Kirchhoff artifacts

Given one of our pair of Kirchoff operations, we can manufacture data from models. With the other, we try to reconstruct the original model. This is called imaging. It does not work perfectly. Observed departures from perfection are called ``artifacts''.

Reconstructing the earth model with the adjoint option yields the result in Figure 4.

 

skmig
Figure 4 Left is the original model. Right is the reconstruction.

The reconstruction generally succeeds but is imperfect in a number of interesting ways. Near the bottom and right side, the reconstruction fades away, especially where the dips are steeper. Bottom fading results because in modeling the data we abandoned arrivals after a certain maximum time. Thus energy needed to reconstruct dipping beds near the bottom was abandoned. Likewise along the side we abandoned rays shooting off the frame.

Unlike the example shown here, real data is notorious for producing semicircular artifacts. The simplest explanation is that real data has impulsive noises that are unrelated to primary reflections. Here we have controlled everything fairly well so no such semicircles are obvious, but on a video screen I can see some semicircles.