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Transformation Jacobians

True-ampliude migration and the pseudo-unitary modeling/migration pair make use of the diagonal operator of the imaging Jacobian. In this section, we derive the analytical expression of this operator.

The two methods used to compute ADCIGs differ by the stage at which they operate: after imaging for ADCIGs with output in reflection-angle, and before imaging for ADCIGs with output in offset ray-parameter. Imaging takes place in different spaces as well: at constant kh for reflection-angle image gathers, and at constant ph for offset ray-parameter image gathers. Consequently, the imaging Jacobians have different expressions.

 
angam
angam
Figure 9
Ideal angle-gather for wide temporal frequency and pull implementation of RTT. From left to right, Fourier-domain, space-domain, and amplitude response.
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next up previous print clean
Next: Angle-gathers Up: Sava and Biondi: Amplitude-preserved Previous: Incorrect imaging condition
Stanford Exploration Project
4/30/2001