes and their accompanying natural disasters pose significant risks to humanity. Yet due to the nonlinear feedbacks, strategic interactions and complex structure of the Earth system, the understanding and in particular the predicting of such disruptive events represent formidable challenges for both scientific and policy communities. During the past years, the emergence and evolution of Earth system science has attracted much attention and produced new concepts and frameworks. Especially, novel statistical physics and complex networks-based techniques have been developed and implemented to substantially advance our knowledge for a better understanding of the Earth system, including climate extreme events, earthquakes and Earth geometric relief features, leading to substantially improved predictive performances. We present here a comprehensive review on the recent scientific progress in the development and application of how combined statistical physics and complex systems science approaches such as, critical phenomena, network theory, percolation, tipping points analysis, as well as entropy can be applied to complex Earth systems (climate, earthquakes, etc.). Notably, these integrating tools and approaches provide new insights and perspectives for understanding the dynamics of the Earth systems. The overall aim of this review is to offer readers the knowledge on how statistical physics approaches can be useful in the field of Earth system science.
Every year, more and more objects are sent to space. While staying in orbit at high altitudes, objects at low altitudes reenter the atmosphere, mostly disintegrating and adding material to the upper atmosphere. The increasing number of countries with space programs, advancing commercialization, and ambitious satellite constellation projects raise concerns about space debris in the future and will continuously increase the mass flux into the atmosphere. In this study, we compare the mass influx of human-made (anthropogenic) objects to the natural mass flux into Earth's atmosphere due to meteoroids, originating from solar system objects like asteroids and comets. The current and near future significance of anthropogenic mass sources is evaluated, considering planned and already partially installed large satellite constellations. Detailed information about the mass, composition, and ablation of natural and anthropogenic material are given, reviewing the relevant literature. Today, anthropogenic material does make up about 2.8 % compared to the annual injected mass of natural origin, but future satellite constellations may increase this fraction to nearly 40 %. For this case, the anthropogenic injection of several metals prevails the injection by natural sources by far. Additionally, we find that the anthropogenic injection of aerosols into the atmosphere increases disproportionately. All this can have yet unknown effects on Earth's atmosphere and the terrestrial habitat.
The rupture of the interface joining two materials under frictional contact controls their macroscopic sliding. Interface rupture dynamics depend markedly on the mechanical properties of the bulk materials that bound the frictional interface. When the materials are similar, recent experimental and theoretical work has shown that shear cracks described by Linear Elastic Fracture Mechanics (LEFM) quantitatively describe the rupture of frictional interfaces. When the elastic properties of the two materials are dissimilar, many new effects take place that result from bimaterial coupling: the normal stress at the interface is elastodynamically coupled to local slip rates. At low rupture velocities, bimaterial coupling is not very significant and interface rupture is governed by `bimaterial cracks' that are described well by LEFM. As rupture velocities increase, we experimentally and theoretically show how bimaterial cracks become unstable at a subsonic critical rupture velocity, $c_T$. When the rupture direction opposes the direction of applied shear in the softer material, we show that $c_T$ is the subsonic limiting velocity. When ruptures propagate in the direction of applied shear in the softer material, we demonstrate that $c_T$ provides an explanation for how and when slip pulses (new rupture modes characterized by spatially localized slip) are generated. This work completes the fundamental physical description of how the frictional rupture of bimaterial interfaces takes place.
Impact rates in the first 500 Myr of the solar system are critical to an understanding of lunar geological history, but they have been controversial. The widely accepted, post-Apollo paradigm of early lunar impact cratering (ca. 1975-2014) proposed very low or negligible impact cratering in the period from accretion (>4.4 Ga) to about 4.0 Ga ago, followed by a 170-million-year-long spike of cataclysmic cratering, during which most prominent multi-ring impact basins formed at age of about 3.9 Ga. More recent dynamical models suggest very early intense impact rates, declining throughout the period from accretion until an age of about 3.0 Ga. These models remove the basin-forming spike. This shift has important consequences on megaregolith evolution and properties of rock samples that can be collected on the lunar surface today. We adopt the Morbidelli et al. (2018) "accretion tail" model of early intense bombardment, declining as a function of time. We find effects differing from the previous models: early crater saturation and supersaturation; disturbance of magma ocean solidification; deep early megaregolith; and erosive destruction of the earliest multi-ring basins, their impact melts, and their ejecta blankets. Our results explain observations such as differences in numbers of early lunar impact melts vs. numbers of early igneous crustal rocks, highland breccias containing impact melts as old as 4.35 Ga, absence of a 170 Myr-long spike in impact melt ages at 3.9 Ga among lunar and asteroidal meteorites, and GRAIL observations of lunar crustal structure.
The emergence of quantum technologies, including cold atom based accelerometers, offers an opportunity to improve the performances of space geodesy missions. In this context, CNES initiated an assessment study called GRICE (GRadiométrie à Interféromètres quantiques Corrélés pour l'Espace) in order to evaluate the contribution of cold atom technologies to space geodesy and to the end users of geodetic data. In this paper, we present mission scenario for gravity field mapping based on a long baseline gradiometer. The mission is based on a constellation of two satellites, flying at an altitude of 373 km, each equipped with a cold atom accelerometer with a sensitivity of $6 \times 10^{-10}$~m.s$^{-2}$.$\mathrmτ^{-1/2}$. A laser link measures the distance between the two satellites and couples these two instruments in order to produce a correlated differential acceleration measurement. The main parameters, determining the performances of the payload, have been investigated. We carried out a general study of satellite architecture and simulations of the mission performances in terms of restitution of the gravity field. The simulations show that this concept would give its best performance in terms of monthly gravity fields recovery under 1000~km resolution. In the resolution band between 1000 and 222~km, the improvement of the GRICE gradient approach over the traditional range-rate approach is globally in the order of 10 to 25\%.
The quasi-brittle nature of rocks challenges the basic assumptions of linear hydraulic fracture mechanics (LHFM): linear elastic fracture mechanics and smooth parallel plates lubrication fluid flow. We relax these hypotheses and investigate the growth of a plane-strain hydraulic fracture in an impermeable medium accounting for a rough cohesive zone and a fluid lag. In addition to a dimensionless toughness and the time-scale of coalescence of the fluid and fracture fronts as in the LHFM case, the solution now also depends on the in-situ-to-cohesive stress ratio and the intensity of the flow deviation induced by aperture roughness. The solution is appropriately described by a nucleation time-scale, which delineates the fracture growth into a nucleation phase, an intermediate stage and a late time stage where convergence toward LHFM predictions finally occurs. A highly non-linear hydro-mechanical coupling takes place as the fluid front enters the rough cohesive zone which itself evolves during the nucleation and intermediate stages. This coupling leads to significant additional viscous flow dissipation. As a result, the fracture evolution deviates from LHFM solutions with shorter fracture lengths, larger widths and net pressures. These deviations ultimately decrease at late times as the lag and cohesive zone fractions both become smaller. The deviations increase with larger dimensionless toughness and in-situ-to-cohesive stress ratio, as both further localize viscous dissipation near the fluid front located in the rough cohesive zone. The convergence toward LHFM can occur at very late time for realistic values of in-situ-to-cohesive stress ratio encountered at depth. The impact of a rough cohesive zone appears to be prominent for laboratory experiments and short in-situ injections in quasi-brittle rocks with ultimately a larger energy demand compared to LHFM predictions.
In this work, we study the dynamics of particles around Bennu. The goal is to understand the stability, evolution, and final outcome of the simulated particles around the asteroid. According to the results, the particle sizes can be divided into two main groups depending on their behavior. Particles smaller than a centimeter are quickly removed from the system by solar radiation pressure, while the dynamics of particles larger than a few centimeters is dominated by the gravitational field of Bennu. Because of its shape and spin period, Bennu has eight equilibrium points around it. The structure of the phase space near its equatorial surface is directly connected to these equilibrium points. Therefore, we performed numerical simulations to obtain information about the orbital evolution near the equilibrium points. The results show that most of the particles larger than a few centimeters fall in the equatorial region close to the Kingfisher area or close to the region diametrically opposite to it. In contrast, almost none of these particles fall in the equatorial region close to the Osprey area. In addition, we also performed computational experiments considering a spherical cloud of particles initially orbiting Bennu. Most of the particles in prograde orbits fall on the surface within our integration period, which was limited to 1.14 years. The particles preferentially fall near high-altitude regions at low equatorial latitudes and close to the north pole. The mid-latitudes are those more depleted of falls, as in the Nightingale and Sandpiper areas.
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