Ray trace tomographic velocity analysis of surface seismic reflection data
<p>Recent development of two technologies allows application of a generalized formulation of travel time inversion to very large data sets, such as the surface reflection surveys collected for oil exploration. This generalized formulation uses very small cell sizes, effectively eliminating...
Summary: | <p>Recent development of two technologies allows application of a generalized
formulation of travel time inversion to very large data sets, such as the surface
reflection surveys collected for oil exploration. This generalized formulation uses
very small cell sizes, effectively eliminating discretization effects. Inversion of an
effective continuum that has no built-in a priori constraints is what places this
technique in the category of tomography.</p>
<p>In reflection surveys, the generalized formulation investigated here treats
the continuous velocity field independently from the reflector locations. The a
priori assumption, common with travel time inversions in seismic exploration data,
is thus not made: that the velocity field is defined as a series of layers with
constant or smoothly varying velocity. This assumption restricts significant
velocity variations to occur only at reflector locations. Velocity parameterized as
layers is merely one of many geologic constraints that can be added optionally in
tomographic inversion.</p>
<p>The technologies that enable this generalized approach to travel time
inversion are: 1) a computer program capable of tracing rays through a 2-
dimensional grid of points and off reflectors with structure, and 2) iterative
schemes that efficiently perform damped, constrained generalized matrix
inversions over a user-specified wide eigenvalue range for very large model and
data sizes. An argument is presented that a variation of Richardson's iteration is
preferred to the Conjugate Gradient Iterative Method for performing the matrix
inversion.</p>
<p>With this generalized formulation, Ray Trace Tomography is a first
approach to tomographic transmission analysis. Travel times and ray paths are a
valid approximation to the wave equation for broad velocity variations. The
method efficiently addresses the characteristics of more general but much more
expensive transmission techniques. For example, Ray Trace Tomography
demonstrates that an iterative application of a transmission velocity analysis
technique, tomography, and a scattering reflector location technique, migration, do
not necessarily converge to the optimal solution. To resolve the ambiguity between
velocity-reflector depth, velocity and reflector locations must be coupled in one
inversion technique. Ray Trace Tomography is able to couple the two. Using it to
indicate the absolute resolution between velocity and reflector depth, we find that
for certain geometries, reflector depths cannot be resolved where most recorded
energy travels within 45° of vertical.</p>
<p>Poor resolution of the velocity-reflector depth ambiguity and other
problems are inherent to reflection surveys. These problems also exist for other
transmission techniques and can be solved only through use of inversion
constraints. Ray Trace Tomography can test constraints for possible use in other
transmission techniques efficiently.</p>
<p>Ray Trace Tomography has difficulty with non-linearities caused by some
types of starting model errors, such as small-scale reflector structure. Improved
performance with non-linearities is an objective we should seek in other
transmission techniques.</p>
<p>Not only is Ray Trace Tomography a useful intellectual exercise as a
preliminary analysis of transmission inversion, but in many cases it is a viable
technique for addressing serious problems with surface seismic reflection data. It
can determine an accurate two-dimensional velocity field for migration, such as in
the case of gas pockets or fault blocks. In addition, it can resolve between certain
velocity and reflector ambiguities such as those occuring in the permafrost region
of Alaska.</p>
<p>As a comparatively efficient technique, Ray Trace Tomography can serve
as a tool for interactive interpretation. The geologist can use the ray tracing to
compare various geologic models with the data and then use the inversion to finetune
the models. The inversion enables the geologist to formulate his geologic
knowledge as constraints in the inversion. By analyzing the inversion results, the
interpreter will develop an understanding of the validity of the various models and
the resolution amoung them.</p> |
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