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.

The Development of a Parallel Ray Launching Algorithm for Wireless Network Planning

2012 ◽  
pp. 466-483
Author(s):  
Zhihua Lai ◽  
Nik Bessis ◽  
Guillaume De La Roche ◽  
Pierre Kuonen ◽  
Jie Zhang ◽  
...  
Keyword(s):  
Ray Tracing ◽  
Wireless Network ◽  
Real World ◽  
Network Planning ◽  
Time Constraint ◽  
Running Time ◽  
Propagation Modeling ◽  
Physical Resources ◽  
Ray Launching

Propagation modeling has attracted much interest because it plays an important role in wireless network planning and optimization. Deterministic approaches such as ray tracing and ray launching have been investigated, however, due to the running time constraint, these approaches are still not widely used. In previous work, an intelligent ray launching algorithm, namely IRLA, has been proposed. The IRLA has proven to be a fast and accurate algorithm and adapts to wireless network planning well. This article focuses on the development of a parallel ray launching algorithm based on the IRLA. Simulations are implemented, and evaluated performance shows that the parallelization greatly shortens the running time. The COST231 Munich scenario is adopted to verify algorithm behavior in real world environments, and observed results show a 5 times increased speedup upon a 16-processor cluster. In addition, the parallelization algorithm can be easily extended to larger scenarios with sufficient physical resources.

Ray Tracing in Layered Anisotropic Media

1991 ◽  
Author(s):  
J. Costa ◽  
M. Schoenberg ◽  
D. Miller
Keyword(s):  
Ray Tracing ◽  
Anisotropic Media

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

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. T281-T289 ◽  
Author(s):  
Qianru Xu ◽  
Weijian Mao
Keyword(s):  
Gaussian Beam ◽  
Ray Tracing ◽  
Initial Conditions ◽  
Anisotropic Media ◽  
Memory Storage ◽  
Ray Tracing Method ◽  
Embedded Discontinuities ◽  
Model Parameterization ◽  
Gaussian Beam Migration ◽  
Tracing Method

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.

scholarly journals Transformation to zero offset in transversely isotropic media

Geophysics ◽  
1996 ◽  
Vol 61 (4) ◽  
pp. 947-963 ◽  
Author(s):  
Tariq Alkhalifah
Keyword(s):  
Ray Tracing ◽  
Impulse Response ◽  
Homogeneous Medium ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Amplitude Distribution ◽  
Isotropic Media ◽  
Zero Offset ◽  
Vertical Inhomogeneity

Nearly all dip‐moveout correction (DMO) implementations to date assume isotropic homogeneous media. Usually, this has been acceptable considering the tremendous cost savings of homogeneous isotropic DMO and considering the difficulty of obtaining the anisotropy parameters required for effective implementation. In the presence of typical anisotropy, however, ignoring the anisotropy can yield inadequate results. Since anisotropy may introduce large deviations from hyperbolic moveout, accurate transformation to zero‐offset in anisotropic media should address such nonhyperbolic moveout behavior of reflections. Artley and Hale’s v(z) ray‐tracing‐based DMO, developed for isotropic media, provides an attractive approach to treating such problems. By using a ray‐tracing procedure crafted for anisotropic media, I modify some aspects of their DMO so that it can work for v(z) anisotropic media. DMO impulse responses in typical transversely isotropic (TI) models (such as those associated with shales) deviate substantially from the familiar elliptical shape associated with responses in homogeneous isotropic media (to the extent that triplications arise even where the medium is homogeneous). Such deviations can exceed those caused by vertical inhomogeneity, thus emphasizing the importance of taking anisotropy into account in DMO processing. For isotropic or elliptically anisotropic media, the impulse response is an ellipse; but as the key anisotropy parameter η varies, the shape of the response differs substantially from elliptical. For typical η > 0, the impulse response in TI media tends to broaden compared to the response in an isotropic homogeneous medium, a behavior opposite to that encountered in typical v(z) isotropic media, where the response tends to be squeezed. Furthermore, the amplitude distribution along the DMO operator differs significantly from that for isotropic media. Application of this anisotropic DMO to data from offshore Africa resulted in a considerably better alignment of reflections from horizontal and dipping reflectors in common‐midpoint gather than that obtained using an isotropic DMO. Even the presence of vertical inhomogeneity in this medium could not eliminate the importance of considering the shale‐induced anisotropy.

Seismic complex ray tracing in 2D/3D viscoelastic anisotropic media by a modified shortest-path method

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. T331-T342
Author(s):  
Xing-Wang Li ◽  
Bing Zhou ◽  
Chao-Ying Bai ◽  
Jian-Lu Wu
Keyword(s):  
Ray Tracing ◽  
Shortest Path ◽  
Anisotropic Medium ◽  
Wave Energy ◽  
Seismic Data ◽  
Seismic Waves ◽  
Effective Means ◽  
Anisotropic Media ◽  
The Real ◽  
Complex Ray

In a viscoelastic anisotropic medium, velocity anisotropy and wave energy attenuation occur and are often observed in seismic data applications. Numerical investigation of seismic wave propagation in complex viscoelastic anisotropic media is very helpful in understanding seismic data and reconstructing subsurface structures. Seismic ray tracing is an effective means to study the propagation characteristics of high-frequency seismic waves. Unfortunately, most seismic ray-tracing methods and traveltime tomographic inversion algorithms only deal with elastic media and ignore the effect of viscoelasticity on the seismic raypath. We have developed a method to find the complex ray velocity that gives the seismic ray speed and attenuation in an arbitrary viscoelastic anisotropic medium, and we incorporate them with the modified shortest-path method to determine the raypath and calculate the real and imaginary traveltime (wave energy attenuation) simultaneously. We determine that the complex ray-tracing method is applicable to arbitrary 2D/3D viscoelastic anisotropic media in a complex geologic model and the computational errors of the real and imaginary traveltime are less than 0.36% and 0.59%, respectively. The numerical examples verify that the new method is an effective and powerful tool for accomplishing seismic complex ray tracing in heterogeneous viscoelastic anisotropic media.

Prestack Gaussian-beam depth migration in anisotropic media

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. S133-S138 ◽  
Author(s):  
Tianfei Zhu ◽  
Samuel H. Gray ◽  
Daoliu Wang
Keyword(s):  
Gaussian Beam ◽  
Ray Tracing ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Elastic Parameters ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Beam Depth ◽  
Dynamic Ray Tracing

Gaussian-beam depth migration is a useful alternative to Kirchhoff and wave-equation migrations. It overcomes the limitations of Kirchhoff migration in imaging multipathing arrivals, while retaining its efficiency and its capability of imaging steep dips with turning waves. Extension of this migration method to anisotropic media has, however, been hampered by the difficulties in traditional kinematic and dynamic ray-tracing systems in inhomogeneous, anisotropic media. Formulated in terms of elastic parameters, the traditional anisotropic ray-tracing systems aredifficult to implement and inefficient for computation, especially for the dynamic ray-tracing system. They may also result inambiguity in specifying elastic parameters for a given medium.To overcome these difficulties, we have reformulated the ray-tracing systems in terms of phase velocity.These reformulated systems are simple and especially useful for general transversely isotropic and weak orthorhombic media, because the phase velocities for these two types of media can be computed with simple analytic expressions. These two types of media also represent the majority of anisotropy observed in sedimentary rocks. Based on these newly developed ray-tracing systems, we have extended prestack Gaussian-beam depth migration to general transversely isotropic media. Test results with synthetic data show that our anisotropic, prestack Gaussian-beam migration is accurate and efficient. It produces images superior to those generated by anisotropic, prestack Kirchhoff migration.

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