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Inverse scattering internal multiple elimination
Adriana C. Ramírez (M-OSRP), Arthur B. Weglein (M-OSRP) and Simon A. Shaw (ConocoPhillips). A part of this project project was done at ConocoPhillips (Summer, 2006). M-OSRP 2006 Annual Meeting, June 5 ~ June 7, 2007 M-OSRP report pages: 1-11
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Key questions What are internal multiples?
Why should they be removed from the data? What are the existing methods? What does the Inverse Scattering internal multiple processing provides?
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Outline Motivation History and background
ISS Internal multiple algorithms Assumptions Characteristics Examples Remarks Acknowledgements
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What are internal multiples?
Events didn’t reflect in the earth FS Reflected in the earth no ghost ghost free surface multiples primaries internal multiples
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“Primaries only” assumption
Why should they be removed from the data? “Primaries only” assumption AVO (amplitudes) Velocity analysis Misinterpretation of events Coherent noise
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What are the existing methods?
What do the Inverse Scattering internal multiple processing algorithms provide? There are many methods that have been developed to deal with internal multiples that are effective within their assumptions. e.g. radon transform, deconvolution, inverse scattering series, layer stripping, etc.
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Inverse Scattering internal multiple algorithms
Require no subsurface information Predict the arrival time of all internal multiples exactly Predict amplitude information of internal multiples
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Internal Multiple Prediction
Predicted multiple Input Result of adaptive subtraction
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Internal Multiple Prediction
The more accurate the predicted multiple, the better the result of multiple attenuation Predicted multiple Input Result of adaptive subtraction
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Outline Motivation History and background
ISS Internal multiple algorithms Assumptions Characteristics Examples Remarks Acknowledgements
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Background Scattering Theory Inverse Scattering series Approach:
Identify task specific subseries Free Surface Multiple Elimination Internal Multiple Elimination Depth imaging Non-linear AVO Data driven algorithms No subsurface information required
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History highlights time Weglein, Boyse and Anderson, 1981
Stolt and Jacobs, 1981 Inverse Scattering Series is introduced to exploration seismology Araújo, 1994 Weglein, Gasparotto, Carvalho and Stolt, 1997 Internal multiple attenuator IMA (model-type independent formulation) Coates and Weglein, 1996 Implementation of the IMA (elastic synthetics) Matson, 1997 Matson, Corrigan, Young, 1998 IMA elastic background formulation & 1st implementation on field data Weglein, Araújo, Carvalho, Stolt, Matson, Coates, Corrigan, Foster, Shaw and Zhang, 2003. Subevent interpretation of the internal multiple algorithm. Topical Review: Inverse Scattering Series IMA displacements formulation & implementation Otnes, Hokstad and Sollie, 2004 Nita and Weglein, 2005 Study of headwaves as subevents in the IMA, 1.5D analytical example. Ramírez and Weglein, 2005 Leading order eliminator IME, amplitude analysis & higher order terms. Kaplan, Innanen, Otnes and Weglein, 2005 Implementation of the IMA machine/architecture adaptive & efficiency improvement
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Outline Motivation History and background
ISS Internal multiple algorithms Assumptions Characteristics Examples Remarks Acknowledgements
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Marine experiment and data preprocessing
FS Pre-processing wavelet deconvolution direct wave removal deghosting FS multiple elimination primaries and internal multiples
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Internal multiple attenuator
Araujo, 1994 and Weglein et al. 1997 where i.e. it is a scaled data. The internal multiple attenuator is a data-driven and model type independent algorithm. It predicts the perfect time and always significantly reduces but doesn’t eliminate the 1st order internal multiples.
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Data IN Multiples OUT Time of = time of + -
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Data IN Multiples OUT Amplitude of = amplitude of *
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Attenuation factor j=1 * = T01T10 T01R2T10 x R1 x T01R2T10 =
T01T T01R2R1R2T10 * True amplitude
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Attenuation factor j=1 j=2 T12T21 (T01T10)2 = T12T21*(T01T10)2*
True amplitude
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T01T10 T12T21 (T01T10)2
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Motivation for multiple elimination
“Primaries only” assumption Adaptive subtraction is not always effective enough. Destructive interference between primaries and multiples The predicted amplitudes of converted waves multiples is 22% or less.
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One multiple prediction
? Correct time Correct amplitude Wrong amplitude
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Inverse Scattering Series
We solve the inverse scattering series by identifying task-specific subseries. The internal multiple attenuator was identified as the first term in an infinite subseries. Strategy Improve the attenuator’s amplitude prediction by: Identifying and selecting higher order terms for the internal multiple elimination series.
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Solution Challenge T01T10 T12T21 (T01T10)2
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Solution Challenge T01T10 DATA attenuator DATA DATA T12T21 (T01T10)2
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Leading order closed form
Ramírez and Weglein, 2005. + + + + … Attenuator Leading order series (main contribution)
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Higher order closed form
Ramírez and Weglein, 2005.
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Outline Motivation History and background
ISS Internal multiple algorithms Assumptions Characteristics Examples Remarks Acknowledgements
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Model 1
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Model 1
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Attenuator True Amplitude of Primary(3.5s) = 0.0686118 p p p p Data
Data with attenuated multiples p p p p p + im =
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Closed form True Amplitude of Primary(3.5s) = 0.0686118 p p p p Data
Attenuator Data with attenuated multiples p p p p p + im =
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Implementation Input Data(x,t) Forward Fourier Transforms Data(kgx,ω)
Multiply by (-2iqs) factor b1(kgx, ω)= -2ikz Data(kgx, ω) Stolt migration b1(kgx,z) Non-linear “w” computation Divide by (-2iqs) factor Data_IM(kgx, ω )=b3(kgx, ω)/(-2iqs) Inverse Fourier Transform
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Divide by (-2iqs) factor Data_IM(kgx, ω )=b3(kgx, ω)/(-2iqs)
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What happens when we have acoustic background and an elastic perturbation?
From Ken Matson’s thesis (1997), the first term in the inverse series with an elastic background is We can write the effective data as The internal multiple attenuator is given by
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What happens when we have acoustic background and an elastic perturbation?
The internal multiple attenuator is given by K. H. Matson 1997
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What happens when we have acoustic background and an elastic perturbation?
The leading order closed form does not eliminate converted-wave multiples
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Internal Multiple Prediction
Output Input Prediction Input
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The inverse scattering internal multiple elimination series is a model type independent theory.
The attenuator is a model-type independent algorithm as well as the leading order eliminator.
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Density only model Data Prediction AGC 1sec
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Outline Motivation History and background
ISS Internal multiple algorithms Assumptions Characteristics Examples Remarks Acknowledgements
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Remarks The first term in the removal series is an attenuator. It predicts the perfect time and always significantly attenuates the 1st order internal multiples. Higher order terms towards elimination are determined by non-linear mathematical expressions that only involve the measured data and the reference medium. The removal series for 1st order internal multiples, based on inverse scattering theory, is model-type independent. A closed form for the leading order subseries allows for the elimination of a type of internal multiples. Explain more , predict more More effective More realism Pushing the boundaries Whenever you can use physics to predict… Don´t give adaptive more responsability
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Acknowledgements I would like to acknowledge the internship opportunity I had at ConocoPhillips (summer 2006), and thank the Subsurface Technology group for the excellent environment and encouragement of this research. Fernanda Araújo, Doug Foster, Bob Keys, Richard Day and Dan Whitmore are thanked for useful discussions. Ken Matson (BP) and Sam Kaplan (Univ. of Alberta) are acknowledged for useful discussions.
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