Offset-continuation stacking: Theory and proof of concept

Coimbra, Tiago A.; Novais, Amélia; Schleicher, Jörg

doi:10.1190/geo2015-0473.1

Cited by 11 publications

(15 citation statements)

References 48 publications

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“…On the other hand, a more appropriate approach would be to consider the offset‐continuation trajectory (OCT) traveltime (Coimbra, Novais and Schleicher ; Coimbra et al . ). It depends on fewer traveltime parameters (two for a 2D prestack data) and has better fitting performance than FO–CRS.…”

Section: Resultsmentioning

confidence: 97%

“…The offset‐continuation trajectory (OCT) traveltime is given by (Coimbra et al . )

T_{OCT} false(m, h, t_{0}, scriptP (t_{0}) false) = t_{h} + A_{h} Δ m,

where

t_{h}

and

A_{h}

are functions of

(h, m_{0}, h_{0}, t_{0})

representing the common‐reflection‐point (CRP) traveltime and the slope (slowness) in midpoint direction, respectively. When

h = h_{0}

, then

t_{h} = t_{0}

and the other values of

t_{h}

are given by the following expression (Santos, Scheicher and Tygel )

\begin{matrix} true \\ right t_{h} & = & left \sqrt{\frac{4 h^{2}}{V^{2}} + \frac{4 h^{2}}{u^{2}} t_{n_{0}}^{2}}, as | h | > | h_{0} |, \\ right t_{h} & = & left \sqrt{\frac{4 h^{2}}{V^{2}} + \frac{u^{2}}{4 h_{0}^{2}} t_{n_{0}}^{2}}, as | h | < | h_{0} |, \end{matrix}

where

\begin{matrix} true \\ right u & = & left \sqrt{{(h + h_{0})}^{2} - (m_{h} - m<...>} \end{matrix}

…”

Section: Resultsmentioning

confidence: 99%

“…In addition, a crucial condition for the functionality of OCT (or OCO stack) is the slope continuation Coimbra et al . () that relates the change of the slopes of the events on the CRP trajectory for each half‐offset value, namely

A_{h} = (\frac{t_{0} t_{n}^{2}}{t_{h} t_{n_{0}}^{2}}) A_{0},

where

t_{n}^{2} = t_{h}^{2} - \frac{4 h^{2}}{V^{2}} .

Figure illustrates a seismic event and the OCT stacking surface following the CRP trajectory parametrized by half offset limited by midpoint‐offset apertures. Furthermore, we can observe that the set of parameters for OCT traveltime is given by

P false(t_{0} false) = false{A_{0} (t_{0}), V (t_{0}) false}

, which satisfies the identity property (

t_{0} = T_{OCT} false(m_{0}, h_{0}, t_{0}, scriptP (t_{0}) false)

), but its metric of stretch is not zero.…”

Section: Resultsmentioning

confidence: 99%

“…Beyond that, FO-CRS depends on a large number of traveltime parameters, five for a twodimensional (2D) pre-stack data, which implies high computational costs to estimate its parameters. On the other hand, a more appropriate approach would be to consider the offsetcontinuation trajectory (OCT) traveltime (Coimbra, Novais and Schleicher 2013;Coimbra et al 2016b). It depends on fewer traveltime parameters (two for a 2D prestack data) and has better fitting performance than FO-CRS.…”

Section: Generalized Normal Moveout Correction In Finite Offset Domainmentioning

confidence: 99%

“…Müller and Höcht () and Gelchinsky, Berkovitch, and Keydar () proposed the common reflection surface (CRS) and multifocusing, respectively, extending the stacking process to consider not only half‐offset apertures but also midpoints apertures. Coimbra, Novaes and Schleicheret () derived an accurate traveltime equation capable of identifying the common reflection point contribution along half offsets and midpoints that can be used in a finite‐offset case. Faccipieri et al .…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Stretch‐free generalized normal moveout correction

Faccipieri

Coimbra

Bloot

2018

Geophysical Prospecting

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The effective application of normal moveout correction processes mainly depends on four factors: the chosen traveltime approximation, the stretching associated with the given traveltime, crossing events and phase changes, the last two being inherent to the seismic data. In this context, we conduct a quantitative analysis on stretching considering a general traveltime expression depending on half‐offset and midpoint coordinates. Through this analysis, we propose a mathematically proven procedure to eliminate stretching, which can be applied to any traveltime approximation. The proposed method is applied to synthetic and real data sets, considering different traveltime approximations and achieved complete elimination of stretching.

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Section: Resultsmentioning

confidence: 97%

“…The offset‐continuation trajectory (OCT) traveltime is given by (Coimbra et al . )

T_{OCT} false(m, h, t_{0}, scriptP (t_{0}) false) = t_{h} + A_{h} Δ m,

where

t_{h}

and

A_{h}

are functions of

(h, m_{0}, h_{0}, t_{0})

representing the common‐reflection‐point (CRP) traveltime and the slope (slowness) in midpoint direction, respectively. When

h = h_{0}

, then

t_{h} = t_{0}

and the other values of

t_{h}

are given by the following expression (Santos, Scheicher and Tygel )

\begin{matrix} true \\ right t_{h} & = & left \sqrt{\frac{4 h^{2}}{V^{2}} + \frac{4 h^{2}}{u^{2}} t_{n_{0}}^{2}}, as | h | > | h_{0} |, \\ right t_{h} & = & left \sqrt{\frac{4 h^{2}}{V^{2}} + \frac{u^{2}}{4 h_{0}^{2}} t_{n_{0}}^{2}}, as | h | < | h_{0} |, \end{matrix}

where

\begin{matrix} true \\ right u & = & left \sqrt{{(h + h_{0})}^{2} - (m_{h} - m<...>} \end{matrix}

…”

Section: Resultsmentioning

confidence: 99%

A_{h} = (\frac{t_{0} t_{n}^{2}}{t_{h} t_{n_{0}}^{2}}) A_{0},

where

t_{n}^{2} = t_{h}^{2} - \frac{4 h^{2}}{V^{2}} .

P false(t_{0} false) = false{A_{0} (t_{0}), V (t_{0}) false}

, which satisfies the identity property (

t_{0} = T_{OCT} false(m_{0}, h_{0}, t_{0}, scriptP (t_{0}) false)

), but its metric of stretch is not zero.…”

Section: Resultsmentioning

confidence: 99%

Section: Generalized Normal Moveout Correction In Finite Offset Domainmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stretch‐free generalized normal moveout correction

Faccipieri

Coimbra

Bloot

2018

Geophysical Prospecting

Self Cite

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show abstract

Time-migration velocity estimation using Fréchet derivatives based on nonlinear kinematic migration/demigration solvers

et al. 2020

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Common-reflection-surface method in weakly anisotropic vertical transverse isotropic media

et al. 2018

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The extraction of kinematic parameters from wave propagation through traveltimes is one of the great challenges in seismic data processing. In this context, we modify the common-reflection-surface (CRS) traveltime to improve its accuracy and also interpret its parameters via paraxial ray theory in an anisotropic medium obtaining information about the wavefront curvatures measured at surface. The proposed method consists of searching for the best stacking parameters that fit the data set followed by the extraction of kinematic information from the measured waves. Numerical tests show the effectiveness of our assumptions and that the results obtained in the fitting and parameter extraction in anisotropic media achieve better accuracy than conventional CRS.

show abstract

Offset-continuation stacking: Theory and proof of concept

Cited by 11 publications

References 48 publications

Stretch‐free generalized normal moveout correction

Stretch‐free generalized normal moveout correction

Time-migration velocity estimation using Fréchet derivatives based on nonlinear kinematic migration/demigration solvers

Common-reflection-surface method in weakly anisotropic vertical transverse isotropic media

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