Estimation of Complex Near Surface Focusing Operators by Global Optimization

Verschuur, D.J.; Marhfoul, B. El

doi:10.3997/2214-4609-pdb.1.a035

Cited by 8 publications

(5 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to extend such a process to the 3D situation, this labour‐intensive interaction should be avoided, so an automatic global optimization method is employed. Initial demonstrations in this direction were described by Marhfoul () and Verschuur and Marhfoul (), although they could obtain results only for a very small and simple 3D synthetic data set. The key element of such a solution is the fact that from one‐way traveltimes between surface and datum locations the two‐way traveltimes can be calculated using Fermat's principle to match the observed traveltimes.…”

Section: D Traveltime Operator Estimationmentioning

confidence: 99%

“…With the above two approximations, the 3D one‐way traveltime t from one point at the surface to many locations along the datum is defined as a semi‐hyperbolic event with a certain apex shift and lateral velocity variations (adapted from the expression proposed in Hindriks and Verschuur and Verschuur and Marhfoul ):

\begin{matrix} true \\ right t (x_{f}, y_{f}, x_{s}, y_{s}) & = & left Δ t (x_{s}, y_{s}) + {{[t_{0} (x_{s}, y_{s}) - Δ t (x_{s}, y_{s})]}^{2} \\ left + A_{x} (x_{f}, x_{s}) + B_{x} (x_{f}, x_{s}) \\ left + A_{y} (y_{f}, y_{s}) + B_{y} (y_{f}, y_{s})}^{1 / 2}, \end{matrix}

where

(x_{s}, y_{s})

is the source (or receiver) point at the surface,

(x_{f}, y_{f})

is the target point at the datum level and,

A_{x}

B_{x}

A_{y}

B_{y}

describe different parts of the traveltime function (negative x, positive x, negative y, positive y) that are given by:

A_{x} (x_{f}, x_{s}) = α_{x} (x_{f}, x_{s}) \times \frac{{(x_{f} - x_{s} + Δ x_{s})}^{2}}{[v_{x} (x_{s}, y_{s})}

…”

Section: D Traveltime Operator Estimationmentioning

confidence: 99%

“…The correct two‐way traveltime should be the one with the smallest value. Actually the shortest traveltime principle is the most prevalent case of Fermat's principle and this is why our method is also named Fermat modelling (Hindriks and Verschuur ; Verschuur and Marhfoul ). In this paper, the one‐way traveltime calculation via Fermat modelling is carried out in a 3D sense, which means all possible reflection points

(x_{f}, y_{f})

are located on a 2D datum.…”

Section: D Traveltime Operator Estimationmentioning

confidence: 99%

See 2 more Smart Citations

Solving the complex near‐surface problem using 3D data‐driven near‐surface layer replacement

Sun

Verschuur

Vrolijk³

2014

Geophysical Prospecting

View full text Add to dashboard Cite

In many land seismic situations, the complex seismic wave propagation effects in the near‐surface area, due to its unconsolidated character, deteriorate the image quality. Although several methods have been proposed to address this problem, the negative impact of 3D complex near‐surface structures is still unsolved to a large extent. This paper presents a complete 3D data‐driven solution for the near‐surface problem based on 3D one‐way traveltime operators, which extends our previous attempts that were limited to a 2D situation. Our solution is composed of four steps: 1) seismic wave propagation from the surface to a suitable datum reflector is described by parametrized one‐way propagation operators, with all the parameters estimated by a new genetic algorithm, the self‐adjustable input genetic algorithm, in an automatic and purely data‐driven way; 2) surface‐consistent residual static corrections are estimated to accommodate the fast variations in the near‐surface area; 3) a replacement velocity model based on the traveltime operators in the good data area (without the near‐surface problem) is estimated; 4) data interpolation and surface layer replacement based on the estimated traveltime operators and the replacement velocity model are carried out in an interweaved manner in order to both remove the near‐surface imprints in the original data and keep the valuable geological information above the datum. Our method is demonstrated on a subset of a 3D field data set from the Middle East yielding encouraging results.

show abstract

Section: D Traveltime Operator Estimationmentioning

confidence: 99%

\begin{matrix} true \\ right t (x_{f}, y_{f}, x_{s}, y_{s}) & = & left Δ t (x_{s}, y_{s}) + {{[t_{0} (x_{s}, y_{s}) - Δ t (x_{s}, y_{s})]}^{2} \\ left + A_{x} (x_{f}, x_{s}) + B_{x} (x_{f}, x_{s}) \\ left + A_{y} (y_{f}, y_{s}) + B_{y} (y_{f}, y_{s})}^{1 / 2}, \end{matrix}

where

(x_{s}, y_{s})

is the source (or receiver) point at the surface,

(x_{f}, y_{f})

is the target point at the datum level and,

A_{x}

B_{x}

A_{y}

B_{y}

describe different parts of the traveltime function (negative x, positive x, negative y, positive y) that are given by:

A_{x} (x_{f}, x_{s}) = α_{x} (x_{f}, x_{s}) \times \frac{{(x_{f} - x_{s} + Δ x_{s})}^{2}}{[v_{x} (x_{s}, y_{s})}

…”

Section: D Traveltime Operator Estimationmentioning

confidence: 99%

(x_{f}, y_{f})

are located on a 2D datum.…”

Section: D Traveltime Operator Estimationmentioning

confidence: 99%

See 1 more Smart Citation

Solving the complex near‐surface problem using 3D data‐driven near‐surface layer replacement

Sun

Verschuur

Vrolijk³

2014

Geophysical Prospecting

View full text Add to dashboard Cite

show abstract

“…These focal operators were used for the multi-level implementation of the focal reconstruction. As done in Verschuur and Marhfoul (2005), the choice of these levels depends on the strongest reflection events in the data. However, the depth levels only have to be roughly in the range of strong reflectors and don't need to follow the varying depths exactly, as was demonstrated in section 4.1.…”

Section: Reconstruction Of the Near-offset Gapmentioning

confidence: 99%

The Double Focal Transformation and its Application to Seismic Data Reconstruction

Kutscha¹

2012

Proceedings

View full text Add to dashboard Cite

“…The generation and updating of the initial Green functions is carried out by a genetic algorithm. In this algorithm the one-way times and Fermat's principle are used to calculate two-way reflection times which are matched in an optimal way with the data (Verschuur et al , 2007). These initial operators are used to construct panels, which are manually picked to fine-tune the operators.…”

Section: Brief Outline Of the Approachmentioning

confidence: 99%

A CFP Approach to Estimate the Shear-wave Velocity Distribution in the Shallow Subsoil

Thorbecke¹,

Ghose²

2007

Near Surface 2007 - 13th EAGE European Meeting of Environmental and Engineering Geophysics

View full text Add to dashboard Cite

The CFP approach has been used to estimate Green functions for a high-resolution shear-wave reflection field dataset. This data set contains lateral variations of the near surface and has very low velocities. To estimate a velocity model for this kind of data is not an easy task. The CFP approach gives one-way Green function times which are accurate as indicated by the flat events at t=0. These Green functions contain all the information needed to build an accurate velocity model.

show abstract

Estimation of Complex Near Surface Focusing Operators by Global Optimization

Cited by 8 publications

References 0 publications

Solving the complex near‐surface problem using 3D data‐driven near‐surface layer replacement

Solving the complex near‐surface problem using 3D data‐driven near‐surface layer replacement

The Double Focal Transformation and its Application to Seismic Data Reconstruction

A CFP Approach to Estimate the Shear-wave Velocity Distribution in the Shallow Subsoil

Contact Info

Product

Resources

About