Can we image complex structures with first‐arrival traveltime?

Geoltrain, Sebastien; Brac, Jean

doi:10.1190/1.1443439

Cited by 118 publications

(71 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For example, in geophysical simulations, first arrivals may not correspond to the most energetic arrivals, and this can cause problems in seismic imaging (12,13).…”

Section: Formulation Of Problemmentioning

confidence: 99%

Fast-phase space computation of multiple arrivals

Fomel

Sethian

2002

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

We present a fast, general computational technique for computing the phase-space solution of static Hamilton-Jacobi equations. Starting with the Liouville formulation of the characteristic equations, we derive ''Escape Equations'' which are static, time-independent Eulerian PDEs. They represent all arrivals to the given boundary from all possible starting configurations. The solution is numerically constructed through a ''one-pass'' formulation, building on ideas from semi-Lagrangian methods, Dijkstra-like methods for the Eikonal equation, and Ordered Upwind Methods. To compute all possible trajectories corresponding to all possible boundary conditions, the technique is of computational order O(N log N), where N is the total number of points in the computational phase-space domain; any particular set of boundary conditions then is extracted through rapid post-processing. Suggestions are made for speeding up the algorithm in the case when the particular distribution of sources is provided in advance. As an application, we apply the technique to the problem of computing first, multiple, and most energetic arrivals to the Eikonal equation.W e present a fast, general computational technique for computing phase-space solutions of static HamiltonJacobi equations. We derive a set of ''Escape Equations'' that are static, time-independent Eulerian partial differential equations which represent all arrivals to the given boundary from all possible starting configurations. Following the strategy proposed in (1) we solve these Escape Equations by systematically constructing space marching the solution in increasing order, using a ''one-pass'' formulation. This means that the solution at each point in the computational mesh is computed only k times, where k does not depend on the number of points in the mesh. The algorithm combines ideas of semi-Lagrangian methods, Dijkstra-like methods for the Eikonal equation, and Ordered Upwind Methods. The method is unconditionally stable, with no time-step restriction, and can be made higher-order accurate. We demonstrate the applicability of this technique by computing multiple arrivals to the Eikonal equation in a variety of settings.The methods presented here are efficient. The Escape Equations are posed time-independent Eulerian equations in phase space, whose solution gives the exit time and location for all possible trajectories, starting from all interior points, initialized in all directions. The computational speed depends on whether one wants to, in fact, obtain results for all possible boundary conditions, or, in fact, only for a particular subset of possibilities.To illustrate, consider a two-dimensional problem consisting of a region and its boundary; we discretize the region with a square mesh with N points on each side. Thus, the physical space corresponding to the interior consists of N 2 points, with N points on the boundary (we ignore constants).In the most general form of boundary conditions, such as those which occur in applications such as tomography and seismic migr...

show abstract

“…For example, in geophysical simulations, first arrivals may not correspond to the most energetic arrivals, and this can cause problems in seismic imaging (12,13).…”

Section: Formulation Of Problemmentioning

confidence: 99%

Fast-phase space computation of multiple arrivals

Fomel

Sethian

2002

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

show abstract

“…which is obtained from initial conditions (14) and (15). This is a signed distance function, satisfying jr x;h /j ¼ 1, to the initial phase space curve…”

Section: Level Set Formulationmentioning

confidence: 99%

“…However, in practice, later arrivals may carry information which is more relevant to applications. In geophysical oil explorations, for example, the first-arrival wavefront may not carry the most energetic part of the wave-field, and later-arrival wavefronts may be more useful for modern high resolution seismic imaging via integral transform in the presence of strong refraction [15,22,25]. In the quantum mechanics, the WKBJ method for the semi-classical limit of the Schr€ odinger www.elsevier.com/locate/jcp Journal of Computational Physics 197 (2004) equation needs multivalued phases to construct the asymptotic expansion of the wave field, where the phases are multivalued solutions of eikonal equations [6,23].…”

Section: Introductionmentioning

confidence: 99%

A level set based Eulerian method for paraxial multivalued traveltimes

Qian

Leung

2004

Journal of Computational Physics

View full text Add to dashboard Cite

We apply the level-set methodology to compute multivalued solutions of the paraxial eikonal equation in both isotropic and anisotropic metrics. This paraxial equation is obtained from 2D stationary eikonal equations by using one of the spatial directions as the artificial evolution direction. The advection velocity field used to move level sets is obtained by the method of characteristics; therefore, the motion of level sets is defined in a phase space, and the zero level set yields the location of bicharacteristic strips in the reduced phase space. The multivalued traveltime is obtained from solving another advection equation with a source term. The complexity of the algorithm is OðN 3 log NÞ in the worst case and OðN 3 Þ in the average case, where N is the number of the sampling points along one of the spatial directions. Numerical experiments including the well-known Marmousi synthetic model illustrate the accuracy and the efficiency of the Eulerian method.

show abstract

“…However, these methods are put forward based on high-frequency approximation theory which requires the value of velocity ranging steadily in a certain wavelength (Geoltrain and Brac, 1993). Often migration model cannot meet this requirement, so it need to be smoothed (Červený, 2005).…”

Section: Introductionmentioning

confidence: 99%

Synthetic Analysis of Model Smoothing’s Influence on Ray Path, Traveltime and Migration Imaging

Sun¹

2017

Appl Ecol Env Res

View full text Add to dashboard Cite

Abstract. Smoothing process might change the value of grid nodes in the migration model, which is essential to seismic imaging. We will study the influence of model smoothing on ray path and traveltime as well as their connections with the migration imaging. A deep-water velocity model is employed for the calculation. The numerical analysis shows that model smoothing has a significant influence on ray path and traveltime, these differences can affect the migration images. Optimal smoothing process is beneficial to achieve high-quality migration images, while inappropriate model smoothing could even change the shape of real geology body and lead to wrong geology structures in the migration sections.

show abstract

Can we image complex structures with first‐arrival traveltime?

Cited by 118 publications

References 4 publications

Fast-phase space computation of multiple arrivals

Fast-phase space computation of multiple arrivals

A level set based Eulerian method for paraxial multivalued traveltimes

Synthetic Analysis of Model Smoothing’s Influence on Ray Path, Traveltime and Migration Imaging

Contact Info

Product

Resources

About