Chapter 4 Seismoelectric Methods of Earth Study B.S. Svetov Geoelectromagnetic Research Center IPE RAS, Troitsk, Moscow Region, Russia
It is well known that the Earth, affected by some physical fields, experiences diverse complex variations. In geophysical respect, these changes can appear in two forms: (1) as changes in physical parameters of a geological medium (effect of the first kind), and (2) as an emergence of physical–chemical processes in the medium that, in turn, gives rise to various physical fields (effect of the second kind). Currently, we are very far from comprehensive understanding of these phenomena, and very often we confine ourselves to their phenomenological description based on the theory of physical fields in continuous, stationary and passive media. In this approach, the complex multi-phase rock structure is ignored and, as a result, a possibility is lost to obtain information about petrophysical parameters of rocks (porosity, fluid permeability, fluid saturation and others). Just the same, the energy state of a geological medium is also neglected in geophysical prospecting.
4.1. SEISMOELECTRIC EFFECT OF THE FIRST KIND Let us dwell on seismoelectric effect (SE) of the first kind implying the elastic (seismic) field influence on a geological medium and the resulting change in its conductivity (Ivanov, 1949). In real conditions, the geological medium is energetically unstable. This instability develops over a wide range of spatial scales – from the scale of porous and polyphase rocks having complex structure to scales of regional geological structures. Therefore, even weak seismic field impacts on the medium can result in its significant changes (in particular, changes in its electric resistivity). Let us show a result of an experiment carried out by geophysicists from Methods in Geochemistry and Geophysics, Volume 40 V.V. Spichak, Editor r 2007 by Elsevier B.V. All rights reserved. ISSN: 0076-6895 DOI: 10.1016/S0076-6895(06)40004-4
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Saratov, USSR, in Near-Caspian depression – a region of widely developed saltdome and fault tectonics (Ozerkov et al., 1998). Fig. 4.1 displays cross sections of apparent resistivity obtained by transient electromagnetic method: (a) before the vibrational impact on the medium, (b) a few minutes after a 3-min operation of seismic vibrator, (c) 24 h after the vibrator operation, and (d) 17 days after the operation. From the dynamics of these cross sections it is clearly seen how sharply the geoelectrical cross section is changing immediately after the vibrational impact, and how slowly and incompletely it is relaxing to its initial state. It is worth noting that such a pattern is observed only within extremely stressed regions; in other experiments the changes of geoelectrical sections were less evident, although still observed sometimes. Similar changes are encountered after and sometimes before earthquakes and are used for earthquake prediction. SE of the first kind caused by controlled seismic impact can be applied in engineering geology as a marker of unstable zones unsuitable for building. Seismic impact is sometimes used to provoke weak and to prevent strong earthquakes. An obstacle for a widespread use of SE of the first kind is its purely empirical foundations and difficulties in creation of a rather rigorous theory.
4.2. SEISMOELECTRIC EFFECT OF THE SECOND KIND: HISTORICAL OUTLINE AND ELEMENTS OF THEORY Situation with SE of second kind is more favorable. During recent decades, certain progress in understanding this phenomenon began to show. Let us consider this effect in more detail. Classical seismic prospecting and acoustic logging were and, up to now, are theoretically based mainly on the equation of elastic waves propagation in continuous media – the Lame equation. In a frequency domain (eiwt) and for isotropic media this can be written in the form mr r u ðl þ 2mÞrðr uÞ o2 u ¼ 0
ð4:1Þ
Here u is a vector of medium displacement, l ¼ K2/3m and m the Lame parameters (m the shear modulus), K the bulk modulus. Solution of this equation in a homogeneous medium is a sum of two elastic waves: longitudinal (potential) and transverse (vortex) ones. In the 1940s, just after the discovery of SE by A.G. Ivanov (1940) Ya.I. Frenkel (1944) gave a first theoretical description to this phenomenon, concurrently laying the foundations to the theory of elastic waves propagation in a porous two-phase medium. Later on, M. Biot (1956) extended this theory and formulated his widely known equations (the Biot equations) describing elastic waves propagation in a two-phase porous fluid- or gas-saturated medium that is a more adequate model of a rock. Written in the form suggested in (D. Schmitt et al., 1988), these equations for an isotropic medium look like mr r us þ Prðr us Þ þ Qrðr uf Þ þ o2 ðg11 us þ g12 uf Þ ¼ 0
ð4:2Þ
Qrðr us Þ þ Rrðr uf Þ þ o2 ðg12 us þ g22 uf Þ ¼ 0
ð4:3Þ
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Fig. 4.1. Seismoelectric effect of the first kind. Sections of apparent resistivity: (a) before the vibrational impact, (b) 5 min after the impact, (c) 24 h later, (d) 17 days later. N, numbers of the sounding points.
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Here us and uf are displacements of a solid and fluid phases in a medium, ð1 fÞð1 f wÞ þ fwK s K f 4 þ m, P ¼ Ks 3 1 f w þ fK s =K f ð1 f wÞfK s Q¼ , 1 f w þ fK s =K f R¼
f2 K s 1 f w þ fK s =K f
where Ks, Kf, Km are bulk moduli of a solid and fluid phases and dry rock skeleton, m the rock skeleton shear modulus, w ¼ Km/Ks, f the porosity of the medium, g11 ¼ r11+ib/o, g12 ¼ r12ib/o, g22 ¼ r22+ib/o, b(o) ¼ f2H1 (o), r22 ¼ f2H2 (o)/o, r12(o) ¼ frfr22(o), r11(o) ¼ (1f)rsr12(o), H1(o)iH2(o) ¼ Z/k(o), n o1 1=2 kðoÞ ¼ k0 1 io=ob M B =2 io=ob is frequency-dependent permeability of a porous medium, M B 2 ð1; 2Þ is a constant depending on a pore shape, ob ¼ f=a1 k0 Z=rf is the Biot critical frequency at which the diffusive motion of a porous fluid changes into the wave motion, rf,rs are densities of a fluid and solid phases, a1 ¼ 1–8 is pore tortuosity, Z the fluid viscosity, k0 the permeability of a medium in a stationary field. The Biot equation’s solution in a homogeneous medium is a sum of three waves: one transverse and two longitudinal (‘‘slow’’ and ‘‘fast’’). Dynamical and kinematical characteristics of these waves depend, as it follows from the equations, not only on the elasticity moduli and densities of a liquid and solid phases but also on pertophysical parameters of the medium and, first of all, on its porosity and permeability. This has opened new informational possibilities for seismic prospecting and, particularly, for acoustic logging. From obvious physical considerations and, in particular, from the Biot equations it follows that the pore fluid moves not in synchronism with a solid phase, but lags behind it. This results in the emergence of a fluid flow relative to a solid rock skeleton, the flow density being w ¼ iofðus uf Þ ¼
kðoÞ 2 ðo rf us rpÞ Z
ð4:4Þ
Bracketed on the right-hand part of this expression is a force that generates the flow and comprises inertial force and pore pressure gradient rp. Selective ion adsorption from a pore solution by a solid rock skeleton results in opposite charging of its liquid and solid phases, therefore their relative motion produces an extraneous electric current with density jext. This current generates an electromagnetic (EM) field. The above is a physical substance of the second kind SE of electrokinetic nature. The value of extraneous current can be expressed in terms of surface-charge density on a solid phase boundary Q, or through zeta-potential z of a pore solution. As it has been already mentioned, the first mathematical description of SE in rocks is given in the work by Ya. Frenkel (1944). Fifty years later, S. Pride (1994) gave a more rigorous description to this phenomenon using a self-consistent system of
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equations comprising the Biot and Maxwell equations. Subsequently, Svetov and Gubatenko (1999) and Svetov (2000) proposed a simpler formulation of this problem allowing for a negligibly weak EM field back influence on the elastic field and reducing to a successive solution of the Biot (4.2, 4.3) and Maxwell equations: ~ oÞE þ j ext ; r H ¼ sðr;
r E ¼ iomH
ð4:5Þ
~ oÞ ¼ s io is a complex electric conductivity of a medium. The extraHere sðr; neous current representation plays an interlinking part between the Biot and Maxwell equations. This representation follows from Onsager thermodynamical relations. Let us write it out in two forms obtained by S. Pride and B. Svetov-V. Gubatenko for a case when the thickness of a diffusional part of a double-layer in a pore solution is much smaller than the pore size: h i ZfLðoÞ j ext ¼ LðoÞ o2 rf us rp ¼ io ðus uf Þ ¼ ioZðus uf Þ ð4:6Þ kðoÞ j ext ¼ ioQðoÞyðus uf Þ ¼ io
QðoÞyðo2 rf us rpÞ
¼ ioZ1 ðus uf Þ ð4:6aÞ iorf 1=2 , Z ¼ ZfL(o)/k(o), Z1 ¼ Q(o)y, Here LðoÞ ¼ f=a1 f z=Z 1 io=ob 2=M B Q(o) is the frequency-dependent surface-charge density on the solid and liquid phase interface, y the specific surface of the pore space. Quantity Z has a sense of a frequency-dependent electrokinetic coefficient since it defines the extraneous electric current generated by the pore fluid flow. This quantity contains basic information about the medium provided by the EM field of electrokinetic origin. For the sake of objectivity it should be mentioned that, as laboratory experiments show (Ageeva et al., 1999), the both of the above expressions give rather crude approximation of processes taking place in the real rocks. Basic importance of these expressions consists in general description of electrokinetic coefficient dependence pattern on pertophysical parameters of a geological medium. Zf kðoÞ
4.3. PHYSICAL INTERPRETATION OF SEISMOELECTRIC PHENOMENA To get a better understanding of what the EM fields develop in a porous fluidsaturated medium (the ‘‘Biot medium’’), let us consider the simplest case of plane elastic waves propagation in such a medium. The medium is assumed homogeneous, then, dependent on the specific exciter type, fast (velocity a1) and slow (velocity a2) longitudinal Biot waves, or transverse wave (velocity b) or both wave types are generated in the medium. Assume these waves to propagate in the 0z axis direction and to have solid phase displacement amplitudes Ap1 ; Ap2 ; As at Z ¼ 0. Then rock skeleton displacements for longitudinal and transverse waves can be written as p
p
upz ¼ Ap1 eik 1 z þ Ap2 eik 2 z
usx ¼ As eik
Sz
ð4:7Þ
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These waves give rise to longitudinal and transverse extraneous currents moving together with the generative waves: p
p
p j ext ¼ Ap1 Zð1 x1 Þeik 1 z þ Ap2 Zð1 x2 Þeik 2 z 1z
kp1
s
s s ik z j ext 1x ¼ A Zð1 gÞe
ð4:8Þ
o=a1 ; kp2
Here ¼ ¼ o=a2 ; ks ¼ o=b are wave numbers of corresponding elastic waves (Re k40), and x1;2 ¼ P a21;2 g11 =a21;2 g12 Q ¼ Q a21;2 g12 =a21;2 g22 R and g ¼ g12 =g22 are the constants defining the ratio of liquid-to solid-phase displacements in the medium that depend on the parameters of the medium (D. Schmitt, 1988). Longitudinal extraneous currents also give rise to longitudinal electric field, not accompanied by a magnetic field and equal to: p p 1 E pz ¼ ½Ap1 Zð1 x1 Þeik 1 z þ Ap2 Zð1 x2 Þeik 2 z ð4:9aÞ s Transverse extraneous current generates transverse electric and magnetic fields:
E sx ¼
s 1 k2e iks s iks z s A Zð1 gÞe ; H ¼ As Zð1 gÞeik z 2 y 2 s2 s k2e ks ke k
ð4:9bÞ
Here ke ¼ ðiomsÞ1=2 is a wave number of EM field. All these fields propagate in a medium with the same velocities as the corresponding elastic waves do, and are non-zero only in that just place crossed by the elastic perturbation at a given moment. This circumstance laid the grounds to call such electric and magnetic waves ‘‘frozen-in’’ (Svetov, 2000). Note that the frozen-in transverse electric fields (Equation (4.9b)) due to ke =ks 1 (over a frequency range of interest) are much smaller than the longitudinal ones (Equation (4.9a)). Now assume longitudinal (Equation (4.9a)) or transverse (Equation (4.9b)) elastic waves orthogonally incident on a plane interface z ¼ 0 of two half-spaces different in their elastic, pertophysical or electric properties. The waves are partially reflected, partially penetrate into the lower half-space without generation of converted waves at orthogonal incidence. In this situation, longitudinal extraneous electric fields will hold the structure of (4.9a), being different in the upper and lower half-spaces only on account of the difference between electrokinetic coefficients and conductivities. The case is another with transverse EM fields. Here, solutions of homogeneous Maxwell equations became non-zero, and general solution to these equations, e.g. in a lower half-space, takes the form E sx ¼
s 1 k2e As Zð1 gÞeik z þ E 0x eike z s k 2 k s2
e
H sy ¼
iks k2e
k
s
s2
As Zð1 gÞeik z þ H 0y eike z
ð4:10Þ
Second summands in Equation (4.10) describe usual EM waves propagating independently on elastic waves at a velocity many times higher than seismic waves. In seismoelectrics such waves can be called ‘‘fast’’ EM waves. The values E 0x and H 0y are found from the continuity conditions for the tangential components of electric
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and magnetic fields at the half-spaces interface. Fast EM waves depend complexly on the contrast in physical and petrophysical characteristics of the medium on either side of the interface. In a highly conducting medium, they decay with the distance to the interface. On the whole, from a geophysical point of view, EM field of electrokinetic origin is much more informative than the parental seismic one. This field includes four wave types differing in their kinematic (velocities) and dynamic characteristics: three waves frozen in their corresponding seismic waves and one fast EM wave. All these waves are differently, and more strongly than the seismic ones, dependent on the pertophysical properties of the medium. If the elastic and electric fields are measured simultaneously as it is usually done in seismoelectrics, a possibility arises to find, directly from measurements, the so-called seismoelectric transfer functions W ðwÞ that are complex ratios, in a frequency domain, of electric field strength to the medium displacement (or the velocity of this displacement) or to the well pressure. Owing to their relative nature they do not depend on the intensity of the excited elastic field and its spectral composition, and therefore these functions are easier to use in the determination of the parameters of the medium than the direct measurements of the field strengths. Functions W ðwÞ differ for different wave types. For frozen-in longitudinal and transverse waves the functions W(w) ¼ E/u equal to 1 W p1 ¼ ð1 x1 ÞZ; s
1 W p2 ¼ ð1 x2 ÞZ; s
Ws ¼
1 k2e ð1 gÞZ ð4:11Þ s k2 ks2 e
Fig. 4.2. Frequency dependences of real (a) and imagery, (b) parts of SE transfer function (p, porosity; pm, permeability).
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They depend on both the petrophysical parameters of the medium and on its elastic and electric properties. Of particular importance seems to be the theoretically predicted possibility of direct determination of rock porosity and permeability from the transfer functions. This possibility shows in different dependences of the real and imaginary parts of SE transfer functions on these parameters. Figure 4.2 displays frequency characteristics of normalized by conductivity real and imagery parts of SE transfer functions for a longitudinal wave. The real part is additionally normalized by o2 , and the imagery by o3 . At not very high frequencies ðRe k40Þ; the real part is proportional to porosity but is practically permeability-independent; quite a contrary, the imaginary part only weakly depends on porosity but is proportional to permeability. Such diverse and rich geophysical information that can be potentially yielded by SE methods destines the prospects of their application in field studies and, particularly, in logging. Note the different character of information provided by the frozen-in and fast EM fields. The frozen-in wave measured by field receivers describes the structure of the medium only within the vicinity of the receiving site. Within the frequency range of field seismoelectrics (60–100 Hz) the size of this area is a few meters to a few dozens of meters, and at SE logging frequencies (2000–10 000 Hz) it amounts to a few meters. Hence, these waves can be used only in shallow (engineer and hydrogeological) field studies and logging. Information about the deeper Earth layers required, e.g., in solving the problems of oil–gas geology, can be obtained only from fast EM waves. However, here the wave absorption along the path from the reflecting boundary to the field receivers should be taken into account.
4.4. MODELING OF SEISMOELECTRIC FIELDS The recent decade was the time of intensive development of theoretical and methodological grounds to field and, particularly, borehole seismoelectrics. Many scientists are involved in this research (S. Pride, M. Haartsen, B. Svetov, V. Gubatenko, P. Aleksandrov, B. Plyuschenkov, M. Markov, V. Verzhbitsky and others). In their works the seismoelectric 1-D problems for horizontally and radially stratified media are solved, corresponding software is built and the solutions are analyzed. Development of the software for 2-D problems solution (vertical well + horizontally stratified medium outside) got started. Experimental field and borehole studies are performed and continue to be carried out. Seismoelectric phenomena are studied by rock sample testing. Here below we shall dwell mainly on the results obtained in the Geoelectromagnetic Research Center IPE RAS. In analytical solution of SE 1-D problems in horizontally and radially stratified media the Biot and Maxwell equations for components of the field or potential are easily scalarized by corresponding integral transforms and reduce to the known ordinary differential equations (the Bessel equations). At interfaces of media with different parameters, the displacement, stress tensor and EM field components
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B.S. Svetov/Seismoelectric Methods of Earth Study Table 4.1. Conjugation conlitions. B–B usr ¼ usr f ufr usr ¼ f ufr usr p¼p cBrr ¼ cBrr cBrz ¼ cBrz uss ¼ uss
W–B (1)
W–B (2)
L–B
ur ¼ usr ð1 fÞ þ fufr
ubr ¼ usr ð1 fÞ þ ufr f
ur ¼ usr ð1 fÞ þ ufr f 0 ¼ ufr usr
upz 0 ¼ cBrr þ p p ¼ cBrr 0 ¼ cBrz
¼
p Ap1 eik1 z
p ¼ cBrr 0 ¼ cBrz
þ
p Ap2 eik2 z
crr ¼ cBrr crz ¼ cBrz uz ¼ usz
satisfy the necessary conjugation conditions. For the Biot equations in a radially stratified medium the conjugation condition are tabulated in Table 4.1. In this table, the columns present the conjugation conditions at interfaces between two Biot media (B–B), between a fluid and a Biot medium with permeable (W–B1) and impermeable (W–B2) interfaces, and between continuous solid medium and a Biot medium (L–B). In the table, an equality is established of the displace^ ¼ fpI^ þ ð1 fÞc^ ment and total stress tensor components in a Biot medium c B s ^ ^ (I is the unit tensor, cs the stress tensor of a solid phase) on either side of the contact media interface. Similar equations can be written for horizontal layers interfaces. Conjugation conditions for EM field consist in the equality of the tangential components of electric and magnetic field. The scientists of the Geoelectromagnetic Research Center developed the software necessary for solving such problems and calculated the SE fields for a series of typical model media. Shown in Figs. 4.3a, b, are the calculation results for the pressure field and vertical component of the electric field in a well enclosed by porous fluid-saturated medium, excited by a radial elastic force transmitter. Base excitation frequency is 10 000 Hz.The abscissa axis is the time of field observation; each wave trace is indexed by the distance to the elastic field source. Fields at each trace are normalized by their maximum values. In the pressure plots (Fig. 4.3a), the longitudinal, transverse and surface (propagating along the drilling mud–porous medium interface) waves successively arriving at the receiver are seen. From these plots, one can find the velocities of these waves and their spatial damping, and that is all what the acoustic logging gives. Using these data geophysicists, to this or that degree of confidence, can separate the geological section in lithology and determine some petrophysical parameters important for gas–oil disposal estimation, e.g. porosity. Fig. 4.3b portrays the wave traces of the electric field. Besides the same types of electric waves frozen in the acoustic fields, also fast EM waves are seen in the plots, instantly and practically simultaneously arriving at electric field receivers spaced by different distances from the source of excitation. These waves originate at a borehole wall (media interface) once it has reached by an acoustic wave. All the geophysical information contained in the acoustic logging persists in the frozen-in electric waves, but this is complemented by new independent data yielded from SE transfer functions and fast waves. Shown in Figs. 4.4a, b, are the results of calculating the vertical components of a solid-phase displacement in a water-saturated medium and electric field strength for
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Fig. 4.3. Calculated acoustograms (well pressure) (a) and electrograms (vertical component of electric field strength), (b) for radially layered medium (well + porous fluid-saturated medium).
an orthogonal intersection of a plane interface of two half-spaces by 2-m-long SE logging facility (the well influence is neglected in calculations). In the right-hand part of this and a series of next figures, the main parameters of the section are given: T layer, location of the section surface; Vp,VS, velocities of longitudinal and transverse seismic waves; ps, solid phase density; mo, porosity; Ks,
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Fig. 4.4. Calculated seismograms (vertical medium displacement) (a) and electrograms, (b) at orthogonal intersection of a plane interface of two halfspaces by SE logging facility.
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solid phase bulk modulus; Vf, elastic waves velocity in a fluid phase of the medium; pf, fluid phase density; ef =e, relative dielectric permittivity of the fluid phase; k, fluid permeability; nu, fluid viscosity; x, pore tortuosity, the value of the M B constant, dzeta, zeta-potential; sigma, conductivity of the medium. The half-spaces have similar elastic and electrical parameters and differ only in their fluid permeability and porosity. The interface is located at z ¼ 0, and the observation point of calculated signals is related to the field receivers. This interface is almost invisible in plots of elastic displacement (on different sides of the interface the wave arrival time changes). In the wave images of electric field, this boundary is clearly manifested in the emergence of reflected waves as the field receivers pass through the interface. Thus, almost invisible in elastic waves, the petrophysical parameters interface is quite distinct in the SE field. Note that the transverse frozen-in waves are practically not apparent in the electric field plots. Similar situation is observed also when the same logging facility intersects a 1-m thick layer that differs from the embedding medium only in porosity and permeability (Figs. 4.5a, b) (the layer boundaries are at z ¼ 70–5 m). On the basis of the carried out calculations, the SE logging sensitivity to petrophysical parameters of the medium was analyzed and compared to that of acoustic logging. Figs. 4.6a, b show the porosity and permeability dependences of pressure P observed in a well (acoustic logging), electric field and absolute values of SE transfer functions for frozen-in fast longitudinal Biot waves. It can be seen from the images that the electric fields and SE transfer functions show substantially higher sensitivity to the petrophysical parameters of the medium. The plots shown above illustrate capabilities of SE logging. Let us present an example of SE field calculation in the context of field seismoelectrics. Traces of vertical component of the displacement and radial component of the electric field excited in a two-layer medium by a pulse of vertical force are depicted in Figs. 4.7 a, b in a similar form. The section is chosen to reproduce the wave pattern observed at one of the segments of experimental profile. The traces are indexed by the distance to the exciter in meters. Besides the frozen-in longitudinal and surface waves, also rapidly damped fast EM waves are seen in the electric field plots at small distances from the exciter. Currently, numerical methods for SE problems solution in 2- and 3-D media based on the use of integral and integral-differential equations are under development in the GEMRC.
4.5. LABORATORY STUDIES OF SEISMOELECTRIC EFFECTS ON ROCK SAMPLES The above stated theory of SE phenomena in a porous fluid-saturated medium and that resulting in geophysical conclusions need an experimental validation and verification. First of all, it is necessary to make sure in the theoretical description adequacy to the real geophysical processes in rocks. This can be done on the basis of laboratory studies of SE effect on rock samples (Ageeva et al., 1999). With this
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Fig. 4.5. Calculated seismograms (vertical medium displacement) (a) and electrograms, (b) at orthogonal intersection of a 1-m-thick layer by SE logging facility.
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Fig. 4.6. Well pressure (a) and SE transfer functions, (b) dependencies on the porosity and permeability of the medium.
purpose, a special facility has been designed for studying elastic and electric fields excited in rock cores by the piezoelectric transmitter of longitudinal waves. Using this equipment, a large set of terrigene and carbonate rocks differing in their porosity and permeability at different levels of water saturation and mineralization of pore solution were tested. In accordance with electrokinetic theory, the intensity of
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Fig. 4.7. Example of calculated seismograms (vertical-medium displacement) (a) and electrograms (horizontal electric-field strength), (b) at different distances to the exciter above a two-layer medium.
SE observed in limestones and sandstones drops with the decrease in fluid saturation of the pattern (Fig. 4.8). This effect is almost missing in dry rock samples. SE transfer functions dependences on petrophysical parameters of the patterns, such as porosity and permeability, were studied. Fig. 4.9 shows the obtained
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Fig. 4.8. SE transfer function dependency on fluid saturation for (a) limestones and (b) sandstones.
porosity dependences of SE transfer function normalized by the pattern conductivity W i ¼ W =s for terrigene rocks. General character of the dependency and the order of magnitudes of the transfer function agree with those theoretically predicted, but a wide spread of the data is apparent (the upper panel). To some extent, this can be explained by imperfection of measurement technique, but there are also another, more fundamental reasons for this. If the whole set of patterns is divided into limestone and sandstone groups, the data scatter reduces and correlation coefficient of linear regression increases (the two bottom panels). This is quite understandable: be the SE theory and its underlying model of the medium ever so perfect, they are incapable of allowing for the whole variety of pore space shapes of rocks and its gas–fluid saturation as well as such important factors as clay contents
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Fig. 4.9. SE transfer function dependency on porosity for (a) sedimentary rocks, (b) limestones, (c) sandstones.
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in rocks, roughness of the solid phase surface and many others. All this necessarily predetermines the spread of SE transfer function values over a set of various patterns not grouped on the basis of any criterion or even united by common linotype. With the reduction of the pattern collection according to some additional features (e.g. geographical or stratigraphical), the resulting regression dependencies become more compact and coefficients of correlation between W i and the studied petrophysical parameters increase. The laboratory studies carried out lead to a conclusion that theoretical expressions for transfer functions like those of Equation (4.11) are capable of characterizing only a few, although important, features of a real relationship between SE effect and petrophysical parameters of the medium. For experimental data interpretation, a parallel arrangement of laboratory studies on the rock samples of the studied object is necessary.
4.6. EXPERIMENTAL FIELD AND BOREHOLE SEISMOELECTRIC STUDIES In order to study the practical possibility of SE measurements in natural conditions and to corroborate their geophysical informativeness following from the theory, necessary equipment has been designed, and field and well measurements were carried out. Fig. 4.10 displays the results of SE logging (Svetov et al., 2001; Svetov et al., 2004) of a well located within an edge zone of the Near-Caspian depression. Measurements were performed at a fixed frequency of 9.5 kHz, the length of the sonde was 0.5 m. Elastic field was excited by magnetostriction transmitter. Shown in the Fig. 4.10a are the recorded curves of pressure and electric field strength measured directly in the well. Electric field signal amounted to hundreds of microvolts and was many times as high as the noise. Within a metal-cased borehole section (down to the depth of 410 m) the signal dropped sharply. Within an open section (Figs. 4.10b, c) the electric field is differential; its variations correlate with changes in the acoustic field intensity and represent the specific features of the geological section known from coring and other logging methods. In particular, the enhanced electric signals (and SE transfer function) are associated with intervals of finest-pored carbonate rocks. Reliability of the obtained results is confirmed by numerous repeated measurements. Detailed field SE studies were carried out at the geophysical test area of the Moscow State University close to v. Aleksandrovka of Kalouga region (Ugra river flood-plain) (Svetov et al., 2001; Svetov et al., 2004). The upper part of the geological section of interest consists of morainic deposits interstratified with layers of limestones, sands and clays. For field SE studies, an eight-channel SE equipment has been designed (four seismic and four electromagnetic channels). Elastic oscillations were excited by the sledge blows. Detection of seismic signals was carried out using seismic detectors SV-20. Electric signals were measured at 1–2 m long grounded lines MN. Measurements of seismic and electric fields at each point of the profile were carried out at progressively increasing separation of the blow site from the fixed
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Fig. 4.10. SE logging results for a borehole in Saratov region: directly measured pressure P and electric field E (a) same data averaged by low-frequency filtering (b) and SE transfer function E/P (c).
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Fig. 4.11. Experimental seismograms (a) and electrograms, (b) obtained at one of the profile points in Aleksandrovka at different distances to the blow point.
measurement point. Fig. 4.11 shows an example of a seismogram of the elastic field vertical component measured at a certain point (a) and an electrogram oriented in the profile direction of the horizontal component of the electric field (b). Separate signal traces are indexed by the distance to the blow point in meters. In the righthand parts of all plots, the maximum values are written of seismic or electric signals
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(in m/s and V/m, correspondingly) that define vertical scales at each of signal traces. From the figure, a conclusion can be drawn about a complex character of seismic (and the more so as to electric) field peculiar to complexly structured near-surface zone. At small time intervals, the refracted waves are recorded (seismic event G1) and at long time intervals intense low-frequency surface waves (seismic event G2). Intermediate time intervals are filled with mutually interfering waves of various types. Seismic waves propagation velocities are low, the values varying from 200–250 m/s (surface waves) to 400–500 m/s (refracted waves). Electric signals show a rather good correlation with seismic signals, which speaks for their frozenness into the elastic field. Fast waves are distinguished only at small spacing r ¼ 4–12 m. Based on the results of the measured data processing (Svetov et al., 2004), the SE transfer function W ¼ E=vðVs=m2 Þ along the profile was plotted (Fig. 4.12). The curve correlates with geological and geophysical data. In particular, the minimum in SE transfer function clearly marks the break in the clay water-resisting rock
Fig. 4.12. SE transfer function along the profile in Aleksandrovka.
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accompanied by the decrease in rock humidity but not revealed by any other methods. Rather large amount of experimental field SE studies are by now carried out with 24-channel SE equipment designed in the GEMRC IPE RAS (12 seismic and 12 electric channels). These works confirmed, in general, the developed theory of SE phenomena and the prospects of seismoelectrics application in solving the problems of engineering, hydro- and mining geology. Resuming the studies carried out, one can say that their main result is the creation of theoretical basics for SE-prospecting studies both in borehole and field modifications, and the experimental verification of a certain adequacy of the developed theory to the really observed phenomena and the yielded from the theory conclusions about new informational possibilities of SE method of geophysical prospecting. To the moment, we believe the major applications of this method to be the logging studies of gas–oil and hydrogeological wells and the study of the upper part of geological section for the purposes of solving the shallow engineering, ecological and hydrogeological problems, although the use of the method in the oil–gas exploration is envisaged in the works by other Russian institute (VNIIGeophysica) with powerful vibrators. Acknowledgments The chapter is based on the results of joint work of the author with his collaborators P. Aleksandrov, V. Ageev, O. Ageeva, S. Karinskii, S. Kevorkyantz, Yu. Kuksa and with the professor of Saratov State Technical University V. Gubatenko to whom the author expresses his deep gratitude. The work was supported by RFBR grant No. 05-03-64467 and Shlumberger Corporation grant CRDF RGE1295.
REFERENCES Ageeva, O.A., Svetov, B.S., Sherman, G.H. and Shipulin, V.V., 1999. Seismoelectric effect of the second kind in rocks (laboratory studies) (in Russian). Novosibirsk. Geol. Geofis., 40, 8: 1251–1257. Biot, M.A., 1956. Theory of propagation of elastic waves in a fluidsaturated porous solids. J. Acoust. Soc. Am., 28: 168–186. Frenkel, Ya. I., 1944. To theory of seismic and seismoelectric phenomena in wet soil (in Russian). Izvestia, Geogr. Geofis., 8, 4: 133–150. Ivanov, A., 1940. Seismoelectric effect of the second kind (in Russian). Izvestiya, Geogr. Geofis., 5: 699–727. Ivanov, A., 1949. Seismoelectric effect of the first kind in near-electrode regions (in Russian). Doklady Akad. Nauk SSSR, 68: 699–727. Ozerkov, E.L., Ageeva, O.A., Osipov, V.G., Svetov, B.S. and Tikshaev, V.V., 1998. On the vibroimpact influence on electric properties of geological medium (in Russian). Geofisika, 3: 30–34. Pride, S.R., 1994. Governing equations for the coupled electromagnetics and acoustics of porous media. Phys. Rev., B, 50: 15678–15696.
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Schmitt, D.P., Bouchon, M. and Bonnet, G., 1988. Full-wave synhtetic acoustic log in radially semiinfinite saturated porous media. Geophysics., 53, 6: 807–823. Svetov, B.S., 2000. To theoretical substantiation of seismoelectric method of geophysical prospecting (in Russian). Geofisika, 1: 28–39. Svetov, B.S. and Gubatenko, V.P., 1999. Electromagnetic field of mechanoelectric origin in porous fluid-saturated rocks: I. Statements of the problem (in Russian). Fis. Zemli, 10: 67–73. Svetov, B.S., Ageeva, O.A. and Lisitsyn, V.S., 2001. Logging studies of seismoelectric phenomena (in Russian). Geofisika, 3: 44–48. Svetov, B.S., Ageev, V.V., Ageeva, O.A., Alexandrov, P.N. and Gubatenko, V.P., 2004. Seismoelectric methods of prospecting and logging (in Russian). Geofisika, 1: 44–48. Svetov, B.S., Ageev, V.V., Alexandrov, P.N. and Ageeva, O.A., 2001. Some results of experimental field seismoelectric studies (in Russian). Geofisika, 6: 47–53.
