Dynamic Ray Tracing Research Articles

Global heat transfer model and dynamic ray tracing algorithm for complex multiple turbine blades of Ni-based superalloys in directional solidification process

High-quality solidification microstructure during directional solidification relies on precise temperature gradient control, so accurate calculation of the temperature field is critical. In this study, a 3D transient global heat transfer model of directional solidification by the Bridgman method based on the finite difference method is developed. The radiation heat in this model is calculated by the discrete transfer method, and a modified method of external surface area for irregular geometric models is proposed to reduce the zigzag shape caused by finite difference grids. Considering the radiative heat transfer between any surface elements of all materials in the directional solidification furnace, a dynamic ray tracing algorithm is developed to simulate the entire process of directional solidification. Then, the simulated results are compared with the theoretical results and experimental results, respectively. Finally, based on the present model and method, the simulation program developed is applied to the directional solidification of actual castings. The simulated results are in good agreement with the experimental results, which indicate that the model and method developed in this study is effective and practical.

Reliability of data-driven wavefront attributes in laterally heterogeneous media

3D wavefront attributes play a major role in many processing steps, such as prestack data enhancement, diffraction separation, and wavefront tomography. For the determination of the 3D wavefront attributes, various stacking operators can be used by adopting semblance optimization. These operators are derived for laterally homogeneous media. In praxis, however, they are applied in real geologic environments with even strong lateral velocity variations such as salt structures. This leads to the question of the quality of the 3D wavefront attributes using these operators when determined in the presence of strong lateral velocity changes. We compared the 3D wavefront attributes determined by 3D common-reflection-surface (CRS) operator (called data-driven wavefront attributes) with the 3D wavefront attributes computed by 3D kinematic and dynamic ray tracing (called model-driven wavefront attributes). For the determination of the 3D CRS wavefront attributes, we have developed a global optimization scheme based on differential evolution. Reflection seismic data of the laterally heterogeneous 3D SEG C3WA salt model are considered, and the model-driven wavefront attributes are computed for a smoothed version of the 3D SEG salt model. The comparison reveals that the wavefront attributes for the normal-incidence-point ray indicate a very good match not only in areas of mild lateral velocity variation but even in regions with strong lateral velocity variations. Approximately 80%–90% of the total picks indicate the good match with a relative error of less than 10% when a semblance threshold of 0.1 is considered in the automatic picking process. This confirms the validity of the determined wavefront attributes even in the presence of strong lateral velocity changes. Using a higher semblance threshold in the automatic picking leads to fewer picks but with an even better match between model- and data-driven wavefront attributes.

3D wavefront attribute determination and conflicting dip processing

The knowledge of 3D wavefront attributes allows many important applications, such as stacking, 5D interpolation, 3D diffraction separation and imaging, and 3D wavefront tomography, just to name a few. For the determination of wavefront attributes, we use the common-reflection-surface (CRS) operator. We adopt a simultaneous search for the determination of wavefront attributes and combine it with conflicting dip processing. For the simultaneous search, we compare three heuristic global optimization algorithms such as particle swarm optimization (PSO), genetic algorithm (GA), and differential evolution (DE). For conflicting dip processing, a dip angle decomposition method for the probed sample is introduced and the simultaneous search is independently performed in specified dip ranges to individually obtain attributes and semblance for each range. Results for the laterally heterogeneous 3D SEG C3WA data indicate that DE has superior performance to determine the 3D wavefront attributes when compared with PSO, GA, and the conventional pragmatic approach because a higher semblance and an improved set of wavefront attributes are achieved. A comparison of the data-driven wavefront attributes obtained from the DE with the model-driven wavefront attributes computed by kinematic and dynamic ray tracing reveals the validity of the data-driven wavefront attributes. Combining the simultaneous search with conflicting dip processing for the 3D CRS stack further improved reflected energy and diffraction details when compared with results without simultaneous search and/or conflicting dip processing.

Implementation of a dynamic ray tracing method in CIVA HealthCare HIFU simulation platform—Application to the propagation in inhomogeneous and heterogeneous tissues

For several years, CEA-LIST has been developing in partnership with INSERM, a HIFU simulation platform, CIVA Healthcare. It provides specific tools for the development and optimization of probes and therapeutic protocols in order to target clinical problematic of specific organs. This platform allows to easily simulate 3D pressure field induced by HIFU, in linear and non-linear regimes, and the corresponding thermal dose in tissues and phantoms. In this communication, we propose a particular focus on the dynamic ray method for linear acoustic propagation. This model enables fast simulations of HIFU propagation in heterogeneous configurations, including soft and hard tissues, made of isotropic and anisotropic medium, with homogeneous or inhomogeneous elastic properties. The contribution of a source point located on the emitting surface is obtained considering the evolution of a pencil of rays centered on the geometrical path linking this source and the observation point. This models takes into account the propagations of bulk waves in each medium and the various reflections and refractions, with and without mode conversion, at each interface. Examples of computation of pressure fields through hard tissues (bones, skull) and in heated soft tissues will be presented. [Work supported by French Nation Research Agency (ANR SATURN -15-CE19-0016).]

An efficient ray-tracing method and its application to Gaussian beam migration in complex multilayered anisotropic media

We have developed a fast ray-tracing method for multiple layered inhomogeneous anisotropic media, based on the generalized Snell’s law. Realistic geologic structures continuously varying with embedded discontinuities are parameterized by adopting cubic B-splines with nonuniformly spaced nodes. Because the anisotropic characteristic is often closely related to the interface configuration, this model parameterization scheme containing the natural inclination of the corresponding layer is particularly suitable for tilted transverse isotropic models whose symmetry axis is generally perpendicular to the direction of the layers. With this model parameterization, the first- and second-order spatial derivatives of the velocity within the interfaces can be effectively obtained, which facilitates the amplitude computation in dynamic ray tracing. By using complex initial conditions for the dynamic ray system and taking the multipath effect into consideration, our method is applicable to Gaussian beam migration. Numerical experiments of our method have been used to verify its effectiveness, practicability, and efficiency in memory storage and computation.

Numerical modeling of Gaussian beam propagation and diffraction in inhomogeneous media based on the complex eikonal equation

Gaussian beam is an important complex geometrical optical technology for modeling seismic wave propagation and diffraction in the subsurface with complex geological structure. Current methods for Gaussian beam modeling rely on the dynamic ray tracing and the evanescent wave tracking. However, the dynamic ray tracing method is based on the paraxial ray approximation and the evanescent wave tracking method cannot describe strongly evanescent fields. This leads to inaccuracy of the computed wave fields in the region with a strong inhomogeneous medium. To address this problem, we compute Gaussian beam wave fields using the complex phase by directly solving the complex eikonal equation. In this method, the fast marching method, which is widely used for phase calculation, is combined with Gauss–Newton optimization algorithm to obtain the complex phase at the regular grid points. The main theoretical challenge in combination of this method with Gaussian beam modeling is to address the irregular boundary near the curved central ray. To cope with this challenge, we present the non-uniform finite difference operator and a modified fast marching method. The numerical results confirm the proposed approach.

A Gaussian beam method for ultrasonic non-destructive evaluation modeling

The propagation of high-frequency ultrasonic body waves can be efficiently estimated with a semi-analytic Dynamic Ray Tracing approach using paraxial approximation. Although this asymptotic field estimation avoids the computational cost of numerical methods, it may encounter several limitations in reproducing identified highly interferential features. Nevertheless, some can be managed by allowing paraxial quantities to be complex-valued. This gives rise to localized solutions, known as paraxial Gaussian beams. Whereas their propagation and transmission/reflection laws are well-defined, the fact remains that the adopted complexification introduces additional initial conditions. While their choice is usually performed according to strategies specifically tailored to limited applications, a Gabor frame method has been implemented to indiscriminately initialize a reasonable number of paraxial Gaussian beams. Since this method can be applied for an usefully wide range of ultrasonic transducers, the typical case of the time-harmonic piston radiator is investigated. Compared to the commonly used Multi-Gaussian Beam model [1], a better agreement is obtained throughout the radiated field between the results of numerical integration (or analytical on-axis solution) and the resulting Gaussian beam superposition. Sparsity of the proposed solution is also discussed.

Characterization of internal waves in synthetic aperture sonar imagery via ray tracing

Synthetic aperture sonar imagery often captures features that appear similar to sand waves but are actually pockets of denser water traveling as isolated waves along the seafloor. These pockets of cold water refract acoustic waves like a lens, causing intensity peaks and shadows that resemble medium to large scale sand waves. This work uses dynamic ray tracing to predict the intensity return as affected by refraction. First, we explore the nature of the intensity pattern created by internal waves of various shapes and sizes. Then, we use an optimization-based approach to solve the inverse problem: given an intensity pattern, determine the size, shape, and location of the internal wave that created it.

Seismic triplication used to reveal slab subduction that had disappeared in the late Mesozoic beneath the northeastern South China Sea

We provided a new study of the seismic velocity structure of the mantle transition zone (MTZ) beneath the northeastern South China Sea using P-wave triplications from two earthquakes at the central Philippines recorded by the Chinese Digital Seismic Network. Through fitting the observed and theoretical triplications modeled by the dynamic ray tracing method for traveltimes, and the reflectivity method for synthetic waveforms using grid-searching method, best-fit velocity models based on IASP91 were obtained to constrain the P-wave velocity structure of the MTZ. The models show that a high-velocity anomaly (HVA) resides at the bottom of MTZ. The HVA is 215km to 225km thick, with a P-wave velocity increment of 1.0% between 450km and 665km or 675km transition and increase by 2.5–3.5% at 665km or 675km depth. The P-wave velocity increment ranges from approximately 0.3% to 0.8% below the 665km or 675km. We proposed that the HVA in the MTZ was caused by the broken fragments of a diving oceanic plate falling into the MTZ at a high angle, and/or by unstable thick continental lithosphere dropping into the MTZ sequentially or almost simultaneously.

Comparison of the anisotropic-ray-theory rays and anisotropic common S-wave rays with the SH and SV reference rays in a velocity model with a split intersection singularity

We describe the behaviour of the anisotropic–ray–theory S–wave rays in a velocity model with a split intersection singularity. The anisotropic–ray–theory S–wave rays crossing the split intersection singularity are smoothly but very sharply bent. While the initial–value rays can be safely traced by solving Hamilton’s equations of rays, it is often impossible to determine the coefficients of the equations of geodesic deviation (paraxial ray equations, dynamic ray tracing equations) and to solve them numerically. As a result, we often know neither the matrix of geometrical spreading, nor the phase shift due to caustics. We demonstrate the abrupt changes of the geometrical spreading and wavefront curvature of the fast anisotropic–ray–theory S wave. We also demonstrate the formation of caustics and wavefront triplication of the slow anisotropic–ray–theory S wave.Since the actual S waves propagate approximately along the SH and SV reference rays in this velocity model, we compare the anisotropic–ray–theory S–wave rays with the SH and SV reference rays. Since the coupling ray theory is usually calculated along the anisotropic common S–wave rays, we also compare the anisotropic common S–wave rays with the SH and SV reference rays.

Development of a treatment simulation platform—Application to probe optimization and tissues characterization

In order to ease the development and optimization of new transducers and therapeutic protocols, a unified tool to easily simulate 3D pressure fields created by HIFU in human tissues has been developed jointly by INSERM and CEA-LIST. This includes three propagation algorithms: 1/ a GPU implementation of Rayleigh integral for fast linear propagation in human soft tissues, 2/ a dynamic ray tracing algorithm for the simulation of propagation in heterogeneous or inhomogeneous media (i.e., bones, skull, heated tissues, etc.), 3/ a Westervelt solver for non-linear propagation. These algorithms have been validated and implemented in a unified graphical user interface and can be easily interchanged to compare the results or to target a specific research topic. A finite volume difference solver for Bio Heat Transfer Equation (BHTE) has also been implemented. It can be used with all the HIFU propagation algorithms. It is used to simulate thermal effects of HIFUs and thermal dose in tissues and phantoms. Parametric s...

Time-to-depth conversion and velocity estimation by image-wavefront propagation

A new strategy for time-to-depth conversion and interval-velocity estimation is based entirely on image-wavefront propagation without the need to follow individual image rays. The procedure has three main features: (1) It computes the velocity field and the traveltime directly, allowing us to dispense with dynamic ray tracing; (2) it requires only the knowledge of the image wavefront at the previous time step; and (3) it inherently smooths the image wavefront, inhibiting the formation of caustics. As a consequence, the method tends to be faster than the usual techniques and does not carry the constraints and limitations inherent to common ray-tracing strategies. Synthetic tests using a Gaussian velocity anomaly as well as the Marmousi velocity model, and two smoothed versions of it show the feasibility of the method. A field-data example demonstrates the use of different numerical procedures. Our results indicate that the present strategy can be used to construct reasonable depth-velocity models that can be used as reliable starting models for velocity-model building in depth migration or for tomographic methods.

Velocity-model estimation with NIP-wave tomography inversion – A real data example

The common-reflection-surface (CRS) stack in addition to high signal-to-noise ratio stacked sections creates the curvature and local dip of a reflector. With this information, so-called kinematic wavefield attributes, it is possible to obtain a subsurface velocity model for laterally inhomogeneous media using normal-incidence-point (NIP) wave inversion. The result of CRS provides some location points on the stacked section as input for the inversion. In each iteration, dynamic ray tracing is applied along the central ray according to an input data point. With this technique, the parameter needed for forward modeling will be obtained. By updating the velocity model and minimizing the misfit between input data and the forward model parameter, it is possible to achieve a final velocity model consistent with input data. In this paper, we applied the CRS method on complex structure in the northeast of Iran, and then we performed the NIP-wave tomography inversion on this data set by means of CRS attributes. The result clearly shows the ability of NIP-wave tomography in velocity-model inversion.

Ray tracing and geodesic deviation of the SH and SV reference rays in a heterogeneous generally anisotropic medium which is approximately uniaxial

The coupling ray theory is usually applied to anisotropic common reference rays, but it is more accurate if it is applied to reference rays which are closer to the actual wave paths. If we know that a medium is close to uniaxial (transversely isotropic), it may be advantageous to trace reference rays which resemble the SH–wave and SV–wave rays. This paper is devoted to defining and tracing these SH and SV reference rays of elastic S waves in a heterogeneous generally anisotropic medium which is approximately uniaxial (approximately transversely isotropic), and to the corresponding equations of geodesic deviation (dynamic ray tracing). All presented equations are simultaneously applicable to ordinary and extraordinary reference rays of electromagnetic waves in a generally bianisotropic medium which is approximately uniaxially anisotropic. The improvement of the coupling–ray–theory seismograms calculated along the proposed SH and SV reference rays, compared to the coupling–ray–theory seismograms calculated along the anisotropic common reference rays, has already been numerically demonstrated by the authors in four approximately uniaxial velocity models.

Numerical synthesis of tri‐reflector CATR with high cross‐polarisation isolation

In this Letter, a tri-reflector compact antenna test range (CATR) with a paraboloidal main reflector and two shaped sub-reflectors is synthesised by the kinematic and dynamic ray tracing method, while the high cross-polarisation isolation is achieved through the proposed system geometry. Numerical simulations by general responsibility assignment software patterns demonstrate that a cross-polarisation isolation >40 dB and a peak-to-peak amplitude (phase) ripple <1 dB (10°) can be achieved on the principal cuts of the designed quiet zone at 90–325 GHz. This clearly shows that the high cross-polarisation isolation in such a tri-reflector CATR can be achieved by the proposed antenna geometry without depolarisation control in the shaping procedure.

Local algorithm for computing complex travel time based on the complex eikonal equation.

The traditional algorithm for computing the complex travel time, e.g., dynamic ray tracing method, is based on the paraxial ray approximation, which exploits the second-order Taylor expansion. Consequently, the computed results are strongly dependent on the width of the ray tube and, in regions with dramatic velocity variations, it is difficult for the method to account for the velocity variations. When solving the complex eikonal equation, the paraxial ray approximation can be avoided and no second-order Taylor expansion is required. However, this process is time consuming. In this case, we may replace the global computation of the whole model with local computation by taking both sides of the ray as curved boundaries of the evanescent wave. For a given ray, the imaginary part of the complex travel time should be zero on the central ray. To satisfy this condition, the central ray should be taken as a curved boundary. We propose a nonuniform grid-based finite difference scheme to solve the curved boundary problem. In addition, we apply the limited-memory Broyden-Fletcher-Goldfarb-Shanno technology for obtaining the imaginary slowness used to compute the complex travel time. The numerical experiments show that the proposed method is accurate. We examine the effectiveness of the algorithm for the complex travel time by comparing the results with those from the dynamic ray tracing method and the Gauss-Newton Conjugate Gradient fast marching method.

Seriate microfluidic droplet coalescence under optical forces in a channel flow

The microfluidic holding and coalescence behaviors of droplets subjected to an optical trap within a channel flow were numerically studied by using the lattice Boltzmann method and the dynamic ray tracing. A tightly focused Gaussian laser beam positioned laterally with respect to the channel flow direction was used as the optical trap. In such a system, seriate droplet coalescence was observed between an optically trapped droplet and the subsequent droplet. The numerically predicted droplet coalescence behavior agreed well with the experimental results. A sufficiently high laser power was required to capture an incoming droplet and induce coalescence with the subsequent droplet. The effects of various flow and optical parameters on the coalescence behavior were investigated.

Common‐shot Fresnel beam migration based on wave‐field approximation in effective vicinity under complex topographic conditions

ABSTRACTGaussian beam migration is a versatile imaging method for geologically complex land areas, which overcomes the limitation of Kirchhoff migration in imaging multiple arrivals and has no steep‐dip limits of one‐way wave‐equation migration. However, its imaging accuracy depends on the geometry of Gaussian beam that is determined by the initial parameter of dynamic ray tracing. As a result, its applications in exploration areas with strong variations in topography and near‐surface velocity are limited. Combined with the concept of Fresnel zone and the theory of wave‐field approximation in effective vicinity, we present a more robust common‐shot Fresnel beam imaging method for complex topographic land areas in this paper. Compared with the conventional Gaussian beam migration for irregular topography, our method improves the beam geometry by limiting its effective half‐width with Fresnel zone radius. Moreover, through a quadratic travel‐time correction and an amplitude correction that is based on the wave‐field approximation in effective vicinity, it gives an accurate method for plane‐wave decomposition at complex topography, which produces good imaging results in both shallow and deep zones. Trials of two typical models and its application in field data demonstrated the validity and robustness of our method.

Gaussian beam prestack depth migration in heterogeneous transversely isotropic media

The transversely isotropic (TI) media approximation is commonly applied to assist in the processing of seismic data acquired in sedimentary environments. Based on anisotropic kinematic and dynamic ray tracing systems, a P-wave Gaussian beam prestack depth migration (GB-PSDM) method for TI media is introduced in this paper. The imaging principle of anisotropic GB-PSDM and the corresponding migration parameters are presented on the basis of the GB-PSDM method in isotropic media. Tests of synthetic and field seismic data show that the method is an accurate and efficient anisotropic prestack depth migration method in TI media.

Lateral migration of a microdroplet under optical forces in a uniform flow

The behavior of a microdroplet in a uniform flow and subjected to a vertical optical force applied by a loosely focused Gaussian laser beam was studied numerically. The lattice Boltzmann method was applied to obtain the two-phase flow field, and the dynamic ray tracing method was adopted to calculate the optical force. The optical forces acting on the spherical droplets agreed well with the analytical values. The numerically predicted droplet migration distances agreed well with the experimentally obtained values. Simulations of the various flow and optical parameters showed that the droplet migration distance nondimensionalized by the droplet radius is proportional to the S number (zd/rp = 0.377S), which is the ratio of the optical force to the viscous drag. The effect of the surface tension was also examined. These results indicated that the surface tension influenced the droplet migration distance to a lesser degree than the flow and optical parameters. The results of the present work hold for the refractive indices of the mean fluid and the droplet being 1.33 and 1.59, respectively.