GNGTS 2019 - Atti del 38° Convegno Nazionale

GNGTS 2019 S essione 3.3 759 In order to study the chosen functions, a 1D three-layered model was used, where the unknown parameters were represented by the wave velocities in the two upper layers: in the reference model, these values were set to 1000 m/s and 1800 m/s. The L2 norm trend obtained from this test is shown in figure 1: some of the main properties of this object function, such as high resolution and presence of local minima due to cycle-skipping can easily be seen. When computing the Wasserstein metric on the same model, in the same velocity ranges, the trend shown in Fig. 2 was obtained. It can be seen that this function is mostly convex, but the valley of the global minimum is quite wide and smooth, so it has a lower resolution than the L2 norm. In this test, the Wasserstein metric required a slightly longer computational time than the L2 norm. Moreover, it was noticed that Instantaneous Envelope misfit has a linear trend, but a lower resolution thanWasserstein metric; Instantaneous Phase, similarly to L2 norm, is affected by the cycle skipping problem; AWI has a wider valley around the global minimum than L2 norm, but it still shows some non-linearities in its trend, and, overall, requires a very long computational time. A more severe test on the Wasserstein norm was finally carried out on a portion of the Marmousi, a synthetic model widely used in reflection seismic to test different modelling and Fig. 1 - Trend of L2 norm misfit when applied to a convolutional model with two unknown velocities. Non-linearity and local minimal are clearly visible. Fig. 2 - Trend of Wasserstein metric misfit when applied to a convolutional model with two unknown velocities. This function shows a more linear trend than L2 norm, but a lower resolution.