Retrieving shallow shear-wave velocity profiles from 2D seismic-reflection data with severely aliased surface waves

The inversion of surface-wave phase-velocity dispersion curves provides a reliable method to derive near-surface shear-wave velocity profiles. In this work, we invert phase-velocity dispersion curves estimated from 2D seismic-reflection data. These data cannot be used to image the first 50 m with seismic-reflection processing techniques due to the presence of indistinct first breaks and significant NMO-stretching of the shallow reflections. A surface-wave analysis was proposed to derive information about the near surface in order to complement the seismic-reflection stacked sections, which are satisfactory for depths between 50 and 700 m. In order to perform the analysis, we had to overcome some problems, such as the short acquisition time and the large receiver spacing, which resulted in severe spatial aliasing. The analysis consists of spatial partitioning of each line in segments, picking of the phase-velocity dispersion curves for each segment in the f-k domain, and inversion of the picked curves using the neighborhood algorithm. The spatial aliasing is successfully circumvented by continuously tracking the surface-wave modal curves in the f-k domain. This enables us to sample the curves up to a frequency of 40 Hz, even though most components beyond 10 Hz are spatially aliased. The inverted 2D VS sections feature smooth horizontal layers, and a sensitivity analysis yields a penetration depth of 20–25 m. The results suggest that long profiles may be more efficiently surveyed by using a large receiver separation and dealing with the spatial aliasing in the described way, rather than ensuring that no spatially aliased surface waves are acquired.Fil: Onnis, Luciano Emanuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Osella, Ana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Carcione, Jose M.. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; Itali

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

Erratum to: Fracture-Induced Anisotropic Attenuation

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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

Biot-Rayleigh theory of wave propagation in double-porosity media

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