An epidemic disease caused by a new coronavirus has spread in Northern Italy with a strong contagion rate. We implement an SEIR model to compute the infected population and the number of casualties of this epidemic. The example may ideally regard the situation in the Italian Region of Lombardy, where the epidemic started on February 24, but by no means attempts to perform a rigorous case study in view of the lack of suitable data and the uncertainty of the different parameters, namely, the variation of the degree of home isolation and social distancing as a function of time, the initial number of exposed individuals and infected people, the incubation and infectious periods, and the fatality rate. First, we perform an analysis of the results of the model by varying the parameters and initial conditions (in order for the epidemic to start, there should be at least one exposed or one infectious human). Then, we consider the Lombardy case and calibrate the model with the number of dead individuals to date (May 5, 2020) and constrain the parameters on the basis of values reported in the literature. The peak occurs at day 37 (March 31) approximately, with a reproduction ratio R 0 of 3 initially, 1.36 at day 22, and 0.8 after day 35, indicating different degrees of lockdown. The predicted death toll is approximately 15,600 casualties, with 2.7 million infected individuals at the end of the epidemic. The incubation period providing a better fit to the dead individuals is 4.25 days, and the infectious period is 4 days, with a fatality rate of 0.00144/day [values based on the reported (official) number of casualties]. The infection fatality rate (IFR) is 0.57%, and it is 2.37% if twice the reported number of casualties is assumed. However, these rates depend on the initial number of exposed individuals. If approximately nine times more individuals are exposed, there are three times more infected people at the end of the epidemic and IFR = 0.47%. If we relax these constraints and use a wider range of lower and upper bounds for the incubation and infectious periods, we observe that a higher incubation period (13 vs. 4.25 days) gives the same IFR (0.6 vs. 0.57%), but nine times more exposed individuals in the first case. Other choices of the set of parameters also provide a good fit to the data, but some of the results may not be realistic. Therefore, an accurate determination of the fatality rate and characteristics of the epidemic is subject to knowledge of the precise bounds of the parameters. Besides the specific example,

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Wave-equation-based redatuming is expensive and requires a detailed knowledge of the shallow velocity field. We derive the analytical expression of a new prestack wavefield extrapolation operator, the Topographic Datuming Operator (TDO), which applies redatuming based on straight-rays approximation above and below a chosen datum. This redatuming operator is directly applied to common-source gathers to downward continue the source and the receivers, simultaneously, to the datum level without resorting to common-receiver gathers. As a result, the method is far more efficient and robust than the conventional wave-equation-based redatuming and does not require an accurate depth-domain interval velocity model. In addition, TDO, unlike wave-equation-based redatuming, requires effective velocities above datum, and thus can be applied using attributes valid for static correction methods. Effective velocities beneath the datum permit us to replace the surface integral, which is needed for wave-equation redatuming with a line integral. In the particular case of infinite (in practice, very high with respect to the shallow layers) velocity beneath the datum, the TDO impulse response collapses to a point, and TDO redatuming is equivalent to conventional static correction, which may, therefore, be regarded as a special case of the newly derived operator. The computational cost of applying TDO is slightly larger than static corrections, yet provides higher quality results partially attributable to the ability of TDO to suppress diffractions emanating from anomalies above datum. Since TDO is an operation based on geometrical optics approximation, velocity after TDO is not biased by the vertical shift correction associated with conventional static correction. Application to a synthetic data set demonstrates the features of the method.