Geology Reference
In-Depth Information
Ground
surface
Fig. 5.23
Idealized observation scheme
for a simple cross-hole seismic
transmission tomography survey. Dots
mark receivers, stars mark sources. For
clarity, only the ray paths from one source
to all receivers (solid lines), and all sources
to one receiver (dashed lines) are shown.
Also shown is the regular grid of elements
for which velocity values are derived.
perimeter of the volume. In the geological case the diffi-
culty lies in getting access to place sources and receivers
at locations distributed uniformly around the volume
under investigation. Multiple vertical boreholes merely
allow the collection of a number of vertical 2D sections
as shown in Fig. 5.23.
The total travel-times for each ray are the basic data
used for interpretation. Each cubic element is assigned
an initial seismic velocity. Assuming a linear ray path
from source and receiver, the time spent by each ray in
each element can be calculated.The velocity assigned to
each individual element can then be adjusted so that the
errors between the observed travel-times and the calcu-
lated ones are minimized. A more sophisticated ap-
proach is to include in the solution the effect of
refraction of the seismic wave as it passes between vol-
ume elements of different velocity. Such a solution has
more variable parameters and requires a dense pattern of
intersecting ray paths within the irradiated section. Note
that the calculation of the true ray path is very difficult. It
cannot be found by applying Snell's Law at the element
boundaries, since these boundaries have no physical
reality. Common methods of solution of the resulting
equations are the
algebraic reconstruction technique
(ART)
and the
simultaneous reconstruction technique
(SIRT). The
details of these techniques are beyond the scope of this
topic, but are well described by Ivansson (1986).
Use of high-frequency sources permits accurate
travel-time determination and consequent high-resolu-
tion imaging of the velocity structure. This is necessary
since a change in velocity in any one element only has a
very small effect on the total travel-time for the ray path.
Less commonly, parameters other than the P-wave trav-
el-times can be analysed. Particular examples would be
the S-wave travel-times, and the attenuation of the seis-
mic wave. The above discussion has only considered
transmission tomography, where the ray path is the sim-
ple minimum travel-time path from source to receiver.
With additional complications, the same basic approach
can be used with more complex ray paths. Reflection
tomography involves the application of tomographic
principles to reflected seismic waves. While it is con-
siderably more complex than conventional seismic
reflection processing, in areas of complex structure, par-
