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Inversion Constraints

Constraints are critical in non-linear problems to limit the number of possible solutions and to increase the chances of finding a solution that satisfies all aspects of the problem. An obvious constraint to be imposed on the inversion is that the computed velocities be within a reasonable interval. In this case I chose 2200 < V <3200 in m/s. This constraint, however, is not enough because we need to account for the velocity-depth trend present in the sonic log. It is a well-known fact that in general wave propagation velocities increase with depth due to several factors such as compaction, cementation, closing of small fractures due to overburden, etc. There may be effects such as overpressure that locally change this behavior, but in average we expect a trend of velocities increasing with depth. When inverting seismic data for interval velocities, it is disappointing to find that this general trend is not recovered. The reason is that the information in the velocity trend would correspond to very low frequencies (lower than, say, 5 Hz) and these low frequencies are not recorded in the standard seismic method. Furthermore, with land data we usually attenuate or eliminate low frequencies because of the detrimental effect of ground-roll on the seismic data. Since this trend is not resolvable by the direct inversion of the seismic trace, it is necessary to impose a second constraint to honor it. This constraint will be discussed in more detail below.
next up previous print clean
Next: Results Up: Velocity Inversion Previous: Convergence Criteria
Stanford Exploration Project
11/11/2002