SMOOTH3D - 3D grid velocity SMOOTHing by the damped least squares

smooth3d <infile >outfile [parameters]

Required Parameters:
n1= number of samples along 1st dimension
n2= number of samples along 2nd dimension
n3= number of samples along 3rd dimension

Optional Parameters:

Smoothing parameters (0 = no smoothing)
r1=0.0 operator length in 1st dimension
r2=0.0 operator length in 2nd dimension
r3=0.0 operator length in 3rd dimension

Sample intervals:
d1=1.0 1st dimension
d2=1.0 2nd dimension
d3=1.0 3rd dimension
iter=2 number of iteration used
time=0 which dimension the time axis is (0 = no time axis)
depth=1 which dimension the depth axis is (ignored when time>0)
mu=1 the relative weight at maximum depth (or time)
verbose=0 =1 for printing minimum wavelengths
slowness=0 =1 smoothing on slowness; =0 smoothing on velocity
vminc=0 velocity values below it are cliped before smoothing
vmaxc=99999 velocity values above it are cliped before smoothing

Notes:
1. The larger the smoothing parameters, the smoother the output velocity.
These parameters are lengths of smoothing operators in each dimension.
2. iter controls the orders of derivatives to be smoothed in the output
velocity. e.g., iter=2 means derivatives until 2nd order smoothed.
3. mu is the multipler of smoothing parameters at the bottom compared to
those at the surface.
4. Minimum wavelengths of each dimension and the total may be printed
for the resulting output velocity is. To compute these parameters for
the input velocity, use r1=r2=r3=0.
5. Smoothing directly on slowness works better to preserve traveltime.
So the program optionally converts the input velocity into slowness ",
and smooths the slowness, then converts back into velocity.



Author: CWP: Zhenyue Liu March 1995

Reference:
Liu, Z., 1994,"A velocity smoothing technique based on damped least squares
in Project Reveiew, May 10, 1994, Consortium Project on
Seismic Inverse Methods for Complex Stuctures.