In general the operator in fitting goals (7) is much more complex than the simple masking operator used in the missing data problem. One of the most attractive potential uses for a range of equiprobable models is in velocity estimation. As a result I decided to next test the methodology on one of the simplest velocity estimation operators, the Dix equation Dix (1955).

Following the methodology of Clapp et al. (1998), I
start from a CMP gather *q*(*t*,*i*) moveout corrected with velocity *v*.
A good starting guess for our RMS velocity function
is the maximum ``instantaneous stack energy'',

(9) |

(10) |

(11) |

(12) |

To test the methodology I took a 2-D line from a 3-D North Sea dataset provided by Unocal. Figure shows four different realizations with varying levels of .

Figure 9

I then chose what I considered a reasonable variability level, and constructed ten equiprobable models (Figure ). Note that the general shapes of the models are very similar. What we see are smaller structural changes. For example, look at the range between .7s and 1.1s. Generally each realization tries to put a high velocity layer in this region, but thickness and magnitude varies in the different realizations.

Figure 10

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