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## Multiple Removal with Local Plane Waves

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**Multiple Removal with Local Plane Waves**Dmitri Lokshtanov**Content**• Motivation • WE multiple suppression operator • Fast 2D/3D WE approach for simple sea-floor • 2D/3D WE approach for irregular sea-floor • Conclusions**Motivation**• Seismic processing and imaging - main challenges: • Velocity model building for sub-salt and sub-basalt imaging • Removal of multiples from strong irregular boundaries**Near offset section**(no AGC)**Depth migration**with water velocity**Multiple suppression**• For multiples from complex boundaries the methods based on periodicity or kinematic discrimination usually don’t work or are not sufficient. • In such cases the main demultiple tools are based on the Surface Related Multiple Elimination (SRME) or Wave-Equation (WE) techniques.**SRME(Berkhout, 1982; Verschuur, 1991) – advantages and**limitations • Does not require any structural information. Predicts all free-surface multiples • As a rule becomes less efficient with increased level of interference of multiples of different orders • Requires the same dense sampling between sources as between receivers • Noise in data and poor sampling significantly degrade the prediction quality • Missing traces required by 3D SRME are reconstructed with least-square Fourier or Radon interpolation; residual NMO correction; DMO/inverse DMO; migration/demigration**WE approach versus SRME**• SRME is the method of preference for data from areas with deep sea-floor, especially when a thick package of strong reflectors is present below the sea-floor • WE approach is especially efficient when the main free-surface multiples are just ‘pure’ water-layer multiples and peg-legs. Gives usually better results than SRME when several orders of multiples are involved • 3D WE approach has less sampling problems than 3D SRME and it gives a flexiblility in methods for wavefield extrapolation depending on complexity of structure**The operator Pg transforms the primary reflection event**recorded at receiver 1 into the multiple event recorded at receiver 2 (Wiggins, 1988; Berryhill & Kim, 1986). The operator Pg transforms the primary reflection event recorded at receiver 1 into the multiple event recorded at receiver 2 (Wiggins, 1988; Berryhill & Kim, 1986).**Wave-equation approach – main features**• All predicted multiples are split into 3 terms, where each term requires the same amplitude correction • All source-side and receiver-side multiples of all orders are suppressed simultaneously in one consistent step • The prediction and the adaptive subtraction of multiples are performed in the same domain • Fast version (WEREM) for a simple sea-floor. Slower version for irregular sea-floor**Why in the tau-p domain**• Easier to apply antialiasing protection • No problems with muting of direct arrival • Easier to define ‘multiple’ zone of tau-p domain and mute it away • Estimated reflection coefficients are explicitly angle dependent**Constant P sections (angle at the surface is about 3º)**Input After Werem After Remul**Constant P sections (angle at the surface is about 15º)**Input After Werem After Remul**Constant P sections (angle at the surface is about 3º)** m. residual Input After Werem**T. Shetland** T. Draupne T. Brent Stack before multiple suppression Stack after Werem**Constant P sections (angle at the surface is about 10º**Input After Werem**Stack before multiple suppression (left) and after**Werem multiple suppression (right). The pink line shows the expected position of the first-order water-layer peg-leg from the Top Cretaceous (black line). The multiple period is about 140 msec.**Constant P sections (angle at the surface is about 8º**Input After Werem multiple suppression Difference**500 m input**WEREM**4000 m input**WEREM**Improving the results - local prediction / subtraction of**multiples • Within the same prediction term, for the same CMP and the same p we have events reflected at different positions along the water bottom • Inconsistency between prediction and subtraction in case of rapid variation of sea-floor reflectivity • The problem is partly solved by applying adaptive subtraction in different time windows • Or by making prediction dependent on both p and offset (window)**3D WEREM – basic features**• 3D data can be represented as a sum of plane waves with different vertical angles and azimuths from the source-side and receiver-side. • Current quasi 3D marine acquisition does not allow full 4D decomposition • Decomposition uniquely defines the direction of propagation from the receiver-side and is an integral over crossline slownesses from the source-side • The result of decomposition are used for exact prediction of multiples from the receiver-side and approximate prediction from the source-side • The approximation is that the crossline slowness from the source-side is the same as from the receiver-side (the same azimuth for 1D structures). The approximation allows us to mix data for flip flop shooting**Constant P section – after prediction / subtraction (small**angles)**Werem - conclusions**• Very efficient when the main assumptions are met: strongest multiples are water-layer multiples and peg-legs and the sea-floor is simple • Very fast - each predicted p trace is simply obtained as a sum of time-delayed input traces with the same p from the neighbour CMPs**WE for irregular sea-floor**• Kinematic prediction of multiples (extrapolation through the water layer) takes into account coupling between incident and reflected / scattered plane waves with different slownesses • Both multiple reflections and diffractions are predicted • The procedure starts from the Radon transformed CS gathers (no interleaving is required) • In 3D exact prediction from the receiver side; approximate prediction from the source side**2D prediction of multiples from the receiver side for**irregular sea-floor**2D prediction of multiples from the source side for**irregular sea-floor