Plane Wave Assumption Research Articles

Non-Stationary Propagation Model for Scattering Volumes With an Application to the Rural LMS Channel

The design of efficient positioning algorithms in navigation satellite systems, like GNSS, operating in land mobile environments demands for detailed models of the radio channel. On the one hand, the models need to accurately describe scattering and shadowing/obstruction caused by vegetation. On the other hand, they have to incorporate the steady change in the propagation constellation due to the receiver displacement. In this paper we propose a model of the non-stationary radio channel in a scenario where a mobile receiver drives past a scattering volume, such as a ball or a cuboid, while the transmitter is elevated, like in satellite positioning applications. Such a volume may represent the canopy of a single tree, the canopies of trees in a grove, or a small forest. Scattering by the volume is characterized by means of multiple point-source scatterers that are assumed to form a marked spatial point process. The system functions of the radio channel are given. An integral form of the time-frequency correlation function of the component in the system functions contributed by the scattering volume is obtained as a direct consequence of Campbell's Theorem. Furthermore, a closed-form approximation of this integral form is derived for time lags corresponding to displacements along the receiver trajectory for which the plane wave assumption holds. The approximation takes into account the steady change in the propagation constellation. The proposed model is validated by means of Monte Carlo simulations and by comparing its prediction capabilities with experimental data in a scenario where a mobile receiver drives past a roadside tree. A good agreement is observed, despite the simplicity of the model.

Validation of experimental whole‐body SAR assessment method in a complex indoor environment

Experimentally assessing the whole-body specific absorption rate (SAR(wb) ) in a complex indoor environment is very challenging. An experimental method based on room electromagnetics theory (accounting only the line-of-sight as specular path) is validated using numerical simulations with the finite-difference time-domain method. Furthermore, the method accounts for diffuse multipath components (DMC) in the total absorption rate by considering the reverberation time of the investigated room, which describes all the losses in a complex indoor environment. The advantage of the proposed method is that it allows discarding the computational burden because it does not use any discretizations. Results show good agreement between measurement and computation at 2.8 GHz, as long as the plane wave assumption is valid, that is, at large distances from the transmitter. Relative deviations of 0.71% and 4% have been obtained for far-field scenarios, and 77.5% for the near field-scenario. The contribution of the DMC in the total absorption rate is also quantified here, which has never been investigated before. It is found that the DMC may represent an important part of the total absorption rate; its contribution may reach up to 90% for certain scenarios in an indoor environment.

A numerical study of a method for measuring the effective in situ sound absorption coefficient

The accuracy of a method [Wijnant et al., Proc. of ISMA 31, Leuven, Belgium (2010), Vol. 31] for measurement of the effective area-averaged in situ sound absorption coefficient is investigated. Based on a local plane wave assumption, this method can be applied to sound fields for which a model is not available. Investigations were carried out by means of finite element simulations for a typical case. The results show that the method is a promising method for determining the effective area-averaged in situ sound absorption coefficient in complex sound fields.

Geomagnetically induced currents in a power grid of northeastern Spain

Using the geomagnetic records of Ebro geomagnetic observatory and taking the plane wave assumption for the external current source and a homogeneous Earth conductivity, a prediction of the effects of the geomagnetic activity on the Catalonian (northeastern Spain) power transmission system has been developed. Although the area is located at midlatitudes, determination of the geoelectric field on the occasion of the largest geomagnetic storms during the last solar cycles indicates amplitudes that are higher than those recorded in southern Africa, where some transformer failures on large transmission systems have been reported. A DC network model of the grid has been constructed, and the geomagnetically induced current (GIC) flows in the power network have been calculated for such extreme events using the electric field at Ebro as a regional proxy. In addition, GICs have been measured at one transformer neutral earthing of the power grid, so that there the accuracy of the model has been assessed. Although the agreement is quite satisfactory, results indicate that better knowledge of the ground conductivity structure is needed. This represents the first attempt to study and measure GICs in southern European power grids, a region considered to have low GIC‐risk up to the present.

Analysis of influence of line array beamforming on the target modulation feature

In the line array sonar, the target signal was obtained after beamforming processing. The beamforming processing could improve the Signal to Noise Ratio (SNR) by using array signal's spatial processing gain. But the distortion would be brought in signal characteristics under non-ideal conditions during line array beamforming in practical application, which increased the difficulty of target characteristics extraction. As an important basis for target classification and recognition, the performance of modulation characteristics detection and extraction is affected by SNR, signal bandwidth, modulation depth and other factors. In this paper, the influence of the time delay error on target characteristics was analyzed based on the conventional beamforming of linear array. And then a method with the combination of theroy and simulation is proposed to analyze the influence of plane wave assumption, azimuth estimation error and disturbance of array shape on modulation characteristics.

Stochastic analysis of tsunami runup due to heterogeneous coseismic slip and dispersion

Most tsunami models apply dislocation models that assume uniform slip over the entire fault plane, followed by standard analytical models based on Volterra's theory of elastic dislocations for the seabed deformation. In contrast, we quantify tsunami runup variability for an earthquake with fixed magnitude but with heterogeneous rupture distribution assuming plane wave propagation (i.e., an infinitely long rupture). A simple stochastic analysis of 500 slip realizations illustrates the expected variability in coseismic slip along a fault plane and the subsequent runup that occurs along a coastline in the near field. Because of the need for systematically analyzing different fault geometries, grid resolutions, and hydrodynamic models, several hundred thousand model runs are required. Thus, simple but efficient linear models for the tsunami generation, propagation, and runup estimation are used. The mean value and variability of the maximum runup is identified for a given coastal slope configuration and is analyzed for different dip angles. On the basis of the ensemble runs, nonhydrostatic effects are discussed with respect to their impact on generation, nearshore propagation, and runup. We conclude that for the geometry and magnitude investigated, nonhydrostatic effects reduce the variability of the runup; that is, hydrostatic models will produce an artificially high variability.

Dispersion analysis of the spectral element method using a triangular mesh

The spectral element method (SEM) is a powerful tool to study wave propagation. Its main advantages are its accuracy and efficiency. Much work has been done to study the accuracy of SEM in quadrilateral elements, but the accuracy of this method using triangular elements is not well understood. In practice triangular elements are preferable to handle irregular geometries, but this introduces additional difficulties when obtaining the interpolation polynomial and quadrature points. In this paper, we show how to circumvent the difficulties using SEM with triangular elements (TSEM), and analyze two different types of nodes (Fekete points and Cohen points). The Fekete points are determined by minimizing the interpolation errors inside the element, while Cohen nodes are obtained by optimizing the accuracy of the quadrature rule. Both nodes have been employed for simulation, but their accuracy has not been studied. Our goal is to analyze the grid dispersion of these two types of nodes by considering the ‘X’ type triangular mesh. The analyses are based on the plane wave assumption by solving an eigenvalue problem. Our results indicate that, considering the same polynomial order, employing Cohen nodes requires more nodes per element but yields more accurate results compared to the Fekete points. Furthermore, the analysis suggests that higher order polynomials will improve the accuracy for both Fekete and Cohen nodes, which is the case for quadrilateral elements.

Horizontal rotation signals detected by “G-Pisa” ring laser for the M w = 9.0, March 2011, Japan earthquake

We report the observation of the ground rotation induced by the Mw=9.0, 11th of March 2011, Japan earthquake. The rotation measurements have been conducted with a ring laser gyroscope operating in a vertical plane, thus detecting rotations around the horizontal axis. Comparison of ground rotations with vertical accelerations from a co-located force-balance accelerometer shows excellent ring laser coupling at periods longer than 100s. Under the plane wave assumption, we derive a theoretical relationship between horizontal rotation and vertical acceleration for Rayleigh waves. Due to the oblique mounting of the gyroscope with respect to the wave direction-of-arrival, apparent velocities derived from the acceleration / rotation rate ratio are expected to be always larger than, or equal to the true wave propagation velocity. This hypothesis is confirmed through comparison with fundamental-mode, Rayleigh wave phase velocities predicted for a standard Earth model.

Three-Dimensional Near-Field Microwave Holography for Tissue Imaging

This paper reports the progress toward a fast and reliable microwave imaging setup for tissue imaging exploiting near-field holographic reconstruction. The setup consists of two wideband TEM horn antennas aligned along each other's boresight and performing a rectangular aperture raster scan. The tissue sensing is performed without coupling liquids. At each scanning position, wideband data is acquired. Then, novel holographic imaging algorithms are implemented to provide three-dimensional images of the inspected domain. In these new algorithms, the required incident field and Green's function are obtained from numerical simulations. They replace the plane (or spherical) wave assumption in the previous holographic methods and enable accurate near-field imaging results. Here, we prove that both the incident field and Green's function can be obtained from a single numerical simulation. This eliminates the need for optimization-based deblurring which was previously employed to remove the effect of realistic non-point-wise antennas.

A Study of the hydrodynamic behavior of cylindrical structure with double porous outer shelters

Porous structure can effectively reduce the loads caused by the water wave, which results in lowering the cost of engineering project. The double porous shelter performs even better. Therefore, it receives much attention from researches. However, most of the previous studies dealing with the analysis of the interaction between water wave are porous structure were based on two-dimensional plane wave assumption. This can hardly reflect the real phenomena of complex wave action. In this paper, a semi-analytical solution to the hydrodynamic interaction between the three-dimensional short-crested wave and the cylindrical structure with double porous shelters is performed by employing the scaled boundary finite element method (SBFEM). The SBFEM possesses the advantages of finite element method (FEM) and boundary element method (BEM): the spatial dimension of the problem is reduced by one, no fundamental solution is needed and no singularity occurs. Meanwhile, this method can meet the infinity of the boundary condition automatically. In the SBFEM, the total computational domain is divided into three sub-domains, two ring-shaped finite sub-domains and one outer infinite sub-domain. A variational principle approach is proposed to establish the SBFE governing equations, which describe the variation of the velocity potential of wave motion in the radial direction. Bessel functions and Hankel functions are chosen as the basis functions for the solution of bounded and unbounded sub-domain problems, respectively. Numerical examples show that the proposed approach achieves very high accuracy and converges rapidly with quite few discretized nodes at the outer boundary. In comparison with the cylindrical structure with single porous shelter, the former performs better for the reduction of the water wave force. In addition, The influences of the wave parameters and the configuration of the structure on the system hydrodynamics, including the wave force, wave and diffracted wave contour are extensively examined. This research provides a valuable insight into the hydrodynamic analysis of cylindrical structure with double porous shelters and their structural design.

선박의 장비 공기소음이 수중소음에 미치는 영향

In research vessels or naval ships, airborne noise from machineries such as diesel engine is the major source of underwater noise at low speed. In this paper, effect of engine noise on underwater noise is studied by considering two paths; sound radiation from hull plate and direct airborne noise transmission through hull plate. SEA (Statistical energy analysis) is used to predict hull plate vibration induced by engine noise, where SEA model consists of only two subsystems; engine room air space and hull plate. The pressure level in water is calculated from sound radiation by plate. Engine noise transmission through hull plate is obtained by assuming plane wave propagation in air-limp plate-water system. Two effects are combined and compared to the measurement, where speaker is used as a source in engine room and sound pressure levels in engine room and water are measured. The hydrophone is located 1 m away from the hull plate. It is found below 1000 Hz, prediction overestimates underwater sound pressure level by 5 to 12 dB.

One-Dimensional Inverse Scattering Problem in Acoustics

We are concerned with the inverse scatter- ing problem (ISP) in acoustics within the Marchenko inversion scheme. The quantum ISP is first discussed and applied in order to exhibit certain characteris- tics and application prospects of the method which could be useful in extending it to classical systems. We then consider the ISP in acoustics by assuming plane waves propagating in an elastic, isotropic, and linear medium. The wave equation is first transformed into a Schrodinger-like equation which can be brought into the Marchenko integral equation for the associated nonlocal kernel the solution of which provides us the full information of the underlying reflective profile. We apply the method in several model problems where the reflection coefficient of the multi-layer reflective medium is used as input to the ISP and in all cases we obtain excellent reproduction of the original structure of the scatterer. We then applied the inverse scatter- ing scheme to construct profiles with certain predeter- mined reflection and transmission characteristics.

Analysis of hearing aid acoustical feedback by means of fast multipole method-boundary element method and the transfer matrix method.

A numerical procedure is investigated for the analysis of hearing aid feedback. The receiver, connecting tubes, ear channel, and vent are considered by means of the standard transfer matrix method. The receiver transfer matrix is obtained experimentally through the two load method, while the transfer matrices representing the other components are obtained by assuming plane waves and taking in account viscous-thermal effects. The radiation impedance of the vent and the transfer function between the vent outlet and the microphone are calculated using the boundary element method and the fast multipole method (FMM-BEM). The use of FMM-BEM solver allows the solution of considerably larger models than standard BEM solvers, which means that finer details of the pinna, vent outlet, and hearing aid microphone may be included in the analysis. Numerical results are compared with experimental data obtained using a hearing aid mounted on the pinna of a manikin, and good agreement is observed.

Scattering by coupled resonating elements in air

Scattering by (a) a single composite scatterer consisting of a concentric arrangement of an outer N-slit rigid cylinder and an inner cylinder which is either rigid or in the form of a thin elastic shell and (b) by a finite periodic array of these scatterers in air has been investigated analytically and through laboratory experiments. The composite scatterer forms a system of coupled resonators and gives rise to multiple low-frequency resonances. The corresponding analytical model employs polar angle dependent boundary conditions on the surface of the N-slit cylinder. The solution inside the slits assumes plane waves. It is shown also that in the low-frequency range the N-slit rigid cylinder can be replaced by an equivalent fluid layer. Further approximations suggest a simple square root dependence of the resonant frequencies on the number of slits and this is confirmed by data. The observed resonant phenomena are associated with Helmholtz-like behaviour of the resonator for which the radius and width of the openings are much smaller than the wavelength. The problem of scattering by a finite periodic array of such coupled resonators in air is solved using multiple scattering techniques. The resulting model predicts band-gap effects resulting from the resonances of the individual composite scatterers below the first Bragg frequency. Predictions and data confirm that use of coupled resonators results in substantial insertion loss peaks related to the resonances within the concentric configuration. In addition, for both scattering problems experimental data, predictions of the analytical approach and predictions of the equivalent fluid layer approximations are compared in the low-frequency interval.

Bistatic Polar Format Algorithm Based on NUFFT Method

Matched filtering of phase history data is the optimum reconstruction algorithm to bistatic synthetic aperture radar (SAR) image formation. However, it comes at great computational expense scaled with complexity O (M 2 N 2), where M N is the number of pixels in the image. Based on the plane wave assumption, bistatic polar format algorithm (PFA) approximates the matched filtering kernel appropriately, so that the computational complexity in image formation is considerably reduced. In this paper, we propose a novel PFA for bistatic SAR processing. This imaging algorithm is to use non-uniform fast Fourier transform (NUFFT) to compute the matched filtering reconstruction image according the plane wave signal model of bistatic SAR, which scales with complexity O (M Nlog2 M N). Numerical simulations are performed to validate the proposed algorithm. The results prove that, compared with the direct computing of matched filtering, the presented algorithm can provide almost identical imaging performance in a relatively very short computation time.

Investigation of groundwater resources using controlled-source radio magnetotellurics (CSRMT) in glacial deposits in Heby, Sweden

We have combined tensor radio magnetotelluric- (RMT, 15–250 kHz) and controlled source tensor magnetotelluric (CSTMT, 1–12 kHz) data for the mapping of aquifers in gravel formations lying in between crystalline bedrock and clay rich sediments in the Heby area some 40 km west of Uppsala in Sweden. The estimated transfer functions, the impedance tensor and the tipper vector generally satisfy 1D or 2D necessary conditions except for the lowest CSTMT frequencies where near field effects become more dominant. The data measured from 8 profiles were inverted with the Rebocc code of Siripunvaraporn and Egbert (2000) assuming plane wave conditions. This meant that only 12 frequencies in the range of 4–180 kHz could be used. The four lowest frequencies of CSTMT in the range of 1–2.8 kHz were excluded because of source effects. Data from all profiles were inverted with a starting model of 100 Ω-m and a relative error floor of 0.02 on apparent resistivity, corresponding to less than 1° on phase. Tipper vectors are generally small except when source effects become dominant in the lowest frequencies of CSTMT and were therefore not used for inversion. Comparing with models derived from vertical electrical soundings, refraction and reflection seismic data as well as ground truth from exploration wells assessed the reliability of the deep part of the models. Furthermore we carried out a non-linear resolution analysis to better quantify the depth extent of the aquifers. The inverted models from the Heby area show well the thickness variations of glacial deposits overlying crystalline bedrock. Generally, the upper 20 m of the models have resistivities below 40 Ω-m, taken to represent clay rich formations. Below the clay layer resistivities increase to about 40–400 Ω-m, interpreted to represent sand/gravel formations with a maximum thickness of about 40 m and a width of several hundred metres. This is a potential aquifer that extends in approximately N–S direction for some kilometres.

Banded acoustic characteristic and optimization of serially connected horns.

When two different diverging and converging horns are serially connected, it is known that the radiation efficiency is increased in a certain frequency range. Because the radiation efficiency of a sound source system can be improved by increasing the horn input impedance, it is used as the performance index of a horn. The input impedance of a horn system can be calculated by using the transfer matrix under the linear plane wave assumption, considering the flare constant, throat area, and length of the horn to know the acoustic characteristics. Exhaustive calculations varying the design parameters revealed that the serially connected horns can be used as an acoustic device improving the radiation efficiency at a desired frequency range. Optimization of the design variables of the two serially connected exponential horns was conducted to increase the efficiency of the horn‐driver assembly, which is the ratio between the radiated sound power and the input electric power. The optimized result showed that the suggested configuration of the two connected horns is better in efficiency at the target frequency band compared to a single exponential horn by sacrificing the low‐frequency range due to the increased cutoff frequency of the horn. [Work supported by BK21.]

Energy flow model considering near field energy for predictions of acoustic energy in low damping medium

The Acoustic Energy Flow Boundary Element Method (AEFBEM) is developed to predict the acoustic energy density and intensity of an engineering system. Up to now, the acoustic energy flow model has been used only for analysis of high frequencies or radiation noise because of plane wave and far-field assumptions. In this research, a new energy flow governing equation that can consider the near field acoustic energy term and spherical wave characteristics is derived successfully to predict the acoustic energy density and intensity of a system in the medium-to-high frequency range. A near field term of acoustic energy in spherical coordinate is added to the relationship between energy density and energy flow. But with the far-field assumption, this term vanishes, so the relationship between energy density and energy flow becomes the same as that of the plane wave. By considering the near field energy term without far-field assumption, the energy density at medium frequencies can be estimated. However, the governing equation has to be numerically manipulated for use in the analysis of complex structures; therefore, the Boundary Element Method (BEM) is implemented. AEFBEM is a numerical analysis method formulated by applying the boundary element method to an acoustic energy flow governing equation. It is very powerful in predicting the acoustic energy density and intensity of complex structures in medium-to-high frequency ranges, and can analyze interior noise and radiating sound. To verify its validity, several numerical results are provided. BEM and AEFBEM were compared with respect to energy density, and the results from both methods were similar.

The electrical conductivity distribution of the Hallandsås Horst, Sweden: a controlled source radiomagnetotelluric study

ABSTRACTWe studied the behaviour of controlled source responses of 2½D synthetic models based on controlled source tensor magnetotelluric ( = 1–12 kHz) and radio magnetotelluric ( = 14–250 kHz) data sets collected along profiles on the Hallandsås Horst, Southern Sweden, with a view to study the depth extent of possible near‐surface fractures zones that might intersect a tunnel under construction. Based upon 2.5D forward modelling of the transverse electric (TE) and transverse magnetic (TM) mode radio magnetotelluric data, a simplified 2D model was constructed such that a dipping conductor was continued down to a depth of 140 m, which is the depth of the tunnel. Based on this extended model, we calculated both plane wave and controlled source responses for the frequency range 1–250 kHz corresponding to the source location in the study. Finally, we inverted both data sets under plane wave assumptions. When comparing synthetic controlled source and plane wave data in the frequency range 1–12 kHz, we find that the controlled source tensor magnetotelluric transfer functions generally deviate from the plane wave condition for frequencies less than 6 kHz. The phases are much more distorted than apparent resistivities. The TM mode phases, in particular, are generally distorted for frequencies less than 6 kHz. Regarding the vertical magnetic fields, we find that at all frequencies the real part of tippers are distorted by source effects but the tipper component along the profile direction is much less affected by the off‐profile lying controlled source tensor magnetotelluric source than the tipper component orthogonal to the profile direction. Based upon synthetic model studies of combined controlled source tensor magnetotelluric and radio magnetotelluric responses, we find that determinant data are less distorted than individual TE‐w and TM‐mode data. On the other hand, TE‐ and TM‐responses have greater resolving power and, when used with care (selecting data that are weakly distorted by source effects), the corresponding models can resolve the conductor down to tunnel depths.

Time-Domain Modelling: Combining ESM and a Finite-Difference Method for Thermoacoustic Devices

Thermoacoustic devices are today mainly simulated using frequency-domain methods. Contrary to frequency-domain methods, time-domain methods may include non-linear effects and time-varying boundary conditions. However, time-domain modelling of thermoacoustic devices is computationally expensive, due to large differences in geometric length scales and time scales. The primary aim of this paper has been to model thermoacoustic devices with computational efficiency by using two different methods. The acoustic field outside the stack, based on the assumption of plane waves, is modelled using the efficient Equivalent Source Method (ESM), whereas the complex acoustic field in the stack is modelled using a finite-difference model. In a previous paper of the authors, ESM and a finite-difference model have been combined to model acoustic wave propagation, though thermal effects and heat flow to the stack plate were excluded. In this paper, however, these effects are included. The performance of the model is studied and compared to linear thermoacoustic theory. The proposed model may provide a useful tool for studying time-varying acoustic fields and temperature distributions in thermoacoustic devices.