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.

MODELING AND ANALYSIS OF AN ACOUSTIC CHANNEL WITH A MOVING SURFACE

2013 ◽  
Vol 21 (04) ◽  
pp. 1350015 ◽  
Author(s):  
YOUNGMIN CHOO ◽  
WOOJAE SEONG
Keyword(s):  
Travel Time ◽  
Ray Tracing ◽  
Path Dependence ◽  
Moving Surface ◽  
Modeling And Analysis ◽  
Surface Movement ◽  
Delay Times ◽  
Tracing Algorithm ◽  
The Difference ◽  
Ray Path

A ray tracing algorithm for moving surfaces is derived to enable the analysis of surface movement effects. For this, a ray tracing algorithm for frozen surface is modified. By comparing the results from frozen and moving surface ray models allows effects of a moving surface to be investigated. The surface movement effects can be seen with the difference between channel impulse responses from the frozen and moving surface ray models. For an investigation of ray path dependence of the surface movement effects, delay times of surface reflective paths from the two ray models are observed according to transmitted ping time. As the ray path from the source to surface gets longer, difference of travel time results from the two ray models increase. This fact indicates that surface movement effects depend on ray path, in particular travel time until a ray meets a surface.

Tsunami Ray Tracing Method for Shortest Travel-Time Path

2021 ◽  
Author(s):  
Tung-Cheng Ho ◽  
Shingo Watada ◽  
Kenji Satake
Keyword(s):  
Travel Time ◽  
Ray Tracing ◽  
Tsunami Wave ◽  
Wave Theory ◽  
Ray Tracing Method ◽  
Tsunami Early Warning ◽  
Time Path ◽  
Long Wave ◽  
Ray Path ◽  
Tracing Method

<p>We propose a ray-tracing method to solve the two-point boundary value problem for tsunamis based on the long-wave theory. In the long-wave theory, the tsunami wave velocity is proportional to the square root of water depth, which is available from global bathymetric atlases. Our method computes the shortest travel times starting from each of the two given points and calculates the local ray direction to trace the ray path. We utilize an explicit, non-iterative tracing scheme that exhibits robust results and applies to any tsunami-accessible locations, and the global-shortest travel-time path is derived. In simple and real bathymetry cases, our method demonstrates stable results with neglectable low uncertainties. The ray-tracing method is then applied to analyze the path of tsunamis from different directions to four important bays in Japan. The result shows that tsunami ray paths are significantly influenced by local bathymetry, and some crucial structures, such as trench and trough, behave as the primary routes of this region. Deploying stations near these routes will be most beneficial for tsunami early warning. The existing tsunami-observing system off the Honshu area works well for tsunamis from the east side but slightly deficient for tsunamis from the west side. The far-field ray tracing shows that tsunamis traveling from Chile to Japan through two main routes—one via north Hawaii and the other via the south— depending on the location of the source.</p>

scholarly journals Non-linear arrival time tomography

1997 ◽  
Vol 40 (1) ◽  
Author(s):  
C. B. Papazachos ◽  
G. Nolet
Keyword(s):  
Ray Tracing ◽  
Large Scale ◽  
Arrival Time ◽  
Local Minima ◽  
Linear Inversion ◽  
3D Ray Tracing ◽  
Non Linear ◽  
Simple Scaling ◽  
Tracing Techniques ◽  
Stepwise Scheme

The use of 1D or pseudo- 3D ray tracing techniques in linearized tomographic problems leads to solutions for which it is difficult to assess the true resolution and error distribution. For this reason, we employ a revised 3D bending algorithm (Moser et al., 1992) and show that it can be used efficiently for a non-linear inversion in a stepwise scheme. Initial paths are determined from graph theory in order to avoid local minima in bending. The importance of 3D ray tracing in inversion studies and the limitations of the standard 1D approach are demonstrated through synthetic examples. The speed of the ray tracing and the simple scaling scheme allow for an implementation in large-scale tomographic problems.

A fast algorithm for two-point seismic ray tracing

1987 ◽  
Vol 77 (3) ◽  
pp. 972-986
Author(s):  
Junho Um ◽  
Clifford Thurber
Keyword(s):  
Travel Time ◽  
Ray Tracing ◽  
Three Dimensional ◽  
Linear Interpolation ◽  
Geometric Interpretation ◽  
Approximate Algorithm ◽  
Velocity Models ◽  
Limit Test ◽  
Ray Path ◽  
Lateral Variations

Abstract A new approximate algorithm for two-point ray tracing is proposed and tested in a variety of laterally heterogeneous velocity models. An initial path estimate is perturbed using a geometric interpretation of the ray equations, and the travel time along the path is minimized in a piecewise fashion. This perturbation is iteratively performed until the travel time converges within a specified limit. Test results show that this algorithm successfully finds the correct travel time within typical observational error much faster than existing three-dimensional ray tracing programs. The method finds an accurate ray path in a fully three-dimensional form even where lateral variations in velocity are severe. Because our algorithm utilizes direct minimization of the travel time instead of solving the ray equations, a simple linear interpolation scheme can be employed to compute velocity as a function of position, providing an added computational advantage.

A New Ray Tracing Method Based on Linear Travel-Time Interpolation

2015 ◽  
Vol 743 ◽  
pp. 845-851
Author(s):  
L.J. Liu ◽  
Z.H. Xie ◽  
C. Yang
Keyword(s):  
Travel Time ◽  
Ray Tracing ◽  
Flaw Detection ◽  
Reverse Direction ◽  
Ray Tracing Method ◽  
Error Accumulation ◽  
Ray Path ◽  
Multiple Cells ◽  
Tracing Method ◽  
Background Area

In the application of industrial flaw detection, the materials to be detected are often a collection of a background area and a small amount of defect areas. In traditional linear travel-time interpolation (LTI) method, the assumption of travel-time linearity will lead to error accumulation when the rays go through multiple cells. In order to reduce the cumulative error in this application, a new ray tracing method is proposed based on linear travel-time interpolation. In our method, calculation points are located on the boundaries between different areas to determine the angle of refraction. Moreover, the minimum travel-time of each point is computed by multidirectional loop strategy, which will make the traced ray path conforms to the condition of minimum travel-time when ray transports from the reverse direction. The simulation results show that using the proposed method to calculate travel-times and paths of tracing rays, it is more rapid and accurate than traditional LTI method and cross-scanning LTI method.

scholarly journals Simple and Exact Closed-Form Expression for Determination of a Penetrated Ray Path in a Ray Tracing

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hyun Wook Moon ◽  
Woojoong Kim ◽  
Sewoong Kwon ◽  
Jaeheung Kim ◽  
Young Joong Yoon
Keyword(s):  
Closed Form ◽  
Approximate Method ◽  
Ray Tracing ◽  
Conventional Method ◽  
Closed Form Expression ◽  
Indoor Environments ◽  
Straight Line ◽  
Ray Path ◽  
Ray Tracing Simulation

A simple and exact closed-form equation to determine a penetrated ray path in a ray tracing is proposed for an accurate channel prediction in indoor environments. Whereas the penetrated ray path in a conventional ray tracing is treated as a straight line without refraction, the proposed method is able to consider refraction through the wall in the penetrated ray path. Hence, it improves the accuracy in ray tracing simulation. To verify the validation of the proposed method, the simulated results of conventional method, approximate method, and proposed method are compared with the measured results. The comparison shows that the proposed method is in better agreement with the measured results than the conventional method and approximate method, especially in high frequency bands.

scholarly journals A simple P-wave polarization analysis: its application to earthquake location

1994 ◽  
Vol 37 (5) ◽  
Author(s):  
B. Alessandrini ◽  
M. Cattaneo ◽  
M. Demartin ◽  
M. Gasperini ◽  
V. Lanza
Keyword(s):  
Ground Motion ◽  
Seismic Wave ◽  
Heterogeneous Media ◽  
Seismic Wave Propagation ◽  
Least Square ◽  
P Wave ◽  
Motion Direction ◽  
Arrival Times ◽  
Hypocentral Location ◽  
Ray Path

We present a method for hypocentral location which takes into account all three components of ground motion and not only the vertical one, as it is usually done by standard least-square techniques applied to arrival times. Assuming that P-wave particle motion direction corresponds to the propagation direction of the seismic wave, we carried out a simple statistical analysis of ground motion amplitudes, carefully using three-component records. We obtained the azimuth and the emersion angle of the seismic ray, which, added to Pg and Sg arrival times, allowed us to find reliable hypocentral coordinates of some local events by means of a ray-tracing technique. We compared our locations to those obtained using a least-square technique: our polarization method's dependence on the accuracy of the model used (on the contrary, the least-square technique proved to be quite stable with respect to changes in the model's velocity parameters) led us to conclude that polarization data provide coherent information on the true ray-path and can be successfully used for both location procedures and seismic wave propagation studizs in strongly heterogeneous media.

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