readme

计算一般形式弹性张量最优化TI近似的C程序 Computing the optimal TI approximation of a general elastic tensor

These programs are released courtesy of BP. They were originally written
by Joe Dellinger in 1997 at the former Amoco Tulsa Technology Center, released
informally in April 2000, and then reworked for more formal release in
March 2005. I would appreciate acknowledgement if you find them useful.
If you want to include this code in some package you are distributing,
then please acknowledge where the code came from, and how what you
are distributing varies from what I distributed.

These programs should work on anything with a reasonable C compiler.

--- Joe Dellinger
BP EPTG, Houston, Texas
Thu Mar 24 19:56:42 CST 2005

------------------------------------------------------------------------------

Copyright notice for SEG distribution:

Copyright (c) 2005 by the Society of Exploration Geophysicists.
For more information, go to http://software.seg.org/2005/0001 .
You must read and accept usage terms at:
http://software.seg.org/disclaimer.txt before use.

------------------------------------------------------------------------------

To compile:
	(using GNU make and GNU cc)
	make

	(ignore any warning about possible use of uninitialized variables
	in titest... it's a bogus warning)


To print man pages:

	nroff -man < titest.mn
	nroff -man < orthotest.mn

To install:
	up to you

To clean up:

	make clean

------------------------------------------------------------------------------

What's here?:

titest, orthotest

What they do:
Titest and orthotest are programs for calculating how close to
transversely isotropic or orthorhombic a set of 21 elastic constants are.
General anisotropy requires 21 velocity parameters to describe.
Orthorhombic media have 3 perpendicular planes of symmetry, and require 9.
Transversely isotropic ("TI") has an axis of rotational symmetry and
requires only 5. There is no proprietary information in these programs;
they merely implement equations described in a paper by Patrick Rasolofosaon
of IFP. (Note there are typos in some equations listed in that paper.)
Those equations define a "distance" measure between two sets of 21 elastic
constants. The only "tricky" coding in these programs is how I do the
search over all possible orientations of the anisotropic symmetry axes.

What they are useful for:
These programs are mostly useful for testing and debugging various other
programs for manipulating and/or inverting elastic constants.

These programs accept as input 21 elastic constants, and output the nearest
TI and orthorhombic equivalents.

------------------------------------------------------------------------------

To test:

titest < TI_TEST_INPUT

Here is an example of program "titest". The input is in fact TI, but
its coordinate system has been rotated to obscure this fact. The
constants have been (accidentally) perturbed and rotated from constants
in: L. E. A. Jones and H. F. Wang, 1981, Ultrasonic velocities in
Cretaceous shales from the Williston Basin: GEOPHYSICS, 46, 288-297.

Input C matrix:
      331.3         128       112.3      -1.304      -23.33      -1.922 
        128       339.4       108.7      -9.835      -4.084      -1.994 
      112.3       108.7       226.2      0.4475       1.101       1.748 
     -1.304      -9.835      0.4475       56.89        1.27      -9.889 
     -23.33      -4.084       1.101        1.27        59.5      -3.662 
     -1.922      -1.994       1.748      -9.889      -3.662       103.7 


Rotated C matrix:
        341         129         107  -6.207e-05  -3.986e-05  -0.0002278 
        129         341         107  -3.395e-07   1.949e-05   4.203e-05 
        107         107         227   5.273e-06  -2.096e-05  -0.0001103 
 -6.207e-05  -3.395e-07   5.273e-06          54   1.381e-05   4.175e-05 
 -3.986e-05   1.949e-05  -2.096e-05   1.381e-05          54   1.415e-05 
 -0.0002278   4.203e-05  -0.0001103   4.175e-05   1.415e-05         106 

TI approximation:
        341         129         107           0           0           0 
        129         341         107           0           0           0 
        107         107         227           0           0           0 
          0           0           0          54           0           0 
          0           0           0           0          54           0 
          0           0           0           0           0         106 

TI approximation in original coordinate system:
      331.3         128       112.3      -1.304      -23.33      -1.922 
        128       339.4       108.7      -9.835      -4.084      -1.994 
      112.3       108.7       226.2      0.4474       1.101       1.748 
     -1.304      -9.835      0.4474       56.89        1.27      -9.889 
     -23.33      -4.084       1.101        1.27        59.5      -3.662 
     -1.922      -1.994       1.748      -9.889      -3.662       103.7 

Normalized deviation from TI in original coordinate system, in percent:
    -0.0000     -0.0000     -0.0000     -0.0000      0.0000      0.0000 
    -0.0000      0.0001      0.0000     -0.0000     -0.0000      0.0000 
    -0.0000      0.0000     -0.0000      0.0000      0.0000      0.0000 
    -0.0000     -0.0000      0.0000     -0.0000      0.0000      0.0000 
     0.0000     -0.0000      0.0000      0.0000      0.0000      0.0000 
     0.0000      0.0000      0.0000      0.0000      0.0000     -0.0000 

distance from TI = 0.000 percent
Symmetry axis: (0.1981, 0.0805, 0.9769)
theta = 67.890,   phi = 12.345

------------------------------------------------------------------------------

Here is an example of program "orthotest". This example comes from a
paper by Robert Vestrum, then at the University of Calgary:
Vestrum, R., Brown, J., and Easley, D. T., 1996,
From group or phase velocities to the general anisotropic stiffness tensor,
in Seismic Anisotropy, edited by J. Rathore, p. 101-140, published by the SEG.

Rob measured 21 elastic constants for a laboratory sample, a synthetic
medium made of resin and burlap that was designed to have orthorhombic
symmetry. This program finds that his elastic constants are indeed very
close to being orthorhombic and shows the orientation of the sample.
If the medium was in fact not only orthorhombic but TI, this program also
detects that by trying out each orthorhombic symmetry axis to see how
well it works as a TI axis of symmetry.

In this example we see the medium is not terribly orthorhombic... one of
the orthorhombic axes found is quite close to also being a TI symmetry axis.

orthotest < VESTRUM_TEST_INPUT

Input C matrix:
      16.85        7.88        6.81        0.07       -0.18        0.12 
       7.88       16.03        6.51           0       -0.26       -0.08 
       6.81        6.51       11.14           0       -0.05       -0.04 
       0.07           0           0        3.03        0.01        0.04 
      -0.18       -0.26       -0.05        0.01         3.4       -0.01 
       0.12       -0.08       -0.04        0.04       -0.01        3.89 


Rotated C matrix:
      16.05       7.881       6.497     -0.1896    -0.01734     -0.0446 
      7.881       16.89       6.789    -0.01128     0.08461    0.008745 
      6.497       6.789       11.14     0.07228    -0.01369    -0.06715 
    -0.1896    -0.01128     0.07228       3.389    -0.01637    -0.01323 
   -0.01734     0.08461    -0.01369    -0.01637       3.036     0.07561 
    -0.0446    0.008745    -0.06715    -0.01323     0.07561       3.862 

Orthorhombic approximation:
      16.05       7.881       6.497           0           0           0 
      7.881       16.89       6.789           0           0           0 
      6.497       6.789       11.14           0           0           0 
          0           0           0       3.389           0           0 
          0           0           0           0       3.036           0 
          0           0           0           0           0       3.862 

Orthorhombic approximation in original coordinates:
      16.86       7.891       6.789    0.002643     -0.1654      0.1098 
      7.891       16.04       6.503     0.01784    -0.07036     -0.0364 
      6.789       6.503       11.15    0.002313     -0.1208     0.02525 
   0.002643     0.01784    0.002313       3.041     0.03028     -0.0423 
    -0.1654    -0.07036     -0.1208     0.03028       3.388  -0.0004675 
     0.1098     -0.0364     0.02525     -0.0423  -0.0004675       3.873 

Normalized deviation from Orthorhombic in original coordinates, in percent:
    -0.0180     -0.0320      0.0629      0.2021     -0.0438      0.0307 
    -0.0320     -0.0445      0.0222     -0.0535     -0.5690     -0.1308 
     0.0629      0.0222     -0.0438     -0.0069      0.2125     -0.1958 
     0.2021     -0.0535     -0.0069     -0.0338     -0.0608      0.2469 
    -0.0438     -0.5690      0.2125     -0.0608      0.0347     -0.0286 
     0.0307     -0.1308     -0.1958      0.2469     -0.0286      0.0522 

Distance from Orthorhombic = 1.563 percent

X axis: (0.0860, -0.9963, -0.0089)  theta=175.069, phi=90.511, TI dist=13.479%
Y axis: (-0.9950, -0.0863, 0.0496)  theta=-94.957, phi=87.158, TI dist=11.422%
Z axis: (-0.0502, 0.0046, -0.9987)  theta=-84.748, phi=177.112, TI dist=3.464%