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physics.geo-ph

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preprint2017arXiv

Fracture imaging within a granitic rock aquifer using multiple-offset single-hole and cross-hole GPR reflection data

The sparsely spaced highly permeable fractures of the granitic rock aquifer at Stang-er-Brune (Brittany, France) form a well-connected fracture network of high permeability but unknown geometry. Previous work based on optical and acoustic logging together with single-hole and cross-hole flowmeter data acquired in 3 neighboring boreholes (70-100 m deep) have identified the most important permeable fractures crossing the boreholes and their hydraulic connections. To constrain possible flow paths by estimating the geometries of known and previously unknown fractures, we have acquired, processed and interpreted multifold, single- and cross-hole GPR data using 100 and 250 MHz antennas. The GPR data processing scheme consisting of time-zero corrections, scaling, bandpass filtering and F-X deconvolution, eigenvector filtering, muting, pre-stack Kirchhoff depth migration and stacking was used to differentiate fluid-filled fracture reflections from source-generated noise. The final stacked and pre-stack depth-migrated GPR sections provide high-resolution images of individual fractures (dipping 30-90°) in the surroundings (2-20 m for the 100 MHz antennas; 2-12 m for the 250 MHz antennas) of

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preprint2017arXiv

Single-hole GPR reflection imaging of solute transport in a granitic aquifer

Identifying transport pathways in fractured rock is extremely challenging as flow is often organized in a few fractures that occupy a very small portion of the rock volume. We demonstrate that saline tracer experiments combined with single-hole ground penetrating radar (GPR) reflection imaging can be used to monitor saline tracer movement within mm-aperture fractures. A dipole tracer test was performed in a granitic aquifer by injecting a saline solution in a known fracture, while repeatedly acquiring single-hole GPR sections in the pumping borehole located 6 m away. The final depth-migrated difference sections make it possible to identify consistent temporal changes over a 30 m depth interval at locations corresponding to fractures previously imaged in GPR sections acquired under natural flow and tracer-free conditions. The experiment allows determining the dominant flow paths of the injected tracer and the velocity (0.4-0.7 m/min) of the tracer front.

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preprint2016arXiv

Seismic metasurfaces: Sub-wavelength resonators and Rayleigh wave interaction

We consider the canonical problem of an array of rods, which act as resonators, placed on an elastic substrate; the substrate being either a thin elastic plate or an elastic half-space. In both cases the flexural plate, or Rayleigh surface, waves in the substrate interact with the resonators to create interesting effects such as effective band-gaps for surface waves or filters that transform surface waves into bulk waves; these effects have parallels in the field of optics where such sub-wavelength resonators create metamaterials, and metasurfaces, in the bulk and at the surface respectively. Here we carefully analyse this canonical problem by extracting the dispersion relations analytically thereby examining the influence of both the flexural and compressional resonances on the propagating wave. For an array of resonators atop an elastic half-space we augment the analysis with numerical simulations. Amongst other effects, we demonstrate the striking effect of a dispersion curve that transitions from Rayleigh wave-like to shear wave-like behaviour and the resultant change in displacement from surface to bulk waves.

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preprint2016arXiv

An Optical Atmospheric Phenomenon Observed in 1670 over the City of Astrakhan Was not a Mid-Latitude Aurora

It has been recently claimed (Zolotova and Ponyavin, Solar Phys., 291, 2869, 2016, ZP16 henceforth) that a mid-latitude optical phenomenon, which took place over the city of Astrakhan in July 1670, according to Russian chronicles, was a strong aurora borealis. If this was true, it would imply a very strong or even severe geomagnetic storm during the quietest part of the Maunder minimum. However, as we argue in this article, this conclusion is erroneous and caused by a misinterpretation of the chronicle record. As a result of a thorough analysis of the chronicle text, we show that the described phenomenon occurred during the daylight period of the day ("the last morning hour"), in the south direction ("towards noon"), and its description does not match that of an aurora. The date of the event was also incorrectly interpreted. We conclude that this phenomenon was not a mid-latitude aurora but an atmospheric phenomenon, the so-called sundog (or parhelion) which is a particular type of solar halo. Accordingly, the claim about a strong mid-latitude aurora during the deep Maunder minimum is not correct and should be dismissed.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations

The characteristic time-dependent viscosity of the intergranular pore-fluid in Buckingham's grain-shearing (GS) model [Buckingham, J. Acoust. Soc. Am. 108, 2796-2815 (2000)] is identified as the property of rheopecty. The property corresponds to a rare type of a non-Newtonian fluid in rheology which has largely remained unexplored. The material impulse response function from the GS model is found to be similar to the power-law memory kernel which is inherent in the framework of fractional calculus. The compressional wave equation and the shear wave equation derived from the GS model are shown to take the form of the Kelvin-Voigt fractional-derivative wave equation and the fractional diffusion-wave equation respectively. Therefore, an analogy is drawn between the dispersion relations obtained from the fractional framework and those from the GS model to establish the equivalence of the respective wave equations. Further, a physical interpretation of the characteristic fractional order present in the wave equations is inferred from the GS model. The overall goal is to show that fractional calculus is not just a mathematical framework which can be used to curve-fit the complex beha

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preprint2016arXiv

A fiber-bundle model for the continuum deformation of brittle material

The deformation of brittle material is primarily accompanied by micro-cracking and faulting. However, it has often been found that continuum fluid models, usually based on a non-Newtonian viscosity, are applicable. To explain this rheology, we use a fiber-bundle model, which is a model of damage mechanics. In our analyses, yield stress was introduced. Above this stress, we hypothesize that the fibers begin to fail and a failed fiber is replaced by a new fiber. This replacement is analogous to a micro-crack or an earthquake and its iteration is analogous to stick-slip motion. Below the yield stress, we assume that no fiber failure occurs, and the material behaves elastically. We show that deformation above yield stress under a constant strain rate for a sufficient amount of time can be modeled as an equation similar to that used for non-Newtonian viscous flow. We expand our rheological model to treat viscoelasticity and consider a stress relaxation problem. The solution can be used to understand aftershock temporal decay following an earthquake. Our results provide justification for the use of a non-Newtonian viscous flow to model the continuum deformation of brittle materials.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Anomalous decrease of relatively large shocks and increase of the p and b values preceding the April 16, 2016 M7.3 earthquake in Kumamoto, Japan

The 2016 Kumamoto earthquakes started with a magnitude (M) 6.5 quake on Apr 14 on the Hinagu fault zone (FZ), followed by active seismicity including an M6.4 quake. Eventually, an M7.3 quake occurred on Apr 16 on the Futagawa FZ. We investigated if any sign indicative of the M7.3 quake could be found in the space-time changes of seismicity after the M6.5 quake. We determined in advance the threshold magnitude, above which all earthquakes are completely recorded. We then showed that the occurrence rate of relatively large (M >= 3) earthquakes significantly decreased 1 day before the M7.3 quake. Significance of this decrease was evaluated by one standard deviation of sampled changes in the rate of occurrence. We next confirmed that seismicity with M >= 3 was well modeled by the OU law with p ~ 1.5 +/- 0.3, which indicates that the temporal decay of seismicity was significantly faster than a typical decay with p = 1. The larger p value was obtained when we used data of the longer time period in the analysis. This significance was confirmed by a bootstrapping approach. Our detailed analysis shows that the large p value was caused by the rapid decay of the seismicity in the northern are

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Optimal damping ratios of multi-axial perfectly matched layers for elastic-wave modeling in general anisotropic media

The conventional Perfectly Matched Layer (PML) is unstable for certain kinds of anisotropic media. This instability is intrinsic and independent of PML formulation or implementation. The Multi-axial PML (MPML) removes such instability using a nonzero damping coefficient in the direction parallel with the interface between a PML and the investigated domain. The damping ratio of MPML is the ratio between the damping coefficients along the directions parallel with and perpendicular to the interface between a PML and the investigated domain. No quantitative approach is available for obtaining these damping ratios for general anisotropic media. We develop a quantitative approach to determining optimal damping ratios to not only stabilize PMLs, but also minimize the artificial reflections from MPMLs. Numerical tests based on finite-difference method show that our new method can effectively provide a set of optimal MPML damping ratios for elastic-wave propagation in 2D and 3D general anisotropic media.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Activation of MHD reconnection on ideal timescales

Magnetic reconnection in laboratory, space and astrophysical plasmas is often invoked to explain explosive energy release and particle acceleration. However, the timescales involved in classical models within the macroscopic MHD regime are far too slow to match the observations. Here we revisit the tearing instability by performing visco-resistive two-dimensional numerical simulations of the evolution of thin current sheets, for a variety of initial configurations and of values of the Lunquist number $S$, up to $10^7$. Results confirm that when the critical aspect ratio of $S^{1/3}$ is reached in the reconnecting current sheets, the instability proceeds on ideal (Alfvénic) macroscopic timescales, as required to explain observations. Moreover, the same scaling is seen to apply also to the local, secondary reconnection events triggered during the nonlinear phase of the tearing instability, thus accelerating the cascading process to increasingly smaller spatial and temporal scales. The process appears to be robust, as the predicted scaling is measured both in inviscid simulations and when using a Prandtl number $P=1$ in the viscous regime.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Postprocessing Galerkin method applied to a data assimilation algorithm: a uniform in time error estimate

We apply the Postprocessing Galerkin method to a recently introduced continuous data assimilation (downscaling) algorithm for obtaining a numerical approximation of the solution of the two-dimensional Navier-Stokes equations corresponding to given measurements from a coarse spatial mesh. Under suitable conditions on the relaxation (nudging) parameter, the resolution of the coarse spatial mesh and the resolution of the numerical scheme, we obtain uniform in time estimates for the error between the numerical approximation given by the Postprocessing Galerkin method and the reference solution corresponding to the measurements. Our results are valid for a large class of interpolant operators, including low Fourier modes and local averages over finite volume elements. Notably, we use here the 2D Navier-Stokes equations as a paradigm, but our results apply equally to other evolution equations, such as the Boussinesq system of Benard convection and other oceanic and atmospheric circulation models.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

A double-correlation tremor-location method

A double-correlation method is introduced to locate tremor sources based on stacks of complex, doubly-correlated tremor records of multiple triplets of seismographs back projected to hypothetical source locations in a geographic grid. Peaks in the resulting stack of moduli are inferred source locations. The stack of the moduli is a robust measure of energy radiated from a point source or point sources even when the velocity information is imprecise. Application to real data shows how double correlation focuses the source mapping compared to the common single correlation approach. Synthetic tests demonstrate the robustness of the method and its resolution limitations which are controlled by the station geometry, the finite frequency of the signal, the quality of the used velocity information and noise level. Both random noise and signal or noise correlated at time shifts that are inconsistent with the assumed velocity structure can be effectively suppressed. Assuming a surface-wave velocity, we can constrain the source location even if the surface-wave component does not dominate. The method can also in principle be used with body waves in three dimensions, although this requires mo

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Some remarks on resolving and interpretation of the short marine magnetic anomalies

Marine magnetic anomalies of the tiny wiggles (TW) type can be used to solve geohistorical and paleomagnetic problems. The model fields corresponding to Paleocene-Eocene anomalies in the northwestern Indian Ocean, which were formed during the fasts preading stage, were studied. For these fields, widely used interpretation methods were compared. The testing was performed with first the classical block model and then more complex models reflecting actual processes of oceanic accretion and magnetic field variations in the past. Spectral and statistical methods are used to estimate the magnetic anomalies(MA) resolving. Preprocessing of a set profiles based on the maximal correlation is considered.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Control of Rayleigh-like waves in thick plate Willis metamaterials

We explore interactions of elastic waves propagating in plates (with soil parameters) structured with concrete pillars buried in the soil. Pillars are 2 m in diameter, 30 m in depth and the plate is 50 m in thickness. We study the frequency range 5 to 10 Hz, for which Rayleigh wave wavelengths are smaller than the plate thickness. This frequency range is compatible with frequency ranges of particular interest in earthquake engineering. It is demonstrated in this paper that two seismic cloaks' configurations allow for an unprecedented flow of elastodynamic energy associated with Rayleigh surface waves. The first cloak design is inspired by some approximation of ideal cloaks' parameters within the framework of thin plate theory. The second, more accomplished but more involved, cloak design is deduced from a geometric transform in the full Navier equations that preserves the symmetry of the elasticity tensor but leads to Willis' equations, well approximated by a homogenization procedure, as corroborated by numerical simulations. The two cloaks's designs are strikingly different, and the superior efficiency of the second type of cloak emphasizes the necessity for rigor

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Continuum modeling of the effect of surface area growth due to crushing and damage on the permeability of granular rocks

This paper discusses a continuum approach to track the evolution of permeability in granular rocks by accounting for the combined effect of porosity changes, grain breakage and cement bond damage. To account for such a broad range of microscopic processes under general loading paths, the Breakage Mechanics theory is used and the computed mechanical response is linked with the Kozeny equation, i.e. a permeability model able to evaluate the reduction of the hydraulic conductivity resulting from the simultaneous loss of porosity and growth of surface area. In particular, the evolution of the internal variables of the model has been linked to idealized geometric schemes at particle scale, with the goal to distinguish the contribution of the fines generated by the disaggregation of the cement matrix from that of the broken fragments resulting from the crushing of the skeleton. Compression/flow experiments available in the literature for different granular rocks are used to validate the proposed methodology. The analyses illustrate that the drop of the permeability of damaged rocks would be severely underestimated without an accurate computation of the growth of surface area, as well as

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Evaluating the paleomagnetic potential of single zircon crystals using the Bishop Tuff

Zircon crystals offer a unique combination of suitability for high-precision radiometric dating and high resistance to alteration. Paleomagnetic experiments on ancient zircons may potentially constrain the earliest geodynamo, which holds broad implications for the early Earth interior and atmosphere. However, the ability of zircons to record accurately the geomagnetic field has not been fully demonstrated. Here we conduct thermal and room temperature alternating field (AF) paleointensity experiments on 767.1 thousand year old (ka) zircons from the Bishop Tuff, California. The rapid emplacement of these zircons in a well-characterized magnetic field provides a high-fidelity test of the zircons intrinsic paleomagnetic recording accuracy. Successful dual heating experiments on nine zircons measured using a superconducting quantum interference device (SQUID) microscope yield a mean paleointensity of 46.2 +/- 18.8 microtesla (1sigma), which agrees closely with high-precision results from Bishop Tuff whole rock (43.0 +/- 3.2 microtesla). High-resolution quantum diamond magnetic mapping, electron microscopy, and X-ray tomography indicate that the bulk of the remanent magnetization in Bish

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Evaluating the wind-induced mechanical noise on the InSight seismometers

The SEIS (Seismic Experiment for Interior Structures) instrument onboard the InSight mission to Mars is the critical instrument for determining the interior structure of Mars, the current level of tectonic activity and the meteorite flux. Meeting the performance requirements of the SEIS instrument is vital to successfully achieve these mission objectives. Here we analyse in-situ wind measurements from previous Mars space missions to understand the wind environment that we are likely to encounter on Mars, and then we use an elastic ground deformation model to evaluate the mechanical noise contributions on the SEIS instrument due to the interaction between the Martian winds and the InSight lander. Lander mechanical noise maps that will be used to select the best deployment site for SEIS once the InSight lander arrives on Mars are also presented. We find the lander mechanical noise may be a detectable signal on the InSight seismometers. However, for the baseline SEIS deployment position, the noise is expected to be below the total noise requirement >97% of the time and is, therefore, not expected to endanger the InSight mission objectives.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Convection-driven kinematic dynamos at low Rossby and magnetic Prandtl numbers

Most large-scale planetary magnetic fields are thought to be driven by low Rossby number convection of a low magnetic Prandtl number fluid. Here kinematic dynamo action is investigated with an asymptotic, rapidly rotating dynamo model for the plane layer geometry that is intrinsically low magnetic Prandtl number. The thermal Prandtl number and Rayleigh number are varied to illustrate fundamental changes in flow regime, ranging from laminar cellular convection to geostrophic turbulence in which an inverse energy cascade is present. A decrease in the efficiency of the convection to generate a dynamo, as determined by an increase in the critical magnetic Reynolds number, is observed as the buoyancy forcing is increased. This decreased efficiency may result from both the loss of correlations associated with the increasingly disordered states of flow that are generated, and boundary layer behavior that enhances magnetic diffusion locally. We find that the spatial characteristics of $α$, and thus the large-scale magnetic field, is dependent only weakly on changes in flow behavior. However, our results are limited to the linear, kinematic dynamo regime, and future simulations including th

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preprint2016arXiv

Meandering instability of air flow in a granular bed: self-similarity and fluid-solid duality

Meandering instability is familiar to everyone through river meandering or small rivulets of rain flowing down a windshield. However, its physical understanding is still premature, although it could inspire researchers in various fields, such as nonlinear science, fluid mechanics and geophysics, to resolve their long-standing problems. Here, we perform a small-scale experiment in which air flow is created in a thin granular bed to successfully find a meandering regime, together with other remarkable fluidized regimes, such as a turbulent regime. We discover that phase diagrams of the flow regimes for different types of grains can be universally presented as functions of the flow rate and the granular-bed thickness when the two quantities are properly renormalized. We further reveal that the meandering shapes are self-similar as was shown for meandering rivers. The experimental findings are explained by theory, with elucidating the physics. The theory is based on force balance, a minimum-dissipation principle, and a linear-instability analysis of a continuum equation that takes into account the fluid-solid duality, i.e., the existence of fluidized and solidified regions of grains al

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preprint2016arXiv

Energy Release Rate in hydraulic fracture: can we neglect an impact of the hydraulically induced shear stress?

A novel hydraulic fracture (HF) formulation is introduced which accounts for the hydraulically induced shear stress at the crack faces. It utilizes a general form of the elasticity operator alongside a revised fracture propagation condition based on the critical value of the energy release rate. It is shown that the revised formulation describes the underlying physics of HF in a more accurate way and is in agreement with the asymptotic behaviour of the linear elastic fracture mechanics. A number of numerical simulations by means of the universal HF algorithm previously developed in Wrobel & Mishuris (2015) are performed in order to: i) compare the modified HF formulation with its classic counterpart and ii) investigate the peculiarities of the former. Computational advantages of the revised HF model are demonstrated. Asymptotic estimations of the main solution elements are provided for the cases of small and large toughness. The modified formulation opens new ways to analyse the physical phenomenon of HF and also improves the reliability and efficiency of its numerical simulations.

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preprint2016arXiv

A computer code for forward calculation and inversion of the H/V spectral ratio under the diffuse field assumption

During a quarter of a century, the main characteristics of the horizontal-to-vertical spectral ratio of ambient noise HVSRN have been extensively used for site effect assessment. In spite of the uncertainties about the optimum theoretical model to describe these observations, several schemes for inversion of the full HVSRN curve for near surface surveying have been developed over the last decade. In this work, a computer code for forward calculation of H/V spectra based on the diffuse field assumption (DFA) is presented and tested.It takes advantage of the recently stated connection between the HVSRN and the elastodynamic Green's function which arises from the ambient noise interferometry theory. The algorithm allows for (1) a natural calculation of the Green's functions imaginary parts by using suitable contour integrals in the complex wavenumber plane, and (2) separate calculation of the contributions of Rayleigh, Love, P-SV and SH waves as well. The stability of the algorithm at high frequencies is preserved by means of an adaptation of the Wang's orthonormalization method to the calculation of dispersion curves, surface-waves medium responses and contributions of bo

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Interaction prediction between groundwater and quarry extension using discrete choice models and artificial neural networks

Groundwater and rock are intensively exploited in the world. When a quarry is deepened the water table of the exploited geological formation might be reached. A dewatering system is therefore installed so that the quarry activities can continue, possibly impacting the nearby water catchments. In order to recommend an adequate feasibility study before deepening a quarry, we propose two interaction indices between extractive activity and groundwater resources based on hazard and vulnerability parameters used in the assessment of natural hazards. The levels of each index (low, medium, high, very high) correspond to the potential impact of the quarry on the regional hydrogeology. The first index is based on a discrete choice modelling methodology while the second is relying on an artificial neural network. It is shown that these two complementary approaches (the former being probabilistic while the latter fully deterministic) are able to predict accurately the level of interaction. Their use is finally illustrated by their application on the Boverie quarry and the Tridaine gallery located in Belgium. The indices determine the current interaction level as well as the one resulting from

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preprint2016arXiv

Subcritical convection of liquid metals in a rotating sphere using a quasi-geostrophic model

We study nonlinear convection in a rapidly rotating sphere with internal heating for values of the Prandtl number relevant for liquid metals ($Pr\in[10^{-2},10^{-1}]$). We use a numerical model based on the quasi-geostrophic approximation, in which variations of the axial vorticity along the rotation axis are neglected, whereas the temperature field is fully three-dimensional. We identify two separate branches of convection close to onset: (i) a well-known weak branch for Ekman numbers greater than $10^{-6}$, which is continuous at the onset (supercritical bifurcation) and consists of thermal Rossby waves, and (ii) a novel strong branch at lower Ekman numbers, which is discontinuous at the onset. The strong branch becomes subcritical for Ekman numbers of the order of $10^{-8}$. On the strong branch, the Reynolds number of the flow is greater than $10^3$, and a strong zonal flow with multiple jets develops, even close to the nonlinear onset of convection. We find that the subcriticality is amplified by decreasing the Prandtl number. The two branches can co-exist for intermediate Ekman numbers, leading to hysteresis ($Ek=10^{-6}$, $Pr=10^{-2}$). Nonlinear oscillations are observed ne

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preprint2016arXiv

Continuous Time Random Walks for the Evolution of Lagrangian Velocities

We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes persistence of velocities over a characteristic spatial scale, unlike classical random walk methods, which model persistence over a characteristic time scale. We first establish the relation between Eulerian and Lagrangian velocities for both equidistant and isochrone sampling along streamlines, under transient and stationary conditions. Based on this, we develop a space continuous CTRW approach for the spatial and temporal dynamics of Lagrangian velocities. While classical CTRW formulations have non-stationary Lagrangian velocity statistics, the proposed approach quantifies the evolution of the Lagrangian velocity statistics under both stationary and non-stationary conditions. We provide explicit expressions for the Lagrangian velocity statistics, and determine the behaviors of the mean particle velocity, velocity covariance and particle dispersion. We find strong Lagrangian correlation and anomalous dispersion for velocity distributions which are ta

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preprint2010arXiv

Forward and adjoint quasi-geostrophic models of the geomagnetic secular variation

We introduce a quasi-geostrophic model of core dynamics, which aims at describing core processes on geomagnetic secular variation timescales. It extends the formalism of Alfvén torsional oscillations by incorporating non-zonal motions. Within this framework, the magnetohydrodynamics takes place in the equatorial plane; it involves quadratic magnetic quantities, which are averaged along the direction of rotation of the Earth. In addition, the equatorial flow is projected on the core-mantle boundary. It interacts with the magnetic field at the core surface, through the radial component of the magnetic induction equation. That part of the model connects the dynamics and the observed secular variation, with the radial component of the magnetic field acting as a passive tracer. We resort to variational data assimilation to construct formally the relationship between model predictions and observations. Variational data assimilation seeks to minimize an objective function, by computing its sensitivity to its control variables. The sensitivity is efficiently calculated after integration of the adjoint model. We illustrate that framework with twin experiments, performed first in the case of

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