This is an example of fitting gridded velocities and triangulated interfaces by a 3-D model suitable for ray tracing.
We take the gridded velocities and the triangulated interfaces of the SEG/EAGE Salt Model, display the data in VRML, and build two versions of the model suitable for ray tracing using packages MODEL and CRT. In the first example, we construct a smooth model without interfaces, and in the second example a model containing the salt body and some other selected interfaces. We perform several tests in the inverted models, and we display the models in VRML or GOCAD.
This file is a brief manual describing the computations. For details refer to Bulant (2001).
The dimension of array RAM in file 'ram.inc' must be at least 15000000 for the calculations.
History file 'sal-ts.h' transforms given triangulated surfaces from the GOCAD representation to the VRML representation. By default, only the most important surfaces are transformed, and they are displayed together with the salt surface. Optionally, all the files from the SEG/EAGE Salt Model CD-ROM may be displayed.
History file 'sal-ts.h' also writes points of the most important surfaces in the format PTS. The points are then used in 'sal-inv2.h' as the data for inversion.
History file 'sal-vel.h' needs file 'Saltf@@' to be extracted from GZIPped file 'saltf.gz' using the command gzip -d -N saltf.gz. History file 'sal-vel.h' reads the given velocities from the binary file 'Saltf@@', converts them into slownesses, and writes the velocities and slownesses on sparser grids into ascii files. Slownesses and velocities chosen from the original dense grid, slownesses and velocities computed by averaging, and slownesses and velocities with removed artificial reflectors are generated. The files are then used in 'sal-inv1.h' and 'sal-inv2.h' as the data for the inversion, and in 'sal-test.h' for calculation of velocity and slowness deviations of the inverted models.
By default, only files necessary for default calculations in 'sal-inv1.h', 'sal-inv2.h' and 'sal-test.h' are generated. Optionally, files necessary for all computations described in Bulant (2001) and for all optional tests may be generated.
History file 'sal-inv1.h' calculates a smooth version of the SEG/EAGE Salt Model by inversion. The inverted model, parametrized by means of package MODEL, is suitable for ray tracing. By default, only the model considered to be the best one, is calculated. Other models mentioned in Bulant (2001), may be calculated after minor changes of the history file.
After the inversion, Sobolev norm of the slowness field in the inverted model is calculated.
History file 'sal-inv2.h' calculates the Salt Model, version with the most important interfaces. By default, only the model considered to be the best one, is calculated. Other models mentioned in Bulant (2001), may be calculated after minor changes of the history file. In the default calculation, the data for the salt interface are taken from the velocity cube. If the points from GOCAD surface 'salt.ts' should be used, history file 'sal-salt.h' must be run before.
After the inversion, Sobolev norm of the slowness field in the inverted model is calculated.
History file 'sal-test.h' performs numerical tests of the inverted models. At the beginning of the file, the model to be tested must be chosen. By default, the output of 'sal-inv1.h' is tested.
By default, the numerical tests cover the visualization of the data and of the velocity and slowness in the inverted model, calculation and visualization of velocity and slowness deviations on the sparse grid of 100 x 100 x 100 m. Standard velocity deviation and standard relative velocity deviation is calculated on the grid of 60 x 60 x 20 m. Optionally, the deviations on full grid may be calculated. It is also possible to exclude the points located in different complex blocks from the calculation of the deviations. For the models with interfaces, the deviations of the interfaces may be calculated.
Default tests include also the calculation of Lyapunov exponents for the inverted model and three simple tests of ray tracing in the inverted model using the history file 'sal-rays.h'.
History file 'sal-wrl.h' may be used for visualization of the model with interfaces using either VRML or GOCAD.
History file 'sal-salt.h' serves for splitting the points of the GOCAD file 'salt.ts' into two files containing the points at the top of the salt and one file with the points at the bottom of the salt. The resulting files have the format PTS. They may be used as the data for inversion 'sal-inv2.h'.
Program 'ptsselec.for' must be compiled before running 'sal-salt.h'.
We thank the Society of Exploration Geophysicists and European Association of Geoscientists and Engineers for permission to include data files 'bottom.ts', 'fault_a.ts', 'gp2.ts', 'hrz_1.ts', 'salt.ts', 'top.ts' and 'Saltf@@' to this data set.
Aminzadeh, F., Brac, J., Kunz, T.: 3-D Salt and Overthrust Models. SEG/EAGE 3-D Modeling Series No.1., Soc. Explor. Geophysicists, Tulsa, 1997.
Bulant, P.: Sobolev scalar products in the construction of velocity models - application to model Hess, to SEG/EAGE Salt Model, and to model Pluto 1.5. In: Seismic Waves in Complex 3-D Structures, Report 11, pp. 133-159, Dep. Geophys., Charles Univ., Prague, 2001.