TY - JOUR AU - Hu,, Hengshan AB - SUMMARY Seismoelectric measurements are conducted with a synthetic porous rock sample to model an ocean exploration. Two kinds of seismoelectric coupling signals, that is, the interfacial EM wave signal and the coseismic electric signal, have been recorded by the electrodes buried inside a rock sample instead of those located in the fluid or in the solid region near the interface as performed in previous works. These seismoelectric signals are clearly observed and identified with a high signal-to-noise ratio. The characteristics of the measured interfacial EM wave and coseismic electric signals are analysed with the experimental data. We also simulate the seismoelectric conversion fields and make a comparison between the measured and simulated seismoelectric signals. The result shows that the simulated and measured signals match well for both the interfacial EM wave and the coseismic electric fields accompanying the fast P wave. Our results also show that the amplitudes of seismoelectric signals are in the order of tens to hundreds of microvolts with our experimental system. This confirms that the seismoelectric signals are measurable in the interior of the rocks with current measurement techniques, suggesting the seismoelectric measurement to be a potential method for studying characteristics of the material beneath the seafloor. Electrical properties, Body waves, Wave propagation 1 INTRODUCTION The seismoelectric effect is one of the electrokinetic coupling effects occurring in fluid-saturated porous media, involving the transformation from the elastic field to the electromagnetic (EM) field, when a pressure gradient exists in the medium (e.g. Morgan et al. 1989; Pride & Morgan 1991; Alkafeef et al. 1999; Hu et al. 2000; Jaafar et al. 2009; Glover & Jackson 2010; Jouniaux & Ishido 2012; Guan et al. 2013; Walker et al. 2014; Bordes et al. 2015; Wang et al. 2015a, 2016, 2017; Jouniaux & Zyserman 2016). It encompasses two different coupling phenomena: (i) an interfacial EM wave generated at an interface separating two different media, at least one of which is a fluid-saturated porous medium and (ii) the coseismic electric/magnetic fields accompanying seismic waves, which have been predicted in theoretical simulations (e.g. Haartsen & Pride 1997; Revil & Linde 2006; Gao & Hu 2010; Revil & Jardani 2010; Warden et al. 2013; Gao et al. 2014, 2016) and observed in experimental/field measurements (e.g. Thompson & Gist 1993; Butler et al. 1996; Russell et al. 1997; Jouniaux et al. 1999; Zhu et al. 1999; Mikhailov et al. 2000; Garambois & Dietrich 2001; Block & Harris 2006; Bordes et al. 2006; Dupuis et al. 2007, 2009; Haines et al. 2007; Zhu & Toksöz 2013; Guan et al. 2015; Butler et al. 2018; Dietrich et al. 2018, Devi et al. 2018; Liu et al. 2018; Peng et al. 2018, 2019). It should be noted that an S wave, which does not cause any pressure change and gradient, can generate coseismic signals as well. When an S wave travels across an interface separating different media, it can also generate an interfacial EM wave. As explained by previous studies (Zyserman et al. 2017; Monachesi et al. 2018a,b; Gao et al. 2019), such an interfacial EM wave results from the jump of the current densities across the interface. Seismoelectric studies have been conducted to pursue the mechanism and the applications of seismoelectric responses in porous media in the past decades. Since Haartsen & Pride(1997) modelled the interfacial EM wave and coseismic electric/magnetic fields in layered media soon after Pride's theory was presented (Pride 1994; Pride & Haartsen 1996), theoretical simulations have been reported to study the characteristics of the seismoelectric wavefields in various models (e.g. Garambois & Dietrich 2002; Ren et al. 2010; Grobbe & Slob 2016). Recently, Gao et al. (2017) presented a potential new method to estimate the seafloor properties by simulating a theoretical prediction of seismoelectric responses in a fluid/porous medium model. Dietrich et al. (2018) analysed the coseismic electric fields propagation in fluid-filled porous media using a filter theory approach. In the laboratory, Zhu et al. (2000) conducted seismoelectric measurements with artificial porous rocks and confirmed that observed seismoelectric phenomena were different from the piezoelectric effect. Bordes et al. (2006) measured the seismoelectric and seismomagnetic conversions in a low-noise underground laboratory. Liu et al. (2008) measured the seismoelectric signals near a frozen-unfrozen interface in a permafrost in the laboratory. Schakel et al. (2011a) measured the reflected EM waves in the fluid and refracted EM waves in the porous medium, and compared them with the theoretical analysis (Schakel & Smeulders 2010). Zhu et al. (2016) quantitatively analysed the relationship between the amplitudes of the measured EM wave signals and the permeability with an anisotropic porous quartz-sand sample. Peng et al. (2017) recorded the interfacial EM wave signals in wedge and cavity rock models. Devi et al. (2018) discussed the influence of electrode arrays on measuring seismoelectric response signals, and then compared the laboratory coseismic signals observed in homogeneous silica glass-beads with theoretical simulations (Dietrich et al. 2018). Due to the challenging difficulties on the manufacture of rock samples and installation of the sensors inside rock samples, laboratory studies were mostly conducted with electric sensors deployed outside the rocks, for example in the water or in solid region very close to the water-rock interface, which was responsible for production of the interfacial EM wave. The seismoelectric signals were frequently measured outside the rock sample and intensively studied. However, the experimental knowledge of the seismoelectric fields inside rocks is still lacking. In this article, we design a set-up for seismoelectric measurements in the laboratory, then conduct seismoelectric experiments with the electrodes inside a synthetic porous rock sample. Both the coseismic electric signals induced by body waves and the interfacial EM wave signal are clearly observed inside the sample. The experimental results are analysed and compared with the theoretical simulations using the method presented by Gao et al. (2017). Our results show that the experimental observations and theoretical modelling have a good agreement. 2 EXPERIMENTAL SET-UP The rock sample used in the experiments was a synthetic porous sand rock with size of 260 |$\ \times $| 135 |$\ \times $| 62 mm. In order to measure the coseismic seismoelectric field induced by an elastic wave inside a porous medium, the electrodes should be placed inside the medium. If the electrode is installed in a natural porous rock by drilling a small hole, the hole changes the structures of the pores inside the natural rock. Therefore, we manufacture an artificial sand model. Sand grains with different diameters and the electrodes are glued using epoxy. A low-viscosity epoxy (Epo-Tek 301, made by Epoxy Technology) is used here to reduce its effect on the pore structure of the sand model. Because the epoxy is used as little as possible, the epoxy does not block the pores between the sand grains but stabilizes the mechanical strength of the sand model. The electrodes are copper wires electroplated by silver on the surface, and their diameter is 1 mm. They are placed at a horizontal location with a certain space before the glued sand models are cured. After the glued sand is cured, a homogeneous porous medium model is formed with the electrodes inside. We cut a small part of the sample to measure several key physical parameters. The permeability of the rock sample is about |$230 \times {10^{ - 12}}$| m2, which was measured based on Darcy's Law. The P-wave (2100 m s−1) and S-wave (1200 m s−1) velocities were measured by using P-wave (Panametric V101) and S-wave transducers (Panametric V1548), respectively. In addition, the weights of the dry sample, water-saturated sample, and the sample suspended in water are measured to obtain the porosity (23.8 per cent) and density (1710 kg m−3) of the water-saturated samples. The sample was immersed in a water tank as shown in Fig. 1 in the experiments. Eleven point electrodes were buried inside the sample, with seven of them deployed 20 mm beneath the water/rock interface. The distance between any two adjacent electrodes was 20 mm along the horizontal direction. The other four electrodes were deployed along the vertical direction with intervals of 10 mm. A 20 mm thick flat piece of Berea sandstone was placed under the synthetic sample as shown in Fig. 1. Because their surfaces are flat and parallel to each other, these two samples are not glued together but fixed by gravity. Therefore, there are two interfaces formed in our experimental model, one is the interface between water and the upper boundary of the synthetic rock (Interface 1 in Fig. 1), the other is the interface between the sandstone and the lower boundary of the synthetic rock (Interface 2 in Fig. 1). Figure 1. Open in new tabDownload slide The experimental model used for the measurements. Eleven point electrodes were buried inside the synthetic sample, with seven of them deployed along the horizontal direction and four of them deployed along the vertical direction. There are two interfaces formed in our model, one is the interface between water and the upper boundary of the synthetic rock (Interface 1), the other is the interface between the sandstone and the lower boundary of the synthetic rock (Interface 2). Figure 1. Open in new tabDownload slide The experimental model used for the measurements. Eleven point electrodes were buried inside the synthetic sample, with seven of them deployed along the horizontal direction and four of them deployed along the vertical direction. There are two interfaces formed in our model, one is the interface between water and the upper boundary of the synthetic rock (Interface 1), the other is the interface between the sandstone and the lower boundary of the synthetic rock (Interface 2). The acoustic source is a P-wave transducer (Panametric V3034, 3.8 cm diameter), which is mounted perpendicular to the sample surface and placed on a thin sheet of Lucite. The Lucite was fixed by two stents, and used to hold the transducer in the experiments. The vertical distance between source transducer and sample surface was 25 mm as shown in Fig. 1. We use the siphon principle to saturate the samples, because these two samples are too big to use the traditional method as performed for the small samples. The fluid in the tank was Poland Spring water with a PH of |$6.5 \pm 0.3$| and electrical conductivity of |$0.002 \pm 0.0001$|S m-1. The laboratory temperature was about |$19 \pm {0.5\,^ \circ }{\rm{C}}$|⁠. Our instrumentation system in the laboratory consists of a function generator (HP3314A), RF power amplifier (2400 L), a pre-amplifier (OLYMPUS-5662), a bandpass filter (KH3202R) and a 22-bit resolution data acquisition (DAQ) card (NI1073 + 5922) with 1 MS s−1 sample rate. In the measurements, we chose a single sinusoidal pulse as the source signal from the function library of the function generator. Its frequency was 160 kHz, and its peak to peak amplitude was 1.5 V. The other parameters of the signal were set as the default values of the instrument. This signal was first sent to the RF power amplifier with a 50 dB gain. Then the output high voltage pulse (450 V) was applied to the P-wave source transducer. Consequently, the source generated a Pwave, which propagated through the water and into the synthetic porous rock sample. When the seismic wave arrived at the sample, the seismoelectric coupling signals were excited due to the electrokinetic effects. These coupling signals were first detected by the point electrodes buried in the sample, magnified by the pre-amplifier, then sent to a bandpass filter and finally stored by the DAQ system, which was controlled by LabVIEW (https://www.ni.com/en-us/shop/labview.html). Data processing was subsequently conducted in order to analyse the propagation properties of the seismoelectric signals. 3 RESULTS AND DISCUSSIONS To verify the reliability of our test system for the measurements of seismoelectric conversion signals, we conduct acoustic and electric measurements on the top surface of the synthetic sample as shown in Fig. 2. An acoustic receiver (BK-8103 transducer) in Fig. 2(a) and a wire electrode receiver in Fig. 2(b) are used to measure the signals in the experiments. The distance between the source and the acoustic/electric receivers is 9 cm. The recorded signals are plotted as trace 1 and trace 2 in Fig. 3(a), respectively. The first wave group in trace 1 represents the fluid acoustic wave that propagates directly from the source to the transducer, and its arrival time is about |$0.06 \pm 0.001$| ms, which agrees well with the expected arrival for a P-wave velocity of |$1480\,{\rm{m\,s^{-1}}}$| in the water (t = 0.09 m/1480 m s−1 = 0.0608 ms). Figure 2. Open in new tabDownload slide The experimental models for acoustic and electric measurements in water region. (a) The acoustic measurement using a transducer receiver placed on the top surface of the rock sample; (b) the electric measurement using a wire electrode receiver placed on the top surface of the rock sample; (c) the electric measurement using a wire electrode receiver placed in water without rock sample inside the tank. Figure 2. Open in new tabDownload slide The experimental models for acoustic and electric measurements in water region. (a) The acoustic measurement using a transducer receiver placed on the top surface of the rock sample; (b) the electric measurement using a wire electrode receiver placed on the top surface of the rock sample; (c) the electric measurement using a wire electrode receiver placed in water without rock sample inside the tank. Figure 3. Open in new tabDownload slide The recorded signals with experimental models in Fig. 2. (a) The normalized acoustic and electric signals measured in three models; (b) the raw signal measured by the electrode in water without rock sample, which records the interference signal with a zero arrival time; (c) the raw signal measured by the electrode deployed on the top surface of the rock sample, which indicates an interfacial EM wave signal induced at the water/rock interface. Figure 3. Open in new tabDownload slide The recorded signals with experimental models in Fig. 2. (a) The normalized acoustic and electric signals measured in three models; (b) the raw signal measured by the electrode in water without rock sample, which records the interference signal with a zero arrival time; (c) the raw signal measured by the electrode deployed on the top surface of the rock sample, which indicates an interfacial EM wave signal induced at the water/rock interface. Fig. 3(a) shows that there are two obvious wave groups in trace 2; the first one has a zero arrival time and the second one has an arrival time of 0.06 ms. The first one is an electrical interference from the high-voltage pulse used to excite the acoustic transducer (Wang et al. 2015b; Devi et al. 2018). We have conducted another experiment as shown in Fig. 2(c) by taking the rock sample out of the tank after the measurement in Fig. 2(b) in order to confirm this conclusion. The measured electric signal is plotted as trace 3 in Fig. 3(a), which has only one obvious wave group at time zero. Since there is no porous medium in the tank, the seismoelectric signals will not be generated in this model even though acoustic wave travels within the tank. Therefore, the first wave group in trace 2 and trace 3 is the electrical interference or triggering noise. We can see that the second wave group in trace 2 has the same arrival time (0.06 ms) and similar waveform as its counterpart acoustic signal in trace 1. Therefore, we identify that the second wave group in trace 2 is the seismoelectric conversion signal induced by the acoustic wave at the top surface of the sample. Further confirmation can be obtained from a comparison between the signals in trace 2 and trace 3, where the seismoelectric conversion signal is not recorded in trace 3, because the rock sample has been taken out of the tank. We also realize that the signals after the electrical interference in trace 3 is the noise in our experiment, so we plot the unnormalized signals of trace 2 and trace 3 in Figs 3(c) and (b), and obtain the peak–peak amplitudes of 0.04 and 0.002 V for the interfacial EM signal and the noise respectively. This result indicates that the recorded seismoelectric signal has a high signal-to-noise ratio of 20, confirming the reliability of our measurement system. In addition, we also obtain the experimental error bound of |$\pm 0.002{\rm{V}}$| from Fig. 3(b). It should be pointed out that the positive probe of the detector is connected with the target electrode, and the negative probe is connected with the ground in the experiment. In this case, the ground is the reference, so the recorded electric signal is the potential difference between the electrode and the ground. We apply the same method in the following measurements conducted inside the rock sample. Then, we start to conduct the seismoelectric coupling measurements with the electrodes in the horizontal direction as considered in previous work (Zhu et al. 2000; Liu et al. 2008; Devi et al. 2018). Fig. 4(a) shows the raw data recorded by seven horizontal electrodes, which are indicated with triangular marks in Fig. 1. Fig. 4(b) shows the normalized signals with amplitudes scaled by factors of 0.2, 0.25, 0.7, 0.8, 0.8, 0.8 and 1 respectively in order to facilitate their comparison in a single figure. We can identify the electrical interference signal at time zero and other coherent seismoelectric arrivals. Figure 4. Open in new tabDownload slide Seismoelectric coupling signals received in the horizontal direction using the electrodes indicated by triangular marks in Fig. 1. (a) The measured raw data of seismoelectric coupling signals; (b) the normalized signals with amplitudes scaled by factors of 0.2, 0.25, 0.7, 0.8, 0.8, 0.8 and 1. Labels EM and Pf denote the interfacial EM wave and the coseismic electric signal accompanying body P wave, respectively. The dotted line indicates the arrival of the interfacial seismoelectric effect which occurs simultaneously at 0.017 ms across the seven horizontally arranged receivers. Figure 4. Open in new tabDownload slide Seismoelectric coupling signals received in the horizontal direction using the electrodes indicated by triangular marks in Fig. 1. (a) The measured raw data of seismoelectric coupling signals; (b) the normalized signals with amplitudes scaled by factors of 0.2, 0.25, 0.7, 0.8, 0.8, 0.8 and 1. Labels EM and Pf denote the interfacial EM wave and the coseismic electric signal accompanying body P wave, respectively. The dotted line indicates the arrival of the interfacial seismoelectric effect which occurs simultaneously at 0.017 ms across the seven horizontally arranged receivers. Following the interference signal, the first seismoelectric signal is the interfacial EM wave (denoted by ‘EM’ in Fig. 4b). This signal is generated at the fluid/rock interface and radiates outward with the speed of EM-wave in materials. The interfacial EM wave travels much faster than the coseismic electric signals induced by the body waves, and is recorded at the same time by all seven receivers. The arrival time of interfacial EM wave is about |$0.017 \pm 0.001$| ms, agreeing with the theoretical value, which is estimated from the distance between the source and the interface (25 mm) and the acoustic velocity in water (1480 m s−1), that is, t = 0.25 m/1480 m s−1 = 0.0169 ms. This type of EM wave has been measured in previous studies by the receivers located in the fluid region (e.g. Schakel et al. 2011a,b; Zhu & Toksöz 2013; Peng et al. 2017; Liu et al. 2018). Although theoretical modellings (e.g. Haartsen & Pride 1997; Gao et al. 2017) show that the interfacial EM wave can be also record inside a porous medium, it is rarely measured in the laboratory experiments (Schakel et al. 2011a; Devi et al. 2018). With the help of the receiver array, our observation provides new evidence for confirming the existence and detectability of the interfacial EM wave inside the porous medium, which is very important for the application of seismoelectric exploration in layered formations. After the interfacial EM wave, the coseismic electric fields induced by body seismic waves are received and can be identified by calculating their arrival times. The second wave group in Fig. 4(b) is the coseismic electric field accompanying P wave (denoted by ‘Pf’). We can see that the arrival times of Pf signal show a hyperbolic shape, because the distance between the source and the receivers does not increase linearly with the horizontal offset. It can be seen from Fig. 4(b) that the amplitudes of Pf are much bigger in the first three curves than those in curves 4–7. The reason is possibly due to the fact that our source is not an ideal point source or an explosive source as commonly used in theoretical simulations (Gao et al. 2017). It has a finite size and generates an acoustic wave that concentrates the main energy in a certain aperture beneath the transducer, where the first three electrodes are placed in that region. In addition, it is not appropriate to quantitatively analyse the attenuation of seismoelectric signals in Fig. 4 due to the size effect of the source transducer. However, the normalized factors may reflect some information about attenuation of the amplitudes. Previous studies (e.g. Feng & Johnson 1983; Adler & Nagy 1994; Zhu & Popovics 2006; Dalen et al. 2010; Gao et al. 2017) have indicated that the fluid acoustic wave can generate refracted seismic waves in the sample, which can also excite coseismic electric signals due to the seismoelectric effects. This explains why we also record other coseismic electric signals behind the Pf group in Fig. 4(b). However, it is hard to identify what waves those coseismic signals correspond to. Hence, we focus most of our attention on the analysis of interfacial EM wave and coseismic electric field induced by fast P wave in this paper. In addition, when the fast P wave travels to the bottom of the synthetic sample, another interfacial EM signals would be generated at about 0.045 ms (t = 0.017 ms + 0.06 m/2100 m s−1 = 0.045 ms). It is a pity that this EM signal induced at the second interface can't be recognized from Fig. 4. We do not find a wave group with the same arrival time and phase in the time domain waveforms, even though looking for this signal from receivers 5–7. The reason might be that this interfacial EM signal is relative weak compared with other signals, making it difficult to be distinguished from the full waveforms. We have simulated the seismoelectric coupling responses in Fig. 5 using the method presented by Gao et al. (2017) in order to better understand the experimental results. Note that those formulae are only for two half-space models. However, the simulated results are still helpful and can benefit our interpretation of the measured data. The details of the modelling are put in Appendix A. Figure 5. Open in new tabDownload slide The comparison of seismoelectric signals between the simulated data and the measured data with the seven horizontally arranged receivers. (a) The simulated waveforms of seismoelectric signals, where three wave groups are interfacial EM wave and the coseismic electric signal induced by fast P wave and slow P wave, and they are denoted by ‘EM’, ‘Pf’ and ‘Ps’, respectively. The dotted lines show the arrival times of these three wave groups; (b) the comparison of the simulated seismoelectric signals (red) and the experimental signals (black), where the arrival times and waveforms of the theoretical EM and Pf match perfectly with those measured in the experiments. Figure 5. Open in new tabDownload slide The comparison of seismoelectric signals between the simulated data and the measured data with the seven horizontally arranged receivers. (a) The simulated waveforms of seismoelectric signals, where three wave groups are interfacial EM wave and the coseismic electric signal induced by fast P wave and slow P wave, and they are denoted by ‘EM’, ‘Pf’ and ‘Ps’, respectively. The dotted lines show the arrival times of these three wave groups; (b) the comparison of the simulated seismoelectric signals (red) and the experimental signals (black), where the arrival times and waveforms of the theoretical EM and Pf match perfectly with those measured in the experiments. The simulated electric field |${E_x}$| at these seven receivers are plotted in Fig. 5(a), where we can observe three wave groups. To undestand them, we made component analysis on the time domain waveforms. As explained in Appendix A and confirmed by Fig. A1, the first group marked by ‘EM’ is the interfacial EM wave generated by the direct acoustic wave at the fluid-porous medium interface. In order to make the EM wave apparent in each trace, its amplitude is amplified by a factor of 15 in traces 1–3, a factor of 75 in traces 4 and 5, and a factor of 300 in traces 6 and 7. The second group denoted by ‘Pf’ is the coseismic signal accompanying the fast P wave. The third wave group seems to be induced by body S wave. However, previous studies demonstrate that an S wave generally has a weaker ability in generating the electric field than a P wave (Pride & Haartsen 1996; Gao & Hu 2010). To confirm this, we conducted the component analysis (Fig. A1). The results indicate that the coseismic electric field induced by body S wave is much weaker than that induced by the Pf wave and hard to be recognized from the waveforms, and its contribution is mainly concentrated on the coseismic magnetic field. The third wave group is the electric field (denoted by ‘Ps’) produced by the slow P wave. A comparison has been made by plotting the theoretical (red) and experimental (black) seismoelectric signals together in Fig. 5(b). It can be seen that they match excellently for the EM wave and for the Pf signals in both the arrival times and the waveforms. Although the amplitudes of the simulated interfacial EM signals have to be scaled up 10–300 times more than the coseismic arrivals, the experimental results provide comparable amplitudes to those assumed in the simulation. Our synthetic sample and setup allow us to measure the seismoelectric coupling signals within the sample by electrodes distributed vertically. Fig. 6(a) shows the measured seismoelectric coupling signals for five vertical electrodes, which are indicated by circular marks in Fig. 1. There are two obvious wave groups in Fig. 6(a) with a very high signal-to-noise ratio, which are the interfacial EM wave (denoted in the figure by ‘EM’) and the coseismic electric signal induced by fast P wave (denoted by ‘Pf’). The interfacial EM wave can be distinguished easily from the recorded signals, since it arrives at all receivers at the same time with excellent consistency as the same way as those shown in Fig. 4(b). Figure 6. Open in new tabDownload slide The measured seismoelectric signals in the vertical direction using electrodes represented by small circles in Fig. 1. (a) The normalized interfacial EM wave and coseismic electric fields induced by fast P wave, which are denoted by ‘EM’ and ‘Pf’, respectively. The left-hand dotted line indicates the arrival of the interfacial seismoelectric effect which occurs simultaneously at 0.017 ms across the five vertically arranged receivers. The right-hand dotted line's slope represents the P-wave velocity. (b) The raw voltage measured at position z = −2 cm beneath the interface; (c) the raw voltage measured at position z = −3 cm beneath the interface; (d) the calculated electric field using the signals received at z = −2 cm and z = –3 cm. Figure 6. Open in new tabDownload slide The measured seismoelectric signals in the vertical direction using electrodes represented by small circles in Fig. 1. (a) The normalized interfacial EM wave and coseismic electric fields induced by fast P wave, which are denoted by ‘EM’ and ‘Pf’, respectively. The left-hand dotted line indicates the arrival of the interfacial seismoelectric effect which occurs simultaneously at 0.017 ms across the five vertically arranged receivers. The right-hand dotted line's slope represents the P-wave velocity. (b) The raw voltage measured at position z = −2 cm beneath the interface; (c) the raw voltage measured at position z = −3 cm beneath the interface; (d) the calculated electric field using the signals received at z = −2 cm and z = –3 cm. Once again, the coseismic electric signals accompanying fast P wave (Pf) follows after the EM wave signal. It can be seen that the Pf wave groups are very clear in the full waveforms. As expected, their arrival times increase exactly with the receiver depth with a slope of approximately 2100 m s−1 (v = 0.04 m/0.019 ms = 2105 m s−1), corresponding to the fast P-wave velocity in the synthetic rock. In addition, we can see that the amplitudes of the Pf signals decay gradually as the receivers go deeper. But there is an obvious increasing in the amplitude of the Pf signal at z = −6 cm in Fig. 6(a). This is most likely caused by the contributions of seismoelectric signals generated by reflected elastic waves, mostly possibly the reflected P wave, at interface between the rock sample and the Berea sandstone (the interface 2 in Fig. 1), which strengths the seismic P wave and induces a stronger seismoelectric signals. There is also an alternative explanation that the stronger seismoelectric signals at z = −6 cm may be caused by the interfacial EM waves generated at interface 2, when elastic waves reach the interface. The theoretical arrival times of fast and slow P waves at the second interface are about 0.045 ms and 0.074 ms respectively. So two interfacial EM signals will be generated one after another, and radiate into the rock sample. The interfacial EM waves generated at the second interface superpose the coseismic signal accompanying the Pf wave so that the recorded coseismic signals at z = –6 cm are enhanced between 0.05 ms and 0.1 ms (Fig. 6a) However, it is only observed obviously at the position of z = –6 cm, and hard to be distinguished at other receivers far away from the interface. Even though some data processing methods for seismoelectric signals are applied (Butler & Russell 2003; Butler et al. 2007), because the second interfacial signals seems to overlap with other coseismic signals rather than contaminated by the harmonic or laboratory noise. It should be noted that the signals in Fig. 6(a) are normalized with the amplitude of Pf signal at z = −2 cm, where its peak-to-peak value is about |$0.15 \pm 0.002\,{\rm{V}}$| in Fig. 6(b) after 54 dB gain. Consequently, the original value of Pf signal is approximately |$300\,\mu \mathrm{ V}$| (electric potential) with our setup system at z = −2 cm. Because the positive probe of the detector is connected with the electrodes inside the rock sample one by one, while the negative probe is fixed to the ground during the whole experiments. So the non-normalized signal received at the position of z = −3 cm is shown in Fig. 6(c) in order to obtain the potential difference between these two electrodes. By making a subtraction between these signals in Figs 6(b) and (c), the peak-to-peak electric field is calculated approximately as 3 and 10 V m−1 for the interfacial EM signal and Pf signal respectively in Fig. 6(d) with 54 dB gain. Furthermore, we analyse the attenuation of the measured interfacial EM wave and the Pf signals in Fig. 7. It can be seen that they decrease as the receiver goes away from the interface, but the Pf signal attenuates faster than the interfacial EM wave. We also fit the experimental data with the exponential function. The results show that two exponential decay curves have very good fits of R2 = 0.9913 and R2 = 0.9038 with |${y_{\mathrm{ Pf}}} = 69.86 \times \exp( { - 2.21x} ) + 0.15$| and |${y_{\mathrm{ Em}}} = 22.95 \times \exp( { - 1.89x} ) + 0.47$| for the EM wave and Pf signals respectively. This result indicates that the two types of seismoelectric conversion signals decay exponentially as the source–receiver distance increases. Figure 7. Open in new tabDownload slide The normalized amplitudes of the measured seismoelectric signals. The square and circle symbols represent the amplitudes of Pf and interfacial EM wave signals, and the black and red lines are their asymptote curves fitted by the exponential function, respectively. Figure 7. Open in new tabDownload slide The normalized amplitudes of the measured seismoelectric signals. The square and circle symbols represent the amplitudes of Pf and interfacial EM wave signals, and the black and red lines are their asymptote curves fitted by the exponential function, respectively. We have also simulated the seismoelectric waveforms in Fig. 8(a) with the receivers placed vertically. Three obvious wave groups can be seen as the source–receiver distance increases, they are the interfacial EM wave, and the coseismic electric signals accompanying fast P wave (Pf) and slow P wave (Ps) respectively. It should be noted that the amplitudes of simulated EM wave in Fig. 8(a) are amplified by a factor of 15 in each trace in order to make the EM wave apparent. The component analysis of the signals in Fig. 8(a) is shown in Fig. A2, which is similar to the results in Fig. 5(a). Figure 8. Open in new tabDownload slide The comparison of seismoelectric signals between the simulated data and the measured data with the five vertically arranged receivers. (a) The simulated waveforms of seismoelectric signals, where the interfacial EM wave and the coseismic electric signal induced by fast P wave and slow P wave are denoted by ‘EM’, ‘Pf’ and ‘Ps’, respectively. The dotted lines show the arrival times of these three wave groups; (b) the comparison of the simulated seismoelectric signals (red) and the experimental signals (black), where the arrival times and waveforms of the theoretical EM wave and Pf signals match perfectly with those measured in the experiments. Figure 8. Open in new tabDownload slide The comparison of seismoelectric signals between the simulated data and the measured data with the five vertically arranged receivers. (a) The simulated waveforms of seismoelectric signals, where the interfacial EM wave and the coseismic electric signal induced by fast P wave and slow P wave are denoted by ‘EM’, ‘Pf’ and ‘Ps’, respectively. The dotted lines show the arrival times of these three wave groups; (b) the comparison of the simulated seismoelectric signals (red) and the experimental signals (black), where the arrival times and waveforms of the theoretical EM wave and Pf signals match perfectly with those measured in the experiments. Then, the theoretical simulated (red) and experimental measured (black) seismoelectric signals are plotted together in Fig. 8(b) for a comparison. The results show that for the EM wave and the coseismic electric fields accompanying the Pf wave, the synthetic and measured signals match well. The Ps wave arrival can be clearly seen in the simulated signals while it is not so obvious in the measured signals. The reason is that the slow P wave is relatively weak in our experiments, so that the induced Ps signal is much smaller than the Pf signal. Another reason is possibly because the measured Ps wave has much stronger attenuation than simulated Ps wave that is predicted by Biot's theory. A limitation of the Biot model is that the predicted attenuation is smaller than that obtained by experiments. We should admit that although the Biot model is not perfect, it is still the best model that is useful in describing the elastic wave propagation in a porous medium. This remarkable consistency between experimental measurements and theoretical calculations verifies both sets of information. Our results confirm that the seismoelectric coupling signals are measurable with the receivers placed inside a porous medium, which indicates a potential feasibility of offshore seismoelectric explorations. In addition, deploying the receivers in the interior of seafloor can reduce the influence of background noise, which may significantly improve the signal-to-noise ratio of measured seismoelectric signals effectively. 4 CONCLUSIONS We have designed a synthetic porous rock sample and developed a high resolution setup (22 bits resolution and 1 MS s−1 sample rate) for seismoelectric experiments in the laboratory. Contrary to previous laboratory studies that recorded seismoelectric coupling signals either in a fluid or in the solid region near the interface, we conducted seismoelectric measurements with the electrodes buried in the interior of the saturated rock sample. The primary reason for this is to model the possible offshore seismoelectric exploration. The experimental results indicate that both interfacial EM wave and coseismic electric fields are measurable with the electrode receivers placed along the horizontal and vertical directions inside the sample. The quantitative analysis on the recorded seismoelectric coupling signals has been discussed and compared with the theoretical simulations. The comparison shows a good match between the simulated and measured signals for both the interfacial EM wave and the coseismic signals accompanying the Pf wave. In addition, the results also show that the amplitudes of seismoelectric signals are of the order of tens to hundreds microvolts in our experiments, and they decay exponentially as the source–receiver distance increases, which provides helpful information for the design of the equipment system in the industry. Our results reveal the possibility of ocean explorations with seismoelectric techniques for the estimation of characteristics of the subseafloor minerals. ACKNOWLEDGEMENTS This work is supported by National Natural Science Foundation of China (Grant Nos. 41974136, 41674121, 41774048, 41874129 and 11734017). REFERENCES Adler L. , Nagy P.B., 1994 . 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Note that those formulae are only for a two half-space model. However, the synthetic results are still helpful and can benefit our understanding of the measured data. In the simulation, the model consists of a half-space fluid (upper) and a half-space porous medium (lower), whose parameters are listed in Tables A1 and A2. The porosity, permeability, and density of the porous medium match those of the rock sample used in the experiment. The elastic moduli |${K_s}$|⁠, |${K_b}$| and G are chosen with the values that produce Vp = 2100 m s−1 and Vs = 1200 m s−1. The source–receiver configuration is the same as shown in Fig. 1. Different from the source used in the experiment which has a finite size, the source in the simulation is a point explosive source described by a displacement potential function $$\begin{eqnarray*} {\phi ^d}(r,z,\omega ) = {A_0}\frac{1}{R}{\mathrm{ e}^{\mathbf{ i}\omega {s_f}R}}S(\omega ), \end{eqnarray*}$$(A1) in which |${A_0}$| is the source intensity, R is the distance between the source and receiver and |$S(\omega )$| is the spectrum of the source time function |${s_0}(t)$|⁠. In this study, the source is located in the upper fluid, 25 mm above the fluid-porous interface to excite acoustic waves in the water. The source has an intensity of A0 = 10−13 m3 and generates a maximum pressure of 620 Pa at a receiver 25 mm from the source. Table A1. Parameters of the porous medium used for the simulations in this study. Parameter . Symbol . Stiff Sandstone . Porosity |$\phi $| 0.238 Permeability |${\kappa _0}( \times {10^{ - 12}}{{\,\rm{m}}^2})$| 230 Tortuosity |${\alpha _\infty }$| 1.52 Solid grain bulk modulus |${K_s}({\rm{GPa)}}$| 4.99 Frame bulk modulusa |${K_b}({\rm{GPa)}}$| 3.50 Shear modulusa |$G({\rm{GPa)}}$| 2.46 Fluid bulk modulus |${K_f}({\rm{GPa)}}$| 2.25 Solid grain density |${\rho _s}({\rm{kg\,}}{{\rm{m}}^{-3}})$| 1931.8 Fluid density |${\rho _f}({\rm{kg\,}}{{\rm{m}}^{-3}})$| 1000 Magnetic permeability |$\mu\ (\mathrm{ H}\, \mathrm{ m}^{-1})$| |$4\pi \times {10^{ - 7}}$| Solid relative permittivity |${\varepsilon _s}$| 4 Salinity of the pore fluid |${C_{f0}}({\rm{mol\,L^{-1})}}$| 0.00016 Fluid relative permittivityb |${\varepsilon _r}$| 80 Effective permittivity of the porous medium |$\varepsilon\ ( \times {10^{ - 11}}\,{\rm{F\,m^{-1}}})$| 13.8 Fluid viscosityb |$\eta\ ({\rm{Pa}}{\,\rm{s)}}$| 0.001 Zeta potentialb |$\zeta ({\rm{mV)}}$| -67.5 Rock conductivityb |${\sigma _0}({\rm{S\,m^{-1})}}$| 0.0004 Static Electrokinetic coupling coefficientb |${L_0}( \times {10^{ - 10}}{\rm{s}}{\rm{C\,kg^{-1})}}$| 72.6 Pf-wave velocity at 60k Hz |${V_{\mathrm{ pf}}}({\rm{m\,s^{-1})}}$| 2100 S-wave velocity at 60k Hz |${V_s}({\rm{m\,s^{-1})}}$| 1200 Ps-wave velocity at 60k Hz |${V_{\mathrm{ ps}}}({\rm{m\,s^{-1})}}$| 1117.9 EM wave velocity at 60 kHz |${V_{\mathrm{ em}}}({\rm{m\,s^{-1})}}$| 3.59 × 107 Parameter . Symbol . Stiff Sandstone . Porosity |$\phi $| 0.238 Permeability |${\kappa _0}( \times {10^{ - 12}}{{\,\rm{m}}^2})$| 230 Tortuosity |${\alpha _\infty }$| 1.52 Solid grain bulk modulus |${K_s}({\rm{GPa)}}$| 4.99 Frame bulk modulusa |${K_b}({\rm{GPa)}}$| 3.50 Shear modulusa |$G({\rm{GPa)}}$| 2.46 Fluid bulk modulus |${K_f}({\rm{GPa)}}$| 2.25 Solid grain density |${\rho _s}({\rm{kg\,}}{{\rm{m}}^{-3}})$| 1931.8 Fluid density |${\rho _f}({\rm{kg\,}}{{\rm{m}}^{-3}})$| 1000 Magnetic permeability |$\mu\ (\mathrm{ H}\, \mathrm{ m}^{-1})$| |$4\pi \times {10^{ - 7}}$| Solid relative permittivity |${\varepsilon _s}$| 4 Salinity of the pore fluid |${C_{f0}}({\rm{mol\,L^{-1})}}$| 0.00016 Fluid relative permittivityb |${\varepsilon _r}$| 80 Effective permittivity of the porous medium |$\varepsilon\ ( \times {10^{ - 11}}\,{\rm{F\,m^{-1}}})$| 13.8 Fluid viscosityb |$\eta\ ({\rm{Pa}}{\,\rm{s)}}$| 0.001 Zeta potentialb |$\zeta ({\rm{mV)}}$| -67.5 Rock conductivityb |${\sigma _0}({\rm{S\,m^{-1})}}$| 0.0004 Static Electrokinetic coupling coefficientb |${L_0}( \times {10^{ - 10}}{\rm{s}}{\rm{C\,kg^{-1})}}$| 72.6 Pf-wave velocity at 60k Hz |${V_{\mathrm{ pf}}}({\rm{m\,s^{-1})}}$| 2100 S-wave velocity at 60k Hz |${V_s}({\rm{m\,s^{-1})}}$| 1200 Ps-wave velocity at 60k Hz |${V_{\mathrm{ ps}}}({\rm{m\,s^{-1})}}$| 1117.9 EM wave velocity at 60 kHz |${V_{\mathrm{ em}}}({\rm{m\,s^{-1})}}$| 3.59 × 107 aThe frame bulk modulus |${K_b}$| is calculated from the porosity according to the relations between frame modulus and porosity given by Vernik (1998). b|${\varepsilon _r}$|⁠, |$\eta $|⁠, |$\zeta $|⁠, |${\sigma _0}$| and |${L_0}$| vary with the pore fluid salinity |${C_f}$|⁠. They are calculated according to their responding equations in the appendix B of Haartsen & Pride (1997). Open in new tab Table A1. Parameters of the porous medium used for the simulations in this study. Parameter . Symbol . Stiff Sandstone . Porosity |$\phi $| 0.238 Permeability |${\kappa _0}( \times {10^{ - 12}}{{\,\rm{m}}^2})$| 230 Tortuosity |${\alpha _\infty }$| 1.52 Solid grain bulk modulus |${K_s}({\rm{GPa)}}$| 4.99 Frame bulk modulusa |${K_b}({\rm{GPa)}}$| 3.50 Shear modulusa |$G({\rm{GPa)}}$| 2.46 Fluid bulk modulus |${K_f}({\rm{GPa)}}$| 2.25 Solid grain density |${\rho _s}({\rm{kg\,}}{{\rm{m}}^{-3}})$| 1931.8 Fluid density |${\rho _f}({\rm{kg\,}}{{\rm{m}}^{-3}})$| 1000 Magnetic permeability |$\mu\ (\mathrm{ H}\, \mathrm{ m}^{-1})$| |$4\pi \times {10^{ - 7}}$| Solid relative permittivity |${\varepsilon _s}$| 4 Salinity of the pore fluid |${C_{f0}}({\rm{mol\,L^{-1})}}$| 0.00016 Fluid relative permittivityb |${\varepsilon _r}$| 80 Effective permittivity of the porous medium |$\varepsilon\ ( \times {10^{ - 11}}\,{\rm{F\,m^{-1}}})$| 13.8 Fluid viscosityb |$\eta\ ({\rm{Pa}}{\,\rm{s)}}$| 0.001 Zeta potentialb |$\zeta ({\rm{mV)}}$| -67.5 Rock conductivityb |${\sigma _0}({\rm{S\,m^{-1})}}$| 0.0004 Static Electrokinetic coupling coefficientb |${L_0}( \times {10^{ - 10}}{\rm{s}}{\rm{C\,kg^{-1})}}$| 72.6 Pf-wave velocity at 60k Hz |${V_{\mathrm{ pf}}}({\rm{m\,s^{-1})}}$| 2100 S-wave velocity at 60k Hz |${V_s}({\rm{m\,s^{-1})}}$| 1200 Ps-wave velocity at 60k Hz |${V_{\mathrm{ ps}}}({\rm{m\,s^{-1})}}$| 1117.9 EM wave velocity at 60 kHz |${V_{\mathrm{ em}}}({\rm{m\,s^{-1})}}$| 3.59 × 107 Parameter . Symbol . Stiff Sandstone . Porosity |$\phi $| 0.238 Permeability |${\kappa _0}( \times {10^{ - 12}}{{\,\rm{m}}^2})$| 230 Tortuosity |${\alpha _\infty }$| 1.52 Solid grain bulk modulus |${K_s}({\rm{GPa)}}$| 4.99 Frame bulk modulusa |${K_b}({\rm{GPa)}}$| 3.50 Shear modulusa |$G({\rm{GPa)}}$| 2.46 Fluid bulk modulus |${K_f}({\rm{GPa)}}$| 2.25 Solid grain density |${\rho _s}({\rm{kg\,}}{{\rm{m}}^{-3}})$| 1931.8 Fluid density |${\rho _f}({\rm{kg\,}}{{\rm{m}}^{-3}})$| 1000 Magnetic permeability |$\mu\ (\mathrm{ H}\, \mathrm{ m}^{-1})$| |$4\pi \times {10^{ - 7}}$| Solid relative permittivity |${\varepsilon _s}$| 4 Salinity of the pore fluid |${C_{f0}}({\rm{mol\,L^{-1})}}$| 0.00016 Fluid relative permittivityb |${\varepsilon _r}$| 80 Effective permittivity of the porous medium |$\varepsilon\ ( \times {10^{ - 11}}\,{\rm{F\,m^{-1}}})$| 13.8 Fluid viscosityb |$\eta\ ({\rm{Pa}}{\,\rm{s)}}$| 0.001 Zeta potentialb |$\zeta ({\rm{mV)}}$| -67.5 Rock conductivityb |${\sigma _0}({\rm{S\,m^{-1})}}$| 0.0004 Static Electrokinetic coupling coefficientb |${L_0}( \times {10^{ - 10}}{\rm{s}}{\rm{C\,kg^{-1})}}$| 72.6 Pf-wave velocity at 60k Hz |${V_{\mathrm{ pf}}}({\rm{m\,s^{-1})}}$| 2100 S-wave velocity at 60k Hz |${V_s}({\rm{m\,s^{-1})}}$| 1200 Ps-wave velocity at 60k Hz |${V_{\mathrm{ ps}}}({\rm{m\,s^{-1})}}$| 1117.9 EM wave velocity at 60 kHz |${V_{\mathrm{ em}}}({\rm{m\,s^{-1})}}$| 3.59 × 107 aThe frame bulk modulus |${K_b}$| is calculated from the porosity according to the relations between frame modulus and porosity given by Vernik (1998). b|${\varepsilon _r}$|⁠, |$\eta $|⁠, |$\zeta $|⁠, |${\sigma _0}$| and |${L_0}$| vary with the pore fluid salinity |${C_f}$|⁠. They are calculated according to their responding equations in the appendix B of Haartsen & Pride (1997). Open in new tab Table A2. Parameters of the water used for the simulations in this study. Parameter . Symbol . Stiff Sandstone . Bulk modulus |${K_1}({\rm{GPa)}}$| 2.25 Density |${\rho _1}({\rm{kg\,}}{{\rm{m}}^{\rm{-3}}})$| 1000 Relative permittivity |${\varepsilon _1}$| 80 Salinity |${C_{f1}}({\rm{mol\,L^{-1})}}$| 0.00016 Conductivity |${\sigma _1}({\rm{S\,m^{-1})}}$| 0.002 Acoustic wave velocity |${V_f}({\rm{m\,s^{-1})}}$| 1500 EM wave velocity at 60 kHz |${V_{\mathrm{ em}}}({\rm{m\,s^{-1})}}$| 1.62 × 107 Parameter . Symbol . Stiff Sandstone . Bulk modulus |${K_1}({\rm{GPa)}}$| 2.25 Density |${\rho _1}({\rm{kg\,}}{{\rm{m}}^{\rm{-3}}})$| 1000 Relative permittivity |${\varepsilon _1}$| 80 Salinity |${C_{f1}}({\rm{mol\,L^{-1})}}$| 0.00016 Conductivity |${\sigma _1}({\rm{S\,m^{-1})}}$| 0.002 Acoustic wave velocity |${V_f}({\rm{m\,s^{-1})}}$| 1500 EM wave velocity at 60 kHz |${V_{\mathrm{ em}}}({\rm{m\,s^{-1})}}$| 1.62 × 107 Open in new tab Table A2. Parameters of the water used for the simulations in this study. Parameter . Symbol . Stiff Sandstone . Bulk modulus |${K_1}({\rm{GPa)}}$| 2.25 Density |${\rho _1}({\rm{kg\,}}{{\rm{m}}^{\rm{-3}}})$| 1000 Relative permittivity |${\varepsilon _1}$| 80 Salinity |${C_{f1}}({\rm{mol\,L^{-1})}}$| 0.00016 Conductivity |${\sigma _1}({\rm{S\,m^{-1})}}$| 0.002 Acoustic wave velocity |${V_f}({\rm{m\,s^{-1})}}$| 1500 EM wave velocity at 60 kHz |${V_{\mathrm{ em}}}({\rm{m\,s^{-1})}}$| 1.62 × 107 Parameter . Symbol . Stiff Sandstone . Bulk modulus |${K_1}({\rm{GPa)}}$| 2.25 Density |${\rho _1}({\rm{kg\,}}{{\rm{m}}^{\rm{-3}}})$| 1000 Relative permittivity |${\varepsilon _1}$| 80 Salinity |${C_{f1}}({\rm{mol\,L^{-1})}}$| 0.00016 Conductivity |${\sigma _1}({\rm{S\,m^{-1})}}$| 0.002 Acoustic wave velocity |${V_f}({\rm{m\,s^{-1})}}$| 1500 EM wave velocity at 60 kHz |${V_{\mathrm{ em}}}({\rm{m\,s^{-1})}}$| 1.62 × 107 Open in new tab It should be mentioned that althought the source used for excitation in the laboratory is a single sinusoidal pulse whose frequency is |$160\,{\rm{kHz}}$|⁠, spectral analysis of the seismoelectric signals shows that these signals have wide-band frequences from 20 to |$200\,{\rm{kHz}}$|⁠. Therefore, we use the following pulse-type time function that has a finite-frequency band $$\begin{eqnarray*} {s_0}(t) = \left\{ \begin{array}{cc} \displaystyle\frac{1}{2}\left[ {1 + \cos \displaystyle\frac{{2\pi }}{{{T_c}}}\left( {t - \displaystyle\frac{{{T_c}}}{2}} \right)} \right]\cos 2\pi {f_0}\left( {t - \displaystyle\frac{{{T_c}}}{2}} \right),& \quad 0 \le t \le T\\ 0, & \quad\quad t \lt 0\,\mathrm{ or}\,t \gt {T_c} \end{array} \right. \end{eqnarray*}$$(A2) where |${f_0}$| and |${T_c}$| denote the centre frequency and the width of the pulse, respectively. In the simulation, we choose |${f_0} = 60\,{\rm{kHz}}$| and |${T_c} = 2/{f_0}$| and the frequencies vary from 0 to |$200\,{\rm{kHz}}$|⁠. The simulated electric field |${E_x}$| at the seven horizontally aligned receivers are plotted in Fig. 5(a), where we can observe several wave groups. The first one denoted by ‘EM’ is the interfacial EM wave generated by the direct acoustic wave at the fluid-porous medium interface. Such an EM wave has a weaker amplitude than the later coseismic signals and it decays rapidly with the distance. In order to make the EM wave apparent in each trace, its amplitude is amplified by a factor of 15 in traces 1–3, a factor of 75 in traces 4 and 5, and a factor of 300 in traces 6 and 7. The wave group after the ‘EM’ wave is the coseismic signals accompanying the Pf wave, that is, the P wave. Its arrival time is not a straight line since the source–receiver distance is not a linear function of the horizontal offset. There is also a wave group arriving later than the Pf wave. It has stronger amplitude than the coseismic signal accompanying the Pf wave. It does not seem to be generated by the S wave since the electric field generated by the body S wave is usually weaker than that generated by the P wave. As proved by the component analysis shown below, it is the coseismic electric field accompanying the slow P wave (Ps). According to the theoretical formulae and simulations in Gao et al. (2017), the direct acoustic wave from the source can generate four transmitted waves in the porous medium, namely, fast P wave (Pf), slow P wave (Ps), shear wave (SV) and electromagnetic wave (EM). We calculate the electric fields contributed by each of these four transmitted waves and compare them with the total field in Fig. A1. It can be seen that the contributions from the Pf (Fig. A1a) and EM (Fig. A1d) waves respectively agree with the signals marked by ‘Pf’ and ‘EM’ in the total field. As is shown in Fig. A1(c), the contribution from the shear wave is very small and can be neglected. Fig. A1(b) shows that the contribution from the Ps wave coincides with the wave group that has the largest amplitude in the total field, indicating that the third group is the Ps wave. Figure A1. Open in new tabDownload slide Normalized electric field at the horizontally aligned receivers. Panels (a) and (b) show the comparison between the total signal (black lines) and the contribution from each of the four modes of waves (red lines), namely, fast P wave (Pf), slow P wave (Ps), shear wave (SV) and electromagnetic wave (EM). In each of the subgraph, the signals are normalized by the same factor |$0.056\,{\rm{V\,m^{-1}}}$|⁠. In order to make the EM wave apparent, its amplitude is amplified by a factor of 5 in traces 4 and 5, and a factor of 20 in traces 6 and 7. Figure A1. Open in new tabDownload slide Normalized electric field at the horizontally aligned receivers. Panels (a) and (b) show the comparison between the total signal (black lines) and the contribution from each of the four modes of waves (red lines), namely, fast P wave (Pf), slow P wave (Ps), shear wave (SV) and electromagnetic wave (EM). In each of the subgraph, the signals are normalized by the same factor |$0.056\,{\rm{V\,m^{-1}}}$|⁠. In order to make the EM wave apparent, its amplitude is amplified by a factor of 5 in traces 4 and 5, and a factor of 20 in traces 6 and 7. We also simulate the seismoelectric responses at the five vertical receivers. The simulated electric field |${E_z}$| at these receivers are shown in Fig. 8(b), where we observe three wave groups. Similar to the analysis in Fig. A1, we calculate the electric fields contributed by each of these four transmitted waves and compare them with the total field in Fig. A2. It can be inferred that these three wave groups are respectively the EM wave, the coseismic signals accompanying the Pf and Ps waves. Figure A2. Open in new tabDownload slide Normalized electric field at the vertically aligned receivers. Panels (a) and (b) show the comparison between the total signal (black lines) and the contribution from each of the four modes of waves (red lines), namely, fast P wave (Pf), slow P wave (Ps), shear wave (SV) and electromagnetic wave (EM). In each of the subgraph, the signals are normalized by the same factor |$0.17{\rm{V\,m^{-1}}}$|⁠. In order to make the EM wave apparent, its amplitude is amplified by a factor of 15 in each trace. Figure A2. Open in new tabDownload slide Normalized electric field at the vertically aligned receivers. Panels (a) and (b) show the comparison between the total signal (black lines) and the contribution from each of the four modes of waves (red lines), namely, fast P wave (Pf), slow P wave (Ps), shear wave (SV) and electromagnetic wave (EM). In each of the subgraph, the signals are normalized by the same factor |$0.17{\rm{V\,m^{-1}}}$|⁠. In order to make the EM wave apparent, its amplitude is amplified by a factor of 15 in each trace. © The Author(s) 2020. Published by Oxford University Press on behalf of The Royal Astronomical Society. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model) TI - Measurements of the seismoelectric responses in a synthetic porous rock JF - Geophysical Journal International DO - 10.1093/gji/ggaa174 DA - 2020-07-01 UR - https://www.deepdyve.com/lp/oxford-university-press/measurements-of-the-seismoelectric-responses-in-a-synthetic-porous-QgkIPe806h SP - 436 VL - 222 IS - 1 DP - DeepDyve ER -