LEAST-SQUARES INVERSION

In order to recover the correct amplitude after datuming or migration, we can use the least-squares imaging method introduced by Ji(1992) elsewhere in this report. We use conjugate gradient algorithm. Convergence was obtained in less than five iterations. The right side of Figure  shows the datuming inversion result after five iterations. Comparing with the datuming result on the left side in Figure , we can see the wavefield is almost the same as the modeled wavefield on the upper left side in Figure . The right side of Figure  shows the migration inversion result after five iterations of the conjugate gradient algorithm. Comparing with the migration result on the left side in Figure , we can see the noise has been reduced and the reflectors are more clearly imaged.

 

datuminv2
Figure 10 Least squares datuming result for scheme 2. Left : Datuming result by applying the conjugate operator of the modeling ( the same as Figure (c) ). Right : Optimized datuming result by conjugate gradient datuming ( after 10 iteration ).

 

topomiginv
Figure 11 Least squares migration result for scheme 2. Left : Migration result by applying the conjugate operator for the modeling ( the same as Figure (d) ). Right : Optimized migration result by conjugate gradient migration ( after 10 iteration ).