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.