Example

Our synthetic example, Figure 1, is represented by a simple horizontal reflector (top panel) embedded in a velocity model with smooth lateral velocity variation (middle panel). A small perturbation introduced in the velocity model creates an image perturbation which does not violate the Born approximation (bottom panel).

 

imags
Figure 1 Reflectivity model (top), background slowness (middle), and image perturbation (bottom).

We compute the gradient of the objective function in Equation (19) using Equation (25) particularized both for the target image fitting (TIF) and for differential semblance optimization (DSO) criteria. Figure 2 shows the ideal image perturbation (top panel), the gradient for TIF (middle panel), and the gradient for DSO (bottom panel).