Three-dimensional Ray Tracing Research Articles

A study of infrasonic anisotropy and multipathing in the atmosphere using seismic networks

We discuss the use of reverse time migration (RTM) with dense seismic networks for the detection and location of sources of atmospheric infrasound. Seismometers measure the response of the Earth's surface to infrasound through acoustic-to-seismic coupling. RTM has recently been applied to data from the USArray network to create a catalogue of infrasonic sources in the western US. Specifically, several hundred sources were detected in 2007-2008, many of which were not observed by regional infrasonic arrays. The influence of the east-west stratospheric zonal winds is clearly seen in the seismic data with most detections made downwind of the source. We study this large-scale anisotropy of infrasonic propagation, using a winter and summer source in Idaho. The bandpass-filtered (1-5 Hz) seismic waveforms reveal in detail the two-dimensional spread of the infrasonic wavefield across the Earth's surface within approximately 800 km of the source. Using three-dimensional ray tracing, we find that the stratospheric winds above 30 km altitude in the ground-to-space (G2S) atmospheric model explain well the observed anisotropy pattern. We also analyse infrasound from well-constrained explosions in northern Utah with a denser IRIS PASSCAL seismic network. The standard G2S model correctly predicts the anisotropy of the stratospheric duct, but it incorrectly predicts the dimensions of the shadow zones in the downwind direction. We show that the inclusion of finer-scale structure owing to internal gravity waves infills the shadow zones and predicts the observed time durations of the signals. From the success of this method in predicting the observations, we propose that multipathing owing to fine scale, layer-cake structure is the primary mechanism governing propagation for frequencies above approximately 1 Hz and infer that stochastic approaches incorporating internal gravity waves are a useful improvement to the standard G2S model for infrasonic propagation modelling.

Radiation Modeling of a Hydrogen Fueled Scramjet

With the difficulty and cost of full-scale flight experiments, the design of scramjet engines relies heavily on computational simulations. Radiation may play an important role in the wall heating and flow cooling of scramjets. However, very few studies have focused on such. The present analysis is based on three-dimensional turbulent reacting flow simulations of the HyShot II hydrogen fueled scramjet engine running at flight conditions of Mach 7.4. A three-dimensional discrete ordinates method analysis with a narrowband averaged spectral model is employed to determine wall heating and flow cooling from thermal radiation. The discrete ordinates method is verified against a three-dimensional ray tracing method. The radiative species considered are and OH. The radiative heat flux is on the order of , which is 0.1–0.6% of the total convective wall heat flux. Flow cooling due to radiation is found to be on the order of 3 K. Sensitivity analysis shows that radiation is highly dependent on chamber size, temperature, pressure, and radiative species mole fraction. Variations in these factors can explain the differences between previous analyses in the literature that studied hypothetical engines and the current work that models an existing scramjet.

A New Pseudo Three-Dimensional Segment Method Analytical Ray Tracing (3-D SMART) Technique

The new pseudo three-dimensional (3-D) segment method analytical ray tracing technique (3-D SMART) is similar to the 2-D SMART technique however with the added ability to determine the effects of transverse refractive gradients on a ray path. In the past numerical ray tracing techniques using a form of Haselgrove's equations were required for realistic 3-D ray tracing. This new 3-D SMART technique is considerably less computer resource intensive than numerical ray tracing techniques and thus is of particular importance for near real-time applications and the general case where it is necessary to trace a vast number of ray paths.

Interference Aware-Coordinated Beamforming in a Multi-Cell System

In this paper, we propose jointly optimized linear transceiver algorithms called interference aware-coordinated beamforming (IA-CBF) for a two-cell system where each base station is equipped with multiple transmit antennas. To generalize IA-CBF to more than two-cell scenarios, a new beam-switching mechanism combined with IA-CBF is proposed. For a two-cell system, we derive a minimum-mean-square-error-type IA-CBF algorithm based on a lower bound on the achievable sum rate. We propose optimal (under an assumption of zero other-cell interference) and suboptimal transmit/receive beamforming vectors through zero-forcing IA-CBF algorithms. We also investigate the optimality of the proposed IA-CBF algorithms with respect to the number of receive antennas. Numerical results confirm that the proposed system with two transmit/receive antennas achieves the full degrees of freedom (a.k.a. multiplexing gain) of the two-cell multiple-input multiple-output channel while showing a better sum rate performance than competitive solutions such as non-cooperative eigen-beamforming and interference nulling. A three-dimensional ray tracing tool is also used to evaluate the proposed multi-cell IA-CBF algorithm.

Modeling of micro cat’s eye retroreflectors using a matrix-based three-dimensional ray tracing technique

In this paper we develop a three-dimensional (3D) ray tracing tool based on the ABCD ray transfer matrices. With symmetric optical components and under paraxial approximation, two sets of 2×2 ABCD matrices, each for a two-dimensional subspace, can be used to describe the 3D ray propagation completely. Compared to commercial ray-tracing software packages, our tool requires no tedious drawing, and the results for various conditions, such as different device dimensions and incident angles, can be easily obtained by simply changing the parameter values used for the calculation. We have employed this matrix-based 3D ray tracing tool to model cat's eye retroreflectors. The cat's eye performance, including the retroreflection efficiency, acceptance angle (i.e., field of view), and beam divergence and deviation, is fully studied. The application of this 3D ray tracing technique can be further extended to other optical components.

Chorus wave-normal statistics in the Earth's radiation belts from ray tracing technique

Abstract. Discrete ELF/VLF (Extremely Low Frequency/Very Low Frequency) chorus emissions are one of the most intense electromagnetic plasma waves observed in radiation belts and in the outer terrestrial magnetosphere. These waves play a crucial role in the dynamics of radiation belts, and are responsible for the loss and the acceleration of energetic electrons. The objective of our study is to reconstruct the realistic distribution of chorus wave-normals in radiation belts for all magnetic latitudes. To achieve this aim, the data from the electric and magnetic field measurements onboard Cluster satellite are used to determine the wave-vector distribution of the chorus signal around the equator region. Then the propagation of such a wave packet is modeled using three-dimensional ray tracing technique, which employs K. Rönnmark's WHAMP to solve hot plasma dispersion relation along the wave packet trajectory. The observed chorus wave distributions close to waves source are first fitted to form the initial conditions which then propagate numerically through the inner magnetosphere in the frame of the WKB approximation. Ray tracing technique allows one to reconstruct wave packet properties (electric and magnetic fields, width of the wave packet in k-space, etc.) along the propagation path. The calculations show the spatial spreading of the signal energy due to propagation in the inhomogeneous and anisotropic magnetized plasma. Comparison of wave-normal distribution obtained from ray tracing technique with Cluster observations up to 40° latitude demonstrates the reliability of our approach and applied numerical schemes.

PSO and APSO for optimizing coverage in indoor UWB communication system

This article presents a method for determining the required number and locations of transmitting antennas (TXs) to optimize wireless propagation coverage in an indoor ultra wideband (UWB) communication system. In the coverage prediction model, we use the three-dimensional ray-tracing technique associated with a particle swarm optimization (PSO), and asynchronous particle swarm optimization (APSO) for optimizing the TXs location in an indoor environment. The three-dimensional ray tracing and optimization algorithm was applied in indoor environment to find the best location of the TXs by maximizing the power in the coverage area. A deployment is proposed to minimize the TXs and maximize the power in the coverage area. Simulation results illustrate the feasibility of using the integrated ray-tracing, and optimization methods to find the optimal transmitter locations in determining the optimized coverage of a wireless network. The APSO has better optimization results compared to the PSO and numerical results also show that the APSO outperforms the PSO in convergence speed. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.

IONORT: A Windows software tool to calculate the HF ray tracing in the ionosphere

This paper describes an applicative software tool, named IONORT (IONOspheric Ray Tracing), for calculating a three-dimensional ray tracing of high frequency waves in the ionospheric medium. This tool runs under Windows operating systems and its friendly graphical user interface facilitates both the numerical data input/output and the two/three-dimensional visualization of the ray path. In order to calculate the coordinates of the ray and the three components of the wave vector along the path as dependent variables, the core of the program solves a system of six first order differential equations, the group path being the independent variable of integration. IONORT uses a three-dimensional electron density specification of the ionosphere, as well as geomagnetic field and neutral particles–electrons collision frequency models having validity in the area of interest.

Erratum to Velocity Structure of the Tibetan Lithosphere: Constraints from P-Wave Travel Times of Regional Earthquakes

Using data from regional earthquakes recorded by the Hi-CLIMB array in Tibet, we model P-wave arrival times to constrain the velocity structure in the crust and the upper mantle in central and western Tibet. Of more than 30 high-quality, regional seismic profiles that have been assembled, we have selected 10 that show excellent crustal and Pn arrivals for further analysis. Travel times from four events along the Hi-CLIMB array provide details on crustal velocities, and six events at regional distances to the array provide further constraints on Moho structure and upper-mantle-lid velocities. We use three-dimensional ray tracing to model the travel times, and the results indicate that the Moho beneath the Lhasa terrane of southern Tibet is over 73 km deep, with a Pn speed of about 8:2 km=s. The Qiangtang terrane north of the Bangong-Nujiang suture (BNS) shows a thinner crust, by up to 10 km, and a lower Pn speed of 7:8-7:9 km=s. Travel times from events to thewest and east of the array indicate that both Moho structure and mantle-lid velocities in the region are three-dimensional in nature but approximately follow the trend of the BNS. Although only a limited number of events were used for the travel-time modeling, the results are consistent with earlier results from teleseismic imaging using the Hi-CLIMB array.

Optical design in illumination system of digital light processing projector using laser and gradient-index lens

A novel structure of illumination system based on laser sources and gradient-index (GRIN) lens arrays for single-plate digital light processing (DLP) projector is proposed. Under the evaluation of light collection efficiency and illumination uniformity, we designed two different architectures of GRIN lens arrays: the unit lens cross section being either square or circular. Also, we designed the one-to-one coupling mechanism between GRIN lens array and Gaussian beam array. By means of three-dimensional modeling and ray tracing, we simulated the optical characteristics of illumination system, and the optical parameters are evaluated. Results show that the total light collection efficiency is 37.9%, the illumination uniformity is 89.7% and the volume is only 12.4 cm3. Thus we improved optical characteristics and reduced the physical dimension of DLP optical engine.

Gravitational lensing with three-dimensional ray tracing★

High redshift sources suffer from magnification or demagnification due to weak gravitational lensing by large scale structure. One consequence of this is that the distance-redshift relation, in wide use for cosmological tests, suffers lensing-induced scatter which can be quantified by the magnification probability distribution. Predicting this distribution generally requires a method for ray-tracing through cosmological N-body simulations. However, standard methods tend to apply the multiple thin-lens approximation. In an effort to quantify the accuracy of these methods, we develop an innovative code that performs ray-tracing without the use of this approximation. The efficiency and accuracy of this computationally challenging approach can be improved by careful choices of numerical parameters; therefore, the results are analysed for the behaviour of the ray-tracing code in the vicinity of Schwarzschild and Navarro-Frenk-White lenses. Preliminary comparisons are drawn with the multiple lens-plane ray-bundle method in the context of cosmological mass distributions for a source redshift of $z_{s}=0.5$.

A Three-Dimensional Ray Tracing Study on Whistler-Mode Chorus During Geomagnetic Activities

A three-dimensional ray tracing study of a whistler-mode chorus is conducted for different geomagnetic activities by using a global core plasma density model. For the upper-band chorus, the initial azimuthal wave angle affects slightly the projection of ray trajectories onto the plane , but controls the longitudinal propagation. The trajectory of the upper-band chorus is strongly associated with the plasmapause and the magnetic local time (MLT) of chorus source region. For the high geomagnetic activity, the chorus trajectory moves inward together with the plasmapause. In the bulge region, the plasmapause extends outward, while the chorus trajectory moves outward together with the plasmapause. For moderately or high geomagnetic activity, the lower-band chorus suffers low hybrid resonance (LHR) reflection before it reaches the plasmapause, leading to a weak correlation with the geomagnetic activity and magnetic local time of the chorus source region. For low geomagnetic activity, the lower-band chorus may be reflected firstly at the plasmapause instead of suffering LHR reflection, exhibiting a propagation characteristic similar to that of the upper-band chorus. The results provide a new insight into the propagation characteristics of the chorus for different geomagnetic activities and contribute to further understanding of the acceleration of energetic electron by a chorus wave.

Validation of Three-Dimensional Ray-Tracing Algorithm for Indoor Wireless Propagations

A 3D ray tracing simulator has been developed for indoor wireless networks. The simulator uses geometrical optics (GOs) to propagate the electromagnetic waves inside the buildings. The prediction technique takes into account multiple reflections and transmissions of the propagated waves. An interpolation prediction method (IPM) has been proposed to predict the propagated signal and to make the ray-tracing algorithm faster, accurate, and simple. The measurements have been achieved by using a single Wi-Fi network access point as a transmitter and a laptop as a receiver. Measured data had been collected at different positions in indoor environment and compared with predicted signals. The comparison of the predicted and measured received signals gave root mean square error of 2.96 dB and std. deviation of 2.98 dB.

Ionospheric disturbances produced by chemical releases and the resultant effects on short-wave ionospheric propagation

[1] As an effective means to actively modify the ionosphere, chemical releases can produce artificial ionospheric holes as a consequence of ionization reduction, which can have a great impact on radio wave propagation. To investigate the morphology control of ionospheric holes by various chemical releases and the resultant effects on radio wave propagation, a quantitative numerical model is developed on the basis of the approximate solutions of the diffusion equation of single-point release in uniform atmosphere. While single-point release produces ellipsoidal ionospheric holes, multipoint release can produce other types of ionospheric holes (such as parabola-like tubular ones), which is strongly dependent on changes in the release species, release altitude, and mass of released neutral gas. Releases of both H2O and SF6 can produce ionospheric holes with a similar spatial extent, but the latter tends to result in clearer boundaries and more pronounced electron density reductions. In addition, either an increase in released amount or releases at higher altitudes can lead to a broader hole. To evaluate the effects of an ionospheric hole on radio wave propagation, three-dimensional ray tracing simulations are performed. The ellipsoidal ionospheric holes can act as a lens focusing and bending radio waves, leading to multiple wave reflections inside the holes. In contrast, in the paraboloid tubular ionospheric holes, the rays can penetrate the disturbed region or reflect back, showing a strong dependence on radio frequency. It is well demonstrated that chemical releases can efficiently give rise to artificial ionospheric disturbances and thus modify ionospheric propagation of radio waves.

Radio wave propagation effects produced by chemical releases in the ionosphere

As an effective means to actively modify the ionosphere, chemical release can produce artificial ionospheric holes as a consequence of ionization depletion, which can greatly impact on radio wave propagation. In this paper, on the basis of the pre-study results on ionospheric disturbances produced by some representative chemical releases, the radio waves propagation effects of ionospheric holes that are produced by two different release species, water (H2O) and sulfur hexafluoride (SF6), had been investigated and simulated by the three-dimensional (3-D) numerical ray tracing. The results show that ➀ the appearance of various artificial ionospheric holes can lead to certain decrease of critical frequency in the ionosphere, and ➁ when the wave frequency exceeds the critical frequency, the rays should be multiple reflections or penetrate through the ionospheric hole and focus afterwards with the focus altitude elevated for higher frequencies. This work may provide the necessary theoretical support for chemical release experiments and the evaluation of radio wave propagation effects.

Global-scalePwave tomography optimized for prediction of teleseismic and regional travel times for Middle East events: 2. Tomographic inversion

[1] We construct a model of three-dimensional P wave velocity structure in the crust and mantle that is global in extent, but with detailed upper mantle heterogeneities throughout the greater Middle East region. Fully three-dimensional ray tracing is employed to achieve accurate travel time predictions of P and Pn arrivals, requiring the characterization of irregular and discontinuous boundaries. Therefore, we explicitly represent undulating seismic discontinuities in the crust and upper mantle within a spherical tessellation modeling framework. The tessellation-based model architecture is hierarchical in that fine node sampling is achieved by recursively subdividing a base level tessellation. Determining the required node spacing to effectively model a given set of data is problematic, given the uneven sampling of seismic data and the differing wavelengths of actual seismic heterogeneity. To address this problem, we have developed an inversion process called Progressive Multilevel Tessellation Inversion (PMTI) that exploits the hierarchical nature of the tessellation-based design and allows the data to determine the level of model complexity. PMTI serves as an alternative to existing multiresolution approaches and robustly images regional trends while allowing localized details to emerge where resolution is sufficient. To demonstrate our complete modeling concept, we construct a velocity model based on teleseismic P travel time data for global events and regional Pn travel time data for events occurring throughout the Middle East. Input data are a product of the statistical procedure called Bayesloc that simultaneously models all components of a multievent system including event locations, origin times, and arrival times (described in the Myers et al. (2011) companion paper). The initial tomographic image provides a new glimpse of the complex upper mantle velocity anomalies associated with the convergence of the Arabian and Indian plates with Eurasia. More important for event monitoring, the model accurately predicts both teleseismic and regional travel times for events occurring within the Middle East region.

Measurement and modeling of multiuser multiantenna system in aircraft in the presence of electromagnetic noise and interference

This article evaluates the accuracy with which the performance of a multiuser multiantenna system can be predicted with and without considering cochannel interference and noise (Gaussian, α-stable, and Cauchy) using a site-specific three-dimensional (3D) ray tracing algorithm as well as with statistical models with Gaussian and Nakagami-m channel models in small to medium sized aircraft. These models expand on previous statistical channel models such as the hyper-Rayleigh model by including the simultaneous effects of cochannel and adjacent channel interference, antenna matching, efficiency, directivity and polarization as well as (for the 3D model) site-specific multipath effects. Measurements and comparisons are made in a metallic-bodied Beech Baron BE 58P and a composite structure Rockwell T-39 Sabreliner. It was found that the 3D ray tracing model provides a mean capacity within 1% of those measured in the two aircraft in the presence of interference and noise. This was closely followed by the Nakagami-m distribution (m = 1.4), which was within 1–3% of measured capacity in the presence of interference and within 6% for a combination of interference and noise and the Gaussian model which was within 6% of measured capacity in the presence of interference and within 11% for a combination of interference and noise. The Cauchy noise degraded the capacity more than the other types of noise in the aircraft, providing a lower bound for capacity in an aircraft system. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:1137–1144, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25939

Three-Dimensional GPR Ray Tracing Based on Wavefront Expansion With Irregular Cells

A new ray-tracing method in 3-D heterogeneous isotropic media is proposed based on the bilinear travel-time interpolation and wavefront group marching method (GMM). In this method, an irregular cell discretization scheme is used to accurately describe arbitrarily undulant interfaces in a model. The ray tracing is carried out by forward–backward processing. In the forward step, the travel time in an irregular cell is expressed in terms of the bilinear interpolation of the known travel times on the cell's surfaces. Then, the wavefront is evolved from the source to the whole computational domain by using the newly developed travel-time solver and the fast wavefront expansion GMM. In the backward step, each ray path is traced from the receiver by finding the intersection points of potential ray propagation vectors with the surfaces of the relevant cells. The same travel-time solver is used to compute the candidate intersection points on all surfaces of each relevant cell, and the point with the minimum travel time is selected as a ray point from which the similar step is continued until the sources are found. Several numerical experiments are presented to demonstrate that the new algorithm is accurate, efficient, and robust.

An improved 3-D ray tracing method using linear traveltime interpolation

An approach of three-dimensional seismic ray tracing is presented, which is derived from adopting two-dimensional linear traveltime interpolation (LTI). By adjusting the forward process using the partition of grid interface, and backward step by considering more directions, the new approach is suitable for the application of three-dimensional models. The calculation results show that, with the same accuracy, the improved 3-D method is much faster than the method of traditional LTI directly applied in the three-dimensional case.

Analysis and fabrication of corner cube array based on laser direct writing technology

A detailed analysis of corner cube array (CCA) structure is carried out using the commercially available ray-tracing software ZEMAX. The retroreflective properties of CCA for short-range and long-range propagation are compared. An improved CCA structure with a relatively low structural depth (compared with rectangular CCA) is designed and analyzed. Higher retroreflectance (compared with triangular CCA) at a specific incident angle is proved by ray tracing. Two kinds of CCA structures, including the improved CCA, have been fabricated using laser direct writing technology. The fabrication results are qualified by three-dimensional shape measurement and ray tracing.