Local Wavenumber Research Articles

Evaluation of Aeromagnetic Data of Ilesha Area of Oyo State Nigeria using Analytical Signal (ASM) and Local wavenumber (LWN)

This paper presents the analysis and interpretation of an aeromagnetic data of Ilesha area, (Sheet 243) sourced from Nigeria Geological Survey Agency. The area is located between 7.5oN and 8.0oN of latitude and longitude 4.5oE to 5.0oE. Two methods: Analytic Signal Method (ASM) and Local wavenumber (LWN) were used. These methods were used to process and analyse the data so as to generate the depth to magnetic sources as well as the source locations. The results obtained showed a shallower depth range limit for ASM between 0.348 km and 1.28 km, which is less than the result of LWN within the range of 0.478 km-1.51 km. The results also revealed more source locations in ASM result in comparison with LWN. The overall results of the methods have revealed the prospect of the lithology of the area for magnetic mineral exploration in the field of applied geophysics.Keywords: Aeromagnetic survey, Analytic signal, Magnetic Anomaly, Local wave number, lithology

On the sensitivity of teleseismic full-waveform inversion to earth parametrization, initial model and acquisition design

Full-waveform inversion (FWI) is not yet a mature imaging technology for lithospheric imaging from teleseismic data. Therefore, its promise and pitfalls need to be assessed more accurately according to the specifications of teleseismic experiments. Three important issues are related to (1) the choice of the lithospheric parametrization for optimization and visualization, (2) the initial model and (3) the acquisition design, in particular in terms of receiver spread and sampling. These three issues are investigated with a realistic synthetic example inspired by the CIFALPS experiment in the Western Alps. Isotropic elastic FWI is implemented with an adjoint-state formalism and aims to update three parameter classes by minimization of a classical least-squares difference-based misfit function. Three different subsurface parametrizations, combining density (ρ) with P and S wave speeds (Vp and Vs) , P and S impedances (Ip and Is), or elastic moduli (λ and μ) are first discussed based on their radiation patterns before their assessment by FWI. We conclude that the (ρ, λ, μ) parametrization provides the FWI models that best correlate with the true ones after recombining a posteriori the (ρ, λ, μ) optimization parameters into Ip and Is. Owing to the low frequency content of teleseismic data, 1-D reference global models as PREM provide sufficiently accurate initial models for FWI after smoothing that is necessary to remove the imprint of the layering. Two kinds of station deployments are assessed: coarse areal geometry versus dense linear one. We unambiguously conclude that a coarse areal geometry should be favoured as it dramatically increases the penetration in depth of the imaging as well as the horizontal resolution. This results because the areal geometry significantly increases local wavenumber coverage, through a broader sampling of the scattering and dip angles, compared to a linear deployment.

Observation of geodesic acoustic mode in SINP-tokamak and its behaviour with varying edge safety factor

The spectral analysis of floating potential fluctuations measured in the edge plasma region (0.87 < r/a < 1.0) of Saha Institute for Nuclear Physics tokamak (SINP-tokamak) using Langmuir probes reveals the existence of a highly coherent mode with a frequency in the range of 15–21 kHz. Long range correlations in poloidal and toroidal directions are observed over a wide range of plasma discharges having different values of the edge safety factor, from very low qedge (<2) to high qedge (>3). These coherent modes are simultaneously observed in density and radial electric field fluctuation spectra as well. These coherent modes are identified as geodesic acoustic modes (GAMs) having different characteristics over the entire qedge range. In discharges with qedge greater than 3, the local wave number spectra of the mode exhibit the properties of continuum GAM with the observed poloidal and toroidal mode numbers of m ∼ 0 and n ∼ 0, and the mode is radially localized. The observed frequency and its variation with the safety factor for qedge > 3 closely agree with the theoretical predictions using the measured values of temperature. In contrast, for qedge < 3.0, the GAM nature changes from continuum to the Eigenmode as the associated GAM frequency remained uniform at ∼13–17 kHz over the q edge range of 1.5 to 3 and ceased to depend on local temperature. Furthermore, the poloidal wave number of the coherent mode no longer remains zero and is observed to increase when qedge falls below 2.5. Coherent modes in magnetic fluctuations having similar frequencies to those of electrostatic fluctuations are also observed in the discharges with the q edge below 2.5. The coupling of these electrostatic and magnetic modes may be responsible for triggering the Eigenmode GAM.

Nonlocal adiabatic theory. II. Nonlinear frequency shift on an electron plasma wave in a multidimensional inhomogeneous plasma

In this article, we provide a general derivation of the nonlinear frequency shift, δω, for a sinusoidal electron plasma wave (EPW) that varies slowly enough for the results derived in Paper I, on the action distribution function, to apply. We first consider the situation when the EPW monotonously grows and then monotonously decays in a homogeneous plasma. In this situation, we show a hysteresis in the wave frequency, which does not converge back to its linear value as the wave decays to small amplitudes. We then address the derivation of δω for an EPW that keeps growing in a one-dimensional (1-D) inhomogeneous plasma. We show that, usually, the frequency shift does not depend only on the local EPW amplitude and wavenumber but also on the whole history of the density variations, as experienced by the wave. In a multidimensional inhomogeneous plasma, the values assumed by δω are usually different from those derived in 1-D because, due to the transverse electron motion, one must account for the hysteresis in δω in addition to plasma inhomogeneity. Hence, unless the EPW keeps growing in a homogeneous one-dimensional plasma, one cannot derive δω a priori as a function of the local wave amplitude and wavenumber. Due to the nonlocality in the action distribution function, δω depends on the whole history of the variations of the EPW amplitude and plasma density.

Basement structure of the United Arab Emirates derived from an analysis of regional gravity and aeromagnetic database

Gravity and aeromagnetic data covering the whole territory of the United Arab Emirates (UAE) have been used to evaluate both shallow and deep geological structures, in particular the depth to basement since it is not imaged by seismic data anywhere within the UAE. Thus, the aim has been to map the basement so that its structure can help to assess its control on the distribution of hydrocarbons within the UAE. Power spectrum analysis reveals gravity and magnetic signatures to have some similarities, in having two main density/susceptibility interfaces widely separated in depth such that regional-residual anomaly separation could effectively be undertaken. The upper density/susceptibility interface occurs at a depth of about 1.0km while the deeper interface varies in depth throughout the UAE. For gravity, this deeper interface is assumed to be due to the combined effect of lateral changes in density structures within the sediments and in depth of basement while for magnetics it is assumed the sediments have negligible susceptibility and the anomalies unrelated to the volcanic/magmatic bodies result from only changes in depth to basement. The power spectrum analysis over the suspect volcanic/magmatic bodies indicates they occur at ~5km depth. The finite tilt-depth and finite local wavenumber methods were used to estimate depth to source and only depths that agree to within 10% of each other were used to generate the depth to basement map. This depth to basement map, to the west of the UAE-Oman Mountains, varies in depth from 5km to in excess of 15km depth and is able to structurally account for the location of the shear structures, seen in the residual magnetic data, and the location of the volcanic/magmatic centres relative to a set of elongate N-S to NE-SW trending basement highs. The majority of oilfields in the UAE are located within these basement highs. Therefore, the hydrocarbon distribution in the UAE basin appears to be controlled by the location of the basement ridges.

Damage detection on composite structures with standing wave excitation and wavenumber analysis

This paper describes the use of wavenumber filtering for damage detection with a signal-frequency standing wave excitation on composite structures. Using a single, fixed frequency excitation from a mounted piezoelectric transducer, the full steady-state wavefield could be obtained using a Laser Doppler Vibrometer with a mirror-tilting device. After completing the scanning, a wavenumber filtering is applied to determine dominant wavenumber components of the measured wavefield, which could be used for indicative of structural damage. Mapping processes based on local wavenumber filtering is then carried out for damaged area visualization. Also introduced are the comparison of two methods for damage identification and visualization: the local wavenumber mapping and acoustic wavenumber spectroscopy. To demonstrate the proposed techniques, several experiments are performed on composite structures with different types of damage, including debonding and delamination on composite plates. The results demonstrate that the techniques are very effective in localizing damage with the potential for the quick inspection of a variety of composite structural components.

Outward particle transport by coherent mode in the H-mode pedestal in the Experimental Advanced Superconducting Tokamak (EAST)

A coherent mode (CM) in the edge pedestal region has been observed on different fluctuation quantities, including density fluctuation, electron temperature fluctuation and magnetic fluctuation in H mode plasma on the Experimental Advanced Superconducting Tokamak (EAST) tokamak. Measurements at different poloidal positions show that the local poloidal wavenumber is smallest at the outboard midplane and will increase with poloidal angle. This poloidal asymmetry is consistent with the flute-like assumption (i.e. k// ∼ 0) from which the toroidal mode number of the mode has been estimated as between 12 and 17. It was further found that the density fluctuation amplitude of the CM also demonstrated poloidal asymmetry. The appearance of a CM can clearly decrease or even stop the increase in the edge density, while the disappearance of a CM will lead to an increase in the pedestal density and density gradient. Statistical analysis showed there was a trend that as the CM mode amplitude increased, the rate of increase of the edge density decreased and the particle flux (Γdiv) onto the divertor plate increased. The CM sometimes showed burst behavior, and these bursts led bursts on Γdiv with a time of about 230 μs, which is close to the time for particle flow from the outer midplane to the divertor targets along the scrape-off layer magnetic field line. This evidence showed that the CM had an effect on the outward transport of particles.

The one-dimensional acoustic field in a duct with arbitrary mean axial temperature gradient and mean flow

This paper presents an analytical solution for the one-dimensional acoustic field in a duct with arbitrary mean temperature gradient and mean flow. A wave equation for the pressure perturbation is derived which relies on very few assumptions. An analytical solution for this is derived using an adapted WKB approximation. The solution is a superposition of waves travelling in either direction and thus provides physical insight. It is also very easy to calculate. The proposed solution is applied to ducts with a mean temperature profile which varies axially with (i) a linear and (ii) a partial sine wave profile: predictions are compared to those obtained by numerically solving the linearised Euler equations (LEEs). The analytical solution reproduces the acoustic field very accurately across a wide range of flow conditions which span both low and moderate-to-high subsonic Mach numbers. It always performs well when the frequency exceeds a certain value; when the mean temperature profile is linear, it also performs well to very low frequencies. This increased frequency range for linear mean temperature profiles leads to its application to more complicated profiles in a piecewise linear manner, axially segmenting the temperature profile into regions that can be approximated as linear. The acoustic field is predicted very accurately as long as enough segmentation points are used and the condition for the linear mean temperature profile is satisfied: |k0|>|α|, where k0 is the local wave number when there is no mean flow and α is the normalised mean density gradient. The proposed solution is extensively compared to previous analytical solutions, and is found to be more accurate and reliable, especially at higher Mach numbers. The entropy wave generated by communication between the acoustic waves and the distributed mean temperature zone is calculated using the LEEs. It is found to remain very small across all operating conditions, such that both the entropy wave and its impact on the acoustic field can be neglected.

Pattern Formation in Axially Symmetric Landau–Lifshitz–Gilbert–Slonczewski Equations

The Landau-Lifshitz-Gilbert-Slonczewski equation describes magnetization dynamics in the presence of an applied field and a spin polarized current. In the case of axial symmetry and with focus on one space dimension, we investigate the emergence of space-time patterns in the form of wavetrains and coherent structures, whose local wavenumber varies in space. A major part of this study concerns existence and stability of wavetrains and of front- and domain wall-type coherent structures whose profiles asymptote to wavetrains or the constant up-/down-magnetizations. For certain polarization the Slonczewski term can be removed which allows for a more complete charaterization, including soliton-type solutions. Decisive for the solution structure is the polarization parameter as well as size of anisotropy compared with the difference of field intensity and current intensity normalized by the damping.

The relationship between free-stream coherent structures and near-wall streaks at high Reynolds numbers.

The present work is based on our recent discovery of a new class of exact coherent structures generated near the edge of quite general boundary layer flows. The structures are referred to as free-stream coherent structures and were found using a large Reynolds number asymptotic approach to describe equilibrium solutions of the Navier-Stokes equations. In this paper, first we present results for a new family of free-stream coherent structures existing at relatively large wavenumbers. The new results are consistent with our earlier theoretical result that such structures can generate larger amplitude wall streaks if and only if the local spanwise wavenumber is sufficiently small. In a Blasius boundary layer, the local wavenumber increases in the streamwise direction so the wall streaks can typically exist only over a finite interval. However, here it is shown that they can interact with wall curvature to produce exponentially growing Görtler vortices through the receptivity process by a novel nonparallel mechanism. The theoretical predictions found are confirmed by a hybrid numerical approach. In contrast with previous receptivity investigations, it is shown that the amplitude of the induced vortex is larger than the structures in the free-stream which generate it.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'.

Thickness reconstruction of nuclear power plant pipes with flow-accelerated corrosion damage using laser ultrasonic wavenumber imaging

The pipeline is an essential part of nuclear and other power plants. Designed to operate for decades, the pipeline is susceptible to multiple types of damage due to working in a high pressure, high temperature, and highly corrosive environment. Therefore, it requires regular inspection. The issue of many current nondestructive testing systems for pipelines is the use of a one-dimensional scan mechanism along the longitudinal direction of the pipe, which is incompatible with the two-dimensional curvature of elbow pipes, yet it is at these places in which the flow changes directions inside the elbow pipes that a common type of damage occurs: flow-accelerated corrosion damage. In this article, flow-accelerated corrosion damage is visualized using the Ultrasonic Wavenumber Imaging algorithm, which maps the dominant local spectroscopic wavenumber of the wavefield at a particular mode and a particular frequency. In previous studies, the mode and frequency were chosen empirically. In this article, a novel theoretical study is presented to optimize the two input parameters of Ultrasonic Wavenumber Imaging based on a sensitivity analysis of the spectroscopic wavenumber with respect to the change in thickness of the structural base. Additionally, an inverse method is proposed to estimate the thickness of the structure based on the Ultrasonic Wavenumber Imaging map.

Correlation imaging method based on local wavenumber for interpreting magnetic data

Depth estimation is a general task in the interpretation of magnetic data, and local wavenumber is an effective tool to accomplish this task, but this method requires the structural index of causative source when applies it to compute the depth of the source, which is hard to obtain for an unknown area. In this paper, we suggested a correlation imaging method to interpret magnetic data, which uses the correlation coefficient of local wavenumber of real magnetic data and transformative local wavenumber of synthetic magnetic data generated by assumed source to estimate the location of the source, and this method does not require any priori information of the source and does not require solving any matrix. The computation steps as follows, first, we assume that the causative sources are distributed regularly as a rectangular grid, and then separately compute the correlation coefficient of the local wavenumber of real data and local wavenumber of the anomaly generated by each assumed source, and the correlation coefficient gets maximum when the location parameters of the assumed source are in accord with the true locations of real sources. The synthetic tested results show that this method can obtain the location of magnetic source effectively and correctly, and is insensitive to magnetization direction and noise. This method is also applied to measured magnetic data, and get the location parameters of the source.

Suppression of superoscillations by noise

Bandlimited functions can vary faster than their highest Fourier component. Such ‘superoscillations’ result from near-perfect destructive interference among the Fourier components and correspond to large values of the phase gradient (local wavenumber). Superoscillations that are strong and extend over a large interval occur where functions are exponentially small. The associated interference is vulnerable to noise, in particular random phases. Averaging over the phases, modelled as independent Gaussian variables with a specified rms value, enables the suppression of superoscillations to be described quantitatively; very weak phase noise suffices. Strong noise generates functions that are essentially random, and the remaining well-understood superoscillations are localised in small intervals. The theory is illustrated by computations with an explicit superoscillatory function.

The amplitude and phase of the derivatives of the magnetic anomalies of thin dykes and contacts

If the horizontal and vertical derivatives of the total field magnetic anomalies of thin dykes and contacts (and the magnetic anomaly from a thin dyke) are put into an amplitude-phase form, then this can aid in their interpretation. First, it allows derivatives of fractional order to be calculated analytically; second, estimates of the source dip can be made; and finally, the relationships between local wavenumber and source-distance semi-automatic interpretation methods are clarified. The approach is demonstrated on synthetic data and aeromagnetic data from South Africa.

A novel multi-channel quadrature Doppler backward scattering reflectometer on the HL-2A tokamak.

A novel 16-channel fixed frequency Doppler backward scattering (DBS) reflectometer system has been developed on the HL-2A tokamak. This system is based on the filter-based feedback loop microwave source (FFLMS) technique, which has lower phase noise and lower power variation compared with present tunable frequency generation and comb frequency array generation techniques [J. C. Hillesheim et al. Rev. Sci. Instrum. 80, 083507 (2009) and W. A. Peebles et al. Rev. Sci. Instrum. 81, 10D902 (2010)]. The 16-channel DBS system is comprised of four × four-frequency microwave transmitters and direct quadrature demodulation receivers. The working frequencies are 17-24 GHz and 31-38 GHz with the frequency interval of 1 GHz. They are designed to measure the localized intermediate wave-number (k⊥ρ ∼ 1-2, k⊥ ∼ 2-9 cm-1) density fluctuations and the poloidal rotation velocity profile of turbulence. The details of the system design and laboratory tests are presented. Preliminary results of Doppler spectra measured by the multi-channel DBS reflectometer systems are obtained. The plasma rotation and turbulence distribution during supersonic molecular beam injection are analyzed.

Semi-Relativistic Reflection and Transmission Coefficients for Two Spinless Particles Separated by a Rectangular-Shaped Potential Barrier

A generalized Schrödinger approximation, due to Ikhdair & Sever, of the semi-relativistic two-body problem with a rectangular barrier in (1+1) dimensions is compared with exact computations. Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers. The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |ϵ − V0| < 2μc2, where μ is the reduced mass, ϵ the scattering energy, and V0 the barrier top energy. The approximate wave numbers are less accurate.

Interpretation of the magnetic data from Shavaz iron ore using enhanced local wavenumber (ELW) and comparison with Euler deconvolution method

This paper presents an inversion method for the interpretation of 2D magnetic anomaly data, in which uses the enhanced local wavenumber function to estimate the depth and the nature (structural index) of an isolated magnetic source. However, the method is sensitive to noise. In order to lower the effect of noise, I applied upward continuation technique to smooth the anomaly. Tests on synthetic noise-free and noise-corrupted magnetic data show that the method can successfully estimate the depth and the nature of the causative source. The practical application of the technique is applied to measured magnetic anomaly data from Shavaz Iron Ore, center of Iran, and the inversion results are in agreement with the inversion results from Euler deconvolution of the analytic signal and exploratory drilling.

A new dispersion-relation preserving method for integrating the classical Boussinesq equation

In this paper, a dispersion-relation preserving method is proposed for nonlinear dispersive waves, starting from the oldest weakly nonlinear dispersive wave mathematical model in shallow water waves, i.e., the classical Boussinesq equation. It is a semi-analytic procedure, however, which preserves, as a distinctive feature, the dispersion-relation imbedded in the model equation without adding (unwelcome) numerical effects, i.e., the proposed method has the same dispersion-relation as the original classical Boussinesq equation. This remarkable (dispersion-relation) preserving property is proved mathematically for small wave motion in present study. The property is also numerically examined by observing both the local wave number and the local frequency of a slowly varying water-wave group. The dispersion-relation preserving method proposed here is powerful as well for observing nonlinear wave phenomena such as solitary waves and their collision. In fact, the main features of nonlinear wave characteristics are clearly seen through not only a single propagating solitary wave but counter-propagating (head-on) solitary wave collisions. They are compared with known (exact) nonlinear solutions, the results of which represent a major improvement over existing solution formulations in the literature.

On the distribution of wave height in shallow water

The statistical distribution of the height of sea waves in deep water has been modelled using the Rayleigh (Longuet-Higgins, 1952) and Weibull distributions (Forristall, 1978). Depth-induced wave breaking leading to restriction on the ratio of wave height to water depth requires new parameterisations of these or other distributional forms for shallow water. Glukhovskiy (1966) proposed a Weibull parameterisation accommodating depth-limited breaking, modified by van Vledder (1991). Battjes and Groenendijk (2000) suggested a two-part Weibull–Weibull distribution. Here we propose a two-part Weibull-generalised Pareto model for wave height in shallow water, parameterised empirically in terms of sea state parameters (significant wave height, HS, local wave-number, kL, and water depth, d), using data from both laboratory and field measurements from 4 offshore locations. We are particularly concerned that the model can be applied usefully in a straightforward manner; given three pre-specified universal parameters, the model further requires values for sea state significant wave height and wave number, and water depth so that it can be applied. The model has continuous probability density, smooth cumulative distribution function, incorporates the Miche upper limit for wave heights (Miche, 1944) and adopts HS as the transition wave height from Weibull body to generalised Pareto tail forms. Accordingly, the model is effectively a new form for the breaking wave height distribution. The estimated model provides good predictive performance on laboratory and field data.

An Improved Method for Determining the Distance to Magnetic Sources

Previous work has determined the distance r to magnetic sources in various ways, using the ratio of different order analytic signal amplitudes. When the negative of r is plotted then the values closest to zero give the source depth and the locations of these values show the horizontal location of the source. Methods that use higher order derivatives are less susceptible to interference problems than those that use lower order derivatives, but are obviously more sensitive to noise. New methods of determining r are presented here which are based on the local wavenumber. The new method gives a function which increases with distance much more rapidly than r away from the source but becomes equal to the depth Δz of the source at the source location. Hence the new method gives much sharper responses to magnetic sources than did the original source-distance methods. In addition, a method to calculate the distance to the source without specifying the structural index is presented.