Attenuation of multiples in image space |

In complex subsurface areas, attenuation of specular and diffracted multiples in image space (after migration) is an attractive alternative to the industry standard processes of Surface Related Multiple Elimination (SRME) and data space Radon demultiple. There are several reasons: (1) migration increases the signal-to-noise ratio of the data; (2) migration guarantees that the primaries are mapped to coherent events in either Subsurface Offset Domain Common Image Gathers (SODCIGs) or Angle Domain Common Image Gathers (ADCIGs); (3) unlike data space, image space is by construction regular and usually much smaller; (4) the moveout of the multiples in image space is more predictable than in data space for complex geology; (5) attenuating the multiples in data space may leave ``holes'' in the frequency-wavenumber space that generate artifacts and amplitude problems after migration.

In this thesis I exploit the power of prestack wave-equation migration to handle complex wave propagation. I design a robust and efficient method to attenuate the multiples in image space via a Radon transform of ADCIGs.

I demonstrate that specular multiples migrate as primaries and develop the equations for their residual moveout in both SODCIGs and ADCIGs for canonical models. In particular, I develop a new equation for the residual moveout of multiples in ADCIGs that accounts for ray bending at the multiple-generating interface. The new equation improves the accuracy of the tangent-squared approximation for the residual moveout of primaries migrated with the wrong velocity \cite{Biondi04}. The tangent-squared equation is shown to be appropriate for multiples only at small aperture angles. A Radon transform whose kernel is the new equation better focuses the multiples and helps separate them from the primaries. This in turn improves the attenuation of the multiples. Unlike specular multiples, diffracted multiples do not migrate as primaries. That is, they do not map to zero subsurface offset in SODCIGs nor to flat events in ADCIGs even if migrated with their correct velocities. Furthermore, I show that the apex of their residual moveout in ADCIGs is shifted from zero aperture angle similar to their behavior in common midpoint gathers. I design an apex-shifted Radon transform that, for 2D data, maps the 2D ADCIGs to a 3D cube of dimensions depth, curvature and apex-shift distance. I show, with a real 2D dataset from the Gulf of Mexico, that Radon filtering with the apex-shifted transform is effective in attenuating both specular and diffracted multiples.

Estimating a multiple model is the first part of the multiple attenuation process, but it is not the only critical step. In order to estimate the primaries we need to subtract the estimated multiples from the data. Because of amplitude, phase and kinematic errors in the multiple estimate, straight subtraction is inaccurate and some form of adaptive subtraction is often needed. I propose to pose the adaptive matching and subtraction of the multiple model from the data as an iterative least-squares problem that simultaneously matches the estimates of both primaries and multiples to the data. Once converge is achieved, the primary and multiple estimates are updated and the inversion is run again. Standard methods match only the estimate of the multiples. The simultaneous matching of the primaries and the multiples has the advantage of reducing the crosstalk between the matched estimates of the primaries and the matched estimate of the multiples. I demonstrate the method with real and synthetic data and show that it produces better results than the standard multiples-only adaptive subtraction. I also show that the method can be used to tackle similar problems where estimates of signal and noise need to be matched to data containing both, and illustrate it by attenuating spatially-aliased ground-roll from a land shot gather.

In 3D, the multiples exhibit residual moveout in SODCIGs in both the inline and crossline offset directions. They map away from zero subsurface offset when migrated with the faster velocity of the primaries. The ADCIGs are function not only of the aperture angle but also of the reflector azimuth. I show, with a simple 3D synthetic dataset, that the residual moveout of the primaries as a function of the aperture angle is flat for those angles that illuminate the reflector at that reflection azimuth, but appear to have curvature for those reflection azimuth planes that do not illuminate the reflector. The multiples, on the other hand, have residual moveout towards increasing depth for increasing aperture angles at all azimuths. Likewise, as a function of azimuth, and for a given aperture angle, the primaries show good azimuth resolution for large aperture angles that illuminate the reflector. At zero aperture angle there is no azimuth resolution. For the multiples from a reflector with crossline dip there is no azimuth resolution at any aperture angle because, even in constant velocity, the propagation is not on one plane.

I show, with a real 3D dataset from the Gulf of Mexico, that even below salt, where illumination is poor, and where the requirements of 3D-SRME are less likely to be met, there is enough residual moveout in ADCIGs to discriminate and attenuate the multiples with a direct application of the new 2D Radon transform in planes of azimuth-stacked ADCIGs.

- Chapter 1: Introduction [pdf 364K]
- Chapter 2: Image space mapping and attenuation of 2D specular and diffracted multiples [pdf 364K]
- Chapter 3: Simultaneous adaptive matching of primaries and multiples [pdf 364K]
- Chapter 4: Mapping of 3D multiples to image space: Theory and synthetic data example [pdf 364K]
- Chapter 5: Imaging and mapping 3D multiples to image gathers: Example with a Gulf of Mexico dataset [pdf 364K]
- Chapter 6: Conclusions [pdf 364K]
- Appendicies [pdf 364K]

2007-10-24