Fresnel volume ray tracing

Geophysics ◽  
1992 ◽  
Vol 57 (7) ◽  
pp. 902-915 ◽  
Author(s):  
Vlastislav Červený ◽  
José Eduardo P. Soares
Keyword(s):  
Ray Tracing ◽  
High Frequency ◽  
Fresnel Zone ◽  
Body Wave ◽  
Low Frequency ◽  
Algebraic Manipulation ◽  
Ray Method ◽  
Propagator Matrix ◽  
Paraxial Ray ◽  
Fresnel Volumes

The concept of “Fresnel volume ray tracing” consists of standard ray tracing, supplemented by a computation of parameters defining the first Fresnel zones at each point of the ray. The Fresnel volume represents a 3-D spatial equivalent of the Fresnel zone that can also be called a physical ray. The shape of the Fresnel volume depends on the position of the source and the receiver, the structure between them, and the type of body wave under consideration. In addition, the shape also depends on frequency: it is narrow for a high frequency and thick for a low frequency. An efficient algorithm for Fresnel volume ray tracing, based on the paraxial ray method, is proposed. The evaluation of the parameters defining the first Fresnel zone merely consists of a simple algebraic manipulation of the elements of the ray propagator matrix. The proposed algorithm may be applied to any high‐frequency seismic body wave propagating in a laterally varying 2-D or 3-D layered structure (P, S, converted, multiply reflected, etc.). Numerical examples of Fresnel volume ray tracing in 2-D inhomogeneous layered structures are presented. Certain interesting properties of Fresnel volumes are discussed (e.g., the double caustic effect). Fresnel volume ray tracing offers numerous applications in seismology and seismic prospecting. Among others, it can be used to study the resolution of the seismic method and the validity conditions of the ray method.

Amplitude, Fresnel zone, and NMO velocity for PP and SS normal-incidence reflections

Geophysics ◽  
2006 ◽  
Vol 71 (2) ◽  
pp. W1-W14 ◽  
Author(s):  
Einar Iversen
Keyword(s):  
Phase Shift ◽  
Ray Tracing ◽  
Explicit Knowledge ◽  
Fresnel Zone ◽  
Normal Wave ◽  
Normal Incidence ◽  
Geometric Spreading ◽  
Dynamic Ray Tracing ◽  
The One ◽  
Paraxial Ray

Inspired by recent ray-theoretical developments, the theory of normal-incidence rays is generalized to accommodate P- and S-waves in layered isotropic and anisotropic media. The calculation of the three main factors contributing to the two-way amplitude — i.e., geometric spreading, phase shift from caustics, and accumulated reflection/transmission coefficients — is formulated as a recursive process in the upward direction of the normal-incidence rays. This step-by-step approach makes it possible to implement zero-offset amplitude modeling as an efficient one-way wavefront construction process. For the purpose of upward dynamic ray tracing, the one-way eigensolution matrix is introduced, having as minors the paraxial ray-tracing matrices for the wavefronts of two hypothetical waves, referred to by Hubral as the normal-incidence point (NIP) wave and the normal wave. Dynamic ray tracing expressed in terms of the one-way eigensolution matrix has two advantages: The formulas for geometric spreading, phase shift from caustics, and Fresnel zone matrix become particularly simple, and the amplitude and Fresnel zone matrix can be calculated without explicit knowledge of the interface curvatures at the point of normal-incidence reflection.

Prediction of High Frequency Sonic Boom Noise Transmission Into Buildings Using a Hybrid Analytical-Ray Tracing Approach

2012 ◽  
Author(s):  
Joseph M. Corcoran ◽  
Marcel C. Remillieux ◽  
Ricardo A. Burdisso
Keyword(s):  
Ray Tracing ◽  
High Frequency ◽  
Acoustic Radiation ◽  
Low Frequency ◽  
Sonic Boom ◽  
Acoustic Transmission ◽  
Frequency Method ◽  
Low Frequencies ◽  
Sonic Booms ◽  
Acoustic Responses

As part of the effort to renew commercial supersonic flight, a predictive numerical tool to compute sonic boom transmission into buildings is under development. Due to the computational limitations of typical numerical methods used at low frequencies (e.g. Finite Element Method), it is necessary to develop a separate approach for the calculation of acoustic transmission and interior radiation at high frequencies. The high frequency approach can then later be combined with a low frequency method to obtain full frequency vibro-acoustic responses of buildings. An analytical method used for the computation of high frequency acoustic transmission through typical building partitions is presented in this paper. Each partition is taken in isolation and assumed to be infinite in dimension. Using the fact that a sonic boom generated far from the structure will approximate plane wave incidence, efficient analytical solutions for the vibration and acoustic radiation of different types of partitions are developed. This is linked to a commercial ray tracing code to compute the high frequency interior acoustic response and for auralization of transmitted sonic booms. Acoustic and vibration results of this high frequency tool are compared to experimental data for a few example cases demonstrating its efficiency and accuracy.

Wave tracing: Ray tracing for the propagation of band-limited signals: Part 1 — Theory

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE377-VE384 ◽  
Author(s):  
Kenneth P. Bube ◽  
John K. Washbourne
Keyword(s):  
Ray Tracing ◽  
High Frequency ◽  
Characteristic Frequency ◽  
Fresnel Zone ◽  
Imaging Techniques ◽  
Real Data ◽  
New Approach ◽  
Head Waves ◽  
Band Limited ◽  
Ray Bending

Many seismic imaging techniques require computing traveltimes and travel paths. Methods to compute raypaths are usually based on high-frequency approximations. In situations such as head waves, these raypaths minimize traveltime but are not paths along which most of the energy travels. We have developed a new approach to computing raypaths, using a modification of ray bending that we call wave tracing; it computes raypaths and traveltimes that are more consistent with the paths and times for the band-limited signals in real data than the paths and times obtained using high-frequency approximations. Wave tracing shortens the raypath while keeping the raypath within the Fresnel zone for a characteristic frequency of the signal.

scholarly journals Revisiting the shadow of a black hole in the presence of a plasma

2018 ◽  
Vol 27 (12) ◽  
pp. 1850114 ◽  
Author(s):  
Yang Huang ◽  
Yi-Ping Dong ◽  
Dao-Jun Liu
Keyword(s):  
Black Hole ◽  
Ray Tracing ◽  
High Frequency ◽  
Low Frequency ◽  
Ring Structure ◽  
Tracing Algorithm

We study the photon’s motion around a black hole in the presence of a plasma whose density is a function of the radius coordinate by a renewed ray-tracing algorithm and investigate the influence of the plasma on the shadow of the black hole. The presence of plasma affects not only the size but also the shape of the black hole shadow. Furthermore, the influence of plasma on trajectories of photons depends on the frequency of the photons. For the high-frequency photons, the influence is negligible, on the contrary, the trajectories of low-frequency photons are affected significantly by the plasma. Interestingly, it is also found that the black hole image would take on a multi-ring structure due to the presence of plasma.

Paraxial ray Kirchhoff migration

Geophysics ◽  
1988 ◽  
Vol 53 (12) ◽  
pp. 1540-1546 ◽  
Author(s):  
T. H. Keho ◽  
W. B. Beydoun
Keyword(s):  
Ray Tracing ◽  
Green's Functions ◽  
Green’S Functions ◽  
Synthetic Data ◽  
Computation Time ◽  
Ray Method ◽  
Kirchhoff Migration ◽  
Order Of Magnitude ◽  
Vsp Data ◽  
Paraxial Ray

A rapid nonrecursive prestack Kirchhoff migration is implemented (for 2-D or 2.5-D media) by computing the Green’s functions (both traveltimes and amplitudes) in variable velocity media with the paraxial ray method. Since the paraxial ray method allows the Green’s functions to be determined at points which do not lie on the ray, two‐point ray tracing is not required. The Green’s functions between a source or receiver location and a dense grid of thousands of image points can be estimated to a desired accuracy by shooting a sufficiently dense fan of rays. For a given grid of image points, the paraxial ray method reduces computation time by one order of magnitude compared with interpolation schemes. The method is illustrated using synthetic data generated by acoustic ray tracing. Application to VSP data collected in a borehole adjacent to a reef in Michigan produces an image that clearly shows the location of the reef.

Monitoring Seismicity on Mars - the Marsquake Service for InSight

2020 ◽  
Author(s):  
John Clinton ◽  
Domenico Giardini ◽  
Savas Ceylan ◽  
Martin van Driel ◽  
Simon Stähler ◽  
...  
Keyword(s):  
High Frequency ◽  
Body Wave ◽  
A Priori ◽  
Broad Band ◽  
Low Frequency ◽  
Ambient Vibration ◽  
Crustal Layer ◽  
Seismic Waveforms ◽  
Seismic Vibrations ◽  
Back Azimuth

<p>InSight landed on Mars in late November 2018, and the SEIS seismometer package was fully deployed by February 2019. By January 2020, SEIS continues to exceed performance expectations in terms of observed minimum noise. The Marsquake Service (MQS) has been setup to create and curate a seismicity catalogue for Mars over the lifetime of the InSight mission. Seismic waveforms are downloaded daily from the station and are analysed and processed by the MarsQuake Service, with the goal of detecting seismic vibrations not due to local ambient sources. To this end, every precaution is applied to eliminate possible non-seismic sources, such as noise induced by atmospheric phenomena, lander vibrations and orbiter activity. At the date of submission, we have detected 365 events, of different quality and SNR levels. Signal amplitudes remain small and signal can generally only be detected at night. Some events show only low-frequency waves in the 1-10 sec band, others have a high-frequency content up to several Hz, and others have a more broad-band character. A special class of events involves the excitation of a very prominent ambient vibration at 2.4Hz. Despite the scattered nature of the energy, in many cases, distinct phases can be inferred in the waveforms. Body wave character, and back-azimuth, can only be confirmed for 3 broadband events so far.  The MQS approach for determining distances from broadband events identifies phases as mantle P and S-phases and uses an a priori set of several thousand martian models, derived from geophysical, mineralogical and orbital constraints. High frequency events are currently located assuming phases are trapped crustal Pg and Sg and using a simple crustal layer. The MQS works in conjunction with the Mars Structural Service (MSS) on building and adopting updated models. The MQS consists of an international team of seismologists that screen incoming data to identify and characterise any seismicity. In this presentation, we present the MQS, demonstrate how we detect and characterise marsquakes, and describe the challenges we face dealing with the Martian dataset.</p>

Improved applicability of ray tracing in seismic acquisition, imaging, and interpretation

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM261-SM271 ◽  
Author(s):  
Håvar Gjøystdal ◽  
Einar Iversen ◽  
Isabelle Lecomte ◽  
Tina Kaschwich ◽  
Åsmund Drottning ◽  
...  
Keyword(s):  
Ray Tracing ◽  
High Frequency ◽  
Numerical Solutions ◽  
Ray Method ◽  
Rapid Changes ◽  
Exploration And Production ◽  
Seismic Acquisition ◽  
Elementary Waves ◽  
Process Elements ◽  
Frequency Approximation

Ray-based seismic modeling methods can be applied at various stages of the exploration and production process. The standard ray method has several advantages, e.g., computational efficiency and the possibility of simulating propagation of elementary waves. As a high-frequency approximation, the method also has a number of limitations, particularly with respect to a lack of amplitude reliability in the presence of rapid changes of the model functions representing elastic parameters and interfaces. Given the objective of improving the applicability of the standard ray method, we present a strategy that does not require specific extension to finite frequencies. Instead, we define each ray-based process as an element of a system that, as a composite process, is able to obtain better results than the ray-based process applied alone. Other elements of the composite process can be finite-difference modeling or numerical solutions for surface and volume integrals, which are basic constituents of Kirchhoff modeling and imaging. We also include among the process elements recently developed techniques for simulating the migration amplitude on a target reflector and in a local volume, e.g., a reservoir zone. The model is decomposed according to its complexity into volume elements, surface elements, or a combination. The composite process consists of a specified interaction between process elements and model elements, which fits well with the philosophy of modern software design. Model elements that will be exposed to ray-tracing algorithms may need appropriate preparation, e.g., smoothing and resampling. We demonstrate specifically, in a tutorial example, that simulating the seismic response from a reflector by ray-based composite processes can yield better results than applying standard ray tracing alone.

The paraxial ray method

Geophysics ◽  
1987 ◽  
Vol 52 (12) ◽  
pp. 1639-1653 ◽  
Author(s):  
Wafik B. Beydoun ◽  
Timothy H. Keho
Keyword(s):  
Wave Field ◽  
Ray Tracing ◽  
Heterogeneous Media ◽  
Computation Time ◽  
Ray Method ◽  
Ray Tracing Method ◽  
Paraxial Ray ◽  
The Cost ◽  
Seismic Wave Field ◽  
Tracing Method

The paraxial ray method is an economical way of computing approximate Green’s functions in heterogeneous media. The method uses information from the standard dynamic ray‐tracing method to extrapolate the seismic wave field at receivers in the neighborhood of a ray so that two‐point ray tracing is not required. Applicability conditions are explicit: they define where asymptotic (high‐frequency) methods are valid, and how far away from the ray the extrapolation remains accurate. Increasing the density of the ray fan improves accuracy but increases computation time. However, since reasonable accuracy is obtained with relatively few rays, the method yields results similar to the two‐point ray‐tracing method, but at a fraction of the cost. Examples of wave‐field extrapolation from a ray to neighboring receivers show that traveltime extrapolation is more accurate than amplitude extrapolation. Accuracy, robustness, and efficiency tests, comparing paraxial ray synthetic seismograms with acoustic finite‐difference and elastic discrete‐wavenumber synthetics, are judged very satisfactory.

Band-limited beam propagator and its application to seismic migration

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. S311-S319 ◽  
Author(s):  
Shaoyong Liu ◽  
Hanming Gu ◽  
Bingkai Han ◽  
Zhe Yan ◽  
Dingjin Liu ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Ray Tracing ◽  
Seismic Wave ◽  
Fresnel Zone ◽  
Seismic Wave Propagation ◽  
Ray Method ◽  
Ray Tracing Method ◽  
Band Limited ◽  
And Migration ◽  
Tracing Method

The ray-tracing technique under the high-frequency assumption has been widely used in seismic wave propagation and migration. However, the practical use of conventional ray tracing is limited in complicated media especially when seismic data are band limited. Besides, the ray-tracing method also suffers from shadow zones in complex media. To alleviate these problems, we have developed a band-limited beam propagator and we apply it in seismic wave propagation and migration, which is flexible to implement and can be friendly to extract angle gathers. To derive the band-limited beam propagator, the band-limited ray-tracing method is adopted to compute the central ray of the beam. These rays in the first Fresnel zone are weighted to obtain the band-limited ray based on the assumption of a local plane wave. Then, the band-limited ray is extended to the band-limited beam propagator using the paraxial approximation. Because the beam propagator has a certain beam width perpendicular to the central ray, it has better illumination than the conventional ray-tracing method, and it could partially alleviate the problem of shadow zones. Finally, we use the band-limited beam propagator to develop a band-limited beam migration and analyze the angle gathers in complicated areas. Numerical examples on synthetic models indicate that the proposed band-limited beam propagator outperforms the conventional ray method in terms of illumination. Its applications in migration determine that it could enhance the imaging quality and produce better angle gathers in a complex area.

Simulations of high-resolution images of amorphous silicon films

1986 ◽  
Vol 44 ◽  
pp. 544-545
Author(s):  
G. Y. Fan ◽  
J. M. Cowley
Keyword(s):  
Electron Microscope ◽  
High Frequency ◽  
Fourier Transformation ◽  
Amorphous Materials ◽  
Low Frequency ◽  
Chromatic Aberration ◽  
Structure Information ◽  
Frequency Components ◽  
High Resolution Images ◽  
Spatial Frequency Spectrum

It is well known that the structure information on the specimen is not always faithfully transferred through the electron microscope. Firstly, the spatial frequency spectrum is modulated by the transfer function (TF) at the focal plane. Secondly, the spectrum suffers high frequency cut-off by the aperture (or effectively damping terms such as chromatic aberration). While these do not have essential effect on imaging crystal periodicity as long as the low order Bragg spots are inside the aperture, although the contrast may be reversed, they may change the appearance of images of amorphous materials completely. Because the spectrum of amorphous materials is continuous, modulation of it emphasizes some components while weakening others. Especially the cut-off of high frequency components, which contribute to amorphous image just as strongly as low frequency components can have a fundamental effect. This can be illustrated through computer simulation. Imaging of a whitenoise object with an electron microscope without TF limitation gives Fig. 1a, which is obtained by Fourier transformation of a constant amplitude combined with random phases generated by computer.

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