The methodology also nicely lends itself to producing block velocity models.
For example we can produce a velocity model with
linear velocity functions within the layers by rewriting
our fitting goals as:
where is a diagonal matrix of 1s and 0s, 1s at layer boundaries
and 0s everywhere else.
As Figure shows, our velocity function is
approximately linear within
the layers and has a reduced wiggliness compared to the smooth interval velocity curve.
Figure 4 The result of the
inversion for a blocky velocity model using the fitting goals (9).
Figure 5 From left to right: CMP gather, velocity scan with picked RMS velocity within a fairway, smoothed and unsmoothed stacking power, the B function, continuous (dashed) and blocky (solid) interval velocity.