Specific shear-dependent viscoelastic third-grade fluid model

A specific modified constitutive equation for a third-grade fluid is proposed so that the model be suitable for applications where shear-thinning or shear-thickening may occur. For that, we use the Cosserat theory approach reducing the exact three-dimensional equations to a system depending only on time and on a single spatial variable. This one-dimensional system is obtained by integrating the linear momentum equation over the cross-section of the tube, taking a velocity field approximation provided by the Cosserat theory. From this reduced system, we obtain the unsteady equations for the wall shear stress and mean pressure gradient depending on the volume flow rate, Womersley number, viscoelastic coefficient and flow index over a finite section of the tube geometry with constant circular cross-section.

Inversion of ambient seismic noise HVSR to evaluate velocity and structural models of the Lower Tagus Basin, Portugal

During its history, several significant earthquakes have shaken the Lower Tagus Valley (Portugal). These earthquakes were destructive; some strong earthquakes were produced by large ruptures in offshore structures located southwest of the Portuguese coastline, and other moderate earthquakes were produced by local faults. In recent years, several studies have successfully obtained strong-ground motion syntheses for the Lower Tagus Valley using the finite difference method. To confirm the velocity model of this sedimentary basin obtained from geophysical and geological data, we analysed the ambient seismic noise measurements by applying the horizontal to vertical spectral ratio (HVSR) method. This study reveals the dependence of the frequency and amplitude of the low-frequency (HVSR) peaks (0.2–2 Hz) on the sediment thickness. We have obtained the depth of the Cenozoic basement along a profile transversal to the basin by the inversion of these ratios, imposing constraints from seismic reflection, boreholes, seismic sounding and gravimetric and magnetic potentials. This technique enables us to improve the existing three-dimensional model of the Lower Tagus Valley structure. The improved model will be decisive for the improvement of strong motion predictions in the earthquake hazard analysis of this highly populated basin. The methodology discussed can be applied to any other sedimentary basin.