Kinematically equivalent velocity distributions

Abstract

For a layered medium, the seismic velocity model can be vertically heterogeneous within the layers. The traveltime parameters estimated from each reflection must be converted into layer traveltime parameters by using the layer-stripping method. The layer traveltime parameters must be inverted into layer velocity model parameters. Interpretation or inversion of layer traveltime parameters depends on the chosen velocity model within the layer. Different or kinematically equivalent velocity distributions can result in the same traveltime parameters. The inversion problem for traveltime parameters is strongly nonunique even if they are estimated accurately. To evaluate the accuracy of a velocity model, one can choose the phase for the two-way propagator. The discrepancy in this phase factor between the kinematically equivalent velocity models depends on the number of traveltime parameters estimated and increases with spatial frequency. By estimating two traveltime parameters, we approximately preserve the average velocity, regardless of the complexity of the vertically heterogeneous model. By estimating three traveltime parameters, we approximately preserve the average velocity gradient.