Efficient modeling and imaging of pegleg multiples Morgan Brown and Antoine Guitton Stanford University, Department of Geophysics Multiples can be bad… On seismic images, multiples inhibit: Geologic interpretation Velocity analysis Prestack amplitudes Poststack inversion Multiple suppression techniques: Shallow water: predictive decon 2-D Deep water: Delft SRME 3-D: Radon demultiple …but, are they all bad? Unlike other seismic noise, multiples: Reach prospect zone Strong and coherent Highly correlated with signal Imaging with multiples? Are they usable? What do they add? How can we use them? Our answer: combine prestack images of multiples and primaries. Many caveats! See this talk: “Least-squares joint imaging of multiples and primaries” (MUL2, Tuesday, 13:55) Poster Summary ---We introduce an efficient linear operator for the “true relative amplitude” modeling and imaging of pegleg multiples. Applying the forward operator to primary reflections after NMO models the peglegs. Applying the adjoint operator to multiples produces events which are directly comparable to NMO’ed primaries. The kinematic component of our operator is an extension of the NMO equation which images “split” peglegs from a moderately heterogeneous earth. The amplitude component corrects multiples for their differences in angle-dependent reflection strength, relative to a primary. We illustrate the efficacy of our approach on 2D and 3D prestack field examples. Please grab a paper for more details! Near-angle information content s g g g …  prim Multiples almost always contain near angle information not found in primaries. Multiples sample the angle axis more finely than primaries.  prim <  mult  mult primary pegleg multiple Far-angle information content s g g g …  prim In certain cases, multiples contain wide angle information not found in the primaries   prim conventional imaging Prestack multiple imaging offset space time seismic experiment midpoint depth primaries pegleg multiples x/  space  /z imaging for multiples primary image multiple image conventional modeling Prestack multiple modeling offset space time primaries pegleg multiples x/  space  /z modeling for multiples structure, amplitudes consistent primary image multiple image Modeling and imaging are an adjoint pair If d 0 is reflection data containing only primaries, creates a primary image, m 0. Conversely, --.maps from image space to data space. Primary modeling Primary imaging Pegleg modeling Pegleg imaging If d k is reflection data containing only a particular type of pegleg, --.creates a pegleg image, m k. Depending on implementation, the index k may be a function of multiple order, the pegleg “split” (see figure to right), and the multiple generator How to image split peglegs? top salt seabed In a non-1D earth, peglegs split into unique events with different arrival times. Offset How we image split peglegs flat in offset “1.5-D” method (vertical stretch) Moderate structure, no diffractions Requires picking, event tracking Fast (main application is iterative inversion) Good for typical marine 3-D geometries Amplitudes preserved, easy to understand Kinematic component: Heterogeneous Earth Multiple NMO Operator (HEMNO)  TS +  WB  TS xpxp x xmxm 1-D earth  y 0  y0y0 pegleg multiple = “pseudo-primary” y 0 = midpoint y m, y p ? Analytic expressions for each pegleg type.  ( y m )? Pick multiple generator on zero-offset section.  ( y p )? Track event by summing the reflector dip, measured on - ---….--zero-offset section (Fomel, 2002), across midpoint. Equivalent to Levin & Shah’s (1977) equations in small dip limit. x xpxp Derive: d/dt of primary & multiple traveltime equations equal at x, x p, respectively. Amplitude Corrections (more details in paper) More on Amplitudes Assume perfect free surface reflection (-1) Differential geometric spreading correction Estimate and apply space-variant reflection -coefficient of multiple generator Minimize: ||r*primary – multiple|| 2 Assume multiple generator has no AVO Pegleg modeling/imaging = standard NMO.... correction Primary modeling Primary imaging Pegleg modeling Pegleg imaging i,k,m = multiple order, type of split, multiple generator. = apply reflection coefficient of multiple generator = HEMNO operator = Snell Resampling = differential geometric spreading structure, amplitudes consistent Normal moveout (NMO) equation for 1 st -order pegleg: easily generalized to higher-order multiples  y p  xpxp x xmxm ymym When reflectors dip, reflection points move. If the dips are small, most of the movement is vertical. By measuring the zero-offset traveltime at (analytical) “1-D earth” reflection points, we can model vertical reflection point movement. 2-D earth y0y0.. actual raypath HEMNO raypath p(t,x,y) m(t,x,y) r(y)r(y) Snell Resampling: a compression of the offset axis that forces imaged primary and multiple to have the same AVO. Valid in v(z) media.

Efficient modeling and imaging of pegleg multiples Morgan Brown and Antoine Guitton Stanford University, Department of Geophysics Stacked Image Comparison top salt peglegsseabed peglegs primaries Predicting Multiples from Primaries 1)NMO’ed ---primaries 2) model one type of pegleg 3)Add all split peglegs (k) of all desired orders (i), from all desired multiple generators (m) 4) predicted multiples Mississippi Canyon (GoM) 2-D line Our predicted multiples versus SRME (Verschuur et al., 1992) Midpoint Data OursSRME Offset (m) Data OursSRME Medium-offset slice Common-midpoint gather Common 3-D marine acquisition “flip-flop” shooting: midpoint locations from adjacent sail lines (… and …) s s sail line 1 sail line 2 Most efficient way to get -- -regular crossline sampling Crossline CMP fold =1 Sparsity hurts SRME Our strategy: Remove crossline offset axis. Now -effectively a 2-D problem ~ AMO/Common azimuth Assume little feathering inline offset xline offset CMP gather Our predicted multiples on Green Canyon IV (GoM) 3-D data near-offset slice Common-midpoint gather Fomel, S., 2002, Applications of plane-wave destruction filters: Geophysics, 67, 6, Levin, F.K., and Shah, P.M., 1977, Peg-leg multiples and dipping reflections: Geophysics, 42, 5, Verschuur, D.J., Berkhout, A.J., and Wapenaar, C.P.A., 1992, Adaptive surface-related multiple elimination: Geophysics, 57, References We introduced an efficient prestack pegleg imaging/modeling scheme, suitable for joint imaging or multiple suppression applications. Although it is theoretically limited to areas with small reflector dip, the multiples modeled by our method compared favorably to those predicted by the more general SRME method. On a 3D Gulf of Mexico field dataset with some crossline dip, our method performed well. Conclusions We acknowledge WesternGeco for donation of the 2D Mississippi Canyon data, and CGG for donation of the 3D Green Canyon data, as well as all the sponsors of the Stanford Exploration Project. The first author acknowledges Robert Clapp and Clement Kostov for support during Ph.D. research at Stanford. Acknowledgements 1.Sort data into common-midpoint gathers 2.NMO & Stack to obtain zero-offset section a)Pick all “important” multiple generators b)Estimate reflector dip 3.Estimate reflection coefficient for all multiple generators 4.Starting from NMO’ed primaries, forward model all important peglegs to obtain predicted multiples near-offset gap doubles Offset (m)