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From the sonic log, assuming constant density, normal incidence, no multiples
or reverberations and no absorption, a synthetic seismic trace was created.
The reflection coefficients for the trace were simply computed with the
recursion:
| |
(1) |

where *RC*_{i} is the reflection coefficient at the *i*th interface and
*V* and represent velocity and density respectively. The density
was assumed to be constant. The depth-to-time conversion was simply done by
integrating the vertical travel time
| |
(2) |

where represents the thickness of the *j*-th layer. In
this case the layer thickness was kept constant at 10 feet.
Once converted to time, the reflectivity series was interpolated
to a constant time-sampling interval using an 8-point sinc interpolator and
convolved with a Ricker wavelet of 60 Hz peak frequency. The right panel of
Figure 1 shows the resulting synthetic trace with time zero
corresponding to the shallowest depth in the log segment (3600 feet).

**input
**

Figure 1 Left panel: Sub-sampled sonic log used to
generate the synthetic trace on the right panel. The zero of the seismic trace
corresponds to the initial depth of the log.

** Next:** Velocity Inversion
** Up:** Alvarez: Velocity inversion
** Previous:** Preprocessing of the well
Stanford Exploration Project

11/11/2002