Minimum time ray tracing of reflected refracted and diffracted waves in irregular grids

1993 ◽  
Author(s):  
A. Vesnaver
Keyword(s):  
Ray Tracing ◽  
Minimum Time ◽  
Irregular Grids ◽  
Diffracted Waves

Rapid solution of ray tracing problems in heterogeneous media

1980 ◽  
Vol 70 (4) ◽  
pp. 1137-1148 ◽  
Author(s):  
C. H. Thurber ◽  
W. L. Ellsworth
Keyword(s):  
Travel Time ◽  
Ray Tracing ◽  
Heterogeneous Media ◽  
Velocity Structure ◽  
Minimum Time ◽  
Local Minima ◽  
Complex Velocity ◽  
Efficient Manner ◽  
Tracing Techniques ◽  
Ray Path

abstract The determination of local earthquake hypocenters and orgin times from first-P-arrival times by Geiger's method requires a technique for finding the minimum travel time (and derivatives) between the source and the station. Sophisticated ray tracing techniques have been developed for this purpose for use in complex velocity structures. Unfortunately, the two common techniques, shooting and bending, are generally prohibitively expensive for routine use in data analysis. The bending method is also particularly vulnerable to the problem of local minima in travel time. A method has been developed known as the ray initializer, which can be used to circumvent these problems in many cases. First, the technique can find a reasonable estimate of the minimum-time ray path in a quick and efficient manner. The velocity in a region local to the source and receiver is laterally averaged to yield an approximate layered velocity model. One-dimensional ray tracing techniques are used to find the minimum-time path for this layered structure. The ray path estimate can then be used as the starting path in a bending routine, a procedure resulting in more rapid convergence and the avoidance of local minima. Second, the travel time found by numerical integration along the estimated ray path is an excellent approximation to the actual travel time. Thus, in many cases, the ray initializer can be substituted for a three-dimensional ray tracing routine with a tremendous increase in efficiency and only a small loss in accuracy. It is found that the location of an explosion, derived using the ray initializer, is nearly identical to a complete ray tracing solution, even for a highly complex velocity structure.

scholarly journals Seismic ray tracing in anisotropic media: A modified Newton algorithm for solving highly nonlinear systems

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. T1-T7 ◽  
Author(s):  
Yanghua Wang
Keyword(s):  
Nonlinear System ◽  
Ray Tracing ◽  
Anisotropic Media ◽  
Iterative Solution ◽  
Physical Principle ◽  
Time Constraint ◽  
Minimum Time ◽  
Variation Principle ◽  
True Solution ◽  
Highly Nonlinear

Seismic ray tracing with a path-bending method leads to a nonlinear system that has much stronger nonlinearity in anisotropic media than the counterpart in isotropic media. Any path perturbation causes changes to directional velocities, which depend not only upon the spatial position but also upon the local propagation direction in anisotropic media. To combat the high nonlinearity of the problem, the Newton-type iterative algorithm is modified by enforcing Fermat’s minimum-time principle as a constraint for the solution update, instead of conventional error minimization in the nonlinear system. As the algebraic problem is incorporated with the physical principle, it is able to stabilize the solution for such a highly nonlinear problem as ray tracing in realistically complicated anisotropic media. With this modified algorithm, two ray-tracing schemes are presented. The first scheme involves newly derived raypath equations, which are approximate for anisotropic media but the minimum-time constraint will ensure that the solution steadily converges to the true solution. The second scheme is based on the minimal variation principle. It is more efficient than the first one as it solves a tridiagonal system and does not need to compute the Jacobian and its inverse in each iteration. Even in this second scheme, Fermat’s minimum-time constraint is employed for the solution update, so as to guarantee a robust convergence of the iterative solution in anisotropic media.

Reinterpretation by ray tracing of a transverse refraction seismic profile through the California Sierra Nevada, part I

1982 ◽  
Vol 72 (3) ◽  
pp. 889-900
Author(s):  
Bruce A. Bolt ◽  
Rolf Gutdeutsch
Keyword(s):  
Ray Tracing ◽  
San Francisco ◽  
Sierra Nevada ◽  
Seismic Profile ◽  
P Wave ◽  
Travel Times ◽  
Shadow Zone ◽  
Refraction Seismic ◽  
Diffracted Waves ◽  
High Velocity Layer

abstract This study reanalyzes a refraction seismic profile from NTS, Nevada, to San Francisco transverse to the high Sierra Nevada. Three models of the Earth's crust, with an asymmetrical mountain root, constructed by different authors are tested by the use of ray tracing: model CQM (Carer et al., 1970), with a maximum crustal thickness of 35 km centered about 50 km west of the crest of the Sierra; models A and B (Pakiser and Brune, 1980), with a mountain root extending to a depth of 55 km below the Sierra. In the latter, guided and diffracted waves are used to explain seismic Pn energy in the shadow zone of the root. The preferred model A has a high-velocity layer, dipping from west to east in the upper crust, while model B does not. The present study demonstrates how fallacies in interpretation of complicated structures can occur if all ray types are not quantitatively traced. The influence of the P-wave gradient in the upper mantle on the length of the shadow zone is shown to be important, and it is demonstrated that a modified CQM model explains the observed travel times when diffracted waves are included. (CQM does not, however, explain why the Pn travel times on a separate refraction profile along the Sierra Nevada from a Truckee earthquake are so great.) Model B interprets the Pn signals at Δ > 200 km as diffracted waves, but the computed travel times do not fit the observations. The dipping wave guide in model A does not work as expected and perhaps should be ruled out.

GPU Ray Tracing using Irregular Grids

2017 ◽  
Vol 36 (2) ◽  
pp. 477-486 ◽  
Author(s):  
Arsène Pérard-Gayot ◽  
Javor Kalojanov ◽  
Philipp Slusallek
Keyword(s):  
Ray Tracing ◽  
Irregular Grids

New form of Transmission Cross Coefficient for High-Resolution Imaging

1990 ◽  
Vol 48 (1) ◽  
pp. 60-61
Author(s):  
Kazuo Ishizuka
Keyword(s):  
Electron Microscope ◽  
High Resolution ◽  
Transmission Function ◽  
Incident Beam ◽  
Optical Microscope ◽  
Strong Interactions ◽  
Small Range ◽  
Specimen Thickness ◽  
Beam Direction ◽  
Diffracted Waves

It is well known that taking into account spacial and temporal coherency of illumination as well as the wave aberration is important to interpret an image of a high-resolution electron microscope (HREM). This occues, because coherency of incident electrons restricts transmission of image information. Due to its large spherical and chromatic aberrations, the electron microscope requires higher coherency than the optical microscope. On an application of HREM for a strong scattering object, we have to estimate the contribution of the interference between the diffracted waves on an image formation. The contribution of each pair of diffracted waves may be properly represented by the transmission cross coefficients (TCC) between these waves. In this report, we will show an improved form of the TCC including second order derivatives, and compare it with the first order TCC.In the electron microscope the specimen is illuminated by quasi monochromatic electrons having a small range of illumination directions. Thus, the image intensity for each energy and each incident direction should be summed to give an intensity to be observed. However, this is a time consuming process, if the ranges of incident energy and/or illumination direction are large. To avoid this difficulty, we can use the TCC by assuming that a transmission function of the specimen does not depend on the incident beam direction. This is not always true, because dynamical scattering is important owing to strong interactions of electrons with the specimen. However, in the case of HREM, both the specimen thickness and the illumination angle should be small. Therefore we may neglect the dependency of the transmission function on the incident beam direction.

Electron Optical Study of Surface Morphologies of Crystals

1980 ◽  
Vol 38 ◽  
pp. 376-377
Author(s):  
Sumio Iijima ◽  
Tung Hsu
Keyword(s):  
Thin Film ◽  
Optical Study ◽  
Regular Array ◽  
Surface Steps ◽  
Diffracted Waves ◽  
Image Position ◽  
Surface Morphologies

Suppose the thickness of a thin film of a crystal varies periodically like a regular array of surface steps, kinematical intensities of diffracted waves from this crystal are modulated by a shape transform,

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