The slowness in both smooth models without interfaces
is interpolated by natural bicubic
splines in the regular grid of 122 points vertically times
384 points horizontally. The grid spacing is 0.024km in both
directions. The size of the spline grid is thus
2.904km vertically and 9.192km horizontally.
The grid velocities in both models, in m/s, are
available at WWW address
` http://www-rocq.inria.fr/~benamou/testproblem.html `
.
The grid velocities are stored with the inner loop from the top
to the bottom and the outer loop from the left to the right.

Receiver '001' is situated at horizontal distance 0.000 km from the left-hand side, '002' at 0.024 km, '003' at 0.048 km, ... '384' at 9.192 km.

The ** first-arrival travel times ** are, as a rule, calculated
on regular rectangular grids of points,
using the discretized versions of seismic models.
For the calculations presented here, the accurate second-order
method by

The ** ray-theory travel times ** at given receivers
in the ** "smooth" model ** were calculated by the shooting method.
Even the "smooth" model is not sufficiently
smooth for the shooting method: the geometrical spreading, especially
at the leftmost part of the receiver profile, is so great that
there is no take-off angle available within the single precision real
numbers to shoot the ray to that region, see the travel time curves below.
Thus, the shooting method cannot catch all the two-point rays
in this model. It may miss about 20% two-point
rays. On the other hand, if the two-point ray is found, the calculated
ray-theory travel time is probably very accurate.

For more details refer to the manuscript by

The

The

Each file is terminated by a slash.

Note that we have supplemented the receiver names (integer indices in apostrophes) with the receiver coordinates in order to reliably distinguish the applied receiver indexing from indexing '000' to '383'.

You may download the resulting first-arrival travel times
` marsf.dat `
in the "smooth" INRIA Marmousi model.

You may download the ray-theory travel times
` marsr.dat `,
found by the shooting method in the "smooth" INRIA Marmousi model.

You may download the resulting first-arrival travel times
` marhf.dat `
in the "hard" INRIA Marmousi model.

The ray-theory travel time curve in the "hard" model is so complex that the two-point ray tracing makes no sense, see the figures below.

The first-arrival travel times in the "smooth" (

*top travel time*=2.6 s

*bottom travel time*=0.9 s

The two-point ray-theory travel times (*red*) plotted over
the first-arrival travel times (*blue*)
in the "smooth" INRIA bench-mark version of the 2-D Marmousi model.
The first-arrival travel times at receivers where the shooting method
failed remain *blue*.

*top travel time*=5.2 s

*bottom travel time*=0.9 s

136818 initial-value ray-theory travel times (*red*) plotted over
the first-arrival travel times (*blue*)
in the "hard" INRIA bench-mark version of the 2-D Marmousi model.
136818 of 244302 initial-value rays,
shot with the angular increment of 0.000010 radians,
hit the receiver profile.

[reduced travel time] = [travel time] - [hypocentral distance] / [3.2 km/s],

and are displayed in 10 times enlarged scale.

*top reduced travel time*=0.50 s

*bottom reduced travel time*=0.07 s

The first-arrival travel times in the "smooth" (*upper curve*)
and "hard" (*lower curve*)
INRIA bench-mark versions of the 2-D Marmousi model.

*top reduced travel time*=0.50 s

*bottom reduced travel time*=0.07 s

The two-point ray-theory travel times (*red*) plotted over
the first-arrival travel times (*blue*)
in the "smooth" INRIA bench-mark version of the 2-D Marmousi model.
The first-arrival travel times at receivers where the shooting method
failed remain *blue*.

*top reduced travel time*=0.50 s

*bottom reduced travel time*=0.07 s

136818 initial-value ray-theory travel times (*red*) plotted over
the first-arrival travel times (*blue*)
in the "hard" INRIA bench-mark version of the 2-D Marmousi model.
Reduced travel times over 0.5 s are clipped off.

The research has been supported by the Grant Agency of the Czech Republic under Contract 205/95/1465, and by the members of the consortium "Seismic Waves in Complex 3-D Structures".

** Summary ** of the manuscript
**
L. Klimes: Travel times in the INRIA Marmousi models**,
Seismic Waves in Complex 3-D Structures, Report 4,
pp. 53-60, Dep. Geophys., Charles Univ., Prague 1996.

** Abstract ** of the contribution
**
L. Klimes: Traveltimes and their computation **
presented at the workshop
"Computation of multi-valued traveltimes" held
in INRIA Rocquencourt, France, on September 16-18, 1996.