GG450 April 10, 2008
Refraction Procedures
Interpretation
SeisImager loaded on machines in 733:
We'll spend most of our class today in 733
to get you started on the refraction
reduction and analysis.
HOMEWORK due Tuesday - see last
lecture
We will use a modern program
for the analysis of our field lab
data – one that offers three
different methods of
interpretation of the data, and
which applies corrections for
elevation of the ground, and for
non-planar layers.
The models obtained by
inversion of the data are as
good as the data entered and
the as the decisions made
before processing. Noisy data
= noisy results. The following is
from the SeisImager Manual.
The methods of analysis of refraction data are
INVERSE modeling techniques - they use the
data you give the program to find the best-fitting
models possible within the constraints of the
software.
Again, while these models can be very good,
they are only MODELS, and they are not
necessarily correct. This becomes obvious when
you compare the results of the time term method
with those of the tomographic method. Both
methods, as presented in the software are 2-D.
They allow variations in depth and distance along
the profile.
Appendix B - The Time-term Method
The time-term technique is a linear Least-Squares
approach to determining the best descrete-layer solution
to the data. The math behind this technique is
comparatively simple. Referring to the figure below from
the SeisImager manual:
The SLOWNESS, or ray parameter, si=1/vi, is used to obtain
the travel time of a ray where layer boundaries are
horizontal:
t  2S1 cos(ic )z  xS2 , and letting
c = 2S1 cos(ic ), we get
t = 2cz + xS 2
We get t from the travel times and distance (x) from
 the data and we want to solve for z and S2.
The above example assumes that the refractor is
parallel to the ground surface. If we expand this to
the general case – non-parallel, curved surfaces,
as shown below – we end up with three unknowns
rather than two, e.g. z1, z2 and S2.
This geometry gives us: t=cz1+cz2+xS2 , and we can
n
form the linear set of equations:
t j   c jk zk  x j s2
k1
The time-term method then solves the eigenvalue
equation for s2 and zk, the slowness of the lower layer and
the depths to the interface at each geophone. We know all
the tj and xj values.
This (time-term) method ASSUMES that the velocities in
each layer are CONSTANT, and that the changes in travel
time are caused by changes in DEPTH of the interface.
While it is not a general model, it works well and yields
reasonable solutions.
The RECIPROCAL TRAVELTIME inversion method
(Appendix C) is more general and makes fewer
assumptions, but it requires more data (which we have)
and more work from the analyst. Because of the timeconsuming work involved, we won’t use this method.
The TOMOGRAPHIC METHOD (Appendix D) requires an
initial velocity model (such as you might get from the Time
Term Method). Rays are traced through a model made up
of many cells and the velocities in each cell are changed
to improve the fit until acceptably small errors in travel
time are achieved.
Tomographic Inversion can give detailed models of
excellent resolution if you have lots of data.
When working with the analysis of your data, try
the “RayTrace” option in SeisImager. This
option calculates the travel times for the resulting
model and calculates and plots the errors between
the model and the data.
Be sure to see the directions for SeisImager on the
web page, and the Lab directions for what I expect
for your lab report. You will also find the complete
SeisImager Manual in the Seisimager folder on the
computers.
Refraction Field Procedures
The preparation for yesterday's field work
was done for you for efficiency, but you
should know what was involved:
Before doing a survey:
• Motivation:
How deep are you looking? What is the
expected velocity contrast? What
resolution do you need? What will the
results be used for?
• Study the local geologic setting
Compile other data – well logs,
maps, local use history, etc.
• Test equipment. Many surveys
in remote areas fail or cost too
much because of faulty or
forgotten equipment. Test EARLY
- in time to make repairs.
• Plan survey parameters – line lengths,
directions, geophone spacing. Know the
analysis software, and plan the survey to
make it easy to import data.
• Obtain permissions, permits, inform
residents and owners
• Make a list of required equipment and
spares
Guidelines:
• shoot along and perpendicular to
any known strike.
• ALWAYS shoot reversed profiles and
orthogonal lines.
• make line lengths (shot point to far
geophone) at least 3-4 times target
depth.
• stay away from trees, traffic, wind.
• You need clean unambiguous data,
make it as clear as possible.
• bury the geophones if possible. Good
coupling to the ground is essential to get
good data, otherwise the sensor measures
its own motion, not the motion of the ground
• use hammer if target depth less than 50100’
use explosive source if the target is deeper
(requires permits and $)
• check data to be sure target is
obtained before leaving site
• check data to be sure surface
layer is well defined – shoot with
close-spaced geophones if
necessary.
Geophone placement
• In-line spread: most common, shot points on
same line as geophones (this is what we did)
• Offset spread: shot points several feet from
geophones. Requires some correction at closest
phones.
• In-line with center shot: same as in-line with
extra shot at center of spread (we did this also)
• Fan shooting: shots off-line looking for 2dimensional targets, like salt domes or caverns
CORRECTIONS TO DATA:
Our models so far have assumed that the
surface of the earth is flat (all shots and
geophone elevations the same), and that the
layers below are planar. This is not often the
case, and corrections often need to be made
for elevation and thickness of the low-velocity
surface layer. Most models assume that
layer velocities are constant – not changing
with depth inside the layer, or laterally.
Changes in depth of layers and changes in velocity ARE
OFTEN VISIBLE in the data. For example:
B
A
*
*
*
*
*
*
Dist anc e f rom shot
*
•What’s happening near point A? Point B? What might
explain the dip in the travel times near point A and the
increases in travel times near Point B?
*
The waviness of the travel time curve implies variations from
planar layers and/or lateral variations in velocity. The
dashed lines show the arrival times from the top figure.
Since arrival come in earlier than expected in region “A”,
either the velocity of the top layer must be greater than
normal OR the depth the top of the lower layer must be
shallower than elsewhere. In region “B”, the opposite is the
case.
v1
v2
v3
v1
v3
v1
The figure below shows seismograms from a single shot (not our data).
The blue highlighting shows the times of arrival of refractions. Light blue
shows surface waves. Note that in refraction seismology we are usually
interested only in the first arrivals.
0
200
Time (ms)
400
800
1000