In this example, we set equal to with a weight of 9 fold in the least squares solution. This is the last row of matrix in equation 27. It is like the following equation 28 being repeated 9 times in the matrix equation 27:
The effect is to strongly weight these two delay times equal. The OLS solution to Equation 27 is again given by
where, in the case of Equation 27, the vector, , contains the delay times for the shots, receivers, and the refractor slowness.
(30) |
If we want to constrain the refractor velocity there is a way to do that too. Perhaps we lack reverse profiles or a second shot with at least a different angle between the shots and geophones which would yield more than one apparent refractor velocity. Modifying the above situation to include only shot A with a constrained refractor velocity, and a constrained delay time, , we could set up a system like this:
Here, we set the velocity of the refractor at m/s and constrain the shot A delay time to seconds. Both of these values would need to come from some other source, like an intersecting survey that was absent the defects here.
pm 2018-04-08