Finite‐difference calculation of traveltimes in three dimensions

Geophysics ◽  
1990 ◽  
Vol 55 (5) ◽  
pp. 521-526 ◽  
Author(s):  
John E. Vidale
Keyword(s):  
Finite Difference ◽  
Ray Tracing ◽  
Three Dimensional ◽  
Forward Modeling ◽  
Three Dimensions ◽  
Earthquake Location ◽  
Head Waves ◽  
Smooth Model ◽  
Numerical Grid ◽  
Difference Calculation

The traveltimes of first arriving seismic rays through most velocity structures can be computed rapidly on a three‐dimensional numerical grid by finite‐difference extrapolation. Head waves are properly treated and shadow zones are filled by the appropriate diffractions. Differences of less than 0.11 percent are found between the results of this technique and ray tracing for a complex but smooth model. This scheme has proven useful for earthquake location and shows promise as an inexpensive, well‐behaved substitute for ray tracing in forward‐modeling and Kirchhoff inversion applications.

Synthetic reflection seismograms in three dimensions by a locked‐mode approximation

Geophysics ◽  
1989 ◽  
Vol 54 (3) ◽  
pp. 350-358 ◽  
Author(s):  
G. Nolet ◽  
R. Sleeman ◽  
V. Nijhof ◽  
B. L. N. Kennett
Keyword(s):  
Finite Difference ◽  
Born Approximation ◽  
Large Scale ◽  
Layered Medium ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Realistic Model ◽  
Three Dimensions ◽  
Acoustic Response ◽  
Many Sources

We present a simple algorithm for computing the acoustic response of a layered structure containing three‐dimensional (3-D) irregularities, using a locked‐mode approach and the Born approximation. The effects of anelasticity are incorporated by use of Rayleigh’s principle. The method is particularly attractive at somewhat larger offsets, but computations for near‐source offsets are stable as well, due to the introduction of anelastic damping. Calculations can be done on small minicomputers. The algorithm developed in this paper can be used to calculate the response of complicated models in three dimensions. It is more efficient than any other method whenever many sources are involved. The results are useful for modeling, as well as for generating test signals for data processing with realistic, model‐induced “noise.” Also, this approach provides an alternative to 2-D finite‐difference calculations that is efficient enough for application to large‐scale inverse problems. The method is illustrated by application to a simple 3-D structure in a layered medium.

Finite‐difference calculation of direct‐arrival traveltimes using the eikonal equation

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1270-1274 ◽  
Author(s):  
Le‐Wei Mo ◽  
Jerry M. Harris
Keyword(s):  
Finite Difference ◽  
Ray Tracing ◽  
Finite Differences ◽  
Eikonal Equation ◽  
Velocity Model ◽  
Uniform Grid ◽  
Square Grid ◽  
Kirchhoff Migration ◽  
Difference Calculation

Traveltimes of direct arrivals are obtained by solving the eikonal equation using finite differences. A uniform square grid represents both the velocity model and the traveltime table. Wavefront discontinuities across a velocity interface at postcritical incidence and some insights in direct‐arrival ray tracing are incorporated into the traveltime computation so that the procedure is stable at precritical, critical, and postcritical incidence angles. The traveltimes can be used in Kirchhoff migration, tomography, and NMO corrections that require traveltimes of direct arrivals on a uniform grid.

scholarly journals Application Of Finite Difference Eikonal Solver For Traveltime Computation In Forward Modeling And Migration

2021 ◽  
Vol 72 ◽  
pp. 113-122
Author(s):  
Amir Mustaqim Majdi ◽  
◽  
Seyed Yaser Moussavi Alashloo ◽  
Nik Nur Anis Amalina Nik Mohd Hassan ◽  
Abdul Rahim Md Arshad ◽  
...  
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Ray Tracing ◽  
Forward Modeling ◽  
Fast Marching ◽  
Seismic Image ◽  
And Migration ◽  
Ray Path ◽  
Seismic Images ◽  
Tracing Method

Traveltime is one of the propagating wave’s components. As the wave propagates further, the traveltime increases. It can be computed by solving wave equation of the ray path or the eikonal wave equation. Accurate method of computing traveltimes will give a significant impact on enhancing the output of seismic forward modeling and migration. In seismic forward modeling, computation of the wave’s traveltime locally by ray tracing method leads to low resolution of the resulting seismic image, especially when the subsurface is having a complex geology. However, computing the wave’s traveltime with a gridding scheme by finite difference methods able to overcomes the problem. This paper aims to discuss the ability of ray tracing and fast marching method of finite difference in obtaining a seismic image that have more similarity with its subsurface model. We illustrated the results of the traveltime computation by both methods in form of ray path projection and wavefront. We employed these methods in forward modeling and compared both resulting seismic images. Seismic migration is executed as a part of quality control (QC). We used a synthetic velocity model which based on a part of Malay Basin geology structure. Our findings shows that the seismic images produced by the application of fast marching finite difference method has better resolution than ray tracing method especially on deeper part of subsurface model.

A Unified Correction Method for the Acoustic Refraction (UCMAR) Caused by a Three Dimensional Shear Layer

2019 ◽  
Vol 105 (5) ◽  
pp. 732-742
Author(s):  
Lican Wang ◽  
Rongqian Chen ◽  
Yancheng You ◽  
Wenjun Wu ◽  
Ruofan Qiu
Keyword(s):  
Wind Tunnel ◽  
Temperature Gradient ◽  
Shear Layer ◽  
Ray Tracing ◽  
Three Dimensional ◽  
Correction Method ◽  
Three Dimensions ◽  
Acceptable Solution ◽  
One Dimensional ◽  
Planar Shear

The acoustic refraction induced by the shear layer in an open-jet wind tunnel causes a source shift when estimating the source location with beamforming. Traditional correction methods of the shear layer refraction are achieved through a computational eff ort or limited using one-dimensional or planar shear layer. In this paper, the unified correction method for acoustic refraction (UCMAR) is suitable for the three dimensions that covers several traditional forms. Meanwhile, the UCMAR can consider more general configurations, such as the temperature gradient on both sides of the shear layer and the off -axis source in a circular wind tunnel. These configurations are validated through a ray tracing technique and a benchmark example. In addition, the principle of time reverse is integrated with UCMAR. This results in a reverse UCMAR, which can quickly attain an acceptable solution.

Solving Fully Three-Dimensional Microscale Dual Phase Lag Problem Using Mixed-Collocation, Finite Difference Discretization

2012 ◽  
Vol 134 (9) ◽  
Author(s):  
Alaeddin Malek ◽  
Zahra Kalateh Bojdi ◽  
Parisa Nuri Niled Golbarg
Keyword(s):  
Finite Difference ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Finite Difference Approximation ◽  
Stability And Convergence ◽  
Difference Approximation ◽  
Phase Lag ◽  
Dual Phase ◽  
Linear System Of Equations ◽  
Finite Difference Discretization

In the present work, we investigate laser heating of nanoscale thin-films irradiated in three dimensions using the dual phase lag (DPL) model. A numerical solution based on mixed-collocation, finite difference method has been employed to solve the DPL heat conduction equation. Direct substitution in the model transforms the differential equation into a linear system of equations in which related system is solved directly without preconditioning. Consistency, stability, and convergence of the proposed method based on a mixed-collocation, finite difference approximation are proved, and numerical results are presented. The general form of matrices and their corresponding eigenvalues are presented.

A Numerical Method for Solving Momentum Equations in Generalized Coordinates (Its Application to Three-Dimensional Separated Flows)

1985 ◽  
Vol 107 (1) ◽  
pp. 49-54 ◽  
Author(s):  
A. Nakayama
Keyword(s):  
Finite Difference ◽  
Control Volume ◽  
Three Dimensional ◽  
Separated Flow ◽  
Complex Nature ◽  
Tensor Calculus ◽  
Generalized System ◽  
Finite Difference Equations ◽  
Calculation Results ◽  
Difference Calculation

A finite difference calculation procedure has been developed for the calculations of the three-dimensional fully elliptic flows over irregular boundaries. A simple control volume analysis is introduced to reformulate the momentum equations in the generalized velocity and coordinate system, without resorting to any extensive tensor calculus. The finite difference equations are obtained by discretizing the conservation equations in this generalized system. For a practical application of the present finite difference calculation scheme, calculations are carried out on the three-dimensional separated flow in a converging-diverging rectangular duct. The calculation results reveal an extremely complex nature of the three-dimensional separated flow.

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