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

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?

Outline Motivation History and background ISS Internal multiple algorithms Assumptions Characteristics Examples Remarks Acknowledgements

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

“Primaries only” assumption Why should they be removed from the data? “Primaries only” assumption AVO (amplitudes) Velocity analysis Misinterpretation of events Coherent noise

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.

Inverse Scattering internal multiple algorithms Require no subsurface information Predict the arrival time of all internal multiples exactly Predict amplitude information of internal multiples

Internal Multiple Prediction Predicted multiple Input Result of adaptive subtraction

Internal Multiple Prediction The more accurate the predicted multiple, the better the result of multiple attenuation Predicted multiple Input Result of adaptive subtraction

Outline Motivation History and background ISS Internal multiple algorithms Assumptions Characteristics Examples Remarks Acknowledgements

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

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

Outline Motivation History and background ISS Internal multiple algorithms Assumptions Characteristics Examples Remarks Acknowledgements

Marine experiment and data preprocessing FS Pre-processing wavelet deconvolution direct wave removal deghosting FS multiple elimination primaries and internal multiples

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.

Data IN Multiples OUT Time of = time of + -

Data IN Multiples OUT Amplitude of = amplitude of *

Attenuation factor j=1 * = T01T10 T01R2T10 x R1 x T01R2T10 = T01T10 T01R2R1R2T10 * True amplitude

Attenuation factor j=1 j=2 T12T21 (T01T10)2 = T12T21*(T01T10)2* True amplitude

T01T10 T12T21 (T01T10)2

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.

One multiple prediction ? Correct time Correct amplitude Wrong amplitude

 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.

Solution Challenge T01T10 T12T21 (T01T10)2

Solution Challenge T01T10 DATA attenuator DATA DATA T12T21 (T01T10)2

Leading order closed form Ramírez and Weglein, 2005. + + + + … Attenuator Leading order series (main contribution)

Higher order closed form Ramírez and Weglein, 2005.

Outline Motivation History and background ISS Internal multiple algorithms Assumptions Characteristics Examples Remarks Acknowledgements

Model 1

Model 1

Attenuator True Amplitude of Primary(3.5s) = 0.0686118 p p p p Data Data with attenuated multiples p p p p p + im =0.0311329 0.0650167

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 =0.0311329 0.0686118

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

Divide by (-2iqs) factor Data_IM(kgx, ω )=b3(kgx, ω)/(-2iqs)

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

What happens when we have acoustic background and an elastic perturbation? The internal multiple attenuator is given by K. H. Matson 1997

What happens when we have acoustic background and an elastic perturbation? The leading order closed form does not eliminate converted-wave multiples

Internal Multiple Prediction Output Input Prediction Input

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.

Density only model Data Prediction AGC 1sec

Outline Motivation History and background ISS Internal multiple algorithms Assumptions Characteristics Examples Remarks Acknowledgements

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

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.