3D ray tracing using a modified shortest-path method

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. T27-T36 ◽  
Author(s):  
Chao-ying Bai ◽  
Stewart Greenhalgh ◽  
Bing Zhou
Keyword(s):  
Velocity Field ◽  
Ray Tracing ◽  
Error Bound ◽  
Shortest Path ◽  
Maximum Relative Error ◽  
Arrival Times ◽  
Velocity Models ◽  
Modified Method ◽  
3D Ray Tracing ◽  
Grid Nodes

We present an accurate 3D ray-tracing algorithm based on a modified (more flexible and economical) shortest-path method (SPM). Unlike the regular SPM in the 3D case, which uses only primary nodes at the corners of each cell and whose accuracy depends on actual cell size, the new method can work with much larger cell sizes by introducing secondary nodes along all bounding surfaces of the cell. This increases the ray angular coverage and permits detailed specification of the velocity field. The modified SPM simultaneously calculates first-arrival times and gradually locates the related raypaths on all grid nodes as the wave field evolves. Its advantages over the regular SPM are its ability to handle high-contrast velocity models more easily, lower memory requirements and less CPU time, and the capability to calculate a relatively large 3D model without losing accuracy. The maximum relative error bound in the computed traveltimes of the modified SPM is established for a uniform velocity field, which may be considered an upper error bound for the whole model in real problems. The modified method in this study is compared with the regular SPM theoretically and on two specific velocity models. The Marmousi model is used to further test the performance of the new approach for both accuracy and flexibility in a complex velocity field. The study shows that the modified SPM is preferable to regular SPM for real 3D problems.

Wave tracing: Ray tracing for the propagation of band-limited signals: Part 2 — Applications

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE385-VE393 ◽  
Author(s):  
John K. Washbourne ◽  
Kenneth P. Bube ◽  
Pedro Carillo ◽  
Carl Addington
Keyword(s):  
Ray Tracing ◽  
Real Data ◽  
Modeling Method ◽  
Simulation Accuracy ◽  
Arrival Times ◽  
Velocity Models ◽  
Depth Images ◽  
Snell’S Law ◽  
Band Limited ◽  
Snell's Law

Modeling seismic propagation is critically important to our work; unfortunately, we often must trade simulation accuracy for reduced computational expense. We present a new seismic-modeling method that is as simple and computationally efficient as Snell’s law ray tracing but provides propagation paths and arrival times more consistent with finite-bandwidth data. We refer to this modeling method as wave tracing and apply it to nonlinear traveltime tomography and depth imaging. By replacing Snell’s law ray tracing with wave tracing, we get better ray coverage, more robust and faster ray bending (fewer iterations), and a much more robust and faster algorithm for nonlinear tomography (fewer iterations, too). A very significant benefit is increased stability and robustness of tomographic inversion with respect to small changes in model parameterization and regularization. A related benefit is the increased stability of depth images with respect to small changes in velocity, which can increase confidence in interpretation. The velocity models that result from wave tracing match picked arrival times in band-limited data better and generate improved depth images. These advantages of wave tracing relative to conventional Snell’s law ray tracing have been tested on both synthetic and real data examples for crosswell seismic geometry.

scholarly journals APPLICATION OF 3-D VELOCITY MODELS AND RAY TRACING IN DOUBLE DIFFERENCE EARTHQUAKE LOCATION ALGORITHMS: APPLICATION TO THE MYGDONIA BASIN (NORTHERN GREECE)

2004 ◽  
Vol 36 (3) ◽  
pp. 1396 ◽  
Author(s):  
O. C. Galanis ◽  
C. B. Papazachos ◽  
P. M. Hatzidimitriou ◽  
E. M. Scordilis
Keyword(s):  
Ray Tracing ◽  
Velocity Structure ◽  
Test Site ◽  
Earthquake Location ◽  
Double Difference ◽  
Northern Greece ◽  
Local Networks ◽  
Velocity Models ◽  
Earthquake Locations

In the past years there has been a growing demand for precise earthquake locations for seismotectonic and seismic hazard studies. Recently this has become possible because of the development of sophisticated location algorithms, as well as hardware resources. This is expected to lead to a better insight of seismicity in the near future. A well-known technique, which has been recently used for relocating earthquake data sets is the double difference algorithm. In its original implementation it makes use of a one-dimensional ray tracing routine to calculate seismic wave travel times. We have modified the implementation of the algorithm by incorporating a three-dimensional velocity model and ray tracing in order to relocate a set of earthquakes in the area of the Mygdonia Basin (Northern Greece). This area is covered by a permanent regional network and occasionally by temporary local networks. The velocity structure is very well known, as the Mygdonia Basin has been used as an international test site for seismological studies since 1993, which makes it an appropriate location for evaluating earthquake location algorithms, with the quality of the results depending only on the quality of the data and the algorithm itself. The new earthquake locations reveal details of the area's seismotectonic structure, which are blurred, if not misleading, when resolved by standard (routine) location algorithms.

Comparing Higher-dimensional Velocity Models for Seismic Location Accuracy using a Consistent Travel Time Framework

2021 ◽  
Author(s):  
Michael Begnaud ◽  
Sanford Ballard ◽  
Andrea Conley ◽  
Patrick Hammond ◽  
Christopher Young
Keyword(s):  
Travel Time ◽  
Ray Tracing ◽  
Seismic Velocity ◽  
3D Seismic ◽  
Location Accuracy ◽  
Velocity Models ◽  
Higher Dimensional ◽  
1D Model ◽  
Tracing Algorithm ◽  
2D And 3D

<p>Historically, location algorithms have relied on simple, one-dimensional (1D, with depth) velocity models for fast, seismic event locations. The speed of these 1D models made them the preferred type of velocity model for operational needs, mainly due to computational requirements. Higher-dimensional (2D-3D) seismic velocity models are becoming more readily available from the scientific community and can provide significantly more accurate event locations over 1D models. The computational requirements of these higher-dimensional models tend to make their operational use prohibitive. The benefit of a 1D model is that it is generally used as travel-time lookup tables, one for each seismic phase, with travel-time predictions pre-calculated for event distance and depth. This simple, lookup structure makes the travel-time computation extremely fast.</p><p>Comparing location accuracy for 2D and 3D seismic velocity models tends to be problematic because each model is usually determined using different inversion parameters and ray-tracing algorithms. Attempting to use a different ray-tracing algorithm than used to develop a model almost always results in poor travel-time prediction compared to the algorithm used when developing the model.</p><p>We will demonstrate that using an open-source framework (GeoTess, www.sandia.gov/geotess) that can easily store 3D travel-time data can overcome the ray-tracing algorithm hurdle. Travel-time lookup tables (one for each station and phase) can be generated using the exact ray-tracing algorithm that is preferred for a specified model. The lookup surfaces are generally applied as corrections to a simple 1D model and also include variations in event depth, as opposed to legacy source-specific station corrections (SSSCs), as well as estimates of path-specific travel-time uncertainty. Having a common travel-time framework used for a location algorithm allows individual 2D and 3D velocity models to be compared in a fair, consistent manner.</p>

Solving two-point seismic-ray tracing problems in a heterogeneous medium

1980 ◽  
Vol 70 (1) ◽  
pp. 79-99 ◽  
Author(s):  
V. Pereyra ◽  
W. H. K. Lee ◽  
H. B. Keller
Keyword(s):  
Numerical Method ◽  
Ray Tracing ◽  
Finite Difference Methods ◽  
Three Dimensional ◽  
Nonlinear Boundary Conditions ◽  
Variable Order ◽  
Flexible Tool ◽  
Velocity Models ◽  
Jump Discontinuities ◽  
Variable Mesh

abstract A study of two-point seismic-ray tracing problems in a heterogeneous isotropic medium and how to solve them numerically will be presented in a series of papers. In this Part 1, it is shown how a variety of two-point seismic-ray tracing problems can be formulated mathematically as systems of first-order nonlinear ordinary differential equations subject to nonlinear boundary conditions. A general numerical method to solve such systems in general is presented and a computer program based upon it is described. High accuracy and efficiency are achieved by using variable order finite difference methods on nonuniform meshes which are selected automatically by the program as the computation proceeds. The variable mesh technique adapts itself to the particular problem at hand, producing more detailed computations where they are needed, as in tracing highly curved seismic rays. A complete package of programs has been produced which use this method to solve two- and three-dimensional ray-tracing problems for continuous or piecewise continuous media, with the velocity of propagation given either analytically or only at a finite number of points. These programs are all based on the same core program, PASVA3, and therefore provide a compact and flexible tool for attacking ray-tracing problems in seismology. In Part 2 of this work, the numerical method is applied to two- and three-dimensional velocity models, including models with jump discontinuities across interfaces.

scholarly journals Comparison analysis of numerically calculated slip surfaces with measured S-wave velocity field for Just-Tęgoborze landslide in Carpathian flysch

2019 ◽  
Vol 133 ◽  
pp. 01003
Author(s):  
Krzysztof Krawiec ◽  
Paulina Harba
Keyword(s):  
Velocity Field ◽  
Wave Velocity ◽  
Strength Criterion ◽  
Deformation Field ◽  
Comparison Analysis ◽  
S Wave ◽  
Velocity Models ◽  
Characteristic Features ◽  
Analysis Of Dispersion ◽  
Comparison Of The Results

The article presents the comparison analysis between deformation field from numerical model and shear wave (S-wave) velocity field obtained from seismic interferometry (SI). Tests were conducted on active Just-Tęgoborze landslide. Geologically, the study area lies in Magura Nappe in the Outer Carpathians. The landslide’s flysch bedrock is covered by Quaternary colluvium built of clays and weathered clayey-rock deposits. During geotechnical investigation, properties of landslide body were established and failure surfaces were distinguished. In order to obtain S-wave velocity models, one-hour of ambient seismic noise was recorded by 12 broadband seismometers. As a result of data processing with SI method, Rayleigh surface wave propagation was reconstructed. The analysis of dispersion curves allowed to estimate a two dimensional S-wave velocity field. The deformation field were calculated assuming an elastic-plastic Coulomb-Mohr strength criterion. Images of shear strain increment, and values of factor of safety of the slope were obtained as a result of calculation. The comparison of the results indicates the similar characteristic features in the S-wave velocity field and the field of deformation calculated numerically.

A New Parallel Approach for 3D Ray-Tracing Techniques in the Radio Propagation Prediction

2007 ◽  
Vol 5 (5) ◽  
pp. 271-279 ◽  
Author(s):  
Andre Mendes Cavalcante ◽  
Marco Jose de Sousa ◽  
Joao Crisostomo Weyl Albuquerque Costa ◽  
Carlos Renato Lisboa Frances ◽  
Gervasio Protasio dos Santos Cavalcante
Keyword(s):  
Ray Tracing ◽  
Radio Propagation ◽  
3D Ray Tracing ◽  
Propagation Prediction ◽  
Tracing Techniques
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