Method of Effective Specular Points

 Testing with real data.

Here the Method of Effective Specular Points is illustrated 
with simplified but well-verified experiment based upon real marine data (Fig.7):
a sea-bottom is a target under artificial assumption
that a speed of sound in the water is unknown. The problem
is to find the speed and to get a depth image of a sea-bottom,
using a sparse subset of seismic records:
(21 locations of sources/receivers with  x = 150 m on the
segment of the line profile of 3000 meters (Fig.4, left).
All other records have been used as a control subset: on the base of the reconstructed
sea-bottom profile, the rms-misfit of traveltimes measured and
those along Fermat's extremals/lines is evaluated -
the decreasing of the misfit can testify for improving the image.

The result is as follows:

* the velocity estimated is 1499 m/s;
* standard deviations of traveltimes are 0.032 sec for the 1-st image,
0.028 sec for the 2-nd  and 0.025 sec for the final images respectively.

Fig. 7. Real marine data processing.

* Segment of the "near 0-offset" gather (offset is equal to 101 m): left;

* objective function yields an estimate of the sound speed in water:
1499 m/s ( in the middle), and

* sequential depth images of the sea bottom
are displayed on the right.

NB! "Acquisition" is similar to that used for 2D synthetic
experiment (Figure 5): a regular source-receiver grid with distance 150 m;
in comparison with the standard acquisition the data set in use  is reduced in more than 30 times.

   References:

   Ryzhikov, Gennady  and  Biryulina, Marina,  1996
  Method of effective specular points
   58th Mtg. Eur. Assoc. Expl Geophys.,
   Extended Abstracts,  96, Session: P-134

   Biryulina, Marina   and  Ryzhikov, Gennady,  2000
  Imaging of reflectors under uncertainties in macromodel
   62nd Mtg. Eur. Assoc. Expl Geophys.,
   Extended Abstracts,  Session: B-55