Nonlinear wave equation inversions are commonly performed using gradient-based iterative optimization. Each iteration typically consists of three steps. First, calculate the residuals, which requires one nonlinear forward operation. Second, calculate the gradient, which requires one linearized adjoint operation. Finally, determine the step size by a line search, which requires few nonlinear forward operations. For our calculations, we will assume the line search requires three forward operations results in a total per iteration effort of four forward and one adjoint operations.
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