Local Wavenumber Research Articles

Amplitude-phase method for solving Floquet-type problems

The understanding of one-dimensional quantal and dynamical problems is fundamental to problems involving stability of material constructions, quantum tunneling in solids, chemical selection of gas components, electronic properties of material nanostructures. An amplitude-phase method for one-dimensional Schrödinger/Hill-type equations with periodic potentials/coefficients is shown to provide detailed insights into Floquet-type quantal and dynamical problems. Method-independent real and periodic local amplitude and wave-number (or angular frequency) functions are found for bounded Floquet solutions. Regular and weakly singular periodic potentials/coefficients of analytic forms apply.

Isolating spatiotemporally local mixed Rossby-gravity waves using multi-dimensional ensemble empirical mode decomposition

Tropical waves have relatively large amplitudes in and near convective systems, attenuating as they propagate away from the area where they are generated due to the dissipative nature of the atmosphere. Traditionally, nonlocal analysis methods, such as those based on the Fourier transform, are applied to identify tropical waves. However, these methods have the potential to lead to the misidentification of local wavenumbers and spatial locations of local wave activities. To address this problem, we propose a new method for analyzing tropical waves, with particular focus placed on equatorial mixed Rossby-gravity (MRG) waves. The new tropical wave analysis method is based on the multi-dimensional ensemble empirical mode decomposition and a novel spectral representation based on spatiotemporally local wavenumber, frequency, and amplitude of waves. We first apply this new method to synthetic data to demonstrate the advantages of the method in revealing characteristics of MRG waves. We further apply the method to reanalysis data (1) to identify and isolate the spatiotemporally heterogeneous MRG waves event by event, and (2) to quantify the spatial inhomogeneity of these waves in a wavenumber-frequency-energy diagram. In this way, we reveal the climatology of spatiotemporal inhomogeneity of MRG waves and summarize it in wavenumber-frequency domain: The Indian Ocean is dominated by MRG waves in the period range of 8–12 days; the western Pacific Ocean consists of almost equal energy distribution of MRG waves in the period ranges of 3–6 and 8–12 days, respectively; and the eastern tropical Pacific Ocean and the tropical Atlantic Ocean are dominated by MRG waves in the period range of 3–6 days. The zonal wavenumbers mostly fall within the band of 4–15, with Indian Ocean has larger portion of higher wavenumber (smaller wavelength components) MRG waves.

Analysis of the hypersonic cross-flow instability with experimental wavenumber distributions

Stationary cross-flow vortex N-factors were calculated over the surface of a yawed circular cone using computationally predicted and experimentally observed wavenumber distributions. Surface heat-flux data were obtained on a half-angle circular cone to investigate the behaviour of the stationary waves at different angles of attack and Reynolds numbers at Mach 6 under quiet-flow conditions in the Boeing/AFOSR Mach-6 Quiet Tunnel at Purdue University. A wavelet analysis was conducted on the experimental surface heat-flux data to construct a spatial mapping of the local largest amplitude wavenumbers of the stationary cross-flow waves, which were between 40 and 80 per circumference. Significant axial and azimuthal variation was observed. The results from the wavelet analysis were used to inform the stability analysis. The computed integration marching directions demonstrated very good agreement with the experimentally observed paths. N-factors were first calculated by integrating the local amplification rate corresponding to the most amplified experimental wavenumbers. The calculations were repeated based on non-dimensional computationally varying wavenumber ratios, which were dimensionalized by the experimental data. The computed N-factors showed good agreement between the two techniques. N-factors were also computed using the computationally predicted most unstable wavenumbers. The results showed decreased agreement with the other two cases, suggesting that this assumption does not properly model the cross-flow transition process.

Imaging of Lamination Defect in Metallic Plate Based on Local Wavenumber Domain Analysis

In metallic plate structures, a lamination defect is a type of internal defect that is commonly generated in the manufacturing process, which is mostly parallel to the surface of the plate. This study presents a technique of imaging a lamination defect in a metallic plate by using Lamb waves based on the local wavenumber domain analysis method. Owing to the processing technique, an aluminum beam structure is utilized to represent the metallic plate for the detection of the lamination defect. A three-dimensional finite-element model of an aluminum beam with a rectangular lamination defect is constructed with MatLab and ABAQUS commercial software. The propagation characteristics of Lamb waves are discussed by analyzing the simulated wavefield. A complicated wave-propagation phenomenon of multiple reflection and transmission is observed between the interaction of Lamb waves and the lamination. By performing local wavenumber domain analysis on the wavefield, the wavenumber distribution is obtained, from which the location and profile of the lamination defect are identified. An experimental study is carried out to verify the numerical result. A fully non-contact detection system consisting of an electromagnetic acoustic transducer and laser ultrasonic inspection system is established to inspect the artificial machined beam structure. The experimental result is in good agreement with the numerical result.

Gravity study of the Douala sub-basin (Cameroon) using Euler 3D deconvolution, source edge detection (SED) and special function analysis

Gravity data over an extending section of the north west portion of the Douala sedimentary sub-basin have been processed for both shallow and deep geologic contacts. Qualitative analysis, Euler 3D deconvolution, source edge detection (SED) and analysis of some special functions (horizontal gradient magnitude, analytic signal and the local wavenumber) have been carried out. One major peak and two minor peaks were highlighted on the anomaly maps as well as three major zones of anomaly which move from a very high positive anomaly zone in the center through an average positive zone to an average negative zone. Results of Euler 3D deconvolution and SED emphasized the presence of the underlying intrusive body to depths greater than 4 km in this study area and also suggested other geologic contacts above it. Solutions of special function analysis indicated that these geological contacts consist of some major faults with N–S, NE–SW, NW–SE and E–W orientations as well as some minor faults with NW–SE, E–W and NE–SW orientations having dip directions generally pointing away from the center of the study area. The faults and contacts were shown to be buried at a minimum depth of about 2 km with the majority having a structural index value in the range − 0.8 to 0.

Stability of mixed convection in a differentially heated vertical fluid layer with internal heat sources

The linear stability of mixed convection caused by a constant external pressure gradient, buoyancy force and a uniform internal heating in a vertical incompressible fluid layer whose vertical walls are kept at different constant temperatures is studied. The ensuing eigenvalue problem is solved numerically using the Chebyshev collocation method for two-dimensional motions after ensuring the validity of Squire’s theorem. The presence of internal heating introduces the point of inflection as well as reverse flow and increasing in its strength is found to amplify the back flow. The stability characteristics of the system are discussed for three values of Prandtl number representative of liquid mercury, water and oil. Multiple local minimum wave numbers are observed even in the presence of internal heating which facilitates instability of the system for all the values of Reynolds number and the Prandtl number considered. Additionally, the streamlines and isotherms of the perturbation modes are presented for different values of internal heat source strength, the Reynolds number and the Prandtl number. An energy budget analysis is embarked upon to understand the physical mechanisms involved in the flow transition.

The High-Resolution Wavevector Analysis for the characterization of the dynamic response of composite plates

The High Resolution Wavevector Analysis (HRWA) is presented and its application illustrated. Extending the High Resolution Wavenumber Analysis method [1] to 2D signals, it allows the wide-band and local characterization of the linear elastic behavior of anisotropic plates. The method belongs to the family of experimental wavenumber-based characterization methods and uses the high resolution signal processing algorithm ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) and the ESTER criterion (ESTimation of ERror) to overcome some of the limitation of Fourier-based methods. Three experimental applications on composite plate specimens are presented. First (i), from the out-of-plane velocity field of a sandwich plate with a foam core, different wave types (bending, shear and compression) are extracted. The results are compared with numerical predictions. Second (ii), individual layer contributions are separated on a honeycomb sandwich plate by means of the observation of the dependence of the extracted complex wavevectors as a function of wave propagation direction and frequency. Third (iii), a local wavenumber extraction is performed on a 4-layer carbon-epoxy plate made of fiber patches with spatially varying orientations. The local specific bending stiffness of the plate is identified from the extracted wavevectors and compared with theoretical results.

The Universality of the Normalized Vertical Velocity Variance in Contrast to the Horizontal Velocity Variance in the Convective Boundary Layer

AbstractThe vertical turbulent velocity variance normalized by the convective velocity squared as a function of the boundary layer depth–normalized height [i.e., ] in the convective boundary layer (CBL) over a homogeneous surface exhibits a near-universal profile, as demonstrated by field observations, laboratory experiments, and numerical simulations. The profile holds over a wide CBL stability range set by the friction velocity, CBL depth, and surface heating. In contrast, the normalized horizontal turbulent velocity variance increases monotonically with decreasing stability. This study investigates the independence of the profile to changes in CBL stability, or more precisely, wind shear. Large-eddy simulations of several convective and neutral cases are performed by varying surface heating and geostrophic winds. Analysis of the turbulent kinetic energy budgets reveals that the conversion term between and depends almost entirely on buoyancy. This explains why does not vary with shear, which is a source to only. Further analysis through rotational and divergent decomposition suggests that the near-universal profile of is fundamentally related to the dynamics and interactions of local and nonlocal CBL turbulence. Specifically, the preferential interactions between local wavenumbers and the downscale energy cascade of CBL turbulence offer plausible explanations to the universal profile of .

English

Structural features of Ikogosi Warm Spring and its environs have been delineated using qualitative and quantitative interpretation methods. Euler-Deconvolution and local wave number methods were adopted for quantitative and qualitative interpretation of aeromagnetic data sheet 243 by Geological Survey Agency of Nigeria (GSN) in 2008, respectively. Euler solution revealed depth range of -2.98 to -290 m to the magnetic sources, while local wave number method revealed depths to magnetic sources/basements ranging from -2.1 to -1311.4 m of the geologic lineaments in Ikogosi Warm Spring and its environs. Both methods revealed outcrop features characterized by their positive depth values above the mean ground level. Both methods proved efficient way of resolving shallow magnetic source depth giving a very plausible depth of -2.1 m for local wave number and -2.98 m for Euler solution in the area of study. Key words:  Warm-Spring, Ikogosi, lineament. &nbsp

Determination of source parameters of simple-shaped geologic subsurface structures from self-potential anomalies using enhanced local wavenumber method

Simple geometry model structures can be useful in quantitative evaluation of self-potential data. In this paper, we solve local wavenumber equation to estimate the horizontal position, the depth and the type of the causative source geometry by using a linear least-squares approximation. The advantages of the algorithm in determining the horizontal position and depth measure are its independency to shape factor of the sources and also its simple computations. The algorithm is built in Matlab environment. The validity of the algorithm is illustrated on variable noise-free and random noise included synthetic data from two-dimensional (2-D) models where the achieved parametric quantities coincide well with the actual ones. The algorithm is also utilized to real self-potential data from Ergani Copper district, Turkey. The results from the actual data application are in good agreement with the published literature for the study area. The source code of the algorithm is available from the authors on request.

Three-dimensional reconstruction of a small-scale magnetic target from magnetic gradient observations

Abstract A three-dimensional reconstruction method of a small-scale magnetic target is studied in this paper. Firstly, the tilt angle and local wavenumber are calculated from the measured magnetic gradient tensor data, leading to estimates of an approximate horizontal boundary and central depth of the magnetic target. From these, a spatial range of the inversion space and depth weighting function of the magnetic target are determined. Secondly, the inversion space is divided into cuboid cells, and the inversion equations for the magnetic parameters are established. They are regularized subject to the determined spatial range and depth weighting. Finally, a generalized cross validation method is used to obtain optimal regularization parameters, allowing the magnetization intensity of each cuboid to be estimated, and the three-dimensional profile of magnetic target to be delimited. Our simulation and experimental results show that the proposed method can realize, with a high degree of fidelity, the three-dimensional reconstruction of a simple small-scale magnetic target.

High resolution airborne radiometric and magnetic studies of ilesha and its environs, southwestern Nigeria

Abstract The study of the nature of distribution of natural radioelements in Ilesha and its environs with its geological structure has been studied using aeroradiometric data. Aeromagnetic data have also been subjected to three automated gradient techniques to delineate the sub-surface structure of the study area. From the study, it can be found that maximum values of “eU” (ppm) and “eTh” (ppm) fall within the branded gneiss, whereas the maximum value of K (%) falls within porphyritic granite regions. eTh had the highest radioactive content. The environmental dose rate of Ilesha was between 0.1817 and 3.9296 msv/yr. Although there were extreme values, but the mean dose rate was 0.522 ± 0.310 msv/yr (within acceptable safe limit of 1.0 msv/yr). eU/K, eU/eTh and eTh/K ratios were analysed for enrichment or depletion of radioisotopes. eU/eTh >1 showed uranium depletion, while eTh >2 showed eTh enrichment. The magnetic intensity values ranged from -79.41 to 140.93 nT. The horizontal gradient method (HGM) and analytic signal amplitude (ASA) revealed that depth to magnetic sources ranged from 0.478 to 4.112 km and 0.348 to 2.551 km, respectively, whereas local wavenumber (LWN) depth ranged from 0.478 to 5.48 km, which overestimated those compared using HGM and ASA functions. The apparent susceptibility ranged from -0.00325 to 0.00323 SI, showing that ferromagnetic and diamagnetic mineral ranges control apparent susceptibility in Ilesha.

Estimation of Magnetic Contact Location and Depth of Magnetic Sources in a Sedimentary Formation

Abstract The aeromagnetic data of Idogo, Southwestern Nigeria, have been used to study the lithology and to determine the magnetic source parameters within Idogo and its environs. Idogo lies between latitudes 6°30′N and 7°00′N and between longitudes 2°30′E and 3°00′E. The magnetic anomaly map, the regional geology, the analytic signal and the local wavenumber were used to identify the nature and depth of the magnetic sources in the region. Data enhancement was carried out to delineate the residual features relative to the strong regional gradients and intense anomalies due to the basin features. The estimated basement depth using the horizontal gradient method revealed depths ranging between 0.55 km and 2.49 km, while the analytic signal amplitude and local wavenumber methods estimated depth to the magnetic sources to range from 0.57 km to 4.22 km and 0.96 km to 2.43 km, respectively. Depth computations suggested the presence of both shallow and deep sources. The total magnetic intensity values ranged from 3.1 nT to 108.3 nT. The area shows magnetic closures of various sizes in different parts of the area trending West, with prominence at the centre and distributed East–West.

Riemann problems and dispersive shocks in self-focusing media

The dynamical behavior resulting from an initial discontinuity in focusing media is investigated using a combination of numerical simulations and Whitham modulation theory for the focusing nonlinear Schrodinger equation. Initial conditions with a jump in either or both the amplitude and the local wavenumber are considered. It is shown analytically and numerically that the space-time plane divides into expanding domains in which the solution is described by a slow modulation of genus-zero, genus-one or genus-two solutions, their precise arrangement depending on the specifics of the initial datum

Initial beam emission spectroscopy diagnostic system on HL-2A tokamak.

A beam emission spectroscopy system is being developed and deployed on the HL-2A tokamak to measure local low wavenumber (k ⊥ ρ i < 1) density fluctuations by measuring the Doppler-shifted emission from a 50 kV deuterium heating neutral beam. High spatial resolution (Δr ≤ 1 cm, Δz ≤ 1.5 cm) measurements are achieved with customized in-vacuum optics. High frequency, high-gain preamplifiers sample the light intensity at a Nyquist frequency of 1 MHz and achieve a high S/N ratio via high optical throughput, low-noise preamplifiers, and high quantum efficiency photodiodes. A first set of 16 detector channels [configured in an 8 (radial) × 2 (poloidal) array] has been installed and tested at HL-2A, covering the radial range r/a = 0.8-1.1. The frequency and wavenumber spectra have been measured under different plasma conditions. Initial measurements have demonstrated the capability of measuring edge plasma density fluctuation spectra and the poloidal flow velocity fields with a high S/N ratio.

Lamb Wave Local Wavenumber Approach for Characterizing Flat Bottom Defects in an Isotropic Thin Plate

This paper aims to use the Lamb wave local wavenumber approach to characterize flat bottom defects (including circular flat bottom holes and a rectangular groove) in an isotropic thin plate. An air-coupled transducer (ACT) with a special incidence angle is used to actuate the fundamental anti-symmetric mode (A0). A laser Doppler vibrometer (LDV) is employed to measure the out-of-plane velocity over a target area. These signals are processed by the wavenumber domain filtering technique in order to remove any modes other than the A0 mode. The filtered signals are transformed back into the time-space domain. The space-frequency-wavenumber spectrum is then obtained by using three-dimensional fast Fourier transform (3D FFT) and a short space transform, which can retain the spatial information and reduce the magnitude of side lobes in the wavenumber domain. The average wavenumber is calculated, as a real signal usually contains a certain bandwidth instead of the singular frequency component. Both simulation results and experimental results demonstrate that the average wavenumber can be used not only to identify shape, location, and size of the damage, but also quantify the depth of the damage. In addition, the direction of an inclined rectangular groove is obtained by calculating the image moments under grayscale. This hybrid and non-contact system based on the local wavenumber approach can be provided with a high resolution.

ESTIMATION OF SOURCE PARAMETERS IN IBADAN, SOUTH – WESTERN NIGERIA USING DIGITIZED AEROMAGNETIC DATA

Airborne magnetic data covering geographical latitudes of 7000‟N to 7030‟N and longitudes of 3 30′E to 4 00′E within Ibadan area were obtained from Nigeria Geology Survey Agency. The data were ana-lyzed to map the sub surface structure and the source parameters were deduced from the quantitative and qualitative interpretation of magnetic data. The upward continuation technique was used to de-emphasize short – wavelength anomaly while the depth to magnetic sources in the area was deter-mined using local wavenumber technique, the analytic signal was also employed to obtain the depths of the magnetic basement. Analysis involving the local wavenumber, upward continuation and appar-ent magnetic susceptibility techniques significantly improves the interpretation of magnetic data in terms of delineating the geological structure, source parameter and magnetic susceptibility within Iba-dan area.. These depth ranges from 0.607km to 2.48km. The apparent susceptibility map at the cut-off wavelength of 50 m ranges from -0.00012 to 0.00079 which agree with the susceptibility value of some rock types; granite gneiss, migmatite biotite gneiss, biotite muscovite granite, hornblende granite, quartz and schists. The result of the local wavenumber suggests variation along the profiles in the surface of magnetic basement across the study area.

Fast local wavenumber (FLW) method for the inversion of magnetic source parameters

The current local wavenumber methods for the interpretation of magnetic anomalies compute the locations of geological bodies by solving complex matrices. Presently, such methods require to know the structural index, which is a parameter that represents the source type. The structural index is hard to know in real data; consequently, the precision of current methods is low. We present the fast local wavenumber (FLW) method, and define the squared sum of the horizontal and vertical local wavenumbers as the cumulative local wavenumber. The FLW method is the linear combination of the umulative local wavenumberand other wavenumbers, and is used to compute the locations and structural index of the source without a priori information and matrix solution. We apply the FLW method to synthetic magnetic anomalies, and the results suggest that the FLW method is insensitive to background and oblique magnetization. Next, we apply the FLW method to real magnetic data to obtain the location and structural index of the source.

A novel method for the extraction of local gravity wave parameters from gridded three-dimensional data: description, validation, and application

Abstract. For the local diagnosis of wave properties, we develop, validate, and apply a novel method which is based on the Hilbert transform. It is called Unified Wave Diagnostics (UWaDi). It provides the wave amplitude and three-dimensional wave number at any grid point for gridded three-dimensional data. UWaDi is validated for a synthetic test case comprising two different wave packets. In comparison with other methods, the performance of UWaDi is very good with respect to wave properties and their location. For a first practical application of UWaDi, a minor sudden stratospheric warming on 30 January 2016 is chosen. Specifying the diagnostics for hydrostatic inertia–gravity waves in analyses from the European Centre for Medium-Range Weather Forecasts, we detect the local occurrence of gravity waves throughout the middle atmosphere. The local wave characteristics are discussed in terms of vertical propagation using the diagnosed local amplitudes and wave numbers. We also note some hints on local inertia–gravity wave generation by the stratospheric jet from the detection of shallow slow waves in the vicinity of its exit region.

Manyetize Olmuş Jeolojik Yapıların Model Parametrelerinin Belirlenebilmesi için Gelişmiş Lokal Dalga Sayısı Tekniğinin Toplam Alan Manyetik Anomalilere Uygulanması

In this study, enhanced local wave number (ELWN) technique is presented to compute some model parameters of isolated and magnetized geological structures such as horizontal position (exact origin), depth and source geometry using the total field magnetic anomalies (TMAs). The technique uses analytical signal amplitude (ASA) and first- and second-degree horizontal and vertical derivatives of observed TMAs, and then simply computes the model parameters without requiring a priori knowledge about the nature of the causative magnetized body. Additionally, inclination and declination angles of both magnetization and ambient field have no effects on the results. In the ELWN technique source geometry, viz., structural index (contact/fault, dyke, horizontal cylinder and sphere) is determined using the depth and exact origin computed previously. Hypothetic simulations performed using TMAs due to some simple shaped geological models have showed the ability of the technique. Moreover, an actual magnetic data taken over the Kesikköprü iron deposit (Central Turkey), one of the largest iron reserve in Turkey,has been also analysed. A depth of 21.39 m has been computed for the magnetized geological source which includes the mafic rocks rich in magnetic properties, and the iron ore body. The structural indices obtained have indicated a dike-like or an intermediate form between a dike and a horizontal cylinder body for the magnetized source. These findings are compatible with those of a recently published study. Hence, the use of ELWN technique is proposed for rapid and reliable model parameter estimations from TMAs as an alternative or supportive experiment to the inverse modelling studies.