Spurious Structures Research Articles

Non-Parametric Determination of Real-Time Lag Structure between Two Time Series: The 'Optimal Thermal Causal Path' Method

We introduce a novel non-parametric methodology to test for the dynamical time evolution of the lag-lead structure between two arbitrary time series. The method consists in constructing a distance matrix based on the matching of all sample data pairs between the two time series. Then, the lag-lead structure is searched as the optimal path in the distance matrix landscape that minimizes the total mismatch between the two time series, and that obeys a one-to-one causal matching condition. To make the solution robust to the presence of large noise that may lead to spurious structures in the distance matrix landscape, we then generalize this optimal search by introducing a fuzzy search by sampling over all possible paths, each path being weighted according to a multinomial logit or equivalently Boltzmann factor proportional to the exponential of the global mismatch of this path. We present the efficient transfer matrix method that solves the problem and test it on simple synthetic examples to demonstrate its properties and usefulness compared with the standard running-time cross-correlation method. We then apply our Optimal Thermal Causal Path method to the question of the causality between the US stock market and the treasury bond yields and confirm our earlier results on a causal arrow of the stock markets preceding the Federal Reserve Funds adjustments, as well as the yield rates at short maturities in the period 2000-2003. Our application of this technique to inflation, inflation change, GDP growth rate and unemployment rate unearths non-trivial causal relationships: the GDP changes lead inflation especially since the 1980s, inflation changes leads GDP only in the 1980 decade, and inflation leads unemployment rates since the 1970s. In addition, our approach seems to detect multiple competing causality paths in which one can have inflation leading GDP with a certain lag time and GDP feeding back/leading inflation with another lag time.

Non-parametric determination of real-time lag structure between two time series: the ‘optimal thermal causal path’ method

We introduce a novel non-parametric methodology to test for the dynamical time evolution of the lag–lead structure between two arbitrary time series. The method consists of constructing a distance matrix based on the matching of all sample data pairs between the two time series. Then, the lag–lead structure is searched for as the optimal path in the distance matrix landscape that minimizes the total mismatch between the two time series, and that obeys a one-to-one causal matching condition. To make the solution robust to the presence of a large amount of noise that may lead to spurious structures in the distance matrix landscape, we generalize this optimal search by introducing a fuzzy search by sampling over all possible paths, each path being weighted according to a multinomial logit or equivalently Boltzmann factor proportional to the exponential of the global mismatch of this path. We present the efficient transfer matrix method that solves the problem and test it on simple synthetic examples to demonstrate its properties and usefulness compared with the standard running-time cross-correlation method. We then apply our ‘optimal thermal causal path’ method to the question of the lag-dependence between the US stock market and the treasury bond yields and confirm our earlier results on an arrow of the stock markets preceding the Federal Reserve Funds’ adjustments, as well as the yield rates at short maturities in the period 2000–2003. Our application of this technique to inflation, inflation change, GDP growth rate and unemployment rate unearths non-trivial lag relationships: the GDP changes lead inflation especially since the 1980s, inflation changes leads GDP only in the 1980 decade, and inflation leads unemployment rates since the 1970s. In addition, our approach seems to detect multiple competing lag structures in which one can have inflation leading GDP with a certain lag time and GDP feeding back/leading inflation with another lag time.

Crustal Scattering and Some Artifacts in Receiver Function Images

The existing 2D and 3D depth imaging approaches using multichannel teleseismic receiver functions (RFs) can result in significant artifacts caused by misinterpretation of signal-generated noise resulting from broadside scattering within the crust. A synthetic example using acquisition geometry of the 1993 Cascadia experiment shows that scattering of the primary P -wave arrivals from a sedimentary accretionary wedge could produce RF events close to those observed in real data. Quasi-linear crustal structures with significant velocity contrasts near Moho depths, such as subduction zones, should create particularly strong and coherent noise arrivals. Conventional interpretations of these arrivals based on assumptions of their origin in mode conversions could lead to images of spurious dipping structures of landward dips steeper than ∼10° that may be very difficult to distinguish from the true structures. Detailed analysis of prestack, premigration RF data is required for correct identification of the signal-generated noise and validation of the resulting depth images. Identification of scattered events in RF records could also help constrain major crustal structures, such as crustal sutures and subduction fault zones, and particularly those with strong Moho expressions. Manuscript received 10 June 2003.

Echelle-spectrograph as a tool for studies of structured background in flame atomic absorption spectrometry

An echelle-spectrograph with solid-state image detector and active wavelength stabilization was developed. It is used as a tool for investigations of structured background in flame atomic absorption spectrometry (flame-AAS). The simultaneously recordable spectral range of the spectrograph extends from 200 to 465 nm. Its pixel-based bandwidth is λ/80 000. The wavelength stabilization was developed for suppressing spurious structures in the calculated ratios of sample and blank spectra. Such structures arise in case of wavelength shifting during recording of the spectra. The stabilization compensates for spectrum displacements with respect to the pixel matrix of the detector by correction of both position and dispersion of the spectrum. The achievable precision is 1% of the pixel width. By averaging a multitude of measurements, transmittance spectra with high signal-to-noise ratios are obtained. Using an air-acetylene flame, alternate measurement of 50 spectra of both sample and blank results in a transmittance spectrum with a noise level of less than 5×10 −4 (rms). The spectra of highly concentrated samples of H 3PO 4, Fe, and Cu exemplary show the appearance of broad range, narrow structure background phenomena.

On Spurious Vortical Structures

The paper investigates the formation of spurious vortical structures in incompressible flow simulations employing Godunov-type methods. The present work is motivated by the earlier studies of Brown and Minion (1995, J. Comput. Phys.122, 165 and 1997, J. Comput. Phys.138, 734) who demonstrated for a variety of numerical schemes (and for the upwind-biased methods in particular) that spurious vortices can occur in underresolved flow simulations. The aim of our work is threefold: (i) to identify deficiencies in various Godunov-type methods leading to spurious flow structures, (ii) to examine the numerical mechanisms responsible for these artifacts, and (iii) to propose modifications of Godunov-type methods in order to recover the correct solutions even under insufficient grid resolution. Our results reveal that the occurrence of spurious solutions depends strongly on the Godunov-type method employed. We show that in addition to the dissipation properties of a scheme—emphasized by Brown and Minion—there are other factors that can also contribute to numerical artifacts. These include a vortical instability arising from the numerical discretization of the advective terms in the primitive variable formulation of the Navier–Stokes equations, the balance of dissipation among the different discretized terms in a Godunov-type method, as well as order of accuracy of the interpolation used to discretize the wave-speed dependent term of the Godunov flux.

Influence of physical processes on the tangent-linear approximation

A comprehensive set of linear physical parametrizations is developed for the tangent-linear andadjoint versions of ECMWF global forecast model. The following processes are described :vertical diffusion, subgrid-scale orographic effects, large scale condensation, long-wave radiationand deep cumulus convection. The accuracy of a tangent-linear model including these processesis examined by comparing 24-h forecasts obtained from an adiabatic tangent-linear version andpairs of non-linear integrations including full physics. It is shown that for finite size perturbations(analysis increments), the inclusion of physics improves the fit to the non-linear model. Theimprovement is largest for specific humidity, where combined effects of vertical diffusion (nearthe surface), large-scale condensation (in the mid-latitudes troposphere) and moist convection(in the lower tropical troposphere) contribute to a better evolution of moisture increments.Simplications have been designed with respect to the operational non-linear physics, mostly toavoid the growth of spurious unstable modes. Computation of singular vectors has revealedthat the linear package does not contain such spurious unphysical structures. This comprehensiveset of linear parametrizations is currently used in the ECMWF operational 4D-Var assimilationsystem.

Searching critical points of fitted potential energy surfaces

The search for critical points of fitted potential energy surfaces is facilitated by the analytical character of the function and their derivatives, but can become complicated owing to the possible presence of spurious structures generated by the fitting procedure. In this paper, we examine the capability of the gradient extremal path for following techniques in this context. In all the test cases, with this method it was possible to localize all the extrema, allowing a subsequent study of the small minima and saddle points oriented towards elucidating their spurious or true character.

Cluster recursion method of a non-orthogonal basis

We propose a new recursion algorithm which is applicable to the electronic structure calculations of disordered materials using a non-orthogonal basis (NOB) set. This recursion approach is based on matrix algebra (modified Householder method) and takes central cluster states as ‘initial states’ of the calculation of the electronic Green functions. Some example calculations on the electronic density of states (DOS) of regular lattices are presented to demonstrate the applicability of the present method. It is shown that the NOB cluster recursion method is stable in numerical computations and practically does not produce any spurious or unphysical structures both for the site diagonal and intersite Green functions.

Determination of crustal structure in central Australia by inversion of traveltime residuals

Teleseismic traveltime anomalies for events recorded on portable seismograph arrays across the northern and southern margins of the Amadeus Basin in central Australia are inverted to obtain a picture of the velocity structure at a scale on the order of 5–10 km. A modified sirt algorithm is used to iteratively redistribute traveltime anomalies along incoming ray paths, subject to regularization constraints, to obtain a direct estimate of the lithospheric velocity field beneath the arrays. Model structure is assumed to be 2-D, based on the strong east-west strike of surface geology and gravity structure in the area. Spurious structures commonly generated in sirt inversions are suppressed using a filter based on the density of rays. A weighting towards near-surface structure is also applied to test the robustness of the inference of deep structures. The most prominent feature of the solutions for all three lines is a sharp interface between slow and fast regions, dipping away from the basin and beneath the adjacent basement blocks. The fastest region, on the upper side of the interface, corresponds to a belt of high-grade metamorphic rocks where they crop out at the surface. The interface between slow and fast regions extends to at least 50 km depth in all cases, dipping at about 50–60° on the northern lines and 60–80° on the southern line. On the northern lines the interface can be correlated with the Redbank Thrust identified in deep seismic reflection data, but the velocity interface seems to dip more steeply. Secondary features on the profiles include a possible change in dip of the interface on the southern line and a more complex structure on one of the northern lines, suggesting that one or more steeper faults cut through the hanging wall of the thrust there. Predicted gravity profiles derived from the velocity sections using empirical velocity—density relations resemble observed gravity surprisingly well in their style and approximate magnitude, providing support for the general features of the models. The results are consistent with a thick-skinned thrusting model for the deformation of the central segment of the basin margins and indicate that the style of deformation in the Late Proterozoic-Cambrian compressional event at the southern edge of the Amadeus Basin was similar to that in the later Alice Springs Orogeny in the north.

On the convergence of the two-centre AO close-coupling method in ion - atom collisions

Convergence of the two-centre atomic orbital (TCAO) close-coupling method in ion - atom collisions is carefully examined within the semiclassical impact parameter approximation. Calculations were carried out for protons colliding with H(1s) in the impact energy range 15 - 1000 keV. It is shown that the spurious oscillatory structures in previous large scale TCAO close-coupling calculations are due to the simultaneous use of the short-ranged pseudo-continuum states on both collision centres. By including a large number of pseudo-continuum states only at one centre in the TCAO expansion, we demonstrate that the resulting cross sections for excitation, capture and ionization for p + H(1s) collisions vary smoothly with collision energy and are in better agreement with the experimental data.

Spectral Transform Solutions to the Shallow Water Test Set

Solutions to the test case suite proposed by Williamson et al. ( J. Comput. Phys. 102, 211 (1992)), for the shallow water equations in spherical geometry, are presented. The solutions have been generated using a conventional spectral transform technique combined with a semi-implicit time differencing scheme. For several of the test cases, closed-form solutions do not exist. For these cases, high-resolution numerical integrations of the spectral transform model are used to provide reference solutions against which alternative numerical schemes and lower resolution spectral transform solutions can be evaluated. The sensitivity of the high resolution numerical solutions, associated with temporal truncation, spatial truncation, and internal dissipation, are quantified in order to help bound their uncertainty. In almost all of the test cases, the spectral transform method proves to be a highly accurate solution technique. This is particularly the case at resolutions typically associated with atmospheric general circulation models used to simulate the atmosphere's climate. The most serious deficiency of the spectral transform method, in the context of the test cases, is the introduction of spurious minima and maxima into the solution (caused by Gibbs phenomenon), when sharp gradients exist. Although this behavior is not necessarily a problem for accurately simulating fluid flow, it can become a serious problem for atmospheric general circulation models if the spurious wave structures result in nonphysical states such as negative water vapor mixing ratio.

Mechanism for spurious structures in photoionization calculations in the independent-particle approximation.

A mechanism of unphysical structures in photoionization cross sections calculated in the independent-particle approximation (IPA) has been identified, in a study of the nature of near-threshold structures in the energy dependence of the krypton 3p photoionization, generated in the Hartree-Fock-Slater-Latter approximation

Effects of surface waves and ship heave-and-roll on CTD data and processing method for CTD data

The effects of surface waves and ship heave-and-roll on CTD data are discussed. The heave-and-roll produces spurious step-like structures in the CTD data. Derivation of a formula for calculating the probe's fall speed is discussed. Several current techniques for CTD sensor lag correction are analyzed and compared. It is shown the lag correction procedure presented here, which is based on the Giles-McDougall technique, can be employed to treat CTD data from regions with slow or fast T-S variations, for instance, in strong seasonal thermocline. False salinity spikes or humps in data corrected with this procedure are significantly reduced.

A compact gridless channel plate detector for time-of-flight measurements

A compact channel plate detector used as a start detector in heavy ion reaction studies is described. In order to avoid spurious structures in the energy spectra of the detected ions the usual electron accelerating grid is replaced by five electrodes which provide a uniform electric field. The start detector has an intrinsic resolution of 85 ps and efficiency of 90% for medium mass nuclei. The overall time resolution with a solid state detector as stop is 105 ps.

Comparison of interface state density in MIS structure deduced from DLTS and Terman measurements

Interface state impedance has been theoretically predicted to introduce spurious detailed structures in the trap density curves when determined by high-frequency C/V measurements (Terman method). This is experimentally demonstrated on irradiated MOS structures. Terman analysis of these MOS capacitors presents a peak in the trap density near the conduction band, while a flat continuum is found by deep level transient spectroscopy (DLTS). A numerical simulation shows that this discrepancy can be taken into account by the only interface state impedance effect.

Evaluation of image quality in tomographic imaging

Modulation transfer functions (MTE) for tomographic imaging with linear, circular, hypocycloidal and spiral motion are given. They may be determined experimentally from tomographs of slits or line pair test patterns. In some cases calculation of the MTF from the blur pattern by Fourier transformation is possible. All tomographic MTFs show the same oscillatory behaviour as MTFs of focal spots, resulting in spurious structures and contours in the tomogram. A quantity named signal/spurious signal ratio (SSR) is introduced as a figure of merit. Effective exposure angles are determined from the MTF and compared with the commonly used 'geometric' exposure angles which result from maximum tube elongations.

Runs Tests as Predictors of Intermediate Structure in the Continuum

Chance coherences between $S$-matrix elements at neighboring compound-nucleus excitation energies in the continuum are shown to generate spurious intermediate structures and statistical correlations in synthetic analyzing-power excitation functions. Hence, certain runs tests may be unreliable predictors of intermediate structure.