JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, B08302, doi:10.1029/2010JB007958, 2011
Electromagnetic field generated by a finite fault due to electrokinetic effect Hengshan Hu1 and Yongxin Gao1 Received 31 August 2010; revised 29 April 2011; accepted 10 May 2011; published 4 August 2011.
[1] This work investigates surface electromagnetic wavefields generated by a finite fault due to electrokinetic effect with Pride’s theory as the governing equations. A finite fault is discretized into a series of small subfaults, each of which is taken as a point source with different initiation time. The wavefields generated by the whole fault are then synthesized by stacking those generated by all the subfaults. Numerical simulations of a vertical strike‐slip fault with a constant rupturing velocity are then conducted on the basis of the derived formalism. Simulation results show that the rupturing fault generates observable permanent ground motions and electromagnetic field disturbances. Two types of electric field characters are observed in simulations: the coseismic oscillatory variation and the postseismic decaying variation. When the fault rupturing stops and the seismic waves pass far away, the magnetic field vanishes while the electric field remains, decaying slowly and lasting for hundreds of seconds. Adjacent to the free surface the vertical electric field is about 100 times larger than the horizontal one. When the receiving depth increases, the amplitudes of the horizontal electric fields in both the oscillatory and decaying components increase while those of the vertical electric fields decrease. It is also shown that there is no horizontal electric field remnant right at the free surface after the seismic perturbations decay away. The near‐fault electric fields simulated in this paper hold similar features to some field observations in literature. Citation: Hu, H., and Y. Gao (2011), Electromagnetic field generated by a finite fault due to electrokinetic effect, J. Geophys. Res., 116, B08302, doi:10.1029/2010JB007958.
1. Introduction [2] It is known that seismic waves can cause electromagnetic (EM) fields. One of the mechanisms for the coupling between the elastic and EM energies in the shallow crust is the electrokinetic effect. Rocks in the shallow crust are usually porous, with porosity varying from as low as 0.01 in highly consolidated states to as high as 0.35 in unconsolidated states. When a seismic compressional wave propagates in a fluid‐saturated porous medium, a relative fluid‐solid motion as well as skeleton deformation is induced [Biot, 1956]. The flow of excess charges in the electrical diffuse layer appears as an advective current. Consequently a streaming potential and an electric field build up. Refer to Pride and Morgan [1991] and Pride [1994] for a detailed description of the electrokinetic phenomena associated with both compressional and shear waves. Since the first measurement of the electric fields due to seismic waves by Ivanov [1939], electrokinetic effect has gradually drawn attention to geophysicists [Frenkel, 1944; Martner and Sparks, 1959; Broding et al., 1963; Long and Rivers, 1975]. Field and laboratory experiments in recent 1 Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin, China.
Copyright 2011 by the American Geophysical Union. 0148‐0227/11/2010JB007958
years [e.g., Thompson and Gist, 1993; Butler et al., 1996; Mikhailov et al., 1997; Zhu et al., 1999, 2008; Garambois and Dietrich, 2001; Gaffet et al., 2003; Bordes et al., 2006, 2008] provide further evidence for the electrokinetic phenomena. Also, several studies [Thompson and Gist, 1993; Butler et al., 1996; Mikhailov et al., 1997; Garambois and Dietrich, 2001] show that electrokinetic effect has potential applications in oil and gas explorations due to its sensitivity to the physical and electrochemical properties of the subsurface. Pride [1994] derived a set of governing equations for the coupled poroelastic and electromagnetic waves, which is followed by theoretical investigations on seismoelectric exploration on the surface [Haartsen and Pride, 1997; Garambois and Dietrich, 2002; Jardani et al., 2010] and in the borehole [Hu and Liu, 2002; Guan and Hu, 2008]. [3] Electrokinetic effects may also be active during earthquake events [Mizutani et al., 1976; Park et al., 2007]. Fitterman [1978, 1979] presented a quantitative modeling of the electrokinetic effect associated with earthquakes. He showed that the fluid diffusion in the vicinity of the fault can cause observable electric and magnetic anomalies due to the electrokinetic processes. Experiment on saturated sedimental rock samples by Jouniaux and Pozzi [1995] showed a large increase in the electrokinetic coupling coefficient beginning with the onset of the localization of the shear band at about 75% of the yield stress and stopping at the
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failure. Based on observations of coseismic EM fields in earthquakes in recent years, electrokinetic effect has been identified as a possible cause for the coseismic EM disturbances [Johnston et al., 1994; Nagao et al., 2000; Johnston, 2002; Karakelian et al., 2002; Park et al., 2007; Tang et al., 2008]. [4] It is believed that electrokinetic effect is tightly connected to fault since most natural earthquakes are caused by fault slips. Note a fault can be generally taken as a point source when its scale is small relative to the wavelength considered and the source‐receiver distance. The wavefields generated by a fault slip are recognized equivalent to those generated by a double couple [Aki and Richards, 2002]. The seismoelectromagnetic fields generated by such a double couple were investigated by Gao and Hu [2010] in an infinite uniform space. For a finite fault model, Pride et al. [2004a] studied the electric response in a uniform porous crust following a shear dislocation on an internal slip surface. Their work emphasizes how the fluid‐pressure equilibration affects both the stress state and the electric field near the fault after an earthquake. Yet, it still remains unclear how process of the fault rupturing or the propagation of the seismic waves affects electrokinetic effect, and how the associated magnetic field varies. [5] The present paper aims to address these unresolved issues via investigating the EM response in an earthquake due to the electrokinetic effect. Note that the EM fields caused by an earthquake may also result from other mechanisms, such as the electromagnetic induction effect [Honkura et al., 2002; Matsushima et al., 2002; Ujihara et al., 2004], the piezoeletric effect [Ogawa and Utada, 2000; Huang, 2002], and so on. In the present work these effects are not our focuses thus are neglected. The earthquake is modeled as a rupturing fault of finite size. A point source stacking method is applied to calculate the electric and magnetic fields for the seismoelectric coupling case based on Pride’s equations [Pride, 1994; Haartsen and Pride, 1997]. The same approach has been successfully used by Olson and Apsel [1982] to calculate the seismic fields generated by a finite fault. [6] This paper is organized as follows. In section 2, Green’s functions to Pride’s equations are derived in a layered geological configuration for point sources represented by moment tensors. The wavefields generated by a fault are then obtained with an integration. In section 3, a numerical example on seismic, electric and magnetic responses to the slipping of a vertical strike‐slip fault is given. Discussions and conclusions are given in sections 4 and 5, respectively.
2. Mathematical Formulation 2.1. Pride’s Equations [7] Pride [1994] derived a set of macroscopic equations governing the coupled poroelastic and EM fields. Assuming an e−iwt time dependence, these equations in an isotropic homogeneous porous medium can be written as follows [Haartsen and Pride, 1997]: r H ¼ ½ð!Þ i!"E þ Lð!Þ rP þ !2 f u þ f þ C; ð1Þ r E ¼ i!H M;
ð2Þ
!2 u þ f w ¼ r t þ F;
ð3Þ
i!w ¼ Lð!ÞE þ ð!Þ= rP þ !2 f u þ f ;
ð4Þ
t ¼ ½ð H 2GÞr u þ Cr wI
þ G ru þ ruT ;
P ¼ Cr u þ M r w;
ð5Þ ð6Þ
where w is the angular frequency, H is the magnetic field, E is the electric field, u is the average solid displacement, w is the average relative fluid‐solid displacement, t is the bulk stress tensor, P is the pore fluid pressure, I is the identity tensor, and " and m are the electrical permittivity and magnetic permeability of the porous formation, respectively. r = (1 − ) rs + rf is the bulk density, rs is the solid grain density, rf is the pore fluid density, is the porosity, and h is the fluid viscosity. s(w), (w) and L(w) are the dynamic electrical conductivity, the dynamic permeability and the dynamic electrokinetic coupling coefficient, respectively, all of which are complex and frequency dependent. However, in the earthquake wave frequency (less than several hertz) band, the variations of s, and L with the frequency are very small and are taken as their respective static values, i.e., s0, 0 and L0. Their detailed expressions have been given by Pride [1994]. F and f are the average force densities exerted on the bulk material and fluid phase, respectively. C and M are the applied current density and magnetic current sources, respectively. H, C and M are the elastic moduli which are expressed as H ¼ Kb þ 4G=3 þ 2 M ;
ð7Þ
C ¼ M ;
ð8Þ
M ¼ Kf Ks = Ks þ ð ÞKf ;
ð9Þ
¼ 1 Kb =Ks :
ð10Þ
where
Ks and Kf are the bulk moduli of the solid and fluid phases, respectively. Kb and G are the bulk and shear moduli of the framework, respectively. [8] Pride’s equations combine Maxwell equations for electromagnetics and Biot’s equations for poroelasticity, thus providing a tool to model the seismoelectric coupling phenomena in fluid‐saturated porous media. However, it has certain limitations. Due to some assumptions, expressions for the electrokinetic coupling coefficient and the conductance in Pride’s equations are not universal. For example, Pride assumed that ions in the Stern layer do not contribute to the rock conductance, which is not true for shaly sandstones [Block and Harris, 2006]. According to Leroy and Revil [2009] and Wang and Revil [2010], more than half of the countercharges are located in the Stern layer for clays and silica. Revil and Florsch [2010] also considered the Stern layer conductivity in their modeling the frequency‐ dependent electrical conductivity of porous rocks. However,
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an exact quantitative analysis has not been done till now on the effect of the Stern layer conductivity on the streaming potential and on the electrokinetic coupling coefficient. Alkafeef and Alajmi [2007] measured the surface conductivity and the zeta potential for consolidated rock cores. They showed that the total surface conductivity is not ignorable at low salinity, but did not separate the contribution of the Stern layer to surface conductivity from that of the diffuse layer. Another assumption made by Pride is that the diffuse layer is very thin compared with the pore diameter, which is not always true for saturated sedimentary rocks. A lot of efforts have been made toward a better understanding of the coupling mechanism [e.g., Leroy and Revil, 2004; Malama et al., 2009]. Recently, Jardani et al. [2010] inverted the mechanical and electrical parameters of a reservoir from synthesized seismoelectric signals. In their modeling the coupling coefficient is empirically linked to the cation exchange capacity (CEC) which is a parameter characterizing the total excess ions in unit weight of a dry core sample and is measurable in a laboratory. These efforts may lead to the final setting up of a better seismoelectric theory in the future. But presently, the Pride’s theory is still among the best sets of accepted governing equations for seismoelectric coupling. The Pride’s equations are valid if one uses experimentally obtained coefficients. In the earthquake wave frequency (which is less than several hertz) band, the conductivity and the coupling coefficient do not change with frequency and can be measured by experiments as done by Pengra et al. [1999] and Alkafeef and Alajmi [2007]. In our modeling example, we use Pride’s expressions for low‐frequency conductivity and coupling coefficient. More realistic modeling will be pursued in our future studies if experimental data are available. [9] Biot’s theory involved in Pride’s equations is well known for its description of the relative motion between the fluid phase and the solid frame and for its prediction of the existence of the slow compressional wave [Biot, 1956]. At the low‐frequency limit the slow compressional wave equation reduces to diffusion equation, and the “wave” behaves as a diffusion process, in which the pressure diffuses and the pore fluid moves as in filtration. Both relative motion and the slow compressional wave are important for the explanation of earthquake seismoelectric wavefield. Note that since the attenuation predicated by Biot’s theory is smaller than that obtained by experiments [Carcione, 2001; Pride et al., 2004b], the model predicts larger seismic wave amplitudes than true values. This overestimation will not affect our analysis significantly as we are interested only in the earthquake seismic signals not far away from the finite fault, whose frequency is orders lower than exploration seismic and acoustic log frequencies. 2.2. Green’s Functions due to Moment Tensor Point Sources in a Layered Half‐Space [10] Haartsen and Pride [1997] have presented an algorithm to calculate the seismoelectric wavefields generated by point sources in a layered half‐space. However, they did not consider a fault slip which can be represented by a moment tensor. In this paper, we aim to investigate the seismoelectromagnetic fields due to a fault slip, and therefore a moment tensor source must be included. In what
follows, we extend the algorithm given by Haartsen and Pride [1997] to allow for a moment tensor point source. [11] To solve the wavefields excited by a point source in a horizontally stratified formation, the cylindrical coordinate system (r, , z) is adopted, with z indicating the depth. In the frequency domain, the field variable x can be expressed in terms of the vector surface harmonics [Kennett and Kerry, 1979; Haartsen and Pride, 1997] im Rm ez ; k ðr; Þ ¼ Jm ðkrÞe
im ′ Sm er þ k ðr; Þ ¼ iJmðkrÞe
Tm k ðr; Þ ¼
m Jm ðkrÞeim e ; kr
m Jm ðkrÞeim er þ iJm′ ðkrÞeim e ; kr
ð11Þ ð12Þ
ð13Þ
as xðr; ; z; !Þ ¼ r ðr; ; z; !Þer þ ðr; ; z; !Þe þ z ðr; ; z; !Þez Z þ∞ l X
^1 ðk; m; z; !ÞSm ¼ kdk k 0
m¼l
m ^ þ ^2 ðk; m; z; !ÞTm k þ z ðk; m; z; !ÞR k ;
ð14Þ
where Jm(kr) is the mth‐order Bessel function of the first kind, J′m(kr) = 1k dJmdrðkrÞ, k is the horizontal wave number, and er, e and ez are the coordinate unit vectors. The field vector x can be u, w, E, H, t, F, f, C or M. t represents the force vector in a horizontal plane. x^ is the field vector in the new m m coordinates composed of Sm k , Tk and Rk . The order l of the summation is determined by the azimuthal symmetry of the point source. l = 0 if the source is of no azimuthal dependence, like an explosion source or a vertical point force. l = 1 if the source is a point force with a nonzero horizontal component. l ≤ 2 if the source is a moment tensor. [12] The Pride’s equations (1)–(6) are then transformed to @ ðk; m; z; !Þ; Bðk; m; z; !Þ ¼ Aðk; !ÞBðk; m; z; !Þ þ F @z
ð15Þ
where B denotes the displacement‐stress‐EM vector, and F denotes the source vector. The macron () in F is used to distinguish from F, which represents the body force acting on the bulk material in equation (3). A is a matrix dependent on the frequency w, the wave number k and the parameters of the porous formation. The detailed expression of A was given by Haartsen and Pride [1997]. The set of equations shown in equation (15) is then separated into two independent sets. One is the PSVTM set coupling the Pf, Ps, SV and TM waves. The other is the SHTE set coupling the SH and TE waves. The vectors B in the two sets are ^2; E ^1 T ; ^1 ; ^ ^ z ; ^1z ; ^zz ; P; H BV ¼ u uz ; w
ð16Þ
^1; E ^2 T : ^2 ; ^2z ; H BH ¼ u
ð17Þ
The superscripts “V” and “H” correspond to the PSVTM and SHTE systems, respectively, and the superscript “T”
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in the two denotes the transpose. The source vectors F systems are ^ 1 ; F ^z ; ^fz V ðk; m; z; !Þ ¼ 0; 0; ip ^f1 ; f ^f1 F F !~ ~ T ~L ^ ^ ^z M ^ pC ^2 ; þ C z ; Lf1 C1 ; "~ "~
ð18Þ
f ^ ^ p ^ ^ T H ^ ^ f2 F2 ; Lf2 þ C2 Mz ; M1 ; ð19Þ F ðk; m; z; !Þ ¼ 0; ~
where d(z − zs) is the Dirac delta function. The effect of the source is represented by S. The expression of S for a moment tensor source is derived in Appendix A. [13] With all the boundary conditions and the source representation, one can solve the wavefields in the wave number–frequency domain in a way similar to Haartsen and Pride [1997]. With a transform back to the space‐time domain, one obtains Z
z ðr; ; z; t Þ ¼
þ∞ ∞
ei!t d!
Z
þ∞ 0
l X
kdk
Jm ðkrÞ ^z ðk; m; z; !Þeim ;
m¼l
ð29Þ
where p is the horizontal slowness, and ~ ¼ i=½!ð!Þ;
ð20Þ
Z
r ðr; ; z; t Þ ¼
"~ ¼ " þ ið!Þ=! ~L2 ð!Þ:
þ∞
∞
ei!t d!
Z
þ∞
0
kdk
l h X m m¼l
i iJm′ ðkrÞ ^1 ðk; m; z; !Þ eim ;
ð21Þ
kr
Jm ðkrÞ ^2 ðk; m; z; !Þ ð30Þ
At the free surface z = 0, the traction conditions require 2 3 0 7 6 7 6 7 6 7 6 6 ^zz 7 ¼ 6 0 7; 7 6 7 6 5 4 5 4 ^ 0 P 2
^1z
3
Z ð22Þ
for the PSVTM system, and ^2z ¼ 0;
ð23Þ
for the SHTE system. Besides, the continuity condition of the horizontal components of E and H fields must be satisfied at the free surface. Since an underground seismic source is considered, there will be only upgoing EM wave in the topmost half‐space. This half‐space contains only air and for simplicity it is treated as vacuum, with permittivity and permeability as "0 and m0, respectively. The electric and magnetic conditions at z = 0 require ^ 2 þ "0 E ^ 1 ¼ 0; q0 H
ð24Þ
for the PSVTM case, and ^ 1 q0 E ^ 2 ¼ 0; 0 H
ð25Þ
Bðz Þ ¼ Bðzþ Þ:
ð26Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi for the SHTE case, where q0 = 0 "0 p2 is the vertical slowness of the EM wave in the vacuum. E^1 , E^2 , H^1 and H^2 correspond to the values at z = 0 of the porous layer, which is located right below the free surface.On the interface at depth z separating two different porous layers, the boundary condition requires
On the horizontal plane at depth zs, where the source is located, the jump condition of vector B is þ AH; ¼G Sðk; m; !Þ B zþ s B zs
ð28Þ
þ∞
∞
ei!t d!
Z
þ∞ 0
kdk
l h X m m¼l
i þ iJm′ ðkrÞ ^2 ðk; m; z; !Þ eim :
kr
Jm ðkrÞ ^1 ðk; m; z; !Þ ð31Þ
In our numerical calculations, the moment tensor sources are considered. For a given component Mjk of a moment tensor, we first solve the field ^i in the coordinate system consisting m m of Sm k , Tk and Rk using the algorithm introduced before. Then the field bi is calculated in the cylindrical coordinate system using equations (29)–(31). Finally, each field in the cylindrical coordinates (r, , z)can be transformed into the Cartesian coordinates (x, y, z) by the rotation formulas. We denote the Green’s function in a layered half‐space as Gbij,k[r, t; r′, 0], which represents the i component of the field of b(b = u, E, H) type, received at location r and time t and is radiated by the jkth component of a moment tensor source at r′ and initiated at time t = 0. It is easy to get bi = MjkGbij,k[r, t; r′, 0]. The Green’s function will be used to synthesize the wavefields generated by a finite fault in section 2.3. 2.3. Synthetic Wavefield by Point Source Stacking Method [14] A Cartesian coordinate system on the Earth surface is setup, with x, y and z indicating the north, east and downward directions, respectively, as shown in Figure 1. The fault is taken as a rectangular plane with a parallel‐to‐strike length L (x direction) and a downdip length D (y direction). s and d denote the strike and dip angles of the fault. z0 represents the buried depth of the fault. According to Olson and Apsel [1982], the wavefields generated by the whole fault can be expressed as ZZ
ð27Þ
where S is the so‐called displacement‐stress‐EM disconti and H can be obtained from nuity vector for the source. G ð z zs Þ þ H ðk; m; z; !Þ ¼ G @ ð z zs Þ; F @z
ðr; ; z; t Þ ¼
i ðr; tÞ ¼
mjk ðr′ÞG ij;k ½r; t; r′; ~t ðr′Þd Sðr′Þ;
ð32Þ
S
where b = u, E, H indicates the type of the field, the subscript i represents the ith component of the field, r is the position vector of the observation point, t is the time. On the right hand side of equation (32) is an integral over the fault
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Figure 1. Geometry and discretization of the fault surface in the Earth surface Cartesian coordinates. s and d denote the strike and dip angles of the fault, respectively, and z0 is the buried depth of the fault. mjk(r′) is the density of the jkth component of surface S. the moment tensor at the point r′ on the fault surface. b [r, t; r′, ~t(r′)] is the Green’s function due to comGij,k ponent Mjk introduced before. ~t (r′) represents the initiation time of the point source at point r′. [15] As shown in Figure 1, the fault plane is divided into N cells (or subfaults). Both the slip and the initiation time over each cell are uniform. If each cell is sufficiently small, at least smaller than the distance between the source and the receiver as well as the wavelength considered, it can be recognized as a point source. The integral defined as equation (32) can then be rewritten as a summation
i ðr; t Þ ¼
N X
Figure 2. Geological model used for numerical simulation. A vertical strike‐slip fault in a homogeneous half‐space is considered. The fault ruptures from the left to right with a constant velocity Vr = 2.2 km/s. 1 km. The fault ruptures from left to right with a constant velocity Vr = 2.2 km/s. The moment is set to be 1.5 × 1018 Nm which corresponds to a M6 earthquake. The slip time dependence assumed is a ramp function of 1 s duration. The frequency varies in the range 0–1 Hz. [17] Figure 3 shows the temporal evolution of the seismic displacement field in a spatial domain (x 2 [0 km, 38 km], y 2 [−40 km, 58 km], z = 1 m). Each row stands for the response at a specified instant after the initiation of the fault rupture. In Figure 3 from top to bottom, starting at t = 2 s, a snapshot of the system is taken every 4 s. It is clear that the fault generates obvious ground motions. The
Table 1. Parameters of the Porous Medium Used for the Calculation Mjk ðnÞG ij;k ½r; t; r′n ; ~tðr′n Þ;
ð33Þ
n¼1
where Mjk (n) = mjk(r′n)DSn is the amplitude of the moment tensor on the nth cell, DSn and r′n are the area and the central coordinates of the nth cell. ~t (r′n) is the initiating time of the nth cell, which is determined by the rupture velocity of the fault Vr and its location r′n.
3. Numerical Simulations [16] The aforementioned solution in terms of Green’s functions is numerically worked out for a strike‐slip fault with strike s = 90° and dip d = 90° in a homogeneous porous half‐space (Figure 2). Values of the parameters for the porous half‐space are listed in Table 1. Porosity and permeability are taken to be the same as those used by Nagao et al. [2000] and Pride et al. [2004a], which are = 0.01 and 0 = 10−16 m2, respectively. Frame bulk modulus and shear modulus are calculated from porosity by Vernik’s relations [Vernik, 1998]. The zeta potential & is calculated from salinity according to Pride and Morgan [1991]. The electrical conductivity and the electrokinetic coupling coefficient are set to their respective static values s0 and L0 [Pride, 1994], since the frequency considered is less than 1 Hz. The fault has a parallel‐to‐strike length of L = 30 km and a downdip length of D = 5 km. The buried depth is z0 =
Parameter
Value
Porosity Permeability Tortuosity Solid grain bulk modulus Frame bulk modulusa Shear modulusa Fluid bulk modulus Solid grain density Fluid density Fluid viscosity Salinity Zeta potentialb Electrical conductivityc Low‐frequency electrokinetic coupling coefficientc Solid relative permittivity Fluid relative permittivity Velocity of the P waved Velocity of the S waved
= 0.01 0 = 10−16 m2 a∞ = 3 Ks = 35.7 GPa Kb = 17.91 GPa G = 17.79 GPa Kf = 2.25 GPa rs = 2650 kg/m3 rf = 1000 kg/m3 h = 0.001 Pa s C0 = 0.025 mol/L z = −0.0037 V s0 = 7.73 × 10−4 S/m L0 = 7.3486 × 10−11 sC/kg "s = 4 "f = 80 VP = 5405 m/s VS = 3375 m/s
a The frame bulk modulus Kb and shear modulus G are calculated from the porosity according to the Vernik [1998] relations between frame moduli and porosity. b The Zeta potential z is calculated from the salinity according to Pride and Morgan [1991]. c The electrical conductivity s0 and the low‐frequency electrokinetic coupling coefficient L 0 are calculated from the salinity and the zeta potential according to Pride [1994]. d The velocities of the P and S waves are calculated from the Pride’s equations [Pride and Haartsen, 1996]. Here P wave is short for fast compressional wave.
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Figure 3. Snapshots of the displacement in the space domain (x 2 [0 km, 38 km], y 2 [−40 km, 58 km], z = 1 m) generated by the strike‐slip fault in a homogeneous half‐space. maximum amplitudes of the three displacement components are ux, max = 0.0538 m, uy, max = 0.0773 m, and uz, max = 0.0165 m. These values show that the horizontal ground motions are stronger than the vertical one. After the fault rupturing stops and the seismic waves propagate far away, there exist permanent ground displacements in the vicinity of the fault. From the waveforms of the displacement at location (x = 2 km, y = 40 km, z = 1 m) shown in Figure 4, such permanent displacement is on order of 0.01 m for the horizontal components and 0.001 m for the vertical component. Waveforms of the displacement right below the same location at z = 250 m are also plotted in Figure 4. Interestingly, displacements received at the two depths coincide with each other. This shows the displacement is not sensitive to the receiving depth in the shallow subsurface. Bouchon [1980]
investigated the ground motions generated by a strike‐slip fault by using the discrete wave number representation method. The ground motions illustrated in Figure 3 agree with those calculated by Bouchon [1980]. [18] Snapshots of the magnetic field are displayed in Figure 5. Circular wavefronts are recognized immediately in the snapshots of Hx, Hy and Hz starting from t = 10 s. Such circular wavefronts are also found in Figure 3 in the snapshots of ux, uy and uz at the same instants with apparently identical radii. This indicates that the seismic waves generate accompanying magnetic field disturbances during propagation. The maximum disturbance of Hx appears perpendicular to the propagating direction of the fault rupture, while the maximum disturbances of Hy and Hz appear along the propagating direction of the rupture. Opposite to rupture
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Figure 4. Waveforms of the displacement in the time domain at two receiving points, of which the horizontal locations are the same (x = 2 km, y = 40 km) but the depths are z = 1 m and z = 250 m.
propagation direction, the magnetic disturbances seem smaller. The waveforms of the magnetic field at location (x = 2 km, y = 40 km, z = 1 m) are shown in Figure 6, where the amplitude of magnetic field is on the order of 1 mA/m. When the seismic perturbations pass away, the magnetic field immediately reduces to zero. As in the previous case, waveforms of magnetic field at the same place with z = 250 m are also plotted. Its horizontal and vertical magnetic field are slightly weaker and slightly stronger, respectively, than those received at z = 1 m. It seems that the magnetic field is not sensitive to the receiving depth in the shallow subsurface. [19] Snapshots of the electric field in the same domain (x 2 [0 km, 38 km], y 2 [−40 km, 58 km], z = 1 m) are given in Figure 7. It shows that the seismic waves also induce observable accompanying electric fields. The electric disturbances along the direction of the propagation of the rupture are larger than those along the opposite direction. The maximum amplitudes of the electric field disturbances are Ex,max = 2.31 × 10−5 V/m, Ey,max = 6.46 × 10−6 V/m and Ez,max = 1.8 × 10−3 V/m. Note that the vertical component of the electric field is 2 orders of magnitude stronger than the horizontal components. As can been seen from the snapshots of the electric field at t = 26 s, t = 30 s and t = 34 s in Figure 7, the electric field near the fault does not immediately turn to zero after the seismic disturbances. It is an interesting phenomenon that there is remnant electric field in the vicinity of the fault. Such remnant electric field reaches its extreme values near the starting and stopping points of the fault rupture. Meanwhile, the polarizations of the remnant electric field are opposite at the two sides of the fault. [20] Figures 8–10 display the waveforms of the electric fields Ex, Ey and Ez at four receiving points on a vertical line at (x = 2 km, y = 40 km) with z = 0 m, z = 1 m, z = 5 m and z = 20 m. As can be seen from Figure 8, the horizontal electric field Ex received at depth z = 0 m goes to zero when t > 20 s.
Meanwhile, the seismic disturbances have propagated far away. This is not the case for Ex at z = 1 m, where postseismic or remnant electric field following the coseismic oscillation exists. It decays slowly and lasts for more than 200 s. When it gets deeper at z = 5 m and z = 20 m, following the coseismic oscillation, the remnant amplitude of electric field Ex becomes even stronger, decays more slowly and lasts longer. Figure 9 shows the horizontal electric field Ey received at the above mentioned four points. They exhibit a similar behavior; that is, both the remnant amplitude and the decay time increase when the receiving depth increases. Note that no remnant horizontal electric field exists right at the free surface z = 0 m. [21] The vertical electric fields Ez received at the four points are illustrated in Figure 10. Here Ez differs from Ex or Ey in that it has a postseismic remnant value right at the free surface z = 0 m after seismic perturbations. Ez received at a deeper location has a smaller coseismic oscillatory amplitude, a weaker remnant value and apparently a slower decaying rate. It is clear that the vertical electric field is more sensitive to the receiving depth than the horizontal counterparts. As can be seen from Figures 8–10, the maximum oscillatory amplitudes of Ex, Ey and Ez received at (x = 2 km, y = 40 km, z = 1 m) are Ex,max = 0.509 mV/m, Ey,max = 0.631 mV/m, Ez,max = 171 mV/m, respectively. The remnant values of its electric fields at t = 50 s are Ex = 0.0959 mV/m, Ey = 0.0482 mV/m, and Ez = 167 mV/m. These data show that the electric field has a much stronger vertical component than its horizontal components in both the oscillatory amplitude and the remnant value. [22] Figure 11 shows the electric field received on the same vertical line at z = 50 m and z = 250 m. The oscillatory amplitudes of the electric fields received at the two points are of the same order, i.e., 0.1 mV/m. At both receiving depths the remnant electric fields after the seismic distur-
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Figure 5. Snapshots of the magnetic field in the space domain (x 2 [0 km, 38 km], y 2 [−40 km, 58 km], z = 1 m) generated by the strike‐slip fault in a homogeneous half‐space.
bance decay so slowly that it keeps unchanged in Figure 11 and even at the end of our permissible computation time. It seems that they will last for a very long time. Similar results from a quasi‐static point of view are given by Pride et al. [2004a]. [23] Nagao et al. [2000] have measured the coseismic electric field at the Earth surface following earthquakes in Japan using dipole electrode pairs. Main features of the observed coseismic electric field can be summarized as follows: (1) they do not start at the origin time of earthquake but at the arrival time of seismic waves; (2) there are two main types of changes, oscillatory type and decay type; and (3) the vertical electric fields are often stronger than the horizontal ones. The electric fields simulated in the present
paper share the same features to those observed by Nagao et al. [2000].
4. Discussion [24] The existence of the remnant electric field and its slow decay with time can be understood as follows. The earthquake induces an inhomogeneous distribution of fluid pressure in a very short time. The fluid pressure could not be balanced immediately after the earthquake. Instead, it diffuses gradually hence the flow of the charge in the pore fluid causes electric field. This is similar to the cases of streaming potential in water pumping test [Malama et al., 2009], self‐ potential associated with flow of water in a sandbox [Crespy et al., 2008] and the surface electric signal induced by fluid flow into a reservoir during and after hydraulic fracturing in
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Figure 6. Waveforms of the magnetic field in the time domain at two receiving points, of which the horizontal locations are the same (x = 2 km, y = 40 km) but the depths are z = 1 m and z = 250 m.
a borehole [Darnet et al., 2006]. The observations made by Park et al. [2007] on the 2004 Parkfield earthquake show that the streaming potential after the main shock was associated with a fluid flow to the void space in the fault, and the weaker aftershock streaming potentials were associated with fluid flow away from the fault. In our numerical model, no void space is created during the earthquake. The rocks on the two sides of the fault stick to each other during slipping. [25] In the viewpoint of waves, the existence of the remnant electric field as well as its slow decay with time in our simulation is mainly associated with the slow compressional wave (Ps wave), which is converted at the free surface from the fast compressional or shear waves. As was pointed out by Biot [1956] and recapitulated in section 2.1, the slow compressional wave involved in the Biot (and therefore in Pride) equations is in nature a diffusion phenomenon at low frequency [Chandler and Johnson, 1981], and it causes the flow filtration and an electric field. Chandler [1981] used this principle to detect the slow compressional wave by observing the electric signal. In the fluid pressure diffusion process, fluid pressure gradient decreases gradually until it is uniformly distributed and fluid flow stops. At the same time, the electric field strength becomes weaker and weaker, and finally vanishes. Therefore, the after‐earthquake fluid diffusing process is accompanied by gradually decaying electric field. [26] The sensitivity of the electric field to the depth can be explained by the high attenuation and shallow penetration of the Ps wave. Most energies of the Ps wave concentrates at the free surface where the Ps wave is generated. Since the slow compressional wave is equivalent to a quasi‐static fluid flow process at the earthquake frequency [Chandler and Johnson, 1981; Wenzlau and Müller, 2009], the effect of the fluid diffusion diminishes when the depth increases.
Therefore, the remnant electric field at a deeper depth has a longer duration as illustrated in Figures 8–10. [27] There is another phenomenon that should be noticed. We modeled the earthquake as a vertical strike‐slip fault. The fault generates stronger horizontal but smaller vertical ground motions. However, contrary to expectation, the horizontal electric field is weaker than the vertical one in both the oscillatory and remnant components near the free surface. Moreover, in our additional simulation of a dip‐slip fault, which is not presented in this paper, the vertical ground motion is larger than the horizontal ones. The vertical electric field generated by such a dip‐slip fault is still stronger than the horizontal counterpart near the free surface [Gao, 2010]. These show that the relative significance of the vertical component of the electrical field to the horizontal components near the free surface is independent of the strike angle, the dip angle or the slip direction of fault. Therefore, the vertical electric field should be paid more attention to in the field measurement, because it holds stronger amplitude than the horizontal electric field.
5. Conclusions [28] The electric and magnetic responses to a rupturing fault have been simulated in this paper. The seismic and electromagnetic fields generated by such a finite fault are synthesized by the point source stacking method. As a numerical example, a vertical strike‐slip fault is investigated. The results show that there are electric and magnetic perturbations accompanying the seismic wave propagations. For a M6 earthquake, in the vicinity of the fault the maximum amplitude of the vertical electric field at depth z = 1 m is on the order of 10−3 V/m, while the maximum amplitudes of the horizontal electric fields at the same depth are on the order of 10−5 V/m. As the atmospherically generated diurnal
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Figure 7. Snapshots of the electric field in the space domain (x 2 [0 km, 38 km], y 2 [−40 km, 58 km], z = 1 m) generated by the strike‐slip fault in a homogeneous half‐space.
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Figure 8. Waveforms of the horizontal electric field Ex in the time domain at four receiving points, of which the horizontal locations are the same (x = 2 km, y = 40 km) but the depths are z = 0 m, z = 1 m, z = 5 m, and z = 20 m. electric fields which are routinely measured are at the mV/m level, the electric field generated by the fault can be easily measured. The three components of the magnetic field generated by the fault are on the order of about 1 mA/m at depths 1 m to 250 m. The corresponding magnetic induction is on the order of 10−3 nt calculated based on the vacuum permeability m0. The magnetic field in our simulation is smaller than the Earth’s magnetic field, which is on the order of 104 nT. However, the magnetic field generated by the fault is alternating and can be measured on a static background magnetic field. When the seismic waves pass away, the magnetic disturbances vanish, and permanent
displacements exist in the vicinity of the fault. Variation of the electric field has two types of characters, i.e., the coseismic oscillation and the postseismic decay. The electric field does not reduce to zero immediately but holds a remnant value after the seismic perturbation except for the horizontal component right at the free surface. This remnant electric field decays slowly and can last for hundreds of seconds or even longer. When the depth increases, both the oscillatory and remnant amplitudes of the horizontal electric fields increase, while those of the vertical electric field decrease. The horizontal and vertical electric fields become of the same order at a sufficiently deep depth.
Figure 9. Waveforms of the horizontal electric field Ey in the time domain at four receiving points, of which the horizontal locations are the same (x = 2 km, y = 40 km) but the depths are z = 0 m, z = 1 m, z = 5 m, and z = 20 m. 11 of 14
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Figure 10. Waveforms of the vertical electric field Ez in the time domain at four receiving points, of which the horizontal locations are the same (x = 2 km, y = 40 km) but the depths are z = 0 m, z = 1 m, z = 5 m, and z = 20 m.
Figure 11. Waveforms of the electric field in the time domain at two receiving points, of which the horizontal locations are the same (x = 2 km, y = 40 km) but the depths are z = 50 m and z = 250 m. 12 of 14
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[29] We have made a tentative simulation of the electromagnetic response to a fault. It is expected that in the future seismoelectric field associated with a particular real earthquake event can be simulated based on the theoretical model and compared against the electric, magnetic and seismic recordings of the same event.
ðA1Þ
where Mij is the component of the moment tensor, and rs is the position of the point source. The components of the body force F in the surface harmonic coordinates are [Aki and Richards, 2002], ^1 ¼ 1 F 2 ^2 ¼ 1 F 2 ^z ¼ 1 F 2
Z
rdr
0
Z
rdr
0
rdr
0
* d Sm F; k
2
* d Tm F; k
ðA3Þ
2
* d Rm F; k
ðA4Þ
sð!Þ M C ik S ðk; 0; !Þ ¼ 0; Mzz ; Mzz ; Mxx þ Myy 2 D D 2 T 2GM Mzz ; 0; 0; 0; 0 ; ik 1 D V
ðA5Þ
where D = HM − C2, and s(w) is the frequency response to the source time function,
S V ðk; 1; !Þ ¼
T sð!Þ ik 0; Mxy Myx ; 0;0 ; 2 2
ðA6Þ
sð!Þ 1 k iMxz þ Myz ; 0; 0; 0; ðMzx Mxz Þ 2 2G 2 T ik ðA7Þ þ Mzy Myz ; 0; 0; 0 ; 2
S H ðk; 1; !Þ ¼
and SV(k, m, w) and SH(k, m, w) vanish for ∣m∣ > 2. [31] For example, when the double couple Mxz + Mzx is used as source in numerical simulation, the order of summation in equation (14) is l = 1, because Mxz and Mzx contribute to SV(k, ±1, w) and SH(k, ±1, w), but not to SV(k, 0, w), SH(k, 0, w), SV(k, ±2, w) or SH(k, ±2, w). [32] Acknowledgments. We thank the two anonymous reviewers for their constructive comments and Yubao Zhen for polishing the English. This work is supported by the Special Research Funds of Seismology in China (grant 200808072) and the National Natural Science Foundation of China (grant 40874062).
ðA2Þ
where * denotes the complex conjugate. Substituting these body force components to equations (18) and (19) one obtains V for the PSVTM set and F H for the SHTE set, which are F then used to derive the displacement‐stress‐EM discontinuity vectors S(k, m, w) for the moment tensor by equations (27) and (28)
S H ðk; 0; !Þ ¼
T ik sð!Þ k 0; Mxx Myy þ Mxy þ Myx ; 0; 0 ; 2 4 4
References
0
Z
þ∞
2
0
Z
þ∞
0
Z
Z
þ∞
ðA9Þ
ðA10Þ
[ 30 ] According to the representation theory [Aki and Richards, 2002], a moment tensor source is equivalent to a body force F with @ Mij ð!Þ ðr rs Þ ; @rj
sð!Þ ik 0; 0; 0; Mxx Myy 2 4 T k Mxy þ Myx ; 0; 0; 0; 0 ; 4
S H ðk; 2; !Þ ¼
Appendix A: Displacement‐Stress‐EM Discontinuity Vector for Moment Tensor
Fi ðr; !Þ ¼
S V ðk; 2; !Þ ¼
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T sð!Þ Mxz iMyz ; 0; 0; 0 ; 2G 2
ðA8Þ
Aki, K., and P. G. Richards (2002), Quantitative Seismology, Univ. Sci., Sausalito, Calif. Alkafeef, S. F., and A. F. Alajmi (2007), The electrical conductivity and surface conduction of consolidated rock cores, J. Colloid Interface Sci., 309, 253–261, doi:10.1016/j.jcis.2007.02.004. Biot, M. A. (1956), Theory of propagation of elastic waves in a fluid‐ saturated solid. I: Low frequency range, J. Acoust. Soc. Am., 28, 168–178, doi:10.1121/1.1908239. Block, G. I., and J. G. Harris (2006), Conductivity dependence of seismoelectric wave phenomena in fluid‐saturated sediments, J. Geophys. Res., 111, B01304, doi:10.1029/2005JB003798. Bordes, C., L. Jouniaux, M. Dietrich, J.‐P. Pozzi, and S. Garambois (2006), First laboratory measurements of seismo‐magnetic conversions in fluid‐ filled Fontainebleau sand, Geophys. Res. Lett., 33, L01302, doi:10.1029/ 2005GL024582. Bordes, C., L. Jouniaux, S. Garambois, M. Dietrich, J.‐P. Pozzi, and S. Gaffet (2008), Evidence of the theoretically predicted seismo‐magnetic conversion, Geophys. J. Int., 174, 489–504, doi:10.1111/j.1365246X.2008.03828.x. Bouchon, M. (1980), The motion of the ground during an earthquake: 1. The case of a strike slip fault, J. Geophys. Res., 85(B1), 356–366, doi:10.1029/JB085iB01p00356. Broding, R. A., S. D. Buchanan, and D. P. Hearn (1963), Field experiments on the electroseismic effect, Geophysics, 58, 898–903. Butler, K. E., R. D. Russell, A. W. Kepic, and M. Maxwell (1996), Measurement of the seismoelectric response from a shallow boundary, Geophysics, 61, 1769–1778, doi:10.1190/1.1444093. Carcione, J. M. (2001), Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic and Porous Media, Elsevier, New York. Chandler, R. N. (1981), Transient streaming potential measurements on fluid‐saturated porous structures: An experimental verification of Biot’s slow wave in the quasi‐static limit, J. Acoust. Soc. Am., 70, 116–121, doi:10.1121/1.386689. Chandler, R. N., and D. L. Johnson (1981), The equivalence of quasi‐static flow in fluid‐saturated porous media and Biot’s slow wave in the limit of zero frequency, J. Appl. Phys., 52, 3391–3395, doi:10.1063/1.329164. Crespy, A., A. Revil, N. Linde, S. Byrdina, A. Jardani, A. Bolève, and P. Henry (2008), Detection and localization of hydromechanical disturbances in a sandbox using the self‐potential method, J. Geophys. Res., 113, B01205, doi:10.1029/2007JB005042. Darnet, M., G. Marquis, and P. Sailhac (2006), Hydraulic stimulation of geothermal reservoir fluid flow, electric potential and microseismicity relationships, Geophys. J. Int., 166, 438–444. Fitterman, D. V. (1978), Electrokinetic and magnetic anomalies associated with dilatant regions in a layered Earth, J. Geophys. Res., 83, 5923–5928, doi:10.1029/JB083iB12p05923.
13 of 14
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Fitterman, D. V. (1979), Theory of electrokinetic‐magnetic anomalies in a faulted half space, J. Geophys. Res., 84, 6031–6040, doi:10.1029/ JB084iB11p06031. Frenkel, J. (1944), On the theory of seismic and seismoelectric phenomena in a mosit soil (in Russian), J. Phys., 8, 230–241. Gaffet, S., Y. Guglielmi, J. Virieux, G. Waysand, A. Chwala, R. Stolz, C. Emblanch, M. Auguste, D. Boyer, and A. Cavaillou (2003), Simultaneous seismic and magnetic measurements in the Low‐Noise Underground Laboratory (LSBB) of Rustrel, France, during the 2001 January 26 Indian earthquake, Geophys. J. Int., 155, 981–990, doi:10.1111/ j.1365-246X.2003.02095.x. Gao, Y. (2010), Simulation of earthquake‐induced electromagnetic wave field due to the electrokinetic effect, Ph.D. thesis, Harbin Inst. of Technol., Harbin, China. Gao, Y., and H. Hu (2010), Seismoelectromagnetic waves radiated by a double couple source in a saturated porous medium, Geophys. J. Int., 181, 873–896. Garambois, S., and M. Dietrich (2001), Seismoelectric wave conversions in porous media: Field measurements and transfer function analysis, Geophysics, 66, 1417–1430, doi:10.1190/1.1487087. Garambois, S., and M. Dietrich (2002), Full waveform numerical simulations of seismoelectromagnetic wave conversions in fluid‐saturated stratified porous media, J. Geophys. Res., 107(B7), 2148, doi:10.1029/ 2001JB000316. Guan, W., and H. Hu (2008), Finite‐difference modeling of the electroseismic logging in a fluid‐saturated porous formation, J. Comput. Phys., 227, 5633–5648, doi:10.1016/j.jcp.2008.02.001. Haartsen, M. W., and S. R. Pride (1997), Electroseismic waves from point sources in layered media, J. Geophys. Res., 102(B11), 24,745–24,769, doi:10.1029/97JB02936. Honkura, Y., M. Matsushima, N. Oshiman, M. K. Tunçer, Ş. Bariş, A. Ito, Y. Iio, and A. M. Işikara (2002), Small electric and magnetic signals observed before the arrival of seismic wave, Earth Planets Space, 54, 9–12. Hu, H., and J. Liu (2002), Simulation of the converted electric field during acoustoelectric logging, SEG Expanded Abstr., 21, 1817–1820. Huang, Q. (2002), One possible generation mechanism of coseismic electric signals, Proc. Jpn. Acad., 78, 173–178, doi:10.2183/pjab.78.173. Ivanov, A. G. (1939), Effect of electrization of Earth layers by elastic waves passing through them (in Russian), Dokl. Akad. Nauk SSSR, 24, 42–45. Jardani, A., A. Revil, E. Slob, and W. Sollner (2010), Stochastic joint inversion of 2D seismic and seismoelectric signals in linear poroelastic materials, Geophysics, 75(1), N19–N31, doi:10.1190/1.3279833. Johnston, M. J. S. (2002), Electromagnetic fields generated by earthquakes, in International Handbook of Earthquake and Engineering Seismology, Int. Geophys. Ser., vol. 81A, pp. 621–635, Academic, Amsterdam. Johnston, M. J. S., R. J. Mueller, and Y. Sasai (1994), Magnetic field observations in the near‐field the 28 June 1992 Mw 7.3 Landers, California, earthquake, Bull. Seismol. Soc. Am., 84, 792–798. Jouniaux, L., and J.‐P. Pozzi (1995), Streaming potential and permeability of saturated sandstone under triaxial stress: Consequences for electrotelluric anomalies prior to earthquakes, J. Geophys. Res., 100, 10,197–10,209, doi:10.1029/95JB00069. Karakelian, D., G. C. Beroza, S. L. Klemperer, and A. C. Fraser‐Smith (2002), Analysis of ultralow‐frequency electromagnetic field measurements associated with the 1999 M 7.1 Hector Mine, California, earthquake sequence, Bull. Seismol. Soc. Am., 92, 1513–1524, doi:10.1785/ 0120000919. Kennett, B. L. N., and N. J. Kerry (1979), Seismic waves in a stratified half space, Geophys. J. R. Astron. Soc., 57, 557–583. Leroy, P., and A. Revil (2004), A triple‐layer model of the surface electrochemical properties of clay minerals, J. Colloid Interface Sci., 270, 371– 380, doi:10.1016/j.jcis.2003.08.007. Leroy, P., and A. Revil (2009), A mechanistic model for spectral induced polarization of clay materials, J. Geophys. Res., 114, B10202, doi:10.1029/2008JB006114. Long, L. T., and W. K. Rivers (1975), Field measurement of the electroseismic response, Geophysics, 40, 233–245, doi:10.1190/1.1440521. Malama, B., A. Revil, and K. L. Kuhlman (2009), A semi‐analytical solution for transient streaming potentials associated with confined aquifer pumping tests, Geophys. J. Int., 176, 1007–1016, doi:10.1111/j.1365246X.2008.04014.x.
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Martner, S. T., and N. R. Sparks (1959), The electroseismic effect, Geophysics, 24, 297–308, doi:10.1190/1.1438585. Matsushima, M., et al. (2002), Seismoelectromagnetic effect associated with the İzmit earthquake and its aftershocks, Bull. Seismol. Soc. Am., 92, 350–360, doi:10.1785/0120000807. Mikhailov, O. V., M. W. Haartsen, and M. N. Toksöz (1997), Electroseismic investigation of the shallow subsurface: Field measurements and numerical modeling, Geophysics, 62, 97–105, doi:10.1190/1.1444150. Mizutani, H., T. Ishido, T. Yokokura, and S. Ohnishi (1976), Electrokinetic phenomena associated with earthquakes, Geophys. Res. Lett., 3, 365–368, doi:10.1029/GL003i007p00365. Nagao, T., Y. Orihara, T. Yamaguchi, I. Takahashi, K. Hattori, Y. Noda, K. Sayanagi, and S. Uyeda (2000), Co‐seismic geoelectric potential changes observed in Japan, Geophys. Res. Lett., 27, 1535–1538, doi:10.1029/1999GL005440. Ogawa, T., and H. Utada (2000), Co‐seismic piezoelectric effects due to a dislocation: 1. An analytic far and early time field solution in a homogeneous whole space, Phys. Earth Planet. Inter., 121(3–4), 273–288, doi:10.1016/S0031-9201(00)00177-1. Olson, A. H., and R. J. Apsel (1982), Finite faults and inverse theory with applications to the 1979 Imperial Valley earthquake, Bull. Seismol. Soc. Am., 72, 1969–2001. Park, S. K., W. Dalrymple, and J. C. Larsen (2007), The 2004 Parkfield earthquake: Test of the electromagnetic precursor hypothesis, J. Geophys. Res., 112, B05302, doi:10.1029/2005JB004196. Pengra, B. D., S. X. Li, and P. Z. Wong (1999), Determination of rock properties by low‐frequency AC electrokinetics, J. Geophys. Res., 104(B12), 29,485–29,508, doi:10.1029/1999JB900277. Pride, S. R. (1994), Governing equations for the coupled electromagnetics and acoustics of porous media, Phys. Rev. B, 50, 15,678–15,696, doi:10.1103/PhysRevB.50.15678. Pride, S. R., and M. W. Haartsen (1996), Electroseimic wave properties, J. Acoust. Soc. Am., 100, 1301–1315, doi:10.1121/1.416018. Pride, S. R., and F. D. Morgan (1991), Electrokinetic dissipation induced by seismic waves, Geophysics, 56, 914–925, doi:10.1190/1.1443125. Pride, S. R., F. Moreau, and P. Gavrilenko (2004a), Mechanical and electrical response due to fluid‐pressure equilibration following an earthquake, J. Geophys. Res., 109, B03302, doi:10.1029/2003JB002690. Pride, S. R., J. G. Berryman, and J. M. Harris (2004b), Seismic attenuation due to wave‐induced flow, J. Geophys. Res., 109, B01201, doi:10.1029/ 2003JB002639. Revil, A., and N. Florsch (2010), Determination of permeability from spectral induced polarization data in granular media, Geophys. J. Int., 181, 1480–1498. Tang, J., et al. (2008), Coseismic signal associated with aftershock of the Ms 8.0 Wenchuan earthquake (in Chinese), Seismol. Geol., 30, 739–745. Thompson, A. H., and G. A. Gist (1993), Geophysical applications of electrokinetic conversion, Leading Edge, 12, 1169–1173, doi:10.1190/ 1.1436931. Ujihara, N., Y. Honkura, and Y. Ogawa (2004), Electric and magnetic field variations arising from the seismic dynamo effect for aftershocks of the M7.1 earthquake of 26 May 2003 off Miyagi Prefecture, NE Japan, Earth Planets Space, 56, 115–123. Vernik, L. (1998), Acoustic velocity and porosity systematics in siliciclastics, Log Anal., 39, 27–35. Wang, M., and A. Revil (2010), Electrochemical charge of silica surface at high ionic strength in narrow channels, J. Colloid Interface Sci., 343, 381–386, doi:10.1016/j.jcis.2009.11.039. Wenzlau, F., and T. M. Müller (2009), Finite‐difference modeling of wave propagation and diffusion in poroelastic media, Geophysics, 74, T55–T65, doi:10.1190/1.3122928. Zhu, Z., M. W. Haartsen, and M. N. Toksöz (1999), Experimental studies of electrokinetic conversions in fluid‐saturated borehole models, Geophysics, 64, 1349–1356, doi:10.1190/1.1444639. Zhu, Z., M. N. Toksöz, and D. R. Burns (2008), Electroseismic and seismoelectric measurements of rock samples in a water tank, Geophysics, 73, E153–E164, doi:10.1190/1.2952570. Y. Gao and H. Hu, Department of Astronautics and Mechanics, Harbin Institute of Technology, Postbox 344, 92 W. Dazhi St., Harbin 150001, China. (
[email protected];
[email protected])
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