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RAYT2DAN, VELPERTAN, SURELANAN  constitute a form of migration
velocity analysis for anisotropy parameters created by
Debashish Sarkar, Dec 2003                      


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README for RAYT2DAN          Debashish Sarkar	Dec 2003                      

This code depends on the CWP/SU (Seismic Unix) package,
available free from the Center for Wave Phenomena at:
ftp.cwp.mines.edu

The program RAYT2DAN computes traveltime tables for P- and SV-waves
in a transversely isotropic medium with a vertical symmetry axis (VTI)
for arbitary, but smooth, variation in the medium parameters. The output
traveltime tables may be used for modeling and migration.

The demo shows an application of the code for a linear variation
in medium parameters computed for a single shot placed at 1000 m
on the surface. 

Type:

Rayt2dan  -- demo for rayt2dan
Clean.sh  -- clean up after running the demo

The output on the screen allows the user to
monitor progress realtime by showing the shotpoint location
and the takeoff angle off each computed ray.


----
README for RAYT2DAN          Debashish Sarkar   2003

This code depends on the CWP/SU (Seismic Unix) package,
available free from the Center for Wave Phenomena at:
www.cwp.mines.edu/cwpcodes

The demo also depends on the proprietary codes: rayt2dan and surelanan
These codes are available to sponsors of the CWP Consortium project.

The program VELPERTAN computes updates of medium 
parameters by minimizing the variance of the
migrated depths of events in image gathers.

To install VELPERTAN

Edit the Makefile to reflect the needs of your system and
type:

make

Demo for VELPERTAN

The demo shows an application of the code on a
factorized v(x,z) medium with linear gradients in
vertical velocity. To run the demo, type:

Synlv          to create the test dataset
Rayt2dan       to perform the ray tracing for the migration
Sukdmig2d      to perform the migration
Surelanan      to begin the residual moveout analysis

to determine the residual moveout at different cdp 
locations. Then use 

Velpertan      to compute parameter updates. 


To minimize the residual moveout
and to obtain perturbation in the parameters.
You should see something like this:

d_VP0=0.000000e+00 d_kz=2.578647e-01 d_kx=7.929953e-02 d_epsilon=3.494340e-01 d_delta=1.202125e-02

The procedure would follow by adding each of these values to
the corresponding value in the input to rayt2dan in the shell
script Rayt2dan. 

The values of d_VP0, d_kz, d_kx, d_epsilon, d_delta are added
to the parameters that are input into unif2 in the portion
of the Rayt2d script reproduced here:

...
 # Create parameter files for raytracing.
 # Make VP0
 # note: add computed d_VP0 to V00 here
 # add computed d_kx to dvdx, and add d_kz to dvdz here.
 unif2 < test >VP0  ninf=$ninf  npmax=$npmax \
        nz=$nz dz=$dz fz=$fz nx=$nx dx=$dx fx=$fx \
        v00=2000 dvdz=0.3 dvdx=0.1
 smooth2 < VP0 r1=$r1 r2=$r2 n1=$nz n2=$nx > VP0sm

 # Make epsilon
 # note: add the computed value of d_epsilon to v00 here
 unif2 < test >epsilon ninf=$ninf npmax=$npmax \
        nz=$nz dz=$dz fz=$fz nx=$nx dx=$dx fx=$fx \
        v00=0.0
 smooth2 < epsilon r1=$r1 r2=$r2 n1=$nz n2=$nx > epsilonsm

 # Make delta
 # note: add the computed value of d_delta to v00 here
 unif2 < test >delta  ninf=$ninf  npmax=$npmax \
        nz=$nz dz=$dz fz=$fz nx=$nx dx=$dx fx=$fx \
        v00=0.0
 smooth2 < delta r1=$r1 r2=$r2 n1=$nz n2=$nx > deltasm
....


The user would then repeat the procedure beginning
by running Rayt2dan, Sukdmig2d, Surelanan, and Velpertan, until
the user is satisfied that the migrated image gathers are flat.

For this particular demo, three iterations of this procedure should
completely flatten the migrated image gathers.

----

README for RAYT2DAN          Debashish Sarkar   2003

This code depends on the CWP/SU (Seismic Unix) package,
available free from the Center for Wave Phenomena at:
www.cwp.mines.edu/cwpcodes

This code also depends on the proprietary code rayt2dan, available
to sponsors of the CWP Consortium. Contanct CWP for further information.

The program SURELANAN allows the user to determine coefficients
r1 and r2 that are necessary to describe residual moveout of migrated 
events in depth. r1 and r2 are substituted in the equation 

z(h)^2=z(0)^2+r1*h^2+r2*h^4/[h^2+z(0)^2] (Sarkar and Tsvankin, 2003),

to obtain estimates of the residual moveout.

Installation:

To install, edit the Makefile to reflect the needs of your system
and type:

make

Running the Demo:

This demo depends on the program  

rayt2dan 

This program must be installed before you can run this demo.

The demo shows an application of the code on one
overcorrected event at two CDP locations. To run the demo
execute the following shell scripts.

Susynlvfti  -- to generate test data
Rayt2dan    -- to generate traveltime tables for migration
Sukdmig2d   -- to migrate the data.

Surelanan   -- to begin the interactive demo for residual moveout
               picking


Start by picking 12 points (this number may be changed, 
if needed, in the script Surelanan) on the stacked image of  
one reflector. By doing so the reflector is delineated
and an estimate of z(0) is gleaned along the reflector. 
These picks are stored in file refl.1. At the selected CDP
locations pick the maxima on the two-parameter semblance
panels, which gives estimates of r1 and r2. 

These picks are
stored in the file cig.par along with the midpoint locations,
and may be used along with the code VELPERTAN to compute 
parameter updates

The file cig.par is the final output of this demo. This file
contains the coefficients that are necessary to describe the
residual moveout. This is example of the contents of cig.par
that you might see.  

cdp1=2000,-0.450038,-0.372307
cdp1=2500,-0.227943,-0.388967

The second and third values in each line correspond to the r1,r2 values
in the equation:

 z(h)*z(h) = z(0)*z(0) + r1*h^2 + r2*h^4/[h^2+z(0)^2] 

which is the non-hyperbolic moveout in depth for VTI anisotropic media.


Reference:
----------
Sarkar and Tsvankin, 2003, Analysis of image gathers in factorized VTI media:
Geophysics, 68, 2016-2025.

John Stockwell	 | [e-mail]
Center for Wave Phenomena (The Home of Seismic Un*x)
Colorado School of Mines
Golden, CO 80401 | http://www.cwp.mines.edu/cwpcodes
voice: [phone]

Our book:
Norman Bleistein, Jack K. Cohen, John W. Stockwell Jr., [2001],
Mathematics of multidimensional seismic imaging, migration, and inversion,
(Interdisciplinary Applied Mathematics, V. 13.), Springer-Verlag, New York.