Frequency-dependent streaming potentials: a review

The interpretation of seismoelectric observations involves the dynamic electrokinetic coupling, which is related to the streaming potential coefficient. We describe the different models of the frequency-dependent streaming potential, mainly the Packard's and the Pride's model. We compare the transition frequency separating low-frequency viscous flow and high-frequency inertial flow, for dynamic permeability and dynamic streaming potential. We show that the transition frequency, on a various collection of samples for which both formation factor and permeability are measured, is predicted to depend on the permeability as inversely proportional to the permeability. We review the experimental setups built to be able to perform dynamic measurements. And we present some measurements and calculations of the dynamic streaming potential

Laboratory monitoring of P-waves in partially saturated sand

International audienceEnergy dissipation is observed on seismic data when a wave propagates through a porous medium, involving different frequency regimes depending on the nature of rock and fluid types. We focus here on the role of partial fluid saturation in unconsolidated porous media, looking in particular at P-wave phase velocity and attenuation. The study consists in running an experiment in a sand-filled tank partially saturated with water. Seismic propagation in the tank is generated in the kHz range by hitting a steel ball on a granite plate. Seismic data are recorded by buried accelerometers and injecting or extracting water controls the partial saturation. Several imbibition/drainage cycles were performed between the water and gas residual saturations. A Continuous Wavelet Transform applied on seismic records allowed us to extract the direct P-wave at each receiver.We observe an hysteresis in phase velocities and inverse quality factors between imbibition and drainage. Phase velocities and inverse quality factors are then jointly inverted to get a final poro-visco-elastic model of the partially saturated sand that satisfactorily reproduces the data. The model formulation consists in generalizing the Biot theory to effective properties of the fluid and medium (permeability and bulk modulus) in order to properly explain the phase velocity variation as a function of the saturation. The strong level of attenuation measured experimentally is further explained by an anelastic effect due to grain to grain sliding, adding to Biot's losses. This study shows that fluid distribution at microscopic scale has strong influence on the attenuation of direct P-waves at macroscopic scale and confirms that seismic prospection may be a powerful tool for the characterization of transport phenomena in porous media

Experimental quantification of the seismoelectric transfer function and its dependence on conductivity and saturation in loose sand

International audienceUnder certain circumstances, seismic propagation within porous media may be associated toa conversion of mechanical into electromagnetical energy known as a seismoelectromagneticphenomemon. The propagation of fast compressional P-waves is more specifically associatedto manifestations of a seismoelectric field linked to fluid flow within the pores. The analysisof seismoelectric phenomena, which requires combining the theory of electrokinetics to Biot’stheory of poroelasticity, provides us with a transfer function noted E/ü that links the coseismicseismoelectric field E to the seismic acceleration u. In order to measure the transfer function,we have developed an experimental set-up enabling seismoelectric laboratory observation inunconsolidated quartz sand within the kilohertz range. The investigation focused on the impactof fluid conductivity and water saturation over the coseismic seismoelectric field. Duringthe experiment, special attention was given to the accuracy of electric field measurements. Weconcluded that, in order to obtain a reliable estimate of the electric field amplitude, the dipolefrom which the potential differences are measured should be of much smaller length than thewavelength of the propagating seismic field. Time-lapse monitoring of the seismic velocitiesand seismoelectric transfer functions were performed during imbibition and drainage experiments.In all cases, the quantitative analysis of the seismoelectric transfer function E=u was ingood agreement with theoretical predictions. While investigating saturation variations from theresidual water saturation to full saturation, we showed that the E/ü ratio undergoes a switchin polarity at a particular saturation S, also implying a sign change of the filtration, traducinga reversal of the relative fluid displacement with respect to the frame. This sign change atcritical saturation S stresses a particular behaviour of the poroelastic medium: the droppingof the coseismic electric field to zero traduces the absence of relative pore/fluid displacementsrepresentative of a Biot dynamically compatible medium.We concluded from our experimentalstudy in loose sand that measurements of the coseismic seismoelectric coupling may provideinformation on fluid distribution within the pores, and that the reversal of the seismoelectricfield may be used as an indicator of the dynamically compatible state of the medium

First laboratory measurements of seismo-magnetic conversions in fluid-filled Fontainebleau sand

International audienceSeismic wave propagation in fluid-filled porous materials induces electromagnetic effects due to small relative pore-fluid motions. In order to detect the seismo-magnetic couplings theoretically predicted by Pride (1994), we have designed a small-scale experiment in a low-noise underground laboratory which presents exceptional electromagnetic shielding conditions. Our experiment included accelerometers, electric dipoles and induction magnetometers to characterize the seismo-electromagnetic propagation phenomena. To assess the electrokinetic origin of the measured electric and magneticfields, we compared records obtained in dry and fluid-filled sand. Extra care has been taken to ensure the mechanical decoupling between the sand column and the magnetometers to avoid spurious vibrations of the magnetometers and misinterpretations of the recorded signals. Our results show that seismo-electric and seismo-magnetic signals are associated with different wave propagation modes, thus emphasizing the electrokinetic origin of these effects

Seismoelectric wave propagation numerical modelling in partially saturated materials

International audienceTo better understand and interpret seismoelectric measurements acquired over vadose environments, both the existing theory and the wave propagation modelling programmes, available for saturated materials, should be extended to partial saturation conditions. We propose here an extension of Pride's equations aiming to take into account partially saturated materials, in the case of a water-air mixture. This new set of equations was incorporated into an existing seismoelectric wave propagation modelling code, originally designed for stratified saturated media. This extension concerns both the mechanical part, using a generalization of the Biot-Gassmann theory, and the electromagnetic part, for which dielectric permittivity and electrical conductivity were expressed against water saturation. The dynamic seismoelectric coupling was written as a function of the streaming potential coefficient, which depends on saturation, using four different relations derived from recent laboratory or theoretical studies. In a second part, this extended programme was used to synthesize the seismoelectric response for a layered medium consisting of a partially saturated sand overburden on top of a saturated sandstone half-space. Subsequent analysis of the modelled amplitudes suggests that the typically very weak interface response (IR) may be best recovered when the shallow layer exhibits low saturation. We also use our programme to compute the seismoelectric response of a capillary fringe between a vadose sand overburden and a saturated sand half-space. Our first modelling results suggest that the study of the seismoelectric IR may help to detect a sharp saturation contrast better than a smooth saturation transition. In our example, a saturation contrast of 50 per cent between a fully saturated sand half-space and a partially saturated shallow sand layer yields a stronger IR than a stepwise decrease in saturation

Seismic wave propagation in heterogeneous limestone samples

International audienceMimic near-surface seismic field measurements at a small scale, in the laboratory, under a well-controlled environment, may lead to a better understanding of wave propagation in complex media such as in geological materials. Laboratory experiments can help in particular to constrain and refine theoretical and numerical modelling of physical phenomena occurring during seismic propagation, in order to make a better use of the complete set of measurements recorded in the field. We have developed a laser Doppler vibrometer (laser interferometry) platform designed to measure non-contact seismic displacements (or velocities) of a surface. This technology enables to measure displacements as small as a tenth of a nanometer on a wide range of frequencies, from a few tenths to a few megahertz. Our experimental setup is particularly suited to provide high-density spatial and temporal records of displacements on the edge of any vibrating material (aluminum, limestone, ...). We will firstly present experiments in cuboid and cylinders of aluminum (homogeneous) in order to calibrate the seismic sources (radiation diagram, frequency content) and identify the wave arrivals (P, S, converted, surface waves). The measurements will be compared quantitatively to a direct 2D numerical elastodynamic simulation (finite elements, Interior Penalty Discontinuous Galerkin). We will then show wave measurements performed in cylindrical heterogeneous limestone cores of typical diameter size around 10 cm. Tomographic images of velocity (figure 2a) in 2D slices of the limestone cores will be derived based upon the time of first arrivals and implemented in the numerical model. By quantifying the difference between numerical and experimental results, the tomographic velocity model will be reciprocally improved and finally compared to a X − ray tomographic image of that slice. A brief overview of the studies Seismic sources We will explore piezo-electric sources of different frequencies (100 kHZ ∼ 5 M Hz) and test the new laser ablation source whose dominant frequency can reach 2 M Hz in aluminium. Avantages and drawbacks of each technology will be discussed in terms of source and wave propagation characterisation. Wave identification in an aluminium cube of side length 280 mm and seismic source at the center of one face We have identified experimentally P, S, head wave, PS, SP and surface waves measured on the cube surfaces. Meanwhile, direct numerical simulations have helped to quantitatively analyze the kinematics of wave fronts. For example, on the surface where the seismic source is excited, a P front, an S front and a PS head wave front are measured by the laser vibrometer right after the initial seismic impulse. These wavefronts can be understood by both the Huygens' Principle and the Snell-Descartes Law. In Figure 1, the seismic source excits simultaneously at time t = 0 a P wave and an S wave. As time evolves, waves propagate inside the volume and a P-wave propagates along the boundary as well: the latter one acts on the boundary as secondary sources which will emit both P and S waves, creating finally a new PS head wave front nicely measured in the experiments. The colours of magenta and green correspond to null amplitudes

Evidence of the theoretically predicted seismo-magnetic conversion

We acknowledge the Geophysical Journal International and the Association/Society and Blackwell Publishing. The definitive version is available at www.wileyinterscience.com. The reference is : Bordes, C., L. Jouniaux, S. Garambois, M. Dietrich, J.-P. Pozzi, and S. Gaffet, Evidence of the theoretically predicted seismo-magnetic conversion, G.J.I., 174, issue 2, 489-504, doi:10.1111/j.1365-246X.2008.03828.xInternational audienceSeismo-electromagnetic phenomena in porous media arise from seismic wave-induced fluid motion in the pore space, which perturbs the equilibrium of the electric double layer. This paper describes with details the original experimental apparatus built within the ultra-shielded chamber of the Low Noise Underground Laboratory of Rustrel (France). We measured seismo-magnetic conversions in moist sand using two induction magnetometers, and a pneumatic seismic source to generate the seismic wave propagation. We ensured to avoid the magnetometer vibrations, which could induce strong disturbances from induction origin. Interpretation of the data is improved by an analytical description of phase velocities for fast (P_f) and slow (P_s) longitudinal modes, transverse mode (S) as well as the extensional mode due to the cylindrical geometry of the sample. The purpose of this paper is to provide elements to measure correctly co seismic seismomagnetic fields and to specify their amplitude. The seismic arrivals recorded in the sample showing a 1200$-1300 m/s velocity have been associated to P and extensional waves. The measured seismo-magnetic arrivals show a velocity of about 800 m/s consistent with the calculated phase velocity of S waves. Therefore we show that the seismo-magnetic field is associated to the transverse part of the propagation, as theoretically predicted by Pride (1994), but never measured up to now. Moreover, the combined experimental and analytical approaches lead us to the conclusion that the measured seismo-magnetic field is probably about 0.35 nT for a 1 m/s2 seismic source acceleration (0.1 g)

Seismic imaging in laboratory trough laser Doppler vibrometry

International audienceMimic near-surface seismic field measurements at a small scale, in the laboratory, under a well-controlled environment , may lead to a better understanding of wave propagation in complex media such as in geological materials. Laboratory experiments can help in particular to constrain and refine theoretical and numerical modelling of physical phenomena occurring during seismic propagation, in order to make a better use of the complete set of measurements recorded in the field. We have developed a laser Doppler vibrometer (laser interferometry) platform designed to measure non-contact seismic displacements (or velocities) of a surface. This technology enables to measure displacements as small as a tenth of a nanometer on a wide range of frequencies, from a few tenths to a few megahertz. Our experimental setup is particularly suited to provide high-density spatial and temporal records of displacements on the edge of any vibrating material. We will show in particular a study of MHz wave propagation (excited by piezoelectric transducers) in cylindrical cores of typical diameter size around 10 cm. The laser vibrometer measurements will be first validated in homogeneous materials cylinders by comparing the measurements to a direct numerical simulation. Special attention will be given to the comparison of experimental versus numerical amplitudes of displacements. In a second step, we will conduct the same type of study through heterogeneous carbonate cores, possibly fractured. Tomographic images of velocity in 2D slices of the carbonate core will be derived based upon on the time of first arrival. Preliminary attempts of tomographic attenuation maps will also be presented based on the amplitudes of first arrivals. Experimental records will be confronted to direct numerical simulations and tomographic images will be compared to x-ray scanner imaging of the cylindrical cores

Seismic imaging in laboratory trough laser Doppler vibrometry

International audienceMimic near-surface seismic field measurements at a small scale, in the laboratory, under a well-controlled environment , may lead to a better understanding of wave propagation in complex media such as in geological materials. Laboratory experiments can help in particular to constrain and refine theoretical and numerical modelling of physical phenomena occurring during seismic propagation, in order to make a better use of the complete set of measurements recorded in the field. We have developed a laser Doppler vibrometer (laser interferometry) platform designed to measure non-contact seismic displacements (or velocities) of a surface. This technology enables to measure displacements as small as a tenth of a nanometer on a wide range of frequencies, from a few tenths to a few megahertz. Our experimental setup is particularly suited to provide high-density spatial and temporal records of displacements on the edge of any vibrating material. We will show in particular a study of MHz wave propagation (excited by piezoelectric transducers) in cylindrical cores of typical diameter size around 10 cm. The laser vibrometer measurements will be first validated in homogeneous materials cylinders by comparing the measurements to a direct numerical simulation. Special attention will be given to the comparison of experimental versus numerical amplitudes of displacements. In a second step, we will conduct the same type of study through heterogeneous carbonate cores, possibly fractured. Tomographic images of velocity in 2D slices of the carbonate core will be derived based upon on the time of first arrival. Preliminary attempts of tomographic attenuation maps will also be presented based on the amplitudes of first arrivals. Experimental records will be confronted to direct numerical simulations and tomographic images will be compared to x-ray scanner imaging of the cylindrical cores

On the use of a pulsed-laser source in laboratory seismic experiments

International audienceReproduction of large-scale seismic exploration at laboratory-scale with controllable sources is a promising approach that could not only be applied to study small-scale physical properties of the medium, but also contribute to significant progress in wave-propagation understanding and complex media imaging at exploration scale via upscaling methods. We seek to characterize the properties of a laser-generated seismic source for new geophysical experiments at laboratory scale. This consists in generating seismic waves by pulsed-laser impacts and measuring the displacement wavefield by laser vibrometry. Parallel 2D/3D simulations using Discontinuous Galerkin discretization method and analytic predictions have been done to match the experimental data