Dense multi offset reflection tomography

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					Dense multi-offset reflection tomography
John Brittan* and Jerry Yuan, PGS Marine Geophysical

Summary                                                          non-hyperbolic residual curves). In addition, Gray et al.
                                                                 (2001) note that the system of equations solved in most
In seismic reflection tomography, the velocity model of the      reflection tomography algorithms is simultaneously over-
subsurface is updated by back-projecting travel-time             determined and under-determined.
residuals along ray-paths. The travel-time residuals are
picked from the seismic data itself and the methodology          The fundamental under-determination is due to the
used to gather these picks is a fundamental part of any          velocity/depth ambiguity (which the pick parameterisation
velocity inversion workflow. In particular, the density at       will not address); whilst the fundamental over-
which the residuals are picked in the four-dimensional data      determination is a result of many cells of the velocity
space (inline, crossline, offset and depth/time) appears to      model being updated by many different ray paths. This
have a significant effect on the precision of the velocity       over-determination, in principle, is what leads to the
updates that are output from the tomographic inversion.          increase in precision of the velocity model determined from
Dense, single-offset picking samples the residuals in the        dense picks, however this effect will be dependent on the
data space very finely but does not necessarily represent        distribution of this density in the multi-dimensional space
their true values with great accuracy. Dense, multi-offset       in which the picks are parameterised. For example,
picking offers a similarly fine sampling but with greater        employing dense single-picks will increase the sampling in
adherence to the true residual value.           These two        the inline and crossline directions while leaving the offset
methodologies are compared and contrasted on a complex           direction well sampled (as the fitted curve will give a
synthetic dataset.                                               residual value at each offset) but relatively inaccurate. In
                                                                 contrast, employing sparse multi-offset picks will increase
                                                                 the accuracy of the sampling in the offset direction;
Introduction                                                     however the sampling in the inline and crossline directions
                                                                 will remain sparse.
 Reflection tomography is a global optimisation
methodology used in velocity model building for pre-stack        The effect of this different sampling was shown on a
depth migration (Stork, 1992; Kosloff et al., 1996). It          relatively simple synthetic dataset by Etgen (2004). By
commonly uses the residual depth from common-image-              comparing the inversion of a sparse set of multi-offset
gathers (CIG) as input data. Given an offset between a shot      picks with a dense set of single-offset picks over a common
and receiver pair, ray paths are generated from the              2-D model, it was shown that, even with severe
shot/receiver to an image point, and then velocities will be     regularization (smoothing) using the dense single picks
updated in an iterative manner along the ray paths until the     gave a better result than the sparse multi-offset picks. In
residual moveout is flattened.                                   other words, in this model, the over-determination in the
                                                                 CDP direction was more useful in recovering the true
One of the fundamental choices that must be made with a          velocity model than the over-determination in the offset
reflection tomography algorithm is how to pick the residual      direction. It is possible however, that for a different model
depths or times for each pre-stack gather. As discussed by       (e.g. containing a large but heterogeneous anomaly) that
Jones (2003), velocity model building techniques may             this situation may be reversed. Ideally, it would seem that
utilize picks from either migrated or un-migrated data and       utilising dense multi-offset picks (i.e. accurate over-
these picks may be on single offsets (e.g. stacks, near or far   determination in all spatial directions) should give the
offsets) or on multiple offsets within the gather. The           optimum result for all models. However, such picking is in
technique we have chosen to use in this paper is based on        general costly and difficult to QC. In this paper we
residual depth picks from common image gathers. Single           describe a methodology for undertaking such picking, and
offset picking methods (including those which fit a              the application of this methodology to a complex 2-D
hyperbola to the depth residual on each gather) offer a fast     synthetic dataset.
and robust method of supplying a dense set of picks to the
tomographic update. However, Jones (2003) suggested that:        Methodology
(i) dense picks only increase the precision of the velocity
model, not its accuracy (which is effectively determined by       In this study we have compared the results of a reflection
the shot and receiver sampling of seismic acquisition); (ii)     tomography algorithm using dense single offset picks and
single offset picks cannot resolve the same level of sub-        dense multi-offset picks on a common, complex 2-D
surface complexity as multi-offset picks (as the single          synthetic model. The model used was the BP synthetic
offset pick, or fitted hyperbola, cannot accurately represent    dataset supplied for the 2004 EAGE workshop on the
                                            Dense multi-offset reflection tomography

‘Estimation of accurate velocity macro-models in complex            generate ray paths from the picked depth residuals. In
structures’. This model included a number of small-scale            order to speed up the convergence, the tomography
velocity and density heterogeneities that provided a stern          algorithm is designed to simultaneously update velocities
test for any reflection tomography algorithm.                       and depths. In this software design, we use grid-based
                                                                    tomography; although horizons picked from the depth
                                                                    migrated common-offset sections serve as part of the input
                                                                    for ray tracing, the velocity and depth will be updated on a
                                                                    cell-by-cell basis. This allows for a robust and realistic
                                                                    tomographic inversion.

Figure 1: Using a 3-D visualisation system to quality control the
automatic RMO picks. The left-hand side shows the stack data,
the right-hand side shows selected gathers and the underlying
colour map is the picked residual moveout (blue indicates over-
moved out arrivals).

The dense, single-offset picking methodology used an                Figure 2: Using the 3-D visualisation system to pick dense, multi-
automatic residual move-out (RMO) scanning technique.               offset residual moveout. The green surface is a guide horizon used
In this technique, every sample on each common image                to aid the picking; the red spheres are the positions of manual picks
                                                                    and the yellow points represent the picks auto-picked by the
gather is scanned along a moveout equation defined by a
                                                                    visualisation system.
power exponent (e.g. 2 for a parabolic curve) and a number
of trial coefficients of fit. The coefficient that gives the
highest semblance is applied to data at the sample. Once            Data examples
the entire dataset has been scanned the residual moveout
volume can be analysed (Figure 1) and smoothed.                     Figure 3 shows example image gathers from the right-hand
                                                                    end of the example dataset. At this end of the dataset, the
The dense, multi-offset picking methodology utilises the            velocity anomalies within the model are small and laterally
capabilities of a high-end 3-D visualisation system. A              discontinuous, which makes a suitable test for a grid-based
horizon of interest is picked on the migrated and stacked           reflection tomography algorithm. The gathers in Figure
data volume, and the zero-offset depth of this horizon is           3(a) have been depth migrated using a starting model
used as a guide to pick the depth residuals on the pre-stack        derived from a pre-stack time migration of the data. It can
data. (This guide horizon is the green surface in Figure 2).        be seen that at all depths below 1km, the initial velocity
Pre-stack migrated data is loaded into the visualisation            model is incorrect and all events have some residual
system in the form of crossline/offset volumes and depth            moveout.       On many gathers in this dataset, below
residuals surfaces are chosen using a combination of                approximately 2km, the residual moveout becomes very
manual and automatic picks (Figure 2). The surfaces can             difficult to characterise accurately using a single parabolic
be analysed and smoothed interactively within the                   curve. A number of horizons were picked using the two
visualisation system.                                               methodologies described above and the resulting depth
                                                                    residuals were input into the reflection tomography
The picks from both methodologies were input into a                 algorithm. Figure 3(b) shows the same gathers migrated
common reflection tomography inversion algorithm. This              with the velocity field derived using the dense, multi-offset
algorithm uses a modified anisotropic ray tracing code to           depth residual picks. Figure 3(c) shows the same gathers
                                          Dense multi-offset reflection tomography

using the dense single-offset depth residual picks. It is
clear that the dense, single-offset pick result is close to the
multi-offset pick result, however, particularly at depth, the
flattening is inferior. It is also possible that, in a real
survey situation, the remaining move-out on the single-
offset pick gathers would be attributed to the presence of
anisotropy (the model used here was purely isotropic).

A comparison of the velocity models derived using the two
picking methodologies shows that only the dense, multi-
offset picking has the resolution to image the small,
laterally discontinuous velocity anomalies (Figure 4).
These results also appear to confirm the observation by
Etgen (2004) that the horizontal resolution of reflection
tomography is greater than the vertical resolution (the
anomalies have a true vertical extent of approximately

In this paper we present a methodology that utilises a 3-D
high-end visualisation system to provide dense, multi-offset
depth residual picks to a reflection tomography algorithm.
Comparisons on a complex 2-D synthetic model suggest
that possibly as a result of the over-determination in the
inversion using dense multi-offset picks, a more accurate
result is achieved than that using dense, single-offset depth
residual picks.


Etgen, J., 2004. What can migration velocity analysis
resolve? 66th EAGE Conference and exhibition – abstracts             (c)
for workshop on “Estimation of accurate velocity macro-
models in complex structures”.
Gray, S.H., Etgen, J., Dellinger, J. and Whitmore, D., 2001.
Seismic migration problems and solutions. Geophysics, 66,
Jones, I.F, 2003. A review of 3-D PreSDM model building
techniques. First Break, 21, 3, 45-58.
Kosloff, D., Sherwood, J., Koren, Z., MacHet, E. and
Falkovitz, Y., 1996, Velocity and interface depth
determination by tomography of depth migrated gathers.
Geophysics, 61, 1511-1523.
Stork, C., 1992, Reflection tomography in the postmigrated
domain. Geophysics, 57, 680-692.

                                                                  Figure 3: Gathers from the right-hand side of the esxample dataset
We would like to thank BP for providing the synthetic
                                                                  after depth migration with the (a) initial velocity model (b) velocity
dataset. The authors would also like to thank Joel Starr,         model derived from dense, multi-offset depth residual picks and (c)
Shelton Ma, Peter Wijnen, Trong Tang, Chris Taylor, Dave          velocity model derived from dense, single-offset depth residual
King, Sandy Carroll and Jostein Lima for their assistance         picks.
and PGS Marine Geophysical for permission to publish this
                                                 Dense multi-offset reflection tomography


                                                  (b)                                                                 1km

                                                  (c)                                                                  1km

Figure 4: A comparison of the velocity model derived using tomographic inversion of the synthetic dataset using (a) dense, multi-offset depth residuals; (b)
dense, single-offset depth redsiduals and (c) the difference between the two models. Note the compressed velocity scale on the difference plot and that
only a small sub-section of each model is shown. The white arrows on (a) indicate the location of small low velocity anomalies in the subsurface. These
anomalies of are limited lateral (<1000m) and vertical (100-200m) extent. It is clear that only the velocity model derived using dense, multi-offset depth
residuals is able to resolve these features adequately, although the result is constrained by the inherent limit on the vertical resolution of seismic reflection

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