Least-squares Joint Imaging of Primaries and Multiples Morgan Brown Stanford University 2002 SEG, Salt Lake City Stanford Exploration Project Brown

A Stack of the Primaries... Stanford Exploration Project Brown

…and a Stack of the Multiples Stanford Exploration Project Brown

CMP gathers are also consistent primaries multiples Stanford Exploration Project Brown

What information can multiples add? At least redundant: Related AVO behavior Similar structural image Different illumination: Near offsets Shadow zones Stanford Exploration Project Brown

How to exploit the information? Constraint on existing information Integrate additional information Three requirements: Image self-consistency Consistency with data Simplicity of images Stanford Exploration Project Brown

The Gameplan Imaging: “NMO for Multiples” Constraint/Integration: Regularized least-squares inversion Synthetic & Real data tests Stanford Exploration Project Brown

NMO for multiples - kinematics Stanford Exploration Project Brown

NMO for multiples - kinematics Building a pseudo-primary t’ S R 1 t’ t Stanford Exploration Project Brown

NMO for multiples - kinematics Building a pseudo-primary t’ S R 2 t’ t Stanford Exploration Project Brown

NMO for multiples - kinematics Building a pseudo-primary t’ S R 3 t’ t Stanford Exploration Project Brown

NMO for multiples - kinematics Building a pseudo-primary t’ S R 4 t’ t Stanford Exploration Project Brown

NMO for multiples - kinematics Building a pseudo-primary t’ S R t’ t Dx Stanford Exploration Project Brown

NMO for multiples - kinematics primary NMO for multiple 1 Effective RMS velocity Stanford Exploration Project Brown

NMO for multiples - kinematics Stanford Exploration Project Brown

Modeling Amplitudes: Assumptions Constant AVO WB reflection. Free surface R.C. = -1. Ignore geometric spreading. Ignoring primary AVO: multi (-r)i*prim AVO: more later. Stanford Exploration Project Brown

Forward Modeling Equation NMO0 d m0 Stanford Exploration Project Brown

Forward Modeling Equation (-r)*NMO1 d m1 Stanford Exploration Project Brown

Forward Modeling Equation (-r)2*NMO2 d m2 Stanford Exploration Project Brown

Forward Modeling Equation Ni :adjoint of NMO for multiple i. Ri : (-r)iI. mi : pseudo-primary panel i. d : input CMP gather. Stanford Exploration Project Brown

Least-squares objective function Stanford Exploration Project Brown

Least-squares objective function Stanford Exploration Project Brown

Image Simplicity and Crosstalk Ideally, the “simplest” model... N0m0 + N1R1m1 + N2R2m2 “inverse” d m0 m1 m2 Stanford Exploration Project Brown

Model Simplicity and Crosstalk …but this problem is underdetermined. N0m0 + N1R1m1 + N2R2m2 “inverse” d m0 m1 m2 Stanford Exploration Project Brown

Discriminating between crosstalk and signal Self-consistent, flat primaries Stanford Exploration Project Brown

Discriminating between crosstalk and signal Inconsistent, curved crosstalk Stanford Exploration Project Brown

Model Regularization suppresses crosstalk Dm= Difference between pseudo-primary panels. Penalizes inconsistent crosstalk events. Dx= Difference along offset. Penalizes curving events. e1,e2 = Scalar regularization parameters. Stanford Exploration Project Brown

Dm: Modeling AVO of multiples No explicit AVO modeling Model relative primary/multiple AVO dependence. Dm differences at different offsets. Stanford Exploration Project Brown

Dm: Modeling AVO of multiples From forward model Mult(h) ~ prim(hp) * (-r) hp S R t’ h t Stanford Exploration Project Brown

Dm: Modeling AVO of multiples In constant velocity: hp S R t’ h t Stanford Exploration Project Brown

Dm: Modeling AVO of multiples In constant velocity: Curves: hp(t) - - m0 m1 Stanford Exploration Project Brown

Synthetic Data Results Raw primaries Raw mult. 1 Raw mult. 2 Stanford Exploration Project Brown

Synthetic Data Results Est. primaries Est. mult. 1 Est. mult. 2 x(-r) x(-r 2) Stanford Exploration Project Brown

Synthetic Data Results Raw primaries Est. primaries Difference Stanford Exploration Project Brown

Synthetic Data #2 Results Raw primaries Est. primaries Difference Stanford Exploration Project Brown

Real Data Results Raw primaries Est. primaries Difference Stanford Exploration Project Brown

Strengths Good separation…. Amplitude-preserving process ...at near offsets …without a prior noise model Amplitude-preserving process General integration framework Stanford Exploration Project Brown

Weaknesses 1-D earth. Amplitudes - Incomplete Modeling? Parameter sensitivity… …e1, e2, r, velocity. Multiples coherent across offset. NMO stretch. Stanford Exploration Project Brown

The Future Migration…tougher battle, richer spoils Different illumination Amplitudes? Converted waves (PS,PSP). “Tall” operator. One image, many datasets. Prior wavefield separation. Stanford Exploration Project Brown

Acknowledgements ExxonMobil, WesternGeco for data. Biondo Biondi, Bob Clapp, Antoine Guitton. Stanford Exploration Project Brown