Theoretical Seismogram Calculation
Explanation of input parameters for ERZSOL3
ZST format for seismograms and travel times
The calculations use a velocity and attenuation model
in the following form:
- all velocities are in kilometres/second
depths or thicknesses in kilometres
densities in Mg/metre cubed
Model file : ew1.mod
ew1 Model name
4 0 # layers, ndt
3 5.000 2.600 2.70 1.000 0.001 0.002
3 5.000 2.600 2.70 6.000 0.001 0.002
3 5.500 2.700 2.75 5.000 0.001 0.002
3 6.000 2.800 2.80 5.000 0.001 0.002
nr alpha beta rho thick 1/Qa 1/Qb
[P km/s] [S km/s] [Mg/m3] [km]
The index nr controls the number of reverberations in the layer
nr = 0 - no reflection from top of layer = 1 - no internal multiples in layer >= 3 - all internal multiples in layer
(nr > 3 marks reflection boundaries for ray tracing routines)
(nr =2 gives a partial set of internal multiples and is not generally
useful)
The control parameter ndt determines whether the model is specified in terms of the thickness of layers or the depth of boundaries.
ndt = 0 - thickness ndt = 1 - depth
All the internal calculations are carried out in memory for a single seismic component at a time: In the Fortran program erzsol3 - the complex arrays RU(5,2500,600), RV(5,2500,600), RW(5,2500,600) are dimensioned to allow: 600 active frequencies and 2500 slownesses and include the azimuthal components assoaiated with a moment tensor point source.
A seismogram at a particular distance is produced by
a) an integration over slowness at each frequency with a distance
specific slowness factor
b) a Fast Fourier transform over frequency
The restriction on the number of slownesses in a single run to 2500 means that an integration over the full slowness range relevant to all possible arrivals may often be best carried out using 2-4 separate slowness integrations and then summing the seismogram traces at the same distance to produce the final theoretical seismogram. This procedure also allows the sampling in slowness to be reduced for larger slowness and so improve the accuracy of the integration.
The theoretical seismogram program erzs is used with a control file which specifies the model file to be used and the parameters for ray parameters and frequencies and multiples to be used in the calculation erzs < ers.p1.cmd
"ERZSOL3-ew1 " Title "ew1.tx.z" File for T-X seismogram output "ew1.mod" Velocity model file "HS" Surface Condition (HS,H1,WF,WS) 1200 Number of slownesses (<2500) 0.0001 Minimum slowness 0.7001 Maximum slowness 10 Slowness taper plo (n samples) 10 Slowness taper phi (n samples) "WA" Wavelet input or Ricker (WA/RI) "ew.wav" Wavelet file "YE" Exponential damping? (YE/NO) 2048 Number of time points 0.01 Time step 0.01 0.10 Frequency taper (low) 10.0 20.0 Frequency taper (high) 2.0 Dominant frequency [RI] 1.00 0.50 0.00 Moment tensor Components 0.50 0.00 0.00 0.00 0.00 -1.00 3.0 Depth of source "ew.dst" Range and azimuth file 0.0 Reduction slowness 0.000 Start time (reduced) "NO" Debug/frequency-wavenumber (YE/NO) "NO" Debug/waveform (YE/NO)
Note all dimensions are in kilometres and times in seconds
1) Title for Run
Character string to be used as header for run
2) File for T-X seismogram output
Character string for name of file to receive T-X seismogram
output in zst format
3) Velocity model file:
Character string for name of file with model specification
the model file should be in the standard model file format
(ndt = 0 for layer thickness specification)
4) Surface Condition:
The various boundary conditons to be applied at the surface are
specified by mnemonics
A full calculation for a half space with
elastic free surface conditions "HS"
Calculation for a half space with only
first order surface reflections included "H1"
Calculation for a non-reflecting surface
but with displacement corrected for
free surface amplification "WF"
Calculation for a non-reflecting surface "WS"
5) Number of slownesses (<2500)
Integer specifying the number of slownesses to be used.
The slowness interval is divided into equal intervals to
enable the integration over slowness to be performed
Too coarse a slowness choice will give rise to inadequate
sampling which usually gives oscillations in the seismograms
at the highest frequency used.
6) Minimum slowness
Lower edge of slowness band in s/km
7) Maximum slowness
Upper edge of slowness band in s/km
The theoretical seismograms for a single slowness panel will normally
display numerical arrivals with the slownesses of the upper and lower
limits of the window. These can often be of significant amplitude.
However, the adjacent panels will have comparable arrivals of opposite
sign and on summation over the slowness panels the cancellation is
very successful.
For land reflection work slowness bands of
0.0001 - 0.30
0.30 - 0.45
0.45 - 0.60
0.60 - 0.75
will generally be sufficient to cover all arrivals
8) Slowness taper plo (n samples)
Integer specifying the number of samples at the lower end of the
slowness window over which the response is linearly tapered to
zero
9) Slowness taper phi (n samples)
Integer specifying the number of samples at the upper end of the
slowness window over which the response is linearly tapered to
zero
If a several slowness panels are be added together then the number of
samples should be set to zero - this will ensure the cancellation
of numerical arrivals which have opposite sign on adjacent panels
10) Choice of source wavelet
Specified time points - "WA"
Ricker wavelet - "RI"
11) File for wavelet input
Character string for name of file for source wavelet input
(needs to be specified even when "RI" option used)
12) Exponential damping
Specification of exponential damping in time in construction
of seismograms ("YE" or "NO")
If "YE" is specified the calculations are carried out in the
complex frequency domain with an effective exponential damping
applied in time. This improves the situation with aliasing in time
and so shorter total time intervals can often be employed.
However weak spatially aliased arrivals late in the record are
magnified dramatically when exponential gain is applied to recover
the true time response. As a result when exponential gain is used
only the first 3/4 of the time interval has gain recovery applied,
the remaining 1/4 should not be regarded as useful.
If "NO" is specified then the calculations are all performed
for real frequency and care needs to be taken to have the time
interval of calculation long enough to avoid aliasing in time.
13) Number of time points
Integer power of 2 e.g. 2048, specifying the total number of
time points in the theoretical seismograms
14) Time step
Sampling interval in time in seconds i.e. 4 ms sampling is
specified as 0.004
15) Frequency taper (low)
A cosine taper in frequency is applied between the two
specified frequencies e.g. for
0.01 0.10
Zero response is specified for frequencies less than 5 Hz and
unit response for frequencies higher than 7 Hz with a cosine
taper between.
16) Frequency taper (high)
A cosine taper in frequency is applied between the two
specified frequencies e.g. for
10.0 20.0
Unit response is specified for frequencies less than 57 Hz and
zero response for frequencies higher than 7 Hz with a cosine
taper between.
Care should be taken that the number of discrete frequencies in the
pass band of the band-pass filter does not exceed 600 - or array
bound violations will occur with unpredictable results
17) Dominant Frequency for Ricker wavelet ["RI"]
values of dominant ferequency to be used is "RI" wavelet selected
(must be given even when "WA" option used)
18) Components of point moment tensor [x=N, y=E, z=D] in order
Mxx, Mxy, Mxz
Myx, Myy, Myz
Mzx, Mzy, Mzz
For an explosive pressure source specify
MXX=MYY=MZZ= 1.0 , all others zero
19) Depth of source
The depth of the source below the surface in km
Note the program is built around a model of a point source
(an array can be simulated in part by weighting dipole sources
or by summing the response from different sources)
20) File for ranges and azimuths
Character string for name of range and azimuth file
22) Reduction slowness
Value in s/km for the slowness to be used to adjust the time axis
to follow spcific arrivals. Valuable for refraction calculations
but for reflection work set equal to 0.0
22) Start time (reduced)
The beginning of the theoretical seismograms allowing for the
reduction slowness.
Use 0.00 to have the theoretical seismograms starting at the
source instant.
23) Debug/frequency-wavenumber ("YE" or "NO")
24) Debug/waveform ("YE" or "NO")
Setting either of these parameters to "YE" generates copious output
and should not be necessary in normal use
Example of Wavelet file "ew.wav"
Integer number of time points in specification of source waveform
followed by discrete waveform values , e.g.,
3 # of points in waveform /waveform
100.0 0.00 0.00
A complex time signature can be introduced here if desired but
it is just as easy to use a delta function source and then
convolve later with an appropriate source-time function
Example of range and azimuth file "ew.dst"
Integer number of distances
followed by distances in km, azimuth in degrees
10 # of distances /distances
2.00 45.00
4.00 45.00
6.00 45.00
8.00 45.00
10.00 45.00
12.00 45.00
14.00 45.00
16.00 45.00
18.00 45.00
20.00 45.00
22.00 45.00
For seismograms:
nrange - number of distances
ncomp - number of components for each distance
...for each component: (nrange*ncomp records)
range - distance in km
azim - azimuth (degrees)
ichar - component identifier (char*4)
delt - time sampling interval
ntim - number of time points
pcal - reduction slowness for calculation
tcal - start time of calculation (absolute)
smax - maximum value of seismogram
(seis(k),k=1,ntim) - time series
...end component loop
COMMAND FILES:
The command files have a fixed syntax:
commands are read with a2
file names are read with a30
titles, labels with a72
numbers are read free formatted
for each instruction a brief explanation is given
in columns 41-80 for commands,numbers
in columns 72-80 for titles etc