Introduction

The purpose of this note is to compare the fundamental solutions generated using Randall's and Herrmann's codes for Green's functions used for moment tensor studies. There are eight different solutions that must be compared.

For the comparison synthetics will be generated for the CUS model, a source depth of 15 km and an epicentral distance of 500 km. The command sequences use are as follow:

Herrmann

      #!/bin/sh
      HS=15.0
      cat > dfile << EOF
      500.0     1       1024 -1.0 13.0
      EOF
      hprep96 -M CUS.mod -HS ${HS}  -d dfile -ALL
      hspec96
      hpulse96 -V -p -l 1 > file96
      f96tosac -G < file96

The model file is CUS.mod

The Herrmann Greens functions have the names 050000150.RDD 050000150.RHF 050000150.TDS 050000150.ZDD 050000150.ZHF 050000150.RDS 050000150.RSS 050000150.THF 050000150.ZDS 050000150.ZSS 050000150.REX 050000150.RVF 050000150.TSS 050000150.ZEX 050000150.ZVF and are in units of ground velocity of cm/s for a step-like source time function for a seismic moment of 1.0E+20 dyne-cm.

Randall

      time mijkennett << EOF
      rCUS.mod
      EOF
      #
      # -d for displacement, 13 reducing velocity, -1.0 time shift
      #
      #1e9,0.0
      xtsynth -d <

The model file is rCUS.mod

The Randall Greens function have names like r_0500_0015_pz.clv t_0500_0015_pz.clv and z_0500_0015_pz.clv
which are identical.  We use the following files for the comparison: z_0500_0015_pz.clv  z_0500_0015_pz.vds	z_0500_0015_sr.clv  z_0500_0015_sr.vds	z_0500_0015_st.vds
z_0500_0015_pz.iso  z_0500_0015_pz.vss	z_0500_0015_sr.iso  z_0500_0015_sr.vss	z_0500_0015_st.vss
and are in units of ground velocity of cm/s for a step-like source time function for a seismic moment of 1.0E+20 dyne-cm.

Preparation for Comparison




The Green's functions are filtered using the gsac commands 



      hp c 0.01 n 3
      lp c 0.10 n 3




Plots are created showing the first 300 seconds of the traces. Traces in a plot have hte same vertical scale.


Since the Herrmann Green's functions are in units of velocity, these are
integrated for comparison after the filter operations:



      int





The focus of the comparison is on long periods, for which the slight difference in Q models will not be significant. However there will be slight timing differences since Randall's code uses acausal Q for reasons of speed, which the Herrmann code uses causal Q.



Comparison

`




 Green's function
	
Comparison

 Green's function
	
Comparison






	Herrmann
	Randall
	
Randall (red) Herrmann (blue)

	Herrmann
	Randall
	
Randall (red) Herrmann (blue)





	ZDD
	z.clv
	
	RDD
	r.clv
	




	ZDS
	z.vds
	
	RDS
	r.vds
	




	TDS
	t.vds
	
	ZSS
	z.vss
	




	RSS
	r.vss
	
	TSS
	t.vss
	




	ZEX
	z.iso
	
	REX
	r.iso
	





Conclusion


The conclusions from this test are that  the 'z.vds/ZDS', 'r.vds/RDS' and 't.vss/TSS' 
differ only in sign. After sign correction, the amplitudes of all agree.

Thus for the Greens functions form Herrmann's Computer Programs in Seismology can
be used with code which previously use the Randall Green's functions, this difference is
accounted for.



Last changed Tue Feb 23 17:15:41 UTC 2010