More complex velocity anomalies

Inverting for more complex perturbations in focusing operators from $\gamma$ perturbations poses more of a problem. Some insight into the problem can be gained by observing the $\gamma$response to the Gaussian anomaly. The pattern of best focusing $\gamma$ (>1. for reflector positions directly above the anomaly, <1. for positions above the anomaly) similar to the well documented `w' shape observed in stacking velocity Toldi (1985). Looking at the difference between the correct focusing operator and our initial focusing operator (Figure 6) leads to some insight on how to project these $\gamma$ perturbations to the focusing operator. The flat reflector and constant velocity nature of the model lead to the Kjartansson's 1979 `V' pattern response.

 

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Figure 6 Top left, difference between correct focusing operator and initial operator; top right, zero-offset deviations; bottom left, operator deviations directly above the anomaly; and bottom right, response .4 km from center of the anomaly.