The failure of the sounding assumption in electroseismic investigations

The failure of the sounding assumption in electroseismic investigations F.D. Fourie, J.F. Botha Institute for Groundwater Studies, University of the Free State, PO Box 339, Bloemfontein, 9300, South Africa Abstract The electrokinetic sounding (EKS) technique is a surface electroseismic technique based on the assumption that the observed electroseismic signal is generated at positions vertically below the seismic source. However, recent field observations and a simplified electroseismic model cast considerable doubt on the validity of this assumption. The model shows that strong electroseismic signals may be recorded at surface positions vertically above positions where no electroseismic energy conversion takes place. 1. Introduction In contrast to other geophysical techniques routinely used in groundwater exploration, electroseismic methods offer the possibility to detect groundwater directly, since the presence of fluids in the subsurface is required for the generation of signal. This led to the introduction of electrokinetic sounding (EKS) technique for the exploration of groundwater resources (Millar and Clarke, 1997). This technique is based on the sounding assumption, i.e. the signal observed on the surface is directly related to the physical conditions in the subsurface vertically below the seismic source. In 1999, the EKS technique was used in an electroseismic survey of the Campus Test Site at the University of the Free State, which is intersected by a horizontal fracture at a depth of approximately 23 m (Botha et al., 1998). A question arose during the investigation regarding the relation between the strength of the electroseismic signal observed on the surface and the subsurface positions where the signal is generated. This paper discusses the results of the survey and a simplified electroseismic model, which indicates that the sounding assumption may be poor in electroseismic investigations of the earth's subsurface. 2. Physical principles of electroseismic techniques It is known that an electric potential usually exists at the contact between the water and solid in water-saturated porous rocks and that the ions in the fluid separate into an electric double layer (Fitterman, 1978). A mechanical disturbance propagating through such a medium will displace the solid phase relative to the fluid phase, thereby causing a relative motion of the ions in the electric double layer, thus inducing an electric current and hence an electromagnetic field in the medium. This phenomenon is generally known as the electrokinetic effect and the resulting macroscopic electric current as the streaming current. The streaming current is related to the pressure gradient in the fluid through the electrokinetic coupling coefficient, which depends on the properties of both the solid and the fluid. When dilatational and rotational seismic waves propagate in a homogeneous porous medium, the streaming current is cancelled by an equivalent and opposite conduction current, (Haartsen, 1995). However, a seismic wave incident on the interface between dissimilar media causes a variation in the streaming current density across the interface. This variation creates a charge separation that acts as oscillating dipoles spread over the interface, which generate an electromagnetic wave that propagates independently of the seismic wave in the subsurface and can be detected on the surface. A more detailed discussion of these processes can be found in Mikhailov et al. (1997) and Beamish (1999). 3. Fresnel zones in Electroseismic Surveys A monochromatic spherical pressure wave that traverses an interface in the earth s subsurface, as in Fig. 1, will create successive Fresnel zones, i.e. radial zones along the interface for which the one-way distance travelled by the seismic wave differs by less than half a wavelength (λ). The relative fluidsolid motion in each Fresnel zone and its contributions to the generated electroseismic signal are 1

consequently out of phase with the preceding zones and those that follow it. The first Fresnel zone, with smallest offset, therefore contributes the most to the total electroseismic signal observed on the surface. This principle led to the introduction of the sounding assumption and the notion that an essentially three-dimensional problem may be reduced to a one-dimensional problem by using small offset antennæ in electroseismic surveys. Seismic source t+ t t+2 t t D D+λ/2 D+λ First Fresnel zone Fig. 1. Schematic illustration of the Fresnel zones in electroseismic surveys. 4. Electroseismic survey of the Campus Test Site The Campus Test Site covers an area of approximately 180 190 m 2. A total of 30 percussion and 7 core boreholes have been drilled at various positions on the site. Numerous hydraulic and geophysical tests have been performed on the boreholes and the geohydrological conditions on the site are consequently well known. The cores of the core boreholes indicate that the geology is very uniform across the site. An important feature of the site is the bedding plane fracture that occurs at a depth of approximately 23 m. Although the areal extent of the fracture is thought to be considerable, it is not uniformly present. Boreholes intersecting the bedding plane fracture all have high yields (>3 L s 1 ), while those that do not intersect the fracture have low yields (<0.5 L s 1 ). The fracture therefore presents a particular challenge for groundwater studies. Model studies by Haartsen and Pride (1997) show that although seismic reflection from the top and bottom interfaces of a thin geological layer between two half-spaces is subject to destructive interference, the generated electroseismic response is enhanced by a factor of 2. This may prove to be one of the strengths of electroseismic methods and suggests that these methods may be ideally suited to the detection of fracture zones. The Campus Test Site was electroseismically surveyed during 1999 with the EKS technique on a 10 10 m grid. Fig. 2 shows a contour map of the normalized amplitude of the electric field observed during the survey, imposed on the positions of some of the boreholes on the site. The surface positions where strong electroseismic signals were recorded are seen to be very localized. Due to the uniform geology on the Campus Test Site, it is likely that this localization can be attributed to the presence or absence of the fracture. Although there is a general agreement between the known extent of the fracture, determined from the borehole logs and the electroseismic amplitude, none of the rather localized amplitude maxima coincide with the positions of the two boreholes (UO5 and UP16) that had the highest yields at the time the boreholes were drilled. It is possible that the several hundred hydraulic tests performed on these two boreholes since they were drilled in 1992, have caused the fracture to collapse in their vicinity. However, there is another possibility. The radius of the n th Fresnel zone of a monochromatic wave is related to its wavelength, λ, through the equation r n 1 2 2 ( D + n / 2) D ) 2 = λ where D is the depth of the interface, as illustrated in Fig. 1. This means that the first Fresnel zone associated with a seismic wave at the depth of the fracture will have a radius of approximately 23.7 m, assuming that the seismic source has a frequency of 75 Hz and that the seismic velocity in the 2

weathered upper layers of the Campus Test Site is 1 500 m s -1. There is thus a strong possibility that the observed amplitude of the electric field was strongly influenced by the localized nature of the fracture. This conclusion is supported by the analysis of the hydraulic tests, which show that the fracture is completely closed immediately east of Borehole UO5 and south-west of UP16 (Botha et al., 1998). This observation obviously has serious implications for the application of the electrokinetic sounding technique in groundwater studies. A simplified electroseismic model was consequently developed to study the effects that localization in the positions where electroseismic energy conversion takes place may have on the observed electric field. 50.00 40.00 0.9 30.00 0.8 0.7 0.6 20.00 10.00 UO5 0.90 0.80 0.70 0.00 0.5 0.4-10.00 UO16 0.60 0.50 0.3-20.00 0.2-30.00 0.1-40.00-50.00 N -60.00 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 0.40 0.30 0.20 0.10 Well-developed fracture Poorly developed fracture No fracture Fig. 2. Contour map of the normalized amplitude of the electric field observed during the electroseismic survey of the Campus Test Site. 5. A simplified electroseismic model By making a number of simplifying assumptions the surface electric potential generated at localized interfacial zones of energy conversion may be modelled as 2 D f ( vt rsd ) ϕ( r om,t) πσ da (1) 2 3 4 r r where f is the seismic wave function, v the speed at which the seismic wave propagates in the medium above the interface, σ the electrical conductivity of the medium overlying the interface, D the interface depth, r sd the distance from the seismic source to the interfacial dipoles, r dm the distance from the dipoles to the measurement position and Σ the total area of the active zone. The horizontal (x) component of the electric field at the surface is given by ϕ E x ( r om,t) = (2) x A Fortran code based on Simpson s rule was developed to compute the horizontal surface electric fields from Eqs. (1) and (2) for the monochromatic seismic source f(t) = exp(iωt), and two broadband sources a Ricker wavelet f(t) = (1-2u)exp(-u), u = π (1.5 f 0 t) with f 0 the dominant frequency of the wavelet, and an impulsive (Delta) wavelet Σ sd dm 3

f(t) = (1 + n 2 t 2 ), (n = 1 000) with a halfwidth of 2 ms. Since only normalized outputs from the model were examined, the electrical conductivity σ was taken as unity. The effects of seismic wave dispersion and attenuation were neglected in the model. The interface considered in the models consisted of a ring-shaped zone situated at a depth of 40 m between two media with seismic velocities of 800 and 1 000 m s -1. The active domain of the zone the region where electroseismic energy conversion occurs was varied by increasing the radius of the inactive zone (the inner circle of the domain) from 0 m to the radius of the outer zone, which was fixed at 20 m. A (dominant) frequency of 120 Hz was assigned to both the monochromatic source and the Ricker wavelet source. The seismic sources were located vertically above the centre of the ring-shaped zone in the models. Fig. 3 shows the normalized amplitude of E x computed at a distance of 0.5 m from the seismic source as a function of the radius (r i ) of the inactive zone. The amplitudes of the electric fields generated by the monochromatic and impulsive seismic sources decrease monotonically, but slowly for small values of r i, while the amplitude for the Ricker wavelet source displays two maxima. There is thus little doubt that the electrokinetic phenomenon can generate strong electric fields at surface positions vertically above positions where electroseismic energy conversion does not take place. The sounding assumption can therefore easily lead to incorrect interpretations of electroseismic data. Fig. 3. Normalized amplitudes of the surface electric fields at a position 0.5 m in the x-direction from the seismic source as a function of the radius of the inactive zone. Acknowledgements The authors would like to thank the National Research Foundation and Water Research Commission for their financial support of this project. References Beamish, D. (1999) Characteristics of near-surface electrokinetic coupling. Geophysical Journal International. 137, 231-242. Botha, J. F., Verwey, J. P., Van der Voort, I., Vivier, J. J. P., Colliston, W. P. and Loock, J. C. (1998) Karoo Aquifers. Their Geology, Geometry and Physical Behaviour. Water Research Commission, P.O. Box 824, Pretoria 0001. Fitterman, D. V. (1978) Electrokinetic and magnetic anomalies associated with dilatant regions in a layered earth. Journal of Geophysical Research. 83 (B12), 5923-5928. Haartsen, M. W. (1995) Coupled electromagnetic and acoustic wavefield modeling in poro-elastic media and its application in geophysical exploration. Ph.D. thesis. Massachusetts Institute of Technology, Cambridge. Haartsen, M. W. and Pride, S. R. (1997) Electroseismic waves from point sources in layered media. Journal of Geophysical Research. 102 (B11), 24745-24769. 4

Mikhailov, O. V., Haartsen, M. W. and Toksöz, M. N. (1997) Electroseismic investigation of the shallow subsurface: Field measurements and numerical modelling. Geophysics. 62 (1), 97-105. 5