Policy lessons from the Italian pandemic of Covid-19

We analyze the management of the Italian pandemic during the five identified waves. We considered the following problems: (i) The composition of the CTS ("Scientific Technical Committee"), which was composed entirely of doctors, mainly virologists, without mathematical epidemiologists, statisticians, physicists, etc. In fact, a pandemic has a behavior described by mathematical, stochastic and probabilistic criteria; (ii) Political interference in security measures and media propaganda; (iii) The initial stages of the vaccination campaign, ignoring the age factor, and (iv) The persistence of the pandemic due to the population unvaccinated (anti-vax or "no-vax"), which amounts to about six to seven million people, including 10% of anti-vax doctors

A pseudospectral method for the simulation of 3-D ultrasonic and seismic waves in heterogeneous poroelastic borehole environments

We present a novel approach for the comprehensive, flexible and accurate simulation of poroelastic wave propagation in 3-D cylindrical coordinates. An important application of this method is the realistic modelling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, as of yet largely unresolved, problem in exploration geophysics. To this end, we consider a numerical mesh consisting of three concentric domains representing the borehole fluid in the centre followed by the mudcake and/or casing, and the surrounding porous formation. The spatial discretization is based on a Chebyshev expansion in the radial direction and Fourier expansions in the vertical and azimuthal directions as well as a Runge-Kutta integration scheme for the time evolution. Trigonometric interpolation and a domain decomposition method based on the method of characteristics are used to match the boundary conditions at the fluid/porous-solid and porous-solid/porous-solid interfaces as well as to reduce the number of gridpoints in the innermost domain for computational efficiency. We apply this novel modelling approach to the particularly challenging scenario of near-surface borehole environments. To this end, we compare 3-D heterogeneous and corresponding rotationally invariant simulations, assess the sensitivity of Stoneley waves to formation permeability in the presence of a casing and evaluate the effects of an excavation damage zone behind a casing on sonic log recordings. Our results indicate that only first arrival times of fast modes are reasonably well described by rotationally invariant approximations of 3-D heterogenous media. We also find that Stoneley waves are indeed remarkably sensitive to the average permeability behind a perforated PVC casing, and that the presence of an excavation damage zone behind a casing tends to dominate the overall signature of recorded seismogram

Simulation of surface waves in porous media

We present a novel numerical algorithm for the simulation of seismic wave propagation in porous media, which is particularly suitable for the accurate modelling of surface wave-type phenomena. The differential equations of motion are based on Biot's theory of poro-elasticity and solved with a pseudospectral approach using Fourier and Chebyshev methods to compute the spatial derivatives along the horizontal and vertical directions, respectively. The time solver is a splitting algorithm that accounts for the stiffness of the differential equations. Due to the Chebyshev operator the grid spacing in the vertical direction is non-uniform and characterized by a denser spatial sampling in the vicinity of interfaces, which allows for a numerically stable and accurate evaluation of higher order surface wave modes. We stretch the grid in the vertical direction to increase the minimum grid spacing and reduce the computational cost. The free-surface boundary conditions are implemented with a characteristics approach, where the characteristic variables are evaluated at zero viscosity. The same procedure is used to model seismic wave propagation at the interface between a fluid and porous medium. In this case, each medium is represented by a different grid and the two grids are combined through a domain-decomposition method. This wavefield decomposition method accounts for the discontinuity of variables and is crucial for an accurate interface treatment. We simulate seismic wave propagation with open-pore and sealed-pore boundary conditions and verify the validity and accuracy of the algorithm by comparing the numerical simulations to analytical solutions based on zero viscosity obtained with the Cagniard-de Hoop method. Finally, we illustrate the suitability of our algorithm for more complex models of porous media involving viscous pore fluids and strongly heterogeneous distributions of the elastic and hydraulic material propertie

On the evaluation of plane-wave reflection coefficients in anelastic media

Analytical evaluations of the reflection coefficients in anelastic media inherently suffer from ambiguities related to the complex square roots contained in the expressions of the vertical slowness and polarization. This leads to a large number of mathematically correct but physically unreasonable solutions. To identify the physical solution, we compute full-waveform synthetic seismograms and use a frequency-slowness method for evaluating the amplitude and phase of the corresponding reflection coefficient. We perform this analysis for transversely isotropic media. The analytical solution space and its ambiguities are explored by analysing the paths along the Riemann surfaces associated with the square roots. This analysis allows us to choose the correct sign. Although this approach is generally effective, there are some cases that require an alternative solution, because the correct integration path for the vertical slowness does not exist on the corresponding Riemann surface. Closer inspection then shows that these ‘pathological' cases, which are essentially characterized by a higher-attenuation layer overlying a lower-attenuation layer, can readily be resolved through an appropriate change of direction on the Riemann sheet. The thus resulting recipe for the analytical evaluation of plane-wave reflection coefficients in anelastic media is conceptually simple and robust and provides correct solutions beyond the equivalent elastic critical (EEC) angl

Evaluation of the stiffness tensor of a fractured medium with harmonic experiments

A fractured medium behaves as an anisotropic medium when the wavelength is much larger than the distance between fractures. These are modeled as boundary discontinuities in the displacement and particle velocity. When the set of fractures is plane, the theory predicts that the equivalent medium is transversely isotropic and viscoelastic (TIV). We present a novel procedure to determine the complex and frequency-dependent stiffness components. The methodology amounts to perform numerical compressibility and shear harmonic tests on a representative sample of the medium. These tests are described by a collection of elliptic boundary-value problems formulated in the space-frequency domain, which are solved with a Galerkin finite-element procedure. The examples illustrate the implementation of the tests to determine the set of stiffnesses and the associated phase velocities and quality factors.Fil: Santos, Juan Enrique. Universidad de Buenos Aires. Facultad de Ingeniería. Instituto del Gas y del Petróleo; Argentina. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Benedettini, Stefano. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Carcione, José M.. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; Itali

On the group velocity of guided waves in drill strings

A key element to verify the drill-bit signal processing is the estimation of the time delay of the guided waves transmitted through the drill string from the bit to the surface. This delay can be measured from drill-bit vibrations or calculated using the mechanical properties of the drill string. The calculation of the complete solution and the exact dispersion relations requires expensive numerical modeling. In this work, a simple approach to compute the group velocity of extensional and torsional waves by averaging the drill-string properties in the low-frequency approximation is used. The result is a generalization of the group velocity for periodic systems in which stationary distribution of properties is assumed. Results obtained with real strings show that the group velocity in the bottom-hole assembly is greater than the velocity in a uniform rod and lower than the velocity in the drill pipes

Numerical test of the Schoemberg-Muir theory

The Schoenberg-Muir theory states that an equivalent, homogeneous and anisotropic medium can be constructed from a layered medium composed of several thin layers, each anisotropic, under the assumption of stationarity. To test the theory we considered single transversely isotropic layers with different orientations of the symmetry axis and performed numerical simulations of wave propagation with a full-wave solver. The equivalent media have orthorhombic and monoclinic symmetries, respectively. The theory performed very well from the kinematical and dynamical points of view, even for strong anisotropy and layers described by media whose symmetry axes have different orientations.Fil: Carcione, José M.. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Picotti, Stefano. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Cavallini, Fabio. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Santos, Juan Enrique. Universidad de Buenos Aires. Facultad de Ingeniería. Instituto del Gas y del Petróleo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Seismic modeling to monitor CO2 geological storage: The Atzbach-Schwanenstadt gas field

We develop a petro-elastical numerical methodology to compute realistic synthetic seismograms and analyze the sensitivity of the seismic response when injecting carbon dioxide (CO2) in a depleted gas reservoir. The petro-elastical model describes the seismic properties of the reservoir rock saturated with CO2, methane and brine, and allows us to estimate the distribution and saturation of CO2 during the injection process. The gas properties, as a function of the in-situ pressure and temperature conditions, are computed with the Peng-Robinson equation of state, taking into account the absorption of gas by brine. Wave attenuation and velocity dispersion are based on the mesoscopic loss mechanism, which is simulated by an upscaling procedure to obtain an equivalent viscoelastic medium corresponding to partial saturation at the mesoscopic scale. Having the equivalent complex and frequency-dependent bulk (dilatational) modulus, we include shear attenuation and perform numerical simulations of wave propagation at the macroscale by solving the viscoelastic differential equations using the memory-variable approach. The pseudo-spectral modeling method allows general material variability and provides a complete and accurate characterization of the reservoir. The methodology is used to assess the sensitivity of the seismic method for monitoring the CO2 geological storage at the Atzbach-Schwanestadt depleted gas-field in Austria. The objective of monitoring is the detection of the CO2 plume in the reservoir and possible leakages of CO2. The leakages are located at different depths, where the CO2 is present as gaseous, liquid and supercritical phases. Even though the differences can be very subtle, this work shows that seismic monitoring of CO2 from the surface is possible. While the identification of shallow leakages is feasible, the detection of the plume and deep leakages, located in the caprock just above the injection formation, is more difficult, but possible by using repeatability metrics, such as the normalized RMS (NRMS) images. Considering real-data conditions, affected by random noise, a reference detection threshold for deep leakages and the CO 2 plume in the reservoir corresponds to a signal-to-noise ratio of about 10 dB.Fil: Picotti, Stefano. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Carcione, José M.. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Gei, Davide. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Rossi, Giuliana. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Santos, Juan Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Instituto del Gas y del Petróleo; Argentina. Universidad Nacional de La Plata; Argentina. Purdue University; Estados Unido

A New Anelasticity Model for Wave Propagation in Partially Saturated Rocks

Elastic wave propagation in partially saturated reservoir rocks induces fluid flow in multi-scale pore spaces, leading to wave anelasticity (velocity dispersion and attenuation). The propagation characteristics cannot be described by a single-scale flow-induced dissipation mechanism. To overcome this problem, we combine the White patchy-saturation theory and the squirt flow model to obtain a new anelasticity theory for wave propagation. We consider a tight sandstone Qingyang area, Ordos Basin, and perform ultrasonic measurements at partial saturation and different confining pressures, where the rock properties are obtained at full-gas saturation. The comparison between the experimental data and the theoretical results yields a fairly good agreement, indicating the efficacy of the new theory