Left: illustrative sketch of a perturbed and reference cross-covariances ( and C^ref, respectively) and the window function w. Right: the associated cost function X(a,t) in log-scale color with contours where X = 0.1, 1, 10, 100, and 1000. The color scale gives the value of the misfit. To measure τ and A, we need to minimize X, and in this case the minimum is reached for τ = 3 min and A = 1.2. In this plot (left panel) we show only t> 0. This part of the cross-covariance function corresponds to waves propagating from the position x₁ to x₂, and the window function for this wave is zero for t< 0.