Reflectivity Modelling - B.L.N. Kennett

SNERTMAN

Theoretical Seismogram Calculations Using Systematic Approximations to the Seismic Wavefield

Written by: B.L.N. Kennett
R.S.E.S., Australian National University
Canberra, ACT, Australia
July 1985
e-mail: brian@bullen.anu.edu.au

Updated by: A.R. Gorman
Department of Earth and Ocean Sciences, University of British Columbia
Vancouver, BC, Canada
May 1997
Now at: Department of Geology
University of Otago, Dunedin, New Zealand
e-mail: andrew.gorman@stonebow.otago.ac.nz


This hypertext document has been prepared by Andrew Gorman from the original notes of Brian Kennett. Modifications have been made to update the documents and make them more complete.

[For users at UBC: This program is presently compiled on the following directory:
/seis/shire/modelling_1-D/kennett/src/snertc/]


CONTENTS

SNERTC
Program Description
Input Control File (example file)
Input Velocity Model (example file)
Example of Output File
Seismogram Output
Other Notes on the Program
Numerical Integration of Response
Implementation
Plotting of Synthetic Seismograms

SNERTC

Program Description

A set of routines for the calculation of theoretical seismograms for a general point source specified by an arbitrary moment tensor.

The model consists of a set of uniform layers, with the propagation split at a specified level. The depth at which this level is specified will depend on the scale of observation. For example, in mantle or whole-earth studies, the entire crust is considered a zone of low velocities so the separation level would be specified as the Moho. This routine then separates wave propagation effects in the shallow region from those in the deeper region.

The calculation scheme is based on the treatment of split stratification in
Kennett, B.L.N., Seismic Wave Propagation, Chapter 9 in Stratified Media by B.L.N. Kennett, Cambridge University Press (1983)
and amplified in
Kennett, B.L.N., Systematic Approximations to the Seismic Wave Field, Chapter III.1 in Seismological Algorithms, ed. D.J. Doornbos, Academic Press (1988).

The calculation makes use of reflection and transmission matrices calculated for uniform layer models.

The program is designed to run in three linked stages:
1) Construction of response in Transform domain using routines:
MAIN program - input/output
RESPON - construction of reponse from reflection and transmission matrices
MOMTEN - source terms for given moment tensor
SRFACE - reflection coefficients between interfaces
SRTDN - reflection and transmission matrices for downward travelling waves
SRYFUP - reflection and transmission matrices for upward travelling waves
2) reorganisation of transform terms
3) Integration both accomplished in subroutine:
SINT - which also calls the Bessel function routine BESHS0 to supply the asymptotic forms required.
Logical Units:
Input of the velocity model is from lu 4. (The name of this file is defined in the input of the control parameters.)
Input of the control parameters for the run is from lu 5.
Output of monitor information is to lu 6.
The time series of seismograms are sent to lu 11. (The name of this output file is defined in the input of the control parameters.)

INPUT CONTROL FILE (Logical Unit 5)

Input to the program to control the approximations to the wavefield. The positions of recording stations and parameters controling the numerical integration are made from a command file on unit 5, with entries in the following form:

1.GENERAL INFORMATION [FORMAT(20A4)]
A) TITLE OF RUN
B) NAME OF INPUT VELOCITY FILE (Logical Unit 4)
C) NAME OF OUTPUT SEISMOGRAM TIME SERIES FILE (Logical Unit 11)

2. CHOICE OF RESPONSE PARAMETERS ALIASES
A)+++ Choice of far-field waveform
        NWA     =  0     WAVEFORM READ IN                     ISW(4)
                =  1     TRAPEZOIDAL WAVEFORM CONSTRUCTED
B)+++ Choice of phases at source and receiver
        NRS     =  0      FULL RESPONSE                       ISW(5)
                = 10      P and S at source, P at receiver
                = 11      P at source, P at receiver
                = 12      S at source, P at receiver
                = 20      P and S at source, S at receiver
                = 21      P at source, S at receiver
                = 22      S at source, S at receiver
+++ Control of response in upper zone
        NFS     =  0      FULL RESPONSE                       ISW(6)
                =  1      ONLY FIRST ORDER FREE-SURFACE
                          REFLECTIONS
                =  2      NON-REFLECTING SURFACE BUT
                          DISPLACEMENT AS AT FREE SURFACE
                =  3      NON-REFLECTING SURFACE
+++ Control of response for overall structure
        NFZ     =  0      FULL RESPONSE                       ISW(7)
                =  1      ONLY SINGLE SURFACE REFLECTIONS
                              FOR DEEP ENERGY
                =  2      NO SURFACE REFLECTIONS
C)+++ Debug output
        NWF     =  0      NO FREQUENCY/DEBUG OUTPUT           ISW(8)
                =  1      FREQUENCY/DEBUG OUTPUT

                                             ISW(9) - ISW(15)   FREE

3. TIMING - Control of record length and time increment
         NT - TOTAL NUMBER OF TIME POINTS IN SERIES
         NTI - INDEX (NT = 2**NTI)
         DELT - TIME STEP IN TIME SERIES
4. Definition of source level and separation level for splitting response

A) SOURCE DEPTH
         HSS - DEPTH OF SOURCE (in km)
A fictitious interface is needed at the source depth during model specification

B) SEPARATION DEPTH
         HJZ - DEPTH OF SEPARATION LEVEL (in km)
A fictitious interface is needed at the separation depth during model specification

5. Definition of point source components

MOMENT TENSOR COMPONENTS OF SOURCE ON THREE CARDS IN ORDER:
          MXX, MXY, MXZ
          MYX, MYY, MYZ
          MZX, MZY, MZZ
6. Establish far-field waveform and filtering

A (option 1) If NWA [ISW(4)] si equal to 0 - read in wave form
        NDT     -      NUMBER OF POINTS IN WAVEFORM           ISW(2)

        F(k)    -      WAVEFORM TIME SERIES (NDT POINTS)

Values entered are complex i.e. treat as 4(F10.5,10X)

A (option 2) If NWA [ISW(4)] is equal to 1 - construct trapezoidal waveform

FARFIELD SOURCE TIME FUNCTION
         T1 - RISE TIME OF TRAPEZOID
         T2 - DURATION OF CONSTANT PORTION
         T3 - FALL TIME OF TRAPEZOID

In both cases

B) FREQUENCY WINDOW
         FLO - LOWER LIMIT OF FREQUENCY WINDOW
         F1  - LOWER CORNER POINT
         F2  - UPPER CORNER POINT
         FUP - UPPER LIMIT OF FREQUENCY WINDOW
A zero phase filter is applied to the waveform with a cosine taper up from FLO to F1 and a cosine taper down from F2 to FUP

7. Distance and slowness specification

A) STATION LOCATIONS
         NPX     - NUMBER OF STATIONS                     ISW(3)
         XS(1)   - FIRST STATION POSTION (km from source)
         xsincr  - INCREMENT BETWEEN STATION LOCATIONS (km)
B) SLOWNESS WINDOW
         NRP  - NUMBER OF RAY PARAMETERS CONSIDERED
         PMN  - MINIMUM SLOWNESS
         PMX  - MAXIMUM SLOWNESS
         NCUT - I have no idea what the hell this is for, 
	        but it would be great to know!
C) DISPLAY PARAMETERS
         PR    - REDUCTION SLOWNESS
         STMIN - STARTING REDUCED TIME
D) PROFILE PARAMETERS
         AZ    - AZIMUTH OF PROFILE
         TSTAR - ATTENUATION FACTOR

Example of an Input Control File

An example of a command file for upper mantle calculations would be:
  ecr - test                             Title
  vel.mod				 Input Velocity Model Name
  synth.t				 Output Time Series Name
   0                                     Control of waveform input: NWA
  10   1   2                             Response control: NRS, NFS, NFZ
   0                                     Display control: NWF
      1024        10      0.04           No of time pts, index, increment
         15.0                            Depth of source
         50.000                          Depth of separation level
    -0.95     -0.19    -0.17             Moment tensor: Mxx,Mxy,Mxz
    -0.19      0.95     -0.13                           Myx,Myy,Myz
     -0.17     -0.13    0.00                            Mzx,Mzy,Mzz
     3                                    no of pts, waveform
 (100.0,0.0)  (0.0,0.0)  (0.0,0.0)
  0.05       0.10      2.0       3.0     Frequency Filter FLO,F1,F2,FUP
    23                                    no of stations,ranges
 1800.0     1850.0    1900.0    1950.0
 2000.0     2050.0    2100.0    2150.0
 2200.0     2250.0    2300.0    2350.0
 2400.0     2450.0    2500.0    2550.0
 2600.0     2650.0    2700.0    2750.0
 2800.0     2850.0    2900.0
      300    0.078    0.12               NRP, Pmin, Pmax
    0.10     40.0                        Pred, Stmin
   25.0       0.00                       Azimuth, Tstar

Input of Velocity Model

Specification of velocity model is via parameters defined at the base of each uniform layer

The input file has the following structure and is input through Input Unit 4

TITLE OF VELOCITY MODEL
NL - NUMBER OF LAYERS ISW(1)
FOR EACH LAYER A CARD IS REQUIRED WITH -
NR - RAY INDEX
ALF - P WAVE VELOCITY
BET - S WAVE VELOCITY
RHO - DENSITY
ZD - DEPTH AT BASE OF LAYER
QAI - 1.0/QA (ATTENUATION FOR P)
QBI - 1.0/QB (ATTENUATION FOR S)

Notes:
IF QAI and/or QBI ARE LEFT UNSET THE MEDIUM IS TREATED AS PERFECTLY ELASTIC (THIS IS UNWISE, UNLESS A NONZERO TSTAR IS USED)

NR = 0 TRANSMISSION THROUGH LAYER
= 1 PRIMARY REFLECTIONS IN LAYER
= 2 PRIMARY + FIRST MULTIPLES IN LAYER
= 3 ALL POSSIBLE REFLECTIONS IN LAYER

The program is designed to compute the reflection properties of an inhomogeneous region bordered by uniform half spaces with continuity at the limits of the region.

To achieve this, the stack of layers of interest should be overlain by a uniform layer with the surface properties, but with depth zero.

At the source level a fictitious interface must be introduced. Similarly at the separation depth


Example Input Velocity Model

The velocity model used with the command file above was:

 TEST MODEL (Upper Mantle)
   72
3    5.8091    3.4557    2.7157     0.000   0.00100   0.00200
3    5.8091    3.4557    2.7157    15.000   0.00100   0.00200
3    5.8091    3.4557    2.7157    20.000   0.00100   0.00200
3    6.5282    3.7663    2.9074    35.000   0.00100   0.00200
3    8.1080    4.4845    3.3297    40.000   0.00100   0.00200
3    8.1200    4.4845    3.3297    44.000   0.00100   0.00200
3    8.1200    4.4845    3.3297    50.000   0.00100   0.00200
3    8.1563    4.5111    3.3198    52.500   0.00100   0.00200
3    8.1647    4.5158    3.3181    65.000   0.00100   0.00200
3    8.1732    4.5205    3.3163    77.500   0.00100   0.00200
3    8.1817    4.5252    3.3146    90.000   0.00100   0.00200
3    8.1901    4.5299    3.3128   102.500   0.00100   0.00200
3    8.1984    4.5345    3.3111   115.000   0.00100   0.00200
3    8.2066    4.5390    3.3094   127.500   0.00100   0.00200
3    8.2149    4.5436    3.3077   140.000   0.00100   0.00200
3    8.2231    4.5482    3.3061   152.500   0.00100   0.00200
3    8.2314    4.5527    3.3046   165.000   0.00100   0.00200
3    8.2396    4.5573    3.3031   177.500   0.00100   0.00200
3    8.2479    4.5618    3.3016   190.000   0.00100   0.00200
3    8.2550    4.5658    3.3001   198.250   0.00100   0.00200
3    8.2610    4.5691    3.2987   206.500   0.00100   0.00200
3    8.2670    4.5724    3.2972   214.750   0.00100   0.00200
3    8.2730    4.5757    3.2958   223.000   0.00100   0.00200
3    8.8880    4.8043    3.2687   237.133   0.00100   0.00200
3    8.9340    4.8291    3.2768   251.267   0.00100   0.00200
3    8.9800    4.8540    3.2849   265.400   0.00100   0.00200
3    9.0249    4.8782    3.2929   278.500   0.00100   0.00200
3    9.0686    4.9019    3.3006   291.600   0.00100   0.00200
3    9.1124    4.9256    3.3083   304.700   0.00100   0.00200
3    9.1561    4.9493    3.3160   317.800   0.00100   0.00200
3    9.2004    4.9732    3.3238   330.975   0.00100   0.00200
3    9.2451    4.9974    3.3317   344.150   0.00100   0.00200
3    9.2899    5.0215    3.3396   357.325   0.00100   0.00200
3    9.3346    5.0457    3.3475   370.500   0.00100   0.00200
3    9.3813    5.0709    3.3558   384.667   0.00100   0.00200
3    9.4300    5.0972    3.3643   398.834   0.00100   0.00200
3    9.4787    5.1235    3.3729   413.001   0.00100   0.00200
3    9.8034    5.2991    3.4009   428.041   0.00100   0.00200
3    9.9022    5.3525    3.4180   443.081   0.00100   0.00200
3   10.0010    5.4059    3.4351   458.121   0.00100   0.00200
3   10.0998    5.4593    3.4523   473.161   0.00100   0.00200
3   10.1986    5.5127    3.4694   488.201   0.00100   0.00200
3   10.2995    5.5672    3.4869   503.421   0.00100   0.00200
3   10.4025    5.6229    3.5048   518.641   0.00100   0.00200
3   10.5055    5.6786    3.5226   533.861   0.00100   0.00200
3   10.6085    5.7343    3.5405   549.081   0.00100   0.00200
3   10.7115    5.7900    3.5584   564.301   0.00100   0.00200
3   10.8081    5.8422    3.5751   577.481   0.00100   0.00200
3   10.8983    5.8909    3.5908   590.661   0.00100   0.00200
3   10.9885    5.9397    3.6064   603.841   0.00100   0.00200
3   11.0787    5.9885    3.6221   617.021   0.00100   0.00200
3   11.1689    6.0372    3.6378   630.200   0.00100   0.00200
3   11.2399    6.0756    3.6501   645.760   0.00100   0.00200
3   11.2917    6.1036    3.6591   661.321   0.00100   0.00200
3   11.3435    6.1316    3.6681   676.881   0.00100   0.00200
3   11.3953    6.1596    3.6771   692.441   0.00100   0.00200
3   11.4471    6.1876    3.6861   708.001   0.00100   0.00200
3   12.0603    6.7375    3.9580   725.981   0.00100   0.00200
3   12.1509    6.7881    3.9501   743.961   0.00100   0.00200
3   12.2415    6.8387    3.9423   761.941   0.00100   0.00200
3   12.3321    6.8894    3.9345   779.921   0.00100   0.00200
3   12.4227    6.9400    3.9266   797.901   0.00100   0.00200
3   12.5058    6.9864    3.9194   816.181   0.00100   0.00200
3   12.5814    7.0287    3.9129   834.461   0.00100   0.00200
3   12.6570    7.0709    3.9064   852.741   0.00100   0.00200
3   12.7326    7.1131    3.8999   871.021   0.00100   0.00200
3   12.8082    7.1554    3.8934   889.301   0.00100   0.00200
3   12.8866    7.1992    3.8866   911.241   0.00100   0.00200
3   12.9678    7.2445    3.8796   933.181   0.00100   0.00200
3   13.0490    7.2899    3.8725   955.121   0.00100   0.00200
3   13.1302    7.3353    3.8655   977.061   0.00100   0.00200
3   13.2114    7.3806    3.8585   999.000   0.00100   0.00200
3   13.2520    7.4033    3.8550   999.000   0.00100   0.00200

Example of Output File (Logical Unit 6):

Full specifications of the run parameters are sent to lu 6 covering most aspects of the calculation.

For the inputs above, the output will be:

           **  SNERTC  **

           SYNTHETIC SEISMOGRAMS FROM A GENERAL POINT SOURCE
           AT DEPTH IN A MULTILAYERED ELASTIC MEDIUM
           WITH SPLIT STRATIFICATION AND CHOICE OF
           INTERNAL MULTIPLES

           B.L.N. KENNETT    -  JULY  1985

           RUN :  ecr - test


           VELOCITY MODEL: TEST MODEL (Upper Mantle)


           LAYER STRUCTURE

     DEPTH    ALPHA     BETA      RHO      THICK    QAI       QBI     NR
      km       km/s     km/s     mg/m3       km

     0.00    5.8091    3.4557    2.7157      0.00   0.00100   0.00200    3
    15.00    5.8091    3.4557    2.7157     15.00   0.00100   0.00200    3
    20.00    5.8091    3.4557    2.7157      5.00   0.00100   0.00200    3
    35.00    6.5282    3.7663    2.9074     15.00   0.00100   0.00200    3
    40.00    8.1080    4.4845    3.3297      5.00   0.00100   0.00200    3
*** 44.00    8.1200    4.4845    3.3297      4.00   0.00100   0.00200    3
>>> 50.00    8.1200    4.4845    3.3297      6.00   0.00100   0.00200    3
    52.50    8.1563    4.5111    3.3198      2.50   0.00100   0.00200    3
    65.00    8.1647    4.5158    3.3181     12.50   0.00100   0.00200    3
    77.50    8.1732    4.5205    3.3163     12.50   0.00100   0.00200    3
    90.00    8.1817    4.5252    3.3146     12.50   0.00100   0.00200    3
   102.50    8.1901    4.5299    3.3128     12.50   0.00100   0.00200    3
   115.00    8.1984    4.5345    3.3111     12.50   0.00100   0.00200    3
   127.50    8.2066    4.5390    3.3094     12.50   0.00100   0.00200    3
   140.00    8.2149    4.5436    3.3077     12.50   0.00100   0.00200    3
   152.50    8.2231    4.5482    3.3061     12.50   0.00100   0.00200    3
   165.00    8.2314    4.5527    3.3046     12.50   0.00100   0.00200    3
   177.50    8.2396    4.5573    3.3031     12.50   0.00100   0.00200    3
   190.00    8.2479    4.5618    3.3016     12.50   0.00100   0.00200    3
   198.25    8.2550    4.5658    3.3001      8.25   0.00100   0.00200    3
   206.50    8.2610    4.5691    3.2987      8.25   0.00100   0.00200    3
   214.75    8.2670    4.5724    3.2972      8.25   0.00100   0.00200    3
   223.00    8.2730    4.5757    3.2958      8.25   0.00100   0.00200    3
   237.13    8.8880    4.8043    3.2687     14.13   0.00100   0.00200    3
   251.27    8.9340    4.8291    3.2768     14.13   0.00100   0.00200    3
   265.40    8.9800    4.8540    3.2849     14.13   0.00100   0.00200    3
   278.50    9.0249    4.8782    3.2929     13.10   0.00100   0.00200    3
   291.60    9.0686    4.9019    3.3006     13.10   0.00100   0.00200    3
   304.70    9.1124    4.9256    3.3083     13.10   0.00100   0.00200    3
   317.80    9.1561    4.9493    3.3160     13.10   0.00100   0.00200    3
   330.98    9.2004    4.9732    3.3238     13.18   0.00100   0.00200    3
   344.15    9.2451    4.9974    3.3317     13.17   0.00100   0.00200    3
   357.32    9.2899    5.0215    3.3396     13.18   0.00100   0.00200    3
   370.50    9.3346    5.0457    3.3475     13.18   0.00100   0.00200    3
   384.67    9.3813    5.0709    3.3558     14.17   0.00100   0.00200    3
   398.83    9.4300    5.0972    3.3643     14.17   0.00100   0.00200    3
   413.00    9.4787    5.1235    3.3729     14.17   0.00100   0.00200    3
   428.04    9.8034    5.2991    3.4009     15.04   0.00100   0.00200    3
   443.08    9.9022    5.3525    3.4180     15.04   0.00100   0.00200    3
   458.12   10.0010    5.4059    3.4351     15.04   0.00100   0.00200    3
   473.16   10.0998    5.4593    3.4523     15.04   0.00100   0.00200    3
   488.20   10.1986    5.5127    3.4694     15.04   0.00100   0.00200    3
   503.42   10.2995    5.5672    3.4869     15.22   0.00100   0.00200    3
   518.64   10.4025    5.6229    3.5048     15.22   0.00100   0.00200    3
   533.86   10.5055    5.6786    3.5226     15.22   0.00100   0.00200    3
   549.08   10.6085    5.7343    3.5405     15.22   0.00100   0.00200    3
   564.30   10.7115    5.7900    3.5584     15.22   0.00100   0.00200    3
   577.48   10.8081    5.8422    3.5751     13.18   0.00100   0.00200    3
   590.66   10.8983    5.8909    3.5908     13.18   0.00100   0.00200    3
   603.84   10.9885    5.9397    3.6064     13.18   0.00100   0.00200    3
   617.02   11.0787    5.9885    3.6221     13.18   0.00100   0.00200    3
   630.20   11.1689    6.0372    3.6378     13.18   0.00100   0.00200    3
   645.76   11.2399    6.0756    3.6501     15.56   0.00100   0.00200    3
   661.32   11.2917    6.1036    3.6591     15.56   0.00100   0.00200    3
   676.88   11.3435    6.1316    3.6681     15.56   0.00100   0.00200    3
   692.44   11.3953    6.1596    3.6771     15.56   0.00100   0.00200    3
   708.00   11.4471    6.1876    3.6861     15.56   0.00100   0.00200    3
   725.98   12.0603    6.7375    3.9580     17.98   0.00100   0.00200    3
   743.96   12.1509    6.7881    3.9501     17.98   0.00100   0.00200    3
   761.94   12.2415    6.8387    3.9423     17.98   0.00100   0.00200    3
   779.92   12.3321    6.8894    3.9345     17.98   0.00100   0.00200    3
   797.90   12.4227    6.9400    3.9266     17.98   0.00100   0.00200    3
   816.18   12.5058    6.9864    3.9194     18.28   0.00100   0.00200    3
   834.46   12.5814    7.0287    3.9129     18.28   0.00100   0.00200    3
   852.74   12.6570    7.0709    3.9064     18.28   0.00100   0.00200    3
   871.02   12.7326    7.1131    3.8999     18.28   0.00100   0.00200    3
   889.30   12.8082    7.1554    3.8934     18.28   0.00100   0.00200    3
   911.24   12.8866    7.1992    3.8866     21.94   0.00100   0.00200    3
   933.18   12.9678    7.2445    3.8796     21.94   0.00100   0.00200    3
   955.12   13.0490    7.2899    3.8725     21.94   0.00100   0.00200    3
   977.06   13.1302    7.3353    3.8655     21.94   0.00100   0.00200    3
   999.00   13.2114    7.3806    3.8585     21.94   0.00100   0.00200    3

           PARAMETERS
              NL  :    72    NDT :     3    NPX :    23
              NWA :     0
              NFS :    10    NFS :     0    NFZ :     2
              NWF :     0



              NT:      1024     NTI:        10    DELT:   0.04000



           SOURCE PARAMETERS:
             Interface JS:         6     HSS:     44.00

             Layers below source :         66
             Layers above source :          5


           SEPARATION LEVEL:
             Interface JZ:         7     HJZ:     50.00

           Layers below HJZ    :         65
           Layers above HJZ    :          6


           MOMENT TENSOR:
                   -0.9500        -0.1900        -0.1700
                   -0.1900         0.9500        -0.1300
                   -0.1700        -0.1300         0.0000


           FAR-FIELD TIME FUNCTION =

                 100.00      0.00      0.00      0.00      0.00      0.00


           FREQUENCY WINDOW     0.050     0.100  and     2.000     3.000 HZ
             DELF:    0.0244


           PHASE VELOCITY WINDOW
             NRP:       300
             CMX:  12.82052     CMN:   8.33334


           RESPONSE SELECTION

             P at receiver: 1.0     S at receiver: 0.0
             P at source  : 1.0     S at source  : 1.0


            RESPONSE IN UPPER ZONE:

                ISW(6)= 0   Full response


            OVERALL RESPONSE:

                ISW(7)= 2   No surface reflections
                            for deep reflected energy


           INTEGRATION PARAMETERS
             NRP:       300
             PMN:  0.078000     PMX:  0.120000      DP:  0.000140


             Reduction Slowness PR:    0.1000
             Starting Time   STMIN:     40.00


             STATION RANGES


                1800.00   1850.00   1900.00   1950.00   2000.00   2050.00   2100
                2200.00   2250.00   2300.00   2350.00   2400.00   2450.00   2500
                2600.00   2650.00   2700.00   2750.00   2800.00   2850.00   2900

             AZIMUTH OF PROFILE =     25.00
             ATTENUATION VIA TSTAR =      0.10


           SLOWNESS ARRAY

               0.078000    0.078140    0.078280    0.078420    0.078560    0.078
               0.079120    0.079260    0.079400    0.079540    0.079680    0.079
               0.080240    0.080380    0.080520    0.080660    0.080800    0.080
               0.081360    0.081500    0.081640    0.081780    0.081920    0.082
               0.082480    0.082620    0.082760    0.082900    0.083040    0.083
               0.083600    0.083740    0.083880    0.084020    0.084160    0.084
               0.084720    0.084861    0.085001    0.085141    0.085281    0.085
               0.085841    0.085981    0.086121    0.086261    0.086401    0.086
               0.086961    0.087101    0.087241    0.087381    0.087521    0.087
               0.088081    0.088221    0.088361    0.088501    0.088641    0.088
               0.089201    0.089341    0.089481    0.089621    0.089761    0.089
               0.090321    0.090461    0.090601    0.090741    0.090881    0.091
               0.091441    0.091581    0.091721    0.091861    0.092001    0.092
               0.092561    0.092701    0.092841    0.092981    0.093121    0.093
               0.093681    0.093821    0.093961    0.094101    0.094241    0.094
               0.094801    0.094941    0.095081    0.095221    0.095361    0.095
               0.095921    0.096061    0.096201    0.096341    0.096481    0.096
               0.097041    0.097181    0.097322    0.097462    0.097602    0.097
               0.098162    0.098302    0.098442    0.098582    0.098722    0.098
               0.099282    0.099422    0.099562    0.099702    0.099842    0.099
               0.100402    0.100542    0.100682    0.100822    0.100962    0.101
               0.101522    0.101662    0.101802    0.101942    0.102082    0.102
               0.102642    0.102782    0.102922    0.103062    0.103202    0.103
               0.103762    0.103902    0.104042    0.104182    0.104322    0.104
               0.104882    0.105022    0.105162    0.105302    0.105442    0.105
               0.106002    0.106142    0.106282    0.106422    0.106562    0.106
               0.107122    0.107262    0.107402    0.107542    0.107682    0.107
               0.108242    0.108382    0.108522    0.108662    0.108802    0.108
               0.109362    0.109502    0.109643    0.109783    0.109923    0.110
               0.110483    0.110623    0.110763    0.110903    0.111043    0.111
               0.111603    0.111743    0.111883    0.112023    0.112163    0.112
               0.112723    0.112863    0.113003    0.113143    0.113283    0.113
               0.113843    0.113983    0.114123    0.114263    0.114403    0.114
               0.114963    0.115103    0.115243    0.115383    0.115523    0.115
               0.116083    0.116223    0.116363    0.116503    0.116643    0.116
               0.117203    0.117343    0.117483    0.117623    0.117763    0.117
               0.118323    0.118463    0.118603    0.118743    0.118883    0.119
               0.119443    0.119583    0.119723    0.119863


 *** RESPONSE STEP


           FREQUENCY COUNTERS
              NLO:         3     NUP:       123      NW :       121


           DIMENSIONS OF TRANSFORM ARRAY
               NW :       121
              NRP :       300


           SOURCE TERMS in order m=0,+1,-1,+2,-2

            ARRAY PU :
               0.0000    0.0000    0.0015    0.0020    0.0015   -0.0020    0.004
            ARRAY SU :
               0.0000    0.0000    0.0017    0.0023    0.0018   -0.0023    0.005
            ARRAY HU :
               0.0000    0.0000    0.0005    0.0006   -0.0005    0.0006    0.001


           ** TRANSFORMS CALCULATED **



  *** INTEGRATION STAGE

            STATION  :   1800.00
            STATION  :   1850.00
            STATION  :   1900.00
            STATION  :   1950.00
            STATION  :   2000.00
            STATION  :   2050.00
            STATION  :   2100.00
            STATION  :   2150.00
            STATION  :   2200.00
            STATION  :   2250.00
            STATION  :   2300.00
            STATION  :   2350.00
            STATION  :   2400.00
            STATION  :   2450.00
            STATION  :   2500.00
            STATION  :   2550.00
            STATION  :   2600.00
            STATION  :   2650.00
            STATION  :   2700.00
            STATION  :   2750.00
            STATION  :   2800.00
            STATION  :   2850.00
            STATION  :   2900.00



           ** CALCULATION COMPLETE **

SEISMOGRAM OUTPUT (Logical Unit 11):

Three component seismogram time series suitable for plotting are written out to unit 11 by the subroutine "SINT" in the following order. This file is a single record of unformatted output.
NPX, NCOMP,
then for each station position:
XS, AZIM, CZ, DELT, NT, PR, TCAL, SMZ, VERT(1-NT),
XS, AZIM, CR, DELT, NT, PR, TCAL, SMR, RAD(1-NT),
XS, AZIM, CT, DELT, NT, PR, TCAL, SMT, TANG(1-NT).

where:

NPX - number of stations
NCOMP - number of components for each distance (currently hardwired as 3)
XS - station range (in km)
AZIM - azimuth (degrees)
CZ, CR, CT - A character denoting the Z (vertical), R (radial), and T (tangential) components.
DELT - time sampling interval (in s)
NT - total number of time points in series
PR - reduction slowness (in s/km)
TCAL - start time of calculation (in s)
SMZ, SMR, SMT - maximum value of seismogram for the vertical, radial, and tangential components, respectively.
VERT - time series for vertical component
RAD - time series for radial component
TANG - time series for tangential component

Other Notes on the Program

NUMERICAL INTEGRATION OF RESPONSE:

Up to 2048 time points in the time series for the seismograms can be handled and the starting time and reduction slowness should be chosen so as to keep the phases of interest within this window to avoid aliasing.

Although it is possible to work up to the Nyquist frequency, the best results are usually obtained by restricting attention to frequencies less than one half of Nyquist (for this reason only a limited number of active frequencies, currently 200 are allowed). The frequency window is specified on input and cosine tapers applied at each end.

The roughness of the numerical integrands increases with frequency and so finer sampling in slowness is required. The choice of slowness increment can be difficult to judge, but a clear sign of under sampling is the presence of high frequency ripple at the highest allowed frequencies. To avoid numerical arrivals from the end of the slowness interval a linear taper is applied at each end over the last 25 values.

Currently 200 active frequencies and 300 slowness values can be used (requiring 1.75 Mbyte on a 32 bit machine). These may be changed by amending the unlabelled common block and the dimensions of PG in block /INTEG/. The memory requirements of the program can be reduced if intermediate results are written to disc rather than held in memory.

IMPLEMENTATION:

The program is written in FORTRAN 77 for an operating system with external assignments of logical units. This routine has been run on a CONCURRENT (PE) 3230; however, earlier versions of many of the subroutines have been run successfully on a wide range of different machines.

PLOTTING SYNTHETIC SEISMOGRAMS

A plotting routine called plotsec_refl has been developed at UBC which plots synthetic seismograms generated by SNERTC using the plotsec suite of programs.

UBC users will find this program compiled at /seis/shire/gorman/modelling_1-D/kennett/src/plotsec_refl/. It requires that the input dataset be named synth.z and will automatically output three sets of PLOTSEC head.dmp and ps_data.out files - for each of the vertical, radial and transverse co-ordinates - ready for viewing or filtering by other PLOTSEC routines.

See Andrew Gorman for details.


What follows is the documentation of Brian Kennett's plotting routine, which has not been used at UBC.

PLOTTING OF SYNTHETIC SEISMOGRAMS AND/OR TRAVEL TIMES _ WINDOWED OUTPUT

zst.man

written by B.L.N. Kennett
R.S.E.S., Australian National University
Canberra, Australia


   DESCRIPTION:

      This routine is designed to plot synthetic seismograms 
      generated by any of the local calculation routines and
      to allow plotting in a specified window with user 
      specified reduction velocity.

      In addition windowed travel time plots can be made, 
      either separately or superimposed on the seismograms.


   EXECUTION:

      zstrun -$1  < input > output

        @1 = h,m    for Hp,Masscomp plots
        
        Input:
          command file:   
          (data files specified in inputs)
        Output:
           summary of run parameters
        Plot:
           on unit 8: zstpl8


   INPUT:
        a)  A command file

        b)  A  data files (unformatted) in the zst format   

      
       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
      
      
       For travel times:
      
            iray     -    number of ray segments
      
      ...for each ray segment 
            it       -    number of points
            (d(k),t(k),pq(k),k=1,it)
                     -    distance, time,  slowness
      ...end ray segment 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

  COMMAND FILE CONSTRUCTION

  1.  Plot seismograms  (YE/NO)
  2.  Components to be plotted
       ZC,RC,TC    - individual components
       3C          - all three components
       PA,PV,PH,PT - Polarisation 
                     PA - vertical & horizontal plane
                     PV - vertical plane
                     PH - horizontal plane
                     PT - vertical vs tangential  
  3.  Number of seismogram files (<3)
  4.  For each file:
       -   name of file  
  5.  Number of distances to plot  
  6.  Reduction velocity for plot
  7.  Minimum reduced time for any seismogram
  8.  Width of Polarisation window (non zero implies component offset),
      Length of Polarisation window. 
  9.  Pen colours for the components (in order Z,R,T)
  10. Normalise each trace to ame maximum amplitude (YE/NO)
  11. Amplification factor
       amp, b1, b2, xr, eps
      with normalisation only amp used
      otherwise the scale factor for each seismogram is set to
       1000.0*amp*( b1 + b2*(xx/xr))**eps  at range xx
  
  12. Plot travel times (YE/NO)
  13. Number of files for travel times (< 3)
  14.  For each file:
    a)    name of file  
    b)    line or symbol mode (LI/SY)
    c)    pen colour 
  
  15.  Frame style  (FR - full frame, NL - no labels)
  16.  Font number from typset
  17.  Min, Max distance  rmin,rmax
  18.  Length of distance axis
  19.  Min, Max reduced time  trmin,trmax
  20.  Length of time axis
  21.  Spacing between large tic marks on distance, time axes
  22.  Spacing between small tic marks on distance, time axes
  23.  Number of decimals in labels for distance, time axes
  24.  Character size for text, title
  25.  Text string for distance axis
  26.  Text string for time axis
  27.  Text string for title



    SAMPLE COMMAND FILE


YE                               Plot seismograms? (YE/NO)    
ZC				 [se] Plot components (ZC,RC,TC,3C,PA,PV,PH,PT)
1                                [se] Number of files for seismograms(<3)
/g/wkbj/fort.11                  [se] Name of file
21                               [se] Number of distances to plot
10.0                             [se] Reduction velocity for plot
 0.0                             [se] Minimum reduced time for seismograms
0.0   5.0                        [se] Component offset, polarisation window
2 3 4                            [se] Pen colours for seismic components
NO                               [se] Trace normalisation? (YE/NO)
 0.1    1.0  1.0   1.0  0.0      [se] Amp,b1,b2,xr,eps | amp*(b1+b2(xx/xr))**eps
YE                               Plot travel times? (YE/NO)
1                                [tt] number of files for travel times (<3)
/g/wkbj/fort.12                  [tt] Name of file
LI                               [tt] line or symbol mode (LI/SY)
3                                [tt] Pen colour
FR                               Frame: FR - full frame , NL - no labels
3                                [fr] font choice
 1000.00  2900.00                [fr] Rmin, Rmax
   26.00                         [fr] length of R-axis
   10.00    60.00                [fr] Trmin,Trmax
   18.00                         [fr] length of T-axis
  200.00   10.000                [fr] Large Tic spacing R,T
   50.00    5.000                [fr] Small Tic spacing R,T
    0       1                    [fr] # of dec. in label R,T
   0.4300   0.47500              [fr] character size text,title
Distance km                                                              X-txt
Reduced Time s                                                           Y-txt
Herrin Test                                                              Title


Last updated: 5 November 2003
A. R. Gorman (andrew.gorman@stonebow.otago.ac.nz)
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