Spurious Shear Research Articles

The impact of mass map truncation on strong lensing simulations

Strong gravitational lensing is a powerful tool to measure cosmological parameters and to study galaxy evolution mechanisms. However, quantitative strong lensing studies often require mock observations. To capture the full complexity of galaxies, the lensing galaxy is often drawn from high resolution, dark matter only or hydro-dynamical simulations. These have their own limitations, but the way we use them to emulate mock lensed systems may also introduce significant artefacts. In this work we identify and explore the specific impact of mass truncation on simulations of strong lenses by applying different truncation schemes to a fiducial density profile with conformal isodensity contours. Our main finding is that improper mass truncation can introduce undesired artificial shear. The amplitude of the spurious shear depends on the shape and size of the truncation area as well as on the slope and ellipticity of the lens density profile. Due to this effect, the value of H0 or the shear amplitude inferred by modelling those systems may be biased by several percents. However, we show that the effect becomes negligible provided that the lens projected map extends over at least 50 times the Einstein radius.

A mixed B-bar formulation derived by a principle of virtual power for energy–momentum time integrations of fiber-reinforced continua

The optimization of finite element discretizations within energy–momentum time integrations of thermodynamical problems leads to further ‘constraints’ on algorithmic modifications compared to static problems, because each modification must not violate discrete balance laws. In order to preserve each discrete balance law while modifying the space approximation, a mixed version of the principle of virtual power is applied. Besides the reduction of volumetric locking in the matrix material and line locking in the fibers of the considered transversely isotropic continuum, a new space approximation additionally prevents spurious shear deformations in bending dominated problems. This approximation is based on independent fields for the deformation gradient and the first Piola–Kirchhoff stress tensor, leading to a new B-bar operator. The local shape functions for the independent deformation gradient are derived by a new criterion from the finite element shape functions. In this way, linear and quadratic hexahedral finite elements are combined with standard and non-standard shape functions of tetrahedral and prismatic elements. In order to evaluate the performance of this new mixed B-bar method with respect to locking as well as thermodynamical behavior, numerical examples with thin-walled, fiber-reinforced structures are considered. The numerical examples also reveal a new aspect of structure preservation, namely, the goal of a spatial mesh density independent structure preservation.

CONSEQUENCES OF CCD IMPERFECTIONS FOR COSMOLOGY DETERMINED BY WEAK LENSING SURVEYS: FROM LABORATORY MEASUREMENTS TO COSMOLOGICAL PARAMETER BIAS

ABSTRACT Weak gravitational lensing causes subtle changes in the apparent shapes of galaxies due to the bending of light by the gravity of foreground masses. By measuring the shapes of large numbers of galaxies (millions in recent surveys, up to tens of billions in future surveys) we can infer the parameters that determine cosmology. Imperfections in the detectors used to record images of the sky can introduce changes in the apparent shapes of galaxies, which in turn can bias the inferred cosmological parameters. In this paper we consider the effect of two widely discussed sensor imperfections: tree rings, due to impurity gradients that cause transverse electric fields in the charge-coupled devices (CCDs), and pixel size variation, due to periodic CCD fabrication errors. These imperfections can be observed when the detectors are subject to uniform illumination (flat-field images). We develop methods to determine the spurious shear and convergence (due to the imperfections) from the flat-field images. We calculate how the spurious shear when added to the lensing shear will bias the determination of cosmological parameters. We apply our methods to candidate sensors of the Large Synoptic Survey Telescope (LSST) as a timely and important example, analyzing flat-field images recorded with LSST prototype CCDs in the laboratory. We find that tree rings and periodic pixel size variation present in the LSST CCDs will introduce negligible bias to cosmological parameters determined from the lensing power spectrum, specifically w, , and .

On the solvability of incompressible Stokes with viscoplastic rheologies in geodynamics

AbstractPlasticity/failure is an essential ingredient in geodynamics models as earth materials cannot sustain unbounded stresses. However, many questions remain as to appropriate models of plasticity as well as effective solvers for these strongly nonlinear systems. Here we present some simplified model problems designed to elucidate many of the issues involved for the description and solution of viscoplastic problems as currently used in geodynamic modeling. We consider compression and extension of a viscoplastic layer overlying an isoviscous layer and introduce a single plastic yield criterion which includes the most commonly used viscoplasticity models: von Mises, depth‐dependent von Mises, and Drucker‐Prager. We show that for all rheologies considered, successive substitution schemes (aka Picard iteration) often stall at large values of the nonlinear residual, producing spurious solutions. However, combined Picard‐Newton schemes can be effective for rheologies that are independent of the dynamic pressure. Difficulties arise when solving incompressible Stokes problems for rheologies that depend on the dynamic pressure such as Drucker‐Prager viscoplasticity. Analysis suggests that incompressible Stokes can become ill‐posed when the dependence of the deviatoric stress tensor on dynamic pressure (i.e., ) becomes large. We demonstrate empirically that, in these cases, Newton solvers can fail by introducing spurious shear bands and discuss the consequence of interpreting the results of nonconverged computations. Even for problems where solvers converge, Drucker‐Prager viscoplasticity can produce dynamic pressures that deviate significantly from lithostatic and both the velocity and pressure fields should be evaluated to determine whether solutions are geologically reasonable.

Spurious shear induced by the tree rings of the LSST CCDs

We present an analysis of the impact of the tree rings seen in the candidate sensors of the Large Synoptic Survey Telescope (LSST) on galaxy-shape measurements. The tree rings are a consequence of transverse electric fields caused by circularly symmetric impurity gradients in the silicon of the sensors. They effectively modify the pixel area and shift the photogenerated charge around, displacing the observed photon positions. The displacement distribution generates distortions that cause spurious shears correlated with the tree-rings patterns, potentially biasing cosmic shear measurements. In this paper we quantify the amplitude of the spurious shear caused by the tree rings on the LSST candidate sensors, and calculate its 2-point correlation function. We find that 2-point correlation function of the spurious shear on an area equivalent to the LSST field of view is order of about 10−13, providing a negligible contribution to the 2-point correlation of the cosmic shear signal. Additional work is underway, and the final results and analysis will be published elsewhere (Okura et al. (2015), in prep.)

Impact of spurious shear on cosmological parameter estimates from weak lensing observables

Residual errors in shear measurements, after corrections for instrument systematics and atmospheric effects, can impact cosmological parameters derived from weak lensing observations. Here we combine convergence maps from our suite of ray-tracing simulations with random realizations of spurious shear. This allows us to quantify the errors and biases of the triplet $(\Omega_m,w,\sigma_8)$ derived from the power spectrum (PS), as well as from three different sets of non-Gaussian statistics of the lensing convergence field: Minkowski functionals (MF), low--order moments (LM), and peak counts (PK). Our main results are: (i) We find an order of magnitude smaller biases from the PS than in previous work. (ii) The PS and LM yield biases much smaller than the morphological statistics (MF, PK). (iii) For strictly Gaussian spurious shear with integrated amplitude as low as its current estimate of $\sigma^2_{sys}\approx 10^{-7}$, biases from the PS and LM would be unimportant even for a survey with the statistical power of LSST. However, we find that for surveys larger than $\approx 100$ deg$^2$, non-Gaussianity in the noise (not included in our analysis) will likely be important and must be quantified to assess the biases. (iv) The morphological statistics (MF,PK) introduce important biases even for Gaussian noise, which must be corrected in large surveys. The biases are in different directions in $(\Omega_m,w,\sigma_8)$ parameter space, allowing self-calibration by combining multiple statistics. Our results warrant follow-up studies with more extensive lensing simulations and more accurate spurious shear estimates.

Seeing in the dark – I. Multi-epoch alchemy

Weak lensing by large-scale structure is an invaluable cosmological tool given that most of the energy density of the concordance cosmology is invisible. Several large ground-based imaging surveys will attempt to measure this effect over the coming decade, but reliable control of the spurious lensing signal introduced by atmospheric turbulence and telescope optics remains a challenging problem. We address this challenge with a demonstration that point-spread function (PSF) effects on measured galaxy shapes in current ground-based surveys can be corrected with existing analysis techniques. In this work, we co-add existing Sloan Digital Sky Survey imaging on the equatorial stripe in order to build a data set with the statistical power to measure cosmic shear, while using a rounding kernel method to null out the effects of the anisotropic PSF. We build a galaxy catalogue from the combined imaging, characterise its photometric properties, and show that the spurious shear remaining in this catalogue after the PSF correction is negligible compared to the expected cosmic shear signal. We identify a new source of systematic error in the shear-shear auto-correlations arising from selection biases related to masking. Finally, we discuss the circumstances in which this method is expected to be useful for upcoming ground-based surveys that have lensing as one of the science goals, and identify the systematic errors that can reduce its efficacy.

An Automated Method for Depicting Mesocyclone Paths and Intensities

Abstract The location and intensity of mesocyclone circulations can be tracked in real time by accumulating azimuthal shear values over time at every location of a uniform spatial grid. Azimuthal shear at low (0–3 km AGL) and midlevels (3–6 km AGL) of the atmosphere is computed in a noise-tolerant manner by fitting the Doppler velocity observations in the neighborhood of a pulse volume to a plane and finding the slope of that plane. Rotation tracks created in this manner are contaminated by nonmeteorological signatures caused by poor velocity dealiasing, ground clutter, radar test patterns, and spurious shear values. To improve the quality of these fields for real-time use and for an accumulated multiyear climatology, new dealiasing strategies, data thresholding, and multiple hypothesis tracking (MHT) techniques have been implemented. These techniques remove nearly all nonmeteorological contaminants, resulting in much clearer rotation tracks that appear to match mesocyclone paths and intensities closely.

Atmospheric point spread function interpolation for weak lensing in short exposure imaging data

A main science goal for the Large Synoptic Survey Telescope (LSST) is to measure the cosmic shear signal from weak lensing to extreme accuracy. One difficulty, however, is that with the short exposure time ($\simeq$15 seconds) proposed, the spatial variation of the Point Spread Function (PSF) shapes may be dominated by the atmosphere, in addition to optics errors. While optics errors mainly cause the PSF to vary on angular scales similar or larger than a single CCD sensor, the atmosphere generates stochastic structures on a wide range of angular scales. It thus becomes a challenge to infer the multi-scale, complex atmospheric PSF patterns by interpolating the sparsely sampled stars in the field. In this paper we present a new method, PSFent, for interpolating the PSF shape parameters, based on reconstructing underlying shape parameter maps with a multi-scale maximum entropy algorithm. We demonstrate, using images from the LSST Photon Simulator, the performance of our approach relative to a 5th-order polynomial fit (representing the current standard) and a simple boxcar smoothing technique. Quantitatively, PSFent predicts more accurate PSF models in all scenarios and the residual PSF errors are spatially less correlated. This improvement in PSF interpolation leads to a factor of 3.5 lower systematic errors in the shear power spectrum on scales smaller than $\sim13'$, compared to polynomial fitting. We estimate that with PSFent and for stellar densities greater than $\simeq1/{\rm arcmin}^{2}$, the spurious shear correlation from PSF interpolation, after combining a complete 10-year dataset from LSST, is lower than the corresponding statistical uncertainties on the cosmic shear power spectrum, even under a conservative scenario.

Spurious shear in weak lensing with the Large Synoptic Survey Telescope

The complete 10-year survey from the Large Synoptic Survey Telescope (LSST) will image $\sim$ 20,000 square degrees of sky in six filter bands every few nights, bringing the final survey depth to $r\sim27.5$, with over 4 billion well measured galaxies. To take full advantage of this unprecedented statistical power, the systematic errors associated with weak lensing measurements need to be controlled to a level similar to the statistical errors. This work is the first attempt to quantitatively estimate the absolute level and statistical properties of the systematic errors on weak lensing shear measurements due to the most important physical effects in the LSST system via high fidelity ray-tracing simulations. We identify and isolate the different sources of algorithm-independent, \textit{additive} systematic errors on shear measurements for LSST and predict their impact on the final cosmic shear measurements using conventional weak lensing analysis techniques. We find that the main source of the errors comes from an inability to adequately characterise the atmospheric point spread function (PSF) due to its high frequency spatial variation on angular scales smaller than $\sim10'$ in the single short exposures, which propagates into a spurious shear correlation function at the $10^{-4}$--$10^{-3}$ level on these scales. With the large multi-epoch dataset that will be acquired by LSST, the stochastic errors average out, bringing the final spurious shear correlation function to a level very close to the statistical errors. Our results imply that the cosmological constraints from LSST will not be severely limited by these algorithm-independent, additive systematic effects.

Measuring the effects of artificial viscosity in SPH simulations of rotating fluid flows

A commonly cited drawback of SPH is the introduction of spurious shear viscosity by the artificial viscosity term in situations involving rotation. Existing approaches for quantifying its effect include approximate analytic formulae and disc-averaged be- haviour in specific ring-spreading simulations, based on the kinematic effects produced by the artificial viscosity. These methods have disadvantages, in that they typically are applicable to a very small range of physical scenarios, have a large number of simplifying assumptions, and often are tied to specific SPH formulations which do not include corrective (e.g., Balsara) or time-dependent viscosity terms. In this study we have developed a simple, generally applicable and practical technique for evaluating the local effect of artificial viscosity directly from the creation of specific entropy for each SPH particle. This local approach is simple and quick to implement, and it al- lows a detailed characterization of viscous effects as a function of position. Several advantages of this method are discussed, including its ease in evaluation, its greater accuracy and its broad applicability. In order to compare this new method with ex- isting ones, simple disc flow examples are used. Even in these basic cases, the very roughly approximate nature of the previous methods is shown. Our local method pro- vides a detailed description of the effects of the artificial viscosity throughout the disc, even for extended examples which implement Balsara corrections. As a further use of this approach, explicit dependencies of the effective viscosity in terms of SPH and flow parameters are estimated from the example cases. In an appendix, a method for the initial placement of SPH particles is discussed which is very effective in reducing numerical fluctuations.

High-resolution surface wave tomography beneath the Aegean-Anatolia region: constraints on upper-mantle structure

This study provides new constraints on the upper-mantle structure from western Greece to central Anatolia using seismic data of permanent broad-band networks recently installed in Greece and Turkey and from a two-year temporary array (SIMBAAD experiment). We used ∼200 seismic events recorded at 146 broad-band stations with a typical interstation distance of 60-100 km across the study area. The high-resolution 3-D shear wave velocity model of the mantle is obtained by inversion of fundamental-mode Rayleigh wave phase velocity maps for periods between 20 and 195 s. The tomography is based on ray tracing in heterogeneous media taking into account external propagation effects. The horizontal resolution is approximately 100 km, however small heterogeneities may suffer from some horizontal smearing and damping. The vertical resolution is approximately 100 km. The vertical smoothing is necessary to avoid unresolved spurious shear wave velocity oscillations in the upper mantle. The errors on shear wave velocities in our 3-D model (0.02–0.1 km s−1) are significantly smaller than the amplitude of Vs variations (0.3–0.5 km s−1). In spite of the vertical and horizontal smoothing, our model shows details in the upper-mantle structure never reached at regional scale in the area. The overall structure is characterized by a low-velocity zone (80–200 km depth) reflecting a slow and warm asthenosphere underlying a thin lithosphere. The southwesternmost termination of the low-velocity anomaly corresponds to the northward dipping Hellenic slab. The detailed shear velocity structure of the upper mantle beneath Anatolia appears to be far more geometrically complex than revealed in previous tomographic studies of the area. At depths larger than or equal to 160 km, velocities are overall high beneath Anatolia, partly due to the presence of dipping high-velocity anomalies which we tentatively interpret as remnant slabs. The southernmost high-velocity anomaly beneath Anatolia is separated from the eastern edge of the Hellenic slab by a major low-velocity anomaly which we interpret as the trace of asthenospheric mantle material rising inside a vertical slab tear beneath southwestern Anatolia.

Spurious Shear from the Atmosphere in Ground-based Weak-lensing Observations

Weak-lensing observations have the potential to be even more powerful than cosmic microwave background observations in constraining cosmological parameters. However, the practical limits to weak-lensing observations are not known. Most theoretical studies of weak-lensing constraints on cosmology assume that the only limits are shot noise on small scales, and cosmic variance on large scales. For future large surveys, shot noise will be so low that other, systematic errors will likely dominate. Here we examine a potential source of additive systematic error for ground-based observations: spurious power induced by the atmosphere. We show that this limit will not be a significant factor even in future massive surveys such as LSST.

A mixed finite-element method for solving the poroelastic Biot equations with electrokinetic coupling

SUMMARY In this paper, a numerical method for solving the Biot poroelastic equations is developed. These equations comprise acoustic (typically water) and elastic (porous medium frame) equations, which are coupled mainly through fluid/solid drag terms. This wave solution is coupled to a simplified form of Maxwell’s equations, which is solved for the streaming potential resulting from electrokinesis. The ultimate aim is to use the generated electrical signals to provide porosity, permeability and other information about the formation surrounding a borehole. The electrical signals are generated through electrokinesis by seismic waves causing movement of the fluid through pores or fractures of a porous medium. The focus of this paper is the numerical solution of the Biot equations in displacement form, which is achieved using a mixed finite-element formulation with a different finite-element representation for displacements and stresses. The mixed formulation is used in order to reduce spurious displacement modes and fluid shear waves in the numerical solutions. These equations are solved in the time domain using an implicit unconditionally stable time-stepping method using iterative solution methods amenable to solving large systems of equations. The resulting model is embodied in the MODELLING OF ACOUSTICS, POROELASTICS AND ELECTROKINETICS (MAPEK) computer model for electroseismic analysis.

On the application of the additive decomposition of generalized strain measures in large strain plasticity

In the present paper two thermodynamically consistent large strain plasticity models are examined and compared in finite simple shear. The first model (A) is based on the multiplicative decomposition of the deformation gradient, while the second one (B) on the additive decomposition of generalized strain measures. Both models are applied to a rigid-plastic material described by the von Mises-type yield criterion. Since both models include neither hardening nor softening law, a constant shear stress response even for large amounts of shear is expected. Indeed, the model A exhibits the true constant shear stress behavior independent of the elastic material law. In contrast, the model B leads to a spurious shear stress increase or drop such that its applicability under finite shear deformations may be questioned.

On the effects of assuming flow profiles in nonequilibrium simulations

Atomic simulation methods modelling fluid flows often incorporate in the equations of motion the steady state flow profile predicted by Navier–Stokes equations. We show in this work that this may lead to significant errors such as spurious shear induced ordering, unphysical steady state flow profiles or artificial dampening of thermal motion even at shear rates regarded as low in simulation applications. Our results also suggest that nonequilibrium molecular dynamics coupled with the recently developed configurational thermostat, which makes no assumption at all on the flow profile, provides a much more realistic way to study these phenomena.

Numerical breakdown at high Weissenberg number in non-Newtonian contraction flows

Planar contraction flows of non-Newtonian fluids with integral constitutive models are studied to investigate the problem of numerical breakdown at high Weissenberg or Debrorah numbers. Spurious shear stress extrema are found on the wall downstream of the re-entrant corner for both sharp and rounded corners. Moreover, a non-monotonic relation between shear stress and strain rate is found when the Deborah number limit is approached, which correlates with these shear extrema. This strongly suggests that non-monotonicity between shear stress and strain rate may be responsible for the Deborah number limit problem in contraction flow simulations. This non-monotonicity is caused by the inaccuracy of the quadrature, using constitutive equations that do not have shear stress maxima when exactly evaluated. This conclusion agrees with recent analytical findings by others that inaccuracy of the integration along the streamlines – either by numerical integration or asymptotic approximation – makes the problem ill-conditioned, with spurious growth occurring on the wall downstream of the re-entrant corner.

Finite element free vibration analysis of eccentrically stiffened plates

A new finite element model is proposed for free vibration analysis of eccentrically stiffened plates. The formulation allows the placement of any number of arbitrarily oriented stiffeners within a plate element without disturbing their individual properties. A plate-bending element consistent with the Reissner-Mindlin thick plate theory is employed to model the behaviour of the plating. A stiffener element, consistent with the plate element, is introduced to model the contributions of the stiffeners. The applied plate-bending and stiffener elements are based on mixed interpolation of tensorial components (MITC), to avoid spurious shear locking and to guarantee good convergence behaviour. Several numerical examples using both uniform and distorted meshes are given to demonstrate the excellent predictive capability of this approach.

Consistent curved beam element

Curved beam finite elements with shear deformation have required the use of reduced integration to provide improved results for thin beams and arches due to the presence of a spurious shear strain mode. It has been found that the spurious shear strain mode results from an inconsistency in the displacement fields used in the formulation of these elements. A new curved beam element has been formulated. By providing a cubic polynomial for approximation of displacements, and a quadratic polynomial for approximation of rotations a consistent formulation is ensured thereby eliminating the spurious mode. A rotational degree of freedom which varies quadratically through the thickness of the element is included. This allows for a parabolic variation of the shear strain and hence eliminates the need for use of the shear correction factor k as required by the Timoshenko beam theory. This rotational degree of freedom also provides a cubic variation of displacements through the depth of the element. Thus, the normal to the centroidal axis is neither straight nor normal after shearing and bending allowing for warping of the cross section. Material nonlinearities are also incorporated, along with the modified Newton-Raphson method for nonlinear analysis. Comparisons are made with the available elasticity solutions and those predicted by the quadratic isoparametric beam element. The results indicate that the consistent beam element provides excellent predictions of the displacements, stresses and plastic zones for both thin and thick beams and arches.

A bilinear shell element with the cross‐reduced integration technique

AbstractA bilinear shell element is presented. The element is based on the concepts of laminas and fibres. A cross‐reduced integration technique is used to carry out the element integration. In this reduced integration technique, the Gauss points are chosen both on the reference lamina and along the central fibre. Spurious shear strains are averaged on the reference lamina to solve the shear locking problem and to eliminate any zero‐energy mode associated with the rotational degrees of freedom. Due to the integration on the reference lamina, zero‐energy modes associated with the translational degrees of freedom can also be removed. The behaviour of the element is examined in several numerical examples with various loading conditions and boundary conditions.