(13) |

Figure shows the result of applying this procedure on a simple CMP gather. The left panel shows the initial CMP gather and the center panel shows the stack power of various values. We use the maximum within a reasonable fairway (the solid lines overlaying the stack power scan) as our data (dashed lines). The right panel of Figure shows: our auto-picked (solid line), our inverted (dashed lines), and our interval velocity converted back to RMS velocity (dotted line).

Figure 12

Fitting goals (13) again assume a constant variance in our data. This is an incorrect assumption in this case for two very obvious regions. First, the operator applied to our data means that late times are going to be given a much larger weight in our inversion. A solution to this problem is introduce a weighting operator ,which is simply .A second error in the assumption of constant variance is that we know that not all our data ( measurements) are of the same quality. The center panel of Figure shows that there are areas where there are no significant reflectors. In addition, there are areas where our stack power results show an obvious maximum at a given value and other areas where the maximum is much less clear. To try to take into account both of these phenomena I calculated a weighted variance within the fairway shown in the center panel of Figure ,

(14) |

*b*(*i*)- is the beginning sample of the fairway at a given sample
*i*, *e*(*i*)- is the ending sample of the fairway at a given sample
*i*, *v*(*j*)- is the
*v*_{rms}at a given stack power location, *v*_{max}(*i*)- is the velocity associated with the maximum stack power value (our data), and
*s*(*i*,*j*)- is the semblance value at time sample
*i*and some*v*_{vrms}value*j*.

(15) |

Figure 13

7/8/2003