Discontinuous Galerkin methods for solving the acoustic wave equation

In this work we develop a numerical simulator for the propagation of elastic waves by solving the one-dimensional acoustic wave equation with Absorbing Boundary Conditions (ABC’s) on the computational boundaries using Discontinuous Galerkin Finite Element Methods (DGFEM). The DGFEM allows us to easily simulate the presence of a fracture in the elastic medium by means of a linear-slip model. We analize the behaviour of our algorithm by comparing its results against analytic solutions. Furthermore, we show the frequency-dependent effect on the propagation produced by the fracture as appears in previous works. Finally, we present an analysis of the numerical parameters of the method.Fil: Castromán, Gabriel Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas. Departamento de Geofísica Aplicada; ArgentinaFil: Zyserman, Fabio Ivan. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas. Departamento de Geofísica Aplicada; Argentin

Comparisons between sediment transport models and observations made in wave and current flows above plane beds

As a part of the MAST2 G8-M Coastal Morphodynamics project, the predictions of four sediment transport models have been compared with detailed laboratory data sets obtained in the bottom boundary layer beneath regular waves, asymmetrical waves, and regular waves superimposed co-linearly on a current. Each data set was obtained in plane bed, sheet flow, conditions and each of the four untuned numerical models has provided a one-dimensional vertical (1DV), time-varying, representation of the various experimental situations. Comparisons have been made between the model predictions and measurements of both time-dependent sediment concentration, and also wave-averaged horizontal velocity and concentration. For the asymmetrical waves and for the combined wave-current flows, comparisons have been made with vertical profiles of the cycle-averaged sediment flux, and also with the vertically-integrated net sediment transport rate. Each of the turbulence diffusion models gives an accurate estimate of the net transport rate (invariably well within a factor of 2 of the measured value). In contrast, none of the models provides a good detailed description of the time-dependent suspended sediment concentration, due mainly to the inability of conventional turbulence diffusion schemes to represent the entrainment of sediment into suspension by convective events at flow reversal. However, in the cases considered here, this has not seriously affected the model predictions of the net sediment flux, due to the dominance of the near-bed transport. The comparisons in this paper are aimed not only at testing the predictive capability of existing sediment transport modelling schemes, but also at highlighting some of their deficiencies

Reply to ‘Comment on “Dependence of shear wave seismoelectrics on soil textures: a numerical study in the vadose zone by F.I. Zyserman, L.B. Monachesi and L. Jouniaux” by Revil, A.’

In this paper we reply to a the comment made by Revil (2017) on our paper (2017, Geophys. J. Int., 208), where we describe seismoelectric phenomena in the vadose zone based on the theory of Pride empirically extended for unsaturated conditions. We analyse and answer each one of the enumerated critics, and reaffirm the conclusions of our work. In particular, we prove that using the conductivity model suggested by Revil (2017) does not change our predictions significantly, contrary to what was argued in the comment. Further, in the light of previous and new theoretical and experimental results existing in the literature, we confirm the reasonability of having tested a non-monotonic saturation dependent streaming potential coefficient model besides the monotonic one, and discuss the suitability of assuming a linear relation between the permeability and the excess charge.Fil: Zyserman, Fabio Ivan. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas. Departamento de Geofísica Aplicada; ArgentinaFil: Monachesi, Leonardo Bruno. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Río Negro. Sede Alto Valle. Instituto de Investigaciones en Paleobiología y Geología; ArgentinaFil: Jouniaux, L.. Centre National de la Recherche Scientifique; Franci

Seismo-electrics, electro-seismics, and seismo-magnetics for earth sciences

International audienceThe seismo-electromagnetic method (SEM) is used for non-invasive subsurface exploration. It shows interesting results for detecting fluids such as water, ice, oil, gas, CO_2 , and also to better characterise the subsurface in terms of porosity, permeability, and fractures. However, a limitation of this method is the low level of the induced 5 signals. We first describe SEM's theoretical background, and the role of some key parameters. We then detail recent studies on SEM, through theoretical and numerical developments, and through field and laboratory observations, to show that this method can bring advantages compared to classical geophysical methods

Reply to comment by A. Revil on "Seismo-electrics, electro-seismics, and seismo-magnetics for earth sciences" by L.Jouniaux and F.Zyserman

International audienceThe relation between the volumetric charge density Q_V expressed as a function of permeability has not been validated using inde-pendent measurements of permeability and charge density.This equation has been used to calculate Q_V , using permeability values, to deduce that Q_V is inversely related to the permeability. Therefore this approach is considered not appropriate and should not be used. We advice thereader to use the electric current density as a function of the pressure, rather than as a function of the velocity and Q_V

Discontinuous Galerkin methods for solving the acoustic wave equation

In this work we develop a numerical simulator for the propagation of elastic waves by solving the one-dimensional acoustic wave equation with Absorbing Boundary Conditions (ABC’s) on the computational boundaries using Discontinuous Galerkin Finite Element Methods (DGFEM). The DGFEM allows us to easily simulate the presence of a fracture in the elastic medium by means of a linear-slip model. We analize the behaviour of our algorithm by comparing its results against analytic solutions. Furthermore, we show the frequency-dependent effect on the propagation produced by the fracture as appears in previous works. Finally, we present an analysis of the numerical parameters of the method.Facultad de Ciencias Astronómicas y Geofísica

A review on electrokinetically induced seismo-electrics, electro-seismics, and seismo-magnetics for Earth sciences

The seismo-electromagnetic method (SEM) can be used for non-invasive subsurface exploration. It shows interesting results for detecting fluids such as water, oil, gas, CO2, or ice, and also help to better characterise the subsurface in terms of porosity, permeability, and fractures. However, the challenge of this method is the low level of the induced signals. We first describe SEM's theoretical background, and the role of some key parameters. We then detail recent studies on SEM, through theoretical and numerical developments, and through field and laboratory observations, to show that this method can bring advantages compared to classical geophysical methods.Facultad de Ciencias Astronómicas y Geofísica

Analysis of 2D time-domain seismoelectric modeling

This work analyzes the equations for 2D seismoelectric modeling in poroelastic fluid-saturated media. The model involves the simultaneous solution of Biot’s equations of motion and Maxwell’s equations, coupled via an electrokinetc coefficient and employs absorbing boundary conditions at the artificial boundaries. Results on existence and uniqueness of the solution of the differential problem are presented.Facultad de Ciencias Astronómicas y Geofísica

Dependence of shear wave seismoelectrics on soil textures: a numerical study in the vadose zone

In this work, we study seismoelectric conversions generated in the vadose zone, when this region is traversed by a pure SH wave. We assume that the soil is a 1-D partially saturated lossy porous medium and we use the van Genuchten's constitutive model to describe the water saturation profile. Correspondingly, we extend Pride's formulation to deal with partially saturated media. In order to evaluate the influence of different soil textures we perform a numerical analysis considering, among other relevant properties, the electrokinetic coupling, coseismic responses and interface responses (IRs). We propose new analytical transfer functions for the electric and magnetic field as a function of the water saturation, modifying those of Bordes et al. and Garambois & Dietrich, respectively. Further, we introduce two substantially different saturation-dependent functions into the electrokinetic (EK) coupling linking the poroelastic and the electromagnetic wave equations. The numerical results show that the electric field IRs markedly depend on the soil texture and the chosen EK coupling model, and are several orders of magnitude stronger than the electric field coseismic ones. We also found that the IRs of the water table for the silty and clayey soils are stronger than those for the sandy soils, assuming a non-monotonous saturation dependence of the EK coupling, which takes into account the charged air-water interface. These IRs have been interpreted as the result of the jump in the viscous electric current density at the water table. The amplitude of the IR is obtained using a plane SH wave, neglecting both the spherical spreading and the restriction of its origin to the first Fresnel zone, effects that could lower the predicted values. However, we made an estimation of the expected electric field IR amplitudes detectable in the field by means of the analytical transfer functions, accounting for spherical spreading of the SH seismic waves. This prediction yields a value of 15 μV m-1, which is compatible with reported values.Facultad de Ciencias Astronómicas y GeofísicasConsejo Nacional de Investigaciones Científicas y Técnica

SH Seismoelectric Response of a Glacier : An Analytic Study

In this work we derive the analytic solutions to the system of equations modeling, within the framework of Pride's theory, the seismic-to-electromagnetic conversions taking place in a glacial environment. Considering a one-dimensional approach, we set a pure shear horizontal wave seismic source on top of an elastic medium representing the glacier, which overlies a porous medium fully saturated with water, representing the glacier bed. The obtained solutions allow to separately represent and analyze the induced electromagnetic responses, the so called coseismic waves, for both the electric and magnetic fields along with the signals originated at the glacier bottom, the electric interface response, and magnetic interface response. We also propose approximate solutions, useful to be used in a fast inversion algorithm. We analyze the characteristics of the induced electromagnetic signals and their dependence on the type of glacier bed, considering an unconsolidated one and a consolidated one. The main results of the present paper are manifold, on the one hand, the mentioned analytic solutions, on the other hand, that the electric interface response originated at the glacier bottom is proportional to the electric current density at this depth, and depends on textural and electrical properties of the basement. We also showed that the amplitude of the electric interface response is three orders of magnitude higher than the amplitude of the electric coseismic field. This fact reinforces the idea proposed in our previous works that it would be interesting to test shear horizontal seismoelectrics as a possible geophysical prospecting and monitoring tool.Facultad de Ciencias Astronómicas y Geofísica