Coupled seismic and electromagnetic wave propagation

Coupled seismic and electromagnetic wave propagation is studied theoretically and experimentally. This coupling arises because of the electrochemical double layer, which exists along the solid-grain/fluid-electrolyte boundaries of porous media. Within the double layer, charge is redistributed, creating an excess electrical charge in the fluid along the boundary. Electrokinetic theory describes coupled seismic and electromagnetic wave propagation. It predicts that seismic waves disturb the fluid excess charge, thereby creating an electric streaming current (seismoelectric effect). Inversely, the theory predicts that electromagnetic waves generate mechanical/seismic signals (electroseismic effect). Electrokinetic conversions can potentially be used as an effective means of detecting hydrocarbon reservoirs: it inherently combines seismic resolution with electromagnetic hydrocarbon sensitivity. Validating electrokinetic wave theory is therefore of paramount importance. Electrokinetic theory predicts the existence of two seismoelectric effects: (1) a coseismic (electric) field that is coupled to seismic waves, and therefore propagates with seismic wave velocity, and (2) a seismic wave that traverses an interface with a contrast in electrical or mechanical properties and produces electromagnetic (EM) signals that propagate outside the support of the seismic waves with much higher EM-wave speeds. These are called the coseismic and interface response fields, respectively. Electroseismic counterparts of these fields exist as well. In this thesis, electrokinetic theory is reformulated along the lines sketched by Biot (1956a,b). The reformulation employs effective frequency-dependent densities, in which both viscous and electrokinetic coupling are comprised. The reformulated theory predicts the existence of four wave modes within a fluid-saturated porous medium: fast and slow P-waves, a shear wave and an EM-wave. The electrokinetic dispersion relations, which give wave speed and intrinsic attenuation of each wave, are expressed in terms of generalized elastic coefficients and the effective densities. Each of the wave modes has a specific fluid-solid amplitude displacement ratio. These are derived and expressed also in terms of generalized elastic coefficients and effective densities. Each wave mode also has a specific ratio of electric potential and solid displacement potential. These are expressed in terms of the fluid-solid ratios and the so-called (frequency-dependent) electrokinetic coupling coefficient. This coefficient describes the coupling between electric and mechanical fields. When the coupling coefficient is zero, the electrokinetic equations decouple into the familiar Biot’s poroelastic equations and Maxwell’s EM relations. Subsequently, the wave coupling at a fluid/porous-medium interface is theoretically solved, where the modified theoretical formulation is applied. First a straightforward scattering problem of an incident fluid P-wave into fluid electromagnetic and pressure waves, and porous medium waves is considered. Second, the electrokinetic scattering matrix for a fluid/porous-medium interface is derived. This matrix summarizes all electrokinetic reflection and transmission coefficients applicable to this boundary. These coefficients describe how incident P-waves are converted at electrical/mechanical interfaces to electromagnetic signals, and, vice-versa, how electromagnetic signals are converted into acoustic signals. They enter the full-waveform seismoelectric and electroseismic interface response field models. The seismoelectric model employs the Sommerfeld approach, while the electroseismic model uses wavefield (de)composition techniques. These models provide electrokinetic theoretical predictions. Laboratory seismoelectric fluid/porous-medium interface response field measurements are performed as a function of time, space and fluid salinity. These measurements are compared against the seismoelectric model predictions. It is found that the seismoelectric model predictions excellently describe the measured interface response fields in terms of waveform, spatial amplitude pattern, and travel times. One scalar amplitude scaling factor is needed to reconcile the amplitudes of the theoretical predictions and the measurements. The factor is shown to depend on electric conductivity, i.e., predicted amplitudes significantly deviate at low pore fluid conductivity (~10E?3 S/m), while they are close to the actual measurements for higher conductivities (~10E?2 S/m). The poroelastic, electromagnetic and specific electrokinetic parameters that enter the seismoelectric model are independently measured or known from literature. The seismoelectric Sommerfeld integral model incorporates a so-called directivity function that closely resembles the independently measured spatial distribution pattern of the incident acoustic field. As a check, seismoelectric origin of the measured electric potentials is confirmed. Next, an expanded seismoelectric model that predicts interface response fields at different boundaries, as well as coseismic fields, is presented and compared against measurements. The seismoelectric model predictions excellently describe the measured electric potentials in terms of travel times, waveform, polarity, amplitude and spatial amplitude decay, demonstrating that seismoelectric effects are comprehensively described by theory. Finally, an electroseismic laboratory setup is described and electroseismic measurements are presented.GeotechnologyCivil Engineering and Geoscience

Seismoelectric conversion for the detection of porous medium interfaces between wetting and nonwetting fluids

Electromagnetic waves are generated by acoustic waves at interfaces between fluids and fluid-saturated porous media, and at porous medium interfaces between different fluids. These signals can be measured in the laboratory as predicted by theory. A potential application is oil spill remediation monotoring in soils. We designed and developed an experimental setup in which acoustic to electromagnetic (EM) wave conversions at interfaces can be measured. Theoretical results are obtained with an electrokinetic full-waveform theoretical model, where use was made of the Sommerfeld approach. Using bimodal samples, different fluid–solid interface effects and saturating fluids were investigated. The contrast between water and water-saturated porous glass samples is larger than the contrast between water and oil-saturated porous glass samples. The contrast between water and water-saturated Fontainebleau sandstone is larger than the contrast between oil and water-saturated Fontainebleau sandstone

Seismoelectric interface response: Experimental results and forward model

Understanding the seismoelectric interface response is important for developing seismoelectric field methods for oil exploration and environmental/engineering geophysics. The existing seismoelectric theory has never been validated systematically by controlled experiments. We have designed and developed an experimental setup in which acoustic-to-electromagnetic wave conversions at interfaces are measured. An acoustic source emits a pressure wave that impinges upon a porous sample. The reflected electric-wave potential is recorded by a wire electrode. We have also developed a full-waveform electrokinetic theoretical model based on the Sommerfeld approach and have compared it with measurements at positions perpendicular and parallel to the fluid/porous-medium interface. We performed experiments at several salinities. For 10-3 and 10-2 M sodium chloride (NaCl) solutions, both waveforms and amplitudes agree. For 10-4 M NaCl, however, amplitude deviations occur. We found that a single amplitude field scaling factor describes these discrepancies. We also checked the repeatability of experiments. The amplitudes are constant for the duration of an experiment (1–4 hours) but decrease on longer time scales (~24 hours). However, the waveforms and spatial amplitude pattern of the electric wavefield are preserved over time. Our results validate electrokinetic theory for the seismic-to-electromagnetic-wave conversion at interfaces for subsurface exploration purposes.Geoscience & EngineeringCivil Engineering and Geoscience

Seismoelectric fluid/porous-medium interface response model and measurements

Coupled seismic and electromagnetic (EM) wave effects in fluid-saturated porous media are measured since decades. However, direct comparisons between theoretical seismoelectric wavefields and measurements are scarce. A seismoelectric full-waveform numerical model is developed, which predicts both the fluid pressure and the electric wavefields in a fluid in which a porous disc is embedded. An experimental setup, in which pressure and electric signals in the fluid are simultaneously measured, is presented. The setup allows the detection of the EM field that is generated when an acoustic wave crosses the interface between the fluid and the thin porous disc, without interference of electrical fields that are present within seismic body waves. The predicted pressure wavefield agrees well with the measurements in terms of acoustic wave travel times, waveforms, and amplitudes. The electric wavefield predictions agree with the recordings in terms of travel times, waveforms, and spatial amplitude decay. A discrepancy in amplitude of the converted EMsignal is observed. Theoretical amplitudes that are smaller than the measurements were also reported in previous literature. These results seem to validate seismoelectric theory.Geoscience & EngineeringCivil Engineering and Geoscience

Experimental validation of the electrokinetic theory and development of seismoelectric interferometry by cross-correlation

We experimentally validate a relatively recent electrokinetic formulation of the streaming potential (SP) coefficient as developed by Pride (1994). The start of our investigation focuses on the streaming potential coefficient, which gives rise to the coupling of mechanical and electromagnetic fields. It is found that the theoretical amplitude values of this dynamic SP coefficient are in good agreement with the normalized experimental results over a wide frequency range, assuming no frequency dependence of the bulk conductivity. By adopting the full set of electrokinetic equations, a full-waveform wave propagation model is formulated. We compare the model predictions, neglecting the interface response andmodeling only the coseismic fields, with laboratory measurements of a seismic wave of frequency 500 kHz that generates electromagnetic signals. Agreement is observed between measurement and electrokinetic theory regarding the coseismic electric field. The governing equations are subsequently adopted to study the applicability of seismoelectric interferometry. It is shown that seismic sources at a single boundary location are sufficient to retrieve the 1D seismoelectric responses, both for the coseismic and interface components, in a layered model.Geoscience & EngineeringCivil Engineering and Geoscience

Electrokinetic fields and waves: Theory, experiments and numerical modeling

Geoscience & EngineeringCivil Engineering and Geoscience