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Jeremy J. Zimmerman1
Search and Discovery Article #40023 (2001)
1Nuevo Energy Company, Houston, TX ([email protected]).
*Adapted for online presentation from article entitled “It’s All a Matter of Space and Time” by the same author in Geophysical Corner, AAPG Explorer, December, 1996. Appreciation is expressed to the author and to M. Ray Thomasson, former Chairman of the AAPG Geophysical Integration Committee, and Larry Nation, AAPG Communications Director, for their support of this online version.
Most geoscientists in
the petroleum industry are dealing with the problem that seismic
information is
usually displayed in some form of a time section, be it a time stack section or
a time-migrated section. Drillers, engineers, geologists, geophysicists, and
earth scientists in general describe the earth in depth, as in “x” number of
feet to target, “x” number of feet of oil column, etc. How do you get easily
from time to depth? The answer depends on the desired level of complexity, which
is usually dictated by how soon something is needed or how much it will cost.
The overall process is
called depth conversion, although some prefer to be more rigorous and call it
depth migration. The simplest definition of depth conversion is the conversion
of some measurable time quantity into some understandable value in depth. The
old joke of when someone asks how deep is the well and the junior geoscientist
responds that “it’s about three seconds ...” pops into many people’s
minds when dealing with representations of well progress with respect to a
chosen seismic
section. So just how do we convert from time to depth?
The purpose of this article is to introduce geoscientists to some basic ideas about depth conversion as well as give examples of when it is appropriate to use a given method. It is not meant to be a rigorous dissertation of depth migration.
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Click here for sequence of Figures 3 and 7.
Click here for sequence of Figures 4 and 5.
Click here for sequence of Figures 4 and 5.
Click here for sequence of Figures 3 and 7. The
raypath concept is the keystone to Most
A
Typically,
rays are easily influenced by the medium in which they travel. The
characteristic that is of greatest concern to the geoscientist is the
velocity of the different layers through which the rays travel. When
The first type of section (and most often ignored by much of the petroleum industry) is the time stack section. It is seen as confusing because it contains segments of events, events that exaggerate the size of structures and even events that cross each other (the ubiquitous “bow-tie” structure). The time stack image of the depth model (Figure 3) is shown in Figure 4. Note that the flat portion of the model remains flat, but the dipping events are much more complex. The second type of section (and the one most often used by the petroleum industry) is the time migrated section. It is seen as less confusing and more of a realistic depiction of the subsurface. To many geoscientists, this represents a realistic cross-section and therefore can be used to infer structural and tectonic features and stress regime. Many of the models regarding interaction between salt and sediment in the Gulf of Mexico are based on these time migrated sections. As shown in Figure 5, this image is still distorted in comparison to the actual model that produced it. Upon
seeing a time-migrated section, one is apt to describe geologic processes
that have produced such a structure. However, the problem remains that the
section is shown with respect to time. When dealing with flat or slightly
dipping events (less than 10o), a simple depth conversion using
the straight vertical ray assumption can be used. This is done by taking
the vertical time difference between events on a time-migrated If
dips on events exceed 10o and the velocity field is
“well-behaved,” then depth conversion becomes a little more
complicated. The idea that vertical travel times taken from even a
time-migrated section can be used to calculate a depth section using an
interval-velocity value (be it local, regional, constant, or varying) can
lead a geoscientist down the primrose path to a dry hole. What often
happens is an interval velocity map is created for selected horizons at
sample points taken from wells. This interval-velocity map is then
multiplied by the isochron map made on the time differences between the
two selected horizons, and a depth map that matches at the well is created
by this “depth-stretch” method. Of course, this depth map agrees with
the information at the wells; it was derived using that information. The
fallacy of this method is the assumption that the raypath generated by the
If the subsurface reflectors exhibit no dip, then this is a valid assumption. Otherwise, the endpoint at depth for the vertical raypath and the actual raypath for the time-migrated sections differ (Figure 6). The greater the dip, the greater the offset between these two endpoints. What this means is that the lateral placement of the events is wrong, commonly leading to misplaced highs or unplanned lows. An example of errors inherent in using the “depth-stretch” method is shown in Figure 7. The time-migrated section generated previously (Figure 5) was depth-converted using the vertical-ray assumption and the interval velocities in the original model that was used to generate the time-migrated section. Comparison of it to the original depth model in Figure 3 shows lateral errors in placement or reflections on the right side of the small mound. This error is also carried through the deeper horizons on the section, due to bending of the raypath at the interface above. Even though the velocities are gently increasing with each horizon, the dip on the second and the third horizon is such that the resulting reflection is moved horizontally. Snell’s law tells us that small changes in dip and velocity can cause the raypath to refract. To best compensate for this change in raypath direction, depth migration is usually applied. The term “depth migration” is different from “depth conversion” in that the lateral movement of the endpoint of a raypath is taken into account. The best situation is when both the interval velocity model and the depth conversion (read depth migration) takes the refracted raypath into account. The
example shown here is only in two dimensions. A method for creating depth
models based on ray displacements in three dimensions is called map
migration. The usual input into map migration is an interpreter’s time
map created from a series of 2-D time-migrated Many map migration algorithms take the above into account when inverse raytracing the data into the depth domain and calculating a raypath based on the relationship between the time-migrated ray and the depth-migrated ray. Although not rigorous in execution, this type of result is better than a vertical “depth-stretch” based solely on a time-migrated section and interval velocities. Depth migration is not a panacea. Limitations in algorithms, computer power, or the failure of the raypath assumption all contribute to lessening one’s ability to get the perfect solution to imaging problems. Moreover, although the mathematics of depth migration has been around since the turn-of-the-century, the concept and practice are still in their infancy. The hope here is that they will grow slowly, and will find many fans and supporters. Software packages for depth migration are currently available for use on high-end desktop workstations. |