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

Modelado y análisis del flujo de agua en medios porosos heterogéneos total o parcialmente saturados

El presente trabajo de Tesis aborda el problema de la caracterización del flujo de agua en medios porosos heterogéneos mediante el uso de métodos numéricos y soluciones analíticas. En primer lugar, se propone un experimento numérico que simula las técnicas de laboratorio usualmente empleadas para la obtención experimental de las relaciones constitutivas. Con este fin se resuelve la ecuación de flujo no saturado en estado estacionario en dominios bidimensionales y tridimensionales considerando campos de conductividad hidráulica altamente heterogéneos. La linealización del problema se realiza mediante un esquema de Picard y la aproximación numérica mediante métodos híbridos mixtos de elementos finitos. Este procedimiento numérico es utilizado para obtener parámetros hidráulicos efectivos y relaciones constitutivas de rocas fracturadas y rocas heterogéneas con distinto grado de correlación espacial. Se presenta además un análisis comparativo de las diferencias que surgen al representar las heterogeneidades en dos y tres dimensiones. La caracterización hidráulica de rocas fracturadas también es abordada mediante modelos analíticos. Utilizando conceptos de geometría fractal para representar la red de fracturas se derivan dos modelos constitutivos con expresiones analíticas cerradas para una y dos fases (agua y aire). Las expresiones analíticas son analizadas en términos de los parámetros involucrados, y validadas mediante su ajuste con datos experimentales y valores obtenidos con el experimento numérico descrito anteriormente. Por último, se analiza el efecto de la heterogeneidad de la conductividad hidráulica a escala de campo en acuíferos costeros afectados por la marea. Para ello se derivan soluciones analíticas exactas y aproximadas que permiten estimar las fluctuaciones inducidas en pozos para el caso de heterogeneidades lineales de la conductividad hidráulica. Las nuevas soluciones analíticas son comparadas con la correspondiente a un acuífero homogéneo y utilizadas para estimar parámetros hidráulicos a partir de datos experimentales disponibles en la literatura.Facultad de Ciencias Astronómicas y Geofísica

Effective Pore Fluid Bulk Modulus at Patchy Saturation: An Analytic Study

A patchy saturated two-layered porous rock, with each layer filled with a different fluid, is examined. We assume that this system is probed by an elastic wave having a wavelength much larger than the layers' thicknesses. We also assume that the diffusion length is smaller than the thickness of an individual layer, which implies hydraulic disconnection between layers. In the context of Gassmann's fluid substitution theory, we analytically derived an exact expression for the effective fluid bulk modulus assuming that both layers have the same porosity, dry frame, and mineral matrix properties. In addition we derived an approximate solution that works well at relatively high porosities. Both solutions are expressed as a weighted average of the arithmetic and harmonic averages of individual bulk moduli of the pore fluid. These weights are explicitly given as functions of the porosity, the fractional thicknesses of both layers, and the elastic moduli of the constituents. For the approximate solution, one does not require explicit knowledge of the shear modulus of the rock. The comparison with laboratory data showed that, in the case where a porous, isotropic rock is filled with water and gas, the approximate solution can be used to model the measured data for high values of water saturation.Fil: Monachesi, Leonardo Bruno. Universidad Nacional de Río Negro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte. Instituto de Investigación en Paleobiología y Geología; ArgentinaFil: Wollner, Uri. University of Stanford; Estados UnidosFil: Dvorkin, Jack. King Fahd University Of Petroleum And Minerals; Arabia Saudit

An analytical solution to assess the SH seismoelectric response of the vadose zone

We derive an analytical solution of the seismoelectric conversions generated in the vadose zone, when this region is crossed by a pure shear horizontal (SH) wave. Seismoelectric conversions are induced by electrokinetic effects linked to relative motions between fluid and porous media. The considered model assumes a 1D soil constituted by a single layer on top of a half-space in contact at the water table, and a shearing force located at the earth?s surface as the wave source. The water table is an interface expected to induce a seismoelectric interfacial response (IR). The top layer represents a porous rock in which porous space is partially saturated by water and air, while the half-space is completely saturated with water, representing the saturated zone. The analytical expressions for the coseismic fields and the interface responses, both electric and magnetic, are derived by solving Pride's equations with proper boundary conditions. An approximate analytical expression of the solution is also obtained, which is very simple and applicable in a fairly broad set of situations. Hypothetical scenarios are proposed to study and analyse the dependence of the electromagnetic fields on various parameters of the medium. An analysis of the approximate solution is also made together with a comparison to the exact solution. The main result of the present analysis is that the amplitude of the interface response generated at the water table is found to be proportional to the jump in the electric current density, which in turn depends on the saturation contrast, poro-mechanical and electrical properties of the medium and on the amplitude of the solid displacement produced by the source. This result is in agreement with the one numerically obtained by the authors, which has been published in a recent work. We also predict the existence of an interface response located at the surface, and that the electric interface response is several orders of magnitude bigger than the electric coseismic field, whereas it is the opposite using compressional waves as shown by theoretical and experimental results. This fact should encourage the performance of field and laboratory tests to check the viability of SHTE seismoelectrics as a near surface prospecting/monitoring tool.Facultad de Ciencias Astronómicas y Geofísica

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

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

An analytical solution to assess the SH seismoelectric response of the vadose zone

We derive an analytical solution of the seismoelectric conversions generated in the vadose zone, when this region is crossed by a pure shear horizontal (SH) wave. Seismoelectric conversions are induced by electrokinetic effects linked to relative motions between fluid and porous media. The considered model assumes a 1D soil constituted by a single layer on top of a half-space in contact at the water table, and a shearing force located at the earth?s surface as the wave source. The water table is an interface expected to induce a seismoelectric interfacial response (IR). The top layer represents a porous rock in which porous space is partially saturated by water and air, while the half-space is completely saturated with water, representing the saturated zone. The analytical expressions for the coseismic fields and the interface responses, both electric and magnetic, are derived by solving Pride's equations with proper boundary conditions. An approximate analytical expression of the solution is also obtained, which is very simple and applicable in a fairly broad set of situations. Hypothetical scenarios are proposed to study and analyse the dependence of the electromagnetic fields on various parameters of the medium. An analysis of the approximate solution is also made together with a comparison to the exact solution. The main result of the present analysis is that the amplitude of the interface response generated at the water table is found to be proportional to the jump in the electric current density, which in turn depends on the saturation contrast, poro-mechanical and electrical properties of the medium and on the amplitude of the solid displacement produced by the source. This result is in agreement with the one numerically obtained by the authors, which has been published in a recent work. We also predict the existence of an interface response located at the surface, and that the electric interface response is several orders of magnitude bigger than the electric coseismic field, whereas it is the opposite using compressional waves as shown by theoretical and experimental results. This fact should encourage the performance of field and laboratory tests to check the viability of SHTE seismoelectrics as a near surface prospecting/monitoring tool.Facultad de Ciencias Astronómicas y Geofísica

A Fractal Model for Predicting Water and Air Permeabilities of Unsaturated Fractured Rocks

A fractal model to predict water and air permeabilities of unsaturated fractured rocks is presented. The derivation of the model is based on physical and geometric concepts. The pattern of the fracture network is assumed to be fractal and it is described by the Sierpinski carpet. The proposed expressions for the relative water and air permeabilities are closed-form and have five independent parameters: the fractal dimension, the minimum and maximum fracture apertures and the emergence points for water and air flows. The ability of the model to describe experimental data is illustrated by fitting the derived analytical curve to measured data from Grimsel Test Site (Switzerland) and numerical experiments designed by Liu and Bodvarsson (J Hydrol 252:116–125, 2001). In both the cases, the proposed model provides a very good description of water and air permeabilities over several orders of magnitude for the whole range of water saturation.Facultad de Ciencias Astronómicas y Geofísica

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.Facultad de Ciencias Astronómicas y GeofísicasConsejo Nacional de Investigaciones Científicas y Técnica

Un modelo fractal para estimar la conductividad hidráulica no saturada de rocas fracturadas

Durante las últimas dos décadas el estudio y la modelación del flujo de agua en rocas fracturadas no saturadas ha recibido considerable atención por parte de investigadores de distintas áreas como la geología, geofísica e ingeniería. Una de las razones principales para su estudio radica en la búsqueda de formaciones geológicas de baja permeabilidad para la construcción de repositorios de residuos nucleares. Para modelar el flujo de agua cuando se utiliza la aproximación del continuo es necesario contar con relaciones constitutivas del medio poroso considerado. Las relaciones constitutivas son curvas de saturación (S) y conductividad hidráulica (K) en función de la altura de presión (h). En general, la determinación en laboratorio de la curva de saturación no suele presentar mayores inconvenientes. En cambio, la determinación experimental de K(h) resulta difícil y costosa, por lo que se suele recurrir a modelos teóricos para su estimación. Entre los modelos teóricos más utilizados se destacan los de Burdine (Burdine, 1953) y Mualem (Mualem, 1976), los cuales permiten predecir la conductividad hidráulica K a partir de la curva de saturación S. Estos modelos predictivos han sido desarrollados para medios porosos de tipo sedimentario, no existiendo en la literatura modelos específicos para rocas fracturadas. En este trabajo se presenta un modelo fractal simple para predecir la conductividad hidráulica no saturada de rocas fracturadas. La deducción del modelo se basa en la hipótesis de que la red de fracturas puede ser descrita mediante un objeto fractal clásico denominado carpeta de Sierpinski. La expresión propuesta de K es cerrada y depende únicamente de tres parámetros independientes: la dimensión fractal y las aperturas máxima y mínima de las fracturas. Una de las características que presenta el modelo propuesto, y que permite validarlo en forma teórica, es que la curva de conductividad hidráulica relativa es equivalente a la que se obtiene con el modelo de Burdine cuando se asume un factor de tortuosidad unitario. Finalmente, se realiza un estudio comparativo entre el modelo analítico propuesto y las relaciones constitutivas obtenidas mediante simulación numérica por Liu y Bodvarsson (2001). La comparación muestra que el modelo propuesto puede predecir dichas relaciones constitutivas en un amplio rango de valores de saturación de agua, y constituye por lo tanto una validación adicional. El modelo de K(h) propuesto es único en su tipo ya que ha sido derivado íntegramente a partir de leyes físicas clásicas y propiedades geométricas de la red de fracturas.Modeling groundwater flow in unsaturated fractured rocks has received considerable attention in the last two decades. One of the main reasons for focusing on the study of water flow in this type of media is the search for potential safe permanent storage facilities for geological disposal of high-level nuclear wastes. Knowledge of constitutive relations is indispensable for the numerical solution of the equations describing water flow in unsaturated porous media. These relations are saturation (S) and hydraulic conductivity (K) curves, both expressed as functions of the pressure head (h). The experimental determination of K(h) is tedious and time-consuming and the measurements are variables, error-prone, and applicable to only a narrow range of pressure head h. An alternative to direct measurement is to use theoretical models which predict K(h) from the saturation curve S(h) that can be easily measured in laboratory. The majority of the models that predicts K(h) from S(h) have been developed for describing unsaturated flow in sedimentary formations (granular porous media). Predictive models specifically designed for fractured hard rocks are virtually nonexistent. In this study, a hydraulic conductivity model for fractured rocks is derived. The proposed K(h) model is based on the assumption that the fracture pattern is self-similar. The fracture pattern is described using the Sierpinski carpet, a classical fractal object that contains a self-similar geometric pattern of pores. The proposed model has a closed form analytical expression with three independent geometric parameters: the fractal dimension of the Sierpinski carpet and the maximum and minimum fracture apertures. One of the main features of the proposed model that allows its validation is that the expression of K(h) is identical to the one obtained by using the Burdine model with a tortuosity factor equal to one. The proposed model can represent the constitutive relations for fractured rocks obtained by Liu and Bodvarsson (2001) using numerical simulation techniques. The proposed K(h) model is the only existing model which has been completely derived from physical concepts and geometric properties of the fracture pattern.Asociación Argentina de Geofísicos y Geodesta