FWI with different boundary conditions

Gradient comparison

In this section and the next, we will use the 2D Marmousi velocity model to compare FWI results with different boundary conditions. The true velocity model is a modified version of the 2D Marmousi model, with ${12}$ -meter spacing in both $x$ and $z$ . The starting model is a smoothed version of the true model. The survey geometry simulates fixed spread land acquisition. A total of $60$ shots are used with $84$ m shot spacing. Figure 1 a shows the true model with continuation of velocity in the boundary region, figure 1 b shows the starting model with continuation of velocity in the boundary region, and figure 1 c shows the starting model with random velocity values in the boundary region.

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Figure 1. Different velocity models with different boundary regions: a) true velocity with continuation of velocity in the boundary region; b) starting velocity with continuation of velocity in the boundary region; c) starting velocity with random velocity values in the boundary region.

Figure 2 shows gradients of the first iteration using different boundary conditions. Due to the similarity between gradient calculation and RTM image calculation, it can be seen that using a random boundary condition gives a good gradient that is very similar to the ones from using an absorbing boundary condition, except for the usual strong amplitude near source locations. The gradient calculated using continuation of velocity in the boundary region, on the other hand, has some artifacts from reflections in the boundary region. This is particularly obvious in the entire shallow depth region.

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Figure 2. First iteration gradient with different boundary conditions:a) gradient with absorbing boundary condition;b) gradient with random boundary condition;c) gradient with continuation of velocity in the boundary region.

FWI with different boundary conditions