Windowing the Signals
In SAC you window signals using the cut command. This
command operates when the data are read in, so first you set
the cut limits, then you read in the signals, then you save
(write) the signals to keep the window. For regional
seismograms you can use the origin time to define one edge
of the window and a group velocity specification to define
the other. For example, if your data aren't too far away, a
group velocity of 1.0 to 1.5 km/s will usually be adequate
to capture the complete signal. You may want to keep more if
you are going to use a narrow-band filter (which has a long
time-domain response).
If you defined the event origin time in the SAC header
(as described above) you can use the header value "o" (the
letter o) to reference it in the cut command. To get the
other window, you can use the marktime command (again,
provided that the origin time is set). Or you can make the
calculation yourself, as shown in the macro below.
I recommend that you save the original
data before overwriting them as done in the following
macro.
do file wild *bhz
setbb base ( BEFORE "bhz" $file )
r %base%bhz %base%bhn %base%bhe
setbb c0 &1,o
evaluate to c1 &1,dist / vgmin + %c0
*
cut %c0 %c1
r %base%bhz %base%bhn %base%bhe
cut off
*
w over
enddo
Instrument Equalization
To model the signals you have to account for the effects
of instrument response (amplitude, group delay or phase)
which distorts the ground motion. You can either put the
response into your Green's functions or remove the response
from the observations. Usually with broadband data we remove
the instrument response from the seismograms. The SAC
command to do this is called "transfer" and it performs a
frequency domain deconvolution. Deconvolutions are often
unstable so it is often necessary to limit the bandwidth of
the resulting displacement seismogram using a
frequency-domain taper. Technically, if you apply the taper
to the displacements, you should include the same taper in
your synthetics, but as long as you stay away from the
regions where the taper is not unity, you can ignore it, or
at least most people do.
As with all digital processing it is a very good idea, if
not necessary, to remove the mean and taper the signals and
this is a convenient time to do that to our data so I'll
include it in the macro that does the instrument
equalization. For SAC, instrument response is summarized in
an ASCII "polezero" file that can be written out using
RDSEED, or is usually supplied with the seismograms. I
usually keep the names of each component in the polezero
file, for example, the polezero file for ccm.bhz is named
ccm.bhz.pz. I'll assume that is the convention in the
example macro to remove instrument responses. The first two
variables are the low-frequency corners for the frequency
taper (this is set up for a small eastern US earthquake
which does not have strong long-period signals). You should
try to keep as wide a bandwidth as possible so you may need
to experiment with these numbers. The high frequencies are
usually much less of a problem, so I set the taper values to
large values, which results in no high-frequency taper.
setbb c1 0.01
setbb c2 0.02
*
do file wild *bhz
setbb base ( BEFORE ".bhz" $file )
r %base%.bhz
rmean
taper w 0.1
trans from polezero subtype %base%.bhz.pz to none freq %c1 %c2 200 201
w %base%_dsp.z
*
r %base%.bhn
rmean
taper w 0.1
trans from polezero subtype %base%.bhn.pz to none freq %c1 %c2 200 201
w %base%_dsp.n
*
r %base%.bhe
rmean
taper w 0.1
trans from polezero subtype %base%.bhe.pz to none freq %c1 %c2 200 201
w %base%_dsp.e
*
enddo
The above macro assumes that you have three-component
observations for each vertical component and will halt
execution if it encounters a read error.
Rotating the Signals
Once you have the displacements you can convert the two
horizontal components into radial and transverse signals.
This might be a good place to generate a plot of the signals
too, so I'll include that in the macro.
do file wild *_dsp.z
setbb base ( BEFORE "_dsp.z" $file )
*
r %base%_dsp.n %base%_dsp.e
rotate
w %base%_dsp.r %base%_dsp.t
*
r %base%_dsp.r
ch kcmpnm Radial
wh
r %base%_dsp.t
ch kcmpnm Trnsvrs
wh
r %base%_dsp.z
ch kcmpnm Vertical
wh
*
r %base%_dsp.z %base%_dsp.r %base%_dsp.t
p1
*
pause
*
enddo
The macro pauses between stations so that you can inspect
the signals.
Marking the First Arrival Time
For the inversions I align the observed and synthetic
seismograms using the first arrival so the the last step in
the data preparation is to mark the first arrival time. For
regional data I often find it convenient to convolve the
signals with a short-period WWSSN seismometer response
before picking the time. This filters away the microseism
noise and generally cleans up the signal. Here's a macro to
help automate the procedure. In SAC you can pick times using
the PlotPK command and the "a" option. I pick the time on
the vertical seismogram and then copy the value into the
horizontals.
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