Analysis of the natural electric field at different sea depths

The natural electric field at the depth of 0 ∼ 1500 m in high seas of South China Sea is obtained by using a new type of measuring device. The electric field data in the 0.01 ∼ 0.5 Hz and 0.5 ∼ 30 Hz frequency range are analyzed respectively. The results show that the induced electric field generated by the surface wave (about 0.14 Hz in the experiment) is obvious at the depth of 50 m but can be ignored at the depth greater than 100 m. When the depth increases from 50 m to 1500 m, the peak-to-peak value of the natural electric field gradually decreases. At the depth of 1000 m, the peak-to-peak values are 0.04 ∼ 0.08 μV/m in the 0.01 ∼ 0.5 Hz range, and 0.07 ∼ 0.1 μV/m in the 0.5 ∼ 30 Hz range. At last, the natural electric field in coastal water near Sanya City, where the water depth is 15 m, is measured by means of a sinking device. The results show that the peak-to-peak values are about 2 ∼ 4 μV/m in the 0.01 ∼ 0.5 Hz range and 2 μV/m in the 0.5 ∼ 30 Hz range. By comparing the natural electric field in high seas with that of coastal water, we find the latter has a larger peak-to-peak value at nearly the same water depth. In addition, line spectrum noise often occurs in coastal water, while it is rarely observed in high seas when the water depth is more than 50 m.


Introduction
Natural electric field in sea waters has been studied since the last century. For example, Chave [1] and Olsen [2] studied the electric field generated by ocean tides, and the signal period is generally more than one day. Luther [3] and Nilsson [4] studied the electric field generated by the ocean current, and analyzed the current velocity and direction. Eide [5] found that the induced electric field generated by ocean surface waves is mainly in the 0.1 0.5 Hz range based on the analysis of other's previous work. Although the magnitude of electric field generated by the tide, internal wave and other similar phenomena is relatively large, the frequency is far lower than a ship's shaft-rate electric field, whose frequency is concentrated in the 0.5 ∼ 30 Hz range. Analysis of electric field in sea waters is currently used for marine geophysics and oil-gas exploration, such as CSEM (Controlled Source Electromagnetic) method [6].
As for the marine electric field measuring devices, bottom metering systems are usually used both for deep sea and shallow sea. For example, Filloux [7], Håland [8], Flekkøy [9] and Wang Meng [10] used a 3-axis electric field sensor to measure the electric field signal on the seafloor. There are also a small number of other measurement devices, such as Qualls [11], who used an AUV (Autonomous underwater vehicle) equipped with the electric field sensor to measure the electric field near the hull.
It can be seen that most of the studies are based on the analysis of electric field data measured on the ocean floor or near the sea surface, but very few can obtain the electric field data of the entire ocean profile. By measuring the electric field of the entire ocean profile, we can understand the law of electric field changing with depth. As we know, the CSEM signals are often reported to be perturbed by electromagnetic noise in the ocean. The analysis of the electric field at different -1 -

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depths is helpful for data processing. In addition, it is also an important factor in determining the operational depth of towed CSEM receiver.
In this paper, a new type of electric field measurement device based on the autonomous profiling drifter was used for the first time. The experiment was conducted in the high seas area of South China Sea. The natural electric field in the depth range of 0 ∼ 1500 m was measured by this device. Then we analyzed the time-domain and power spectral density (PSD) characteristics of the electric field in the 0.01 ∼ 0.5 Hz and 0.5 ∼ 30 Hz range. To compare the difference of the electric field between the coastal water and high seas, we also measured the underwater electric field in coastal water at the depth of 15 m near Sanya, China. It is worth to note that, in this paper, high seas refer to the area which is far from the mainland with a water depth of several kilometers; while coastal water refers to the area which is close to the mainland with a water depth less than 60 m.
The contents of this paper are arranged as follows: in the second section, the basic structure of the electric field measuring device based on the autonomous profiling drifter, and the condition of sea trial in South China Sea are introduced; in the third section, the electric field at different depths of high sea is analyzed; in the fourth section, a bottom measuring device is used to record the electric field in coastal water near Sanya City and the natural electric field in coastal water is compared with that in high sea; in the fifth section, some conclusions are made based on the analysis.

Measurement technique and sea trial
To measure the natural electric field at different sea depths, an electric field measuring device is used which combines the electric field measuring system with the autonomous profiling drifter, see in figure 1. Note that UEP in figure 1 means underwater electric potential. The autonomous profiling drifter adjusts the buoyancy, making the measuring device move slowly or suspend at a set depth. And the UEP measuring unit is responsible for recording the electric field data at different depths. We use three pairs of low-noise Ag/AgCl electrodes, among them two pairs of electrodes are fixed on horizontal carbon fiber brackets and one pair is fixed on the vertical direction, see in figure 1. By measuring the electric potential difference between the same pair of electrodes, we can get the UEP in the direction of the electrodes. As the electric field is the gradient of electric potential, the underwater electric field can be computed in three directions. In this paper, represents the electric field measured by one certain pair of horizontal Ag/AgCl electrodes; represents the electric field measured by an orthogonal pair of horizontal Ag/AgCl electrodes and represents the vertical electric field. The distance is 3 m between the same pair of horizontal electrodes and 1.6 m for the vertical pair of electrodes.
To avoid the electric field interference caused by the measuring device itself, the electronic instruments of the buoyancy adjusting unit and the electric field measuring unit are all placed in separate glass balls. And these glass balls can resist the pressure of 4000 m water depth. In addition, water-tight cables are used for signal transmission between the electric field sensors and the electric field measuring unit. The workflow is as follows, firstly, the measuring device is power on via a contactless switch outside the glass ball; then the device starts to dive and the underwater electric field is being measured at the same time; when the device dives to the predefined depth, the device begins to rise and finally surfaces; after the device is recovered to the shore, the measurement data is transmitted via Wifi.
The parameters of the electric field measuring unit are as follows. The noise of the Ag/AgCl electrode is measured in a water tank where an electric field with standard intensity is applied, and at the same time the electrodes potential difference is recorded by a high precision measuring system (HIOKI MR8875 [12]). The results show that the noise of the Ag/AgCl electrode is less than 1nV/ √ Hz@1 Hz. We also measure the static potential difference of each pair of electrodes in the same way except that no electric field is applied, and the static potential difference of each pair of electrodes is less than 0.1 mV. The sampling rate of the measuring system is 100 Hz, and the whole measurement system noise is less than 4 nV/ √ Hz@1 Hz. All electric field values reported in this paper refer to peak-to-peak values.
The experiment was carried out in an area 300 km from the coast of southeastern Vietnam in South China Sea, in May 2019. The water depth of this area was about 3000 m, and the sea wave height was about 1.0 m. The sea trial site is shown in figure 2. After the electric field measuring device was placed into the water, it automatically dived and suspended at a depth of 50 m for 1 hour, and then slowly dived to a depth of 2000 m at a speed lower than 0.06 m/s, and finally surfaced to transmit data. In the process of descent, the electric field data of different depths was recorded, and the attitude information was also recorded at the same time by a high precision inertial measuring unit. The inertial measuring unit is BW-AH500 [13], its parameters are as follows: dynamic accuracy of pitch, roll, azimuth angles are 0.1 • , 0.1 • , 0.3 • , respectively. And the resolutions of these three angles are all 0.01 • .  Firstly, the attitude of the measuring device is analyzed. The results show that the measuring device is in a low-frequency shaking state at the depth less than 50 m. The maximum pitch and roll angles both are about 7 • , and the shaking frequency is close to the wave spectrum, about 0.14 Hz; while the azimuth angle (rotating around the vertical direction) changes very slowly, whose time period is more than 2 hours. When the measuring device starts to dive from 50 m, the shaking amplitude starts to decrease rapidly. At the depth of 100 m, the shaking amplitude both of the pitch -4 -and roll angles are less than 0.5 • , while the azimuth angle changes more slowly than before. When the depth is more than 200 m, the shaking amplitude of the measuring device is nearly unchanged although the depth continues to increase.

Natural electric field of high sea
Because the pitch and roll angles will affect the readings of the three components · and , coordinate transformation is necessary for · and . As we know, the underwater magnetic measurement is largely affected by the shaking of the measurement platform because a strong geomagnetic field exists on land and sea. However, no steady electric current exists in the ocean, making the underwater electric field measurement much less affected by the shaking of the measuring unit [14,15]. As a result, the measured data are coordinate-transformed based on the recorded attitude data only when water depth is no more than 100 m. And no coordinate transformation is applied when the depth is more than 100 m because of weak shaking amplitude.
Analysis of the underwater attitude of the measuring device shows that the measuring device is affected by the waves when the depth is less than 50 m. When the depth is greater than 100 m, it is nearly unaffected by the waves. Therefore, the electric field measured at a depth less than 50 m should have components of the induced electric field generated by the shaking of the measuring device itself. The analysis of the electric field at some depths is as follows.

Depth at 50 m
The time-domain and PSD characteristics in the 0.01 ∼ 0.5 Hz range are shown in figure 3 (a) and figure 3 (b), respectively. It can be seen from figure 3 (a) that the peak-to-peak value of the electric field is in the level of μV/m. According to figure 3 (b), the PSD of · and is basically the same level with each other and gradually decreases with the increase of frequency. At around 0.14 Hz, the PSD of and increases significantly, and the PSD of is a little greater than that of . And this phenomenon is more obvious when the depth is 20 m, which is not shown because of limited space.
As we know, the component is more easily affected by the induced electric field generated by the wave motion cutting the north-south geomagnetic field [16,17], as E = −V × B, where E is the electric field, V is the seawater direction and B is the earth magnetic field. As a result, the PSD in figure 3(b) clearly indicates that the electric field at this depth is affected by the surface wave. Note that no obvious increase is seen at around 0.14 Hz in , and this is because the direction of the wave was the same as that of at the measurement time.
At 50 m depth, in addition to the induced electric field generated by the sea wave, the measurement platform is also in a low-frequency shaking state, so it will also generate an induced electric field with the corresponding frequency. As a result, the measured underwater electric field in the experiment will be slightly greater than the actual magnitude of the natural electric field. Figure 4 shows the time-domain and PSD characteristics of electric field in the 0.5 ∼ 30 Hz range. From figure 4(a), it can be seen that the peak-to-peak values of both and are about 0.1 μV/m, while 0.2 μV/m for , which is higher than that of the horizontal components. It can also be seen from figure 4(b) that the PSD of is higher than that of the horizontal components. It is worth to note that the sharp pulses in figure 4(a) and figure 4(b) are generated by the interference of the buoyancy control unit after checking the work record of the buoyancy.    figure 3(a), it can be seen that the peak-to-peak value of the electric field at the depth of 100 m is significantly lower than that of the 50 m. In addition, it can be seen from figure 5 (b) that the electric field energy is mainly concentrated in the frequency band below 0.02 Hz. Comparing figure 5(b) with figure 3(b), we can see that the PSD at depth of 100 m does not increase at around 0.14 Hz, indicating that the natural electric field at this depth is nearly not affected by the surface wave.

Depth at 200 m
The time-domain and PSD characteristics in the 0.5 ∼ 30 Hz range are shown in figure 6. It can be seen that at the depth of 200 m, the peak-to-peak value of the electric field is further reduced compared with that of 100 m. The PSD of is still larger than that of the horizontal components. It has been ruled out that this phenomenon is caused by the circuit board of the measuring device. It shows that the natural electric field in the 0.5 ∼ 30 Hz range is not always dominated by horizontal components in these depths. -7 -

Depth at 1000 m
The natural electric field characteristics in the 0.01 ∼ 0.5 Hz and 0.5 ∼ 30 Hz range are shown in figure 6 and figure 7, respectively. Compared with 200 m depth, the peak-to-peak values of electric field in the 0.01 ∼ 0.5 Hz and 0.5 ∼ 30 Hz range are very weak. Note that the short pulse at 600 s in figure 7(a) is a transient external disturbance. And the line-spectrum in figure 7(b) and figure 8(b) is the result of the digital band pass filtering.

Comparison of the electric field among different depths
To compare the natural electric field characteristics among different depths, the peak-to-peak values of the electric field at different sea depths are summarized as shown in figure 9 and table 1. We can get the following conclusions.

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(1) In 0.01 ∼ 0.5 Hz range, the peak-to-peak value decreases gradually when the depth increases from 50 m to 500 m (See in figure 9), which is mainly due to the following reasons: a. the sea wave strength decreases exponentially with the depth (the attenuation coefficient is 2 / , where is the sea water depth and is the wave wavelength). As a result, the wave induced electric field decays fast at shallow depth; b. external electromagnetic waves decay rapidly in seawater. The skin depth is an important parameter which represents the distance an electromagnetic wave diffuse into a conducting medium, and where the amplitude is −1 of its initial value. Most of the energy of the electromagnetic wave is dissipated within one skin depth [6]. For electric field at 0.3 Hz, its skin depth is about 460 m, so the attenuation trend is obvious within 500 m depth range; c. at 50 m depth, the measuring device is also in a low-frequency shaking state, resulting in a larger electric field strength than the actual, while at depths more than 100 m, the measuring device's shaking is very weak, and the induced electric field generated by the measuring device itself can be ignored. In the 0.5 ∼ 30 Hz range, the peak-to-peak value decreases gradually when the depth increases from 50 m to 200 m (see in figure 9). Since this frequency range does not include the frequency of the surface wave motion, the attenuation trend of the electric field in this frequency range is mainly caused by the attenuation effect of sea water to electromagnetic waves. And the higher frequency electric field signal has a greater attenuation coefficient and a smaller skin depth in sea water compared with lower frequency signals [18,19]. For example, the skin depth of 1 Hz electric field is about 250 m in sea water.
(2) The natural electric field peak-to-peak values in the 0.01 ∼ 0.5 Hz and 0.5 ∼ 30 Hz range are nearly not changing with the depth when their depths exceed 500 m and 200 m, respectively. And these depths exceed the skin depth of the corresponding electric field signal. As most of the energy of the electromagnetic wave is dissipated within one skin depth, the electric field of the two frequency ranges should be less affected by ionosphere at this depth. Except for the ionosphere, this small unchanged peak-to-peak value may also be caused by the underwater magnetic background. Because the water is always moving, even in deep water, the induced electric field will always be generated even at deep depth.
(3) From table 1, the peak-to-peak values in the 0.5 ∼ 30 Hz range are a little bigger than that of 0.01 ∼ 0.5 Hz range when the water depth is within 500 ∼ 1500 m. The underwater magnetic background may lead to the small unchanged peak-to-peak value of the two frequency ranges, but will not make the peak-to-peak value of electric field in the 0.5 ∼ 30 Hz range be bigger than that of 0.01 ∼ 0.5 Hz range. The difference between the peak-to-peak values may be caused by the magnetic pulsation and other unknown reasons which need further research.

Natural electric field of coastal water
In section 3, we measured the natural electric field at different depths, and its measurement area belongs to high seas where the water depth is thousands of meters. To compare it with coastal water where the water depth is less than 60 m, a long-term monitoring experiment was carried out in the shallow sea where the water depth was 15 m near Sanya City in September 2019.
-9 -  -10 -To avoid the electric field interference caused by the measuring device itself, the measuring device was submerged at the sea bottom, and only non-metallic materials such as epoxy resins were used to fix the measuring electrodes(Ag/AgCl electrodes), and the signal was transmitted to the shore through a watertight cable. The measuring platform would not shake with the sea water because a heavy concrete base was used. And the distance between each pair of Ag/AgCl electrodes in three directions was 1 m. The measuring device is shown in figure 10. The filter amplifier circuit was the same as the circuit used in section 3, and the sampling rate was 200 Hz.
We choose the data which has the same surface wave strength as high seas for analysis. Because we mainly study the signals in the 0.01 ∼ 0.5 Hz and 0.5 ∼ 30 Hz range, the influence caused by tides is excluded. The analysis results show that the characteristics of natural electric field in the 0.01 ∼ 0.5 Hz range change little within one day, but the electric field in the 0.5 ∼ 30 Hz range are often affected by artificial line spectrum signals. As a result, we choose the data in one time period near 10:00am to analyze where there are some line spectrum noise signals. In this period, the time-domain and PSD characteristics are shown in figure 11 and figure 12, respectively. -11 -It can be seen from figure 11 that the peak-to-peak value of the electric field in the 0.01 ∼ 0.5 Hz range is about 2 ∼ 4 μV/m. At around 0.12 Hz, the PSD of the three electric field components increase significantly, which is mainly caused by the induced electric field generated by the surface wave.
It can be seen from figure 12 that the peak-to-peak value of the electric field is about 2 μV/m in the 0.5 ∼ 30 Hz range. The PSD of the vertical electric field component is greater than that of the horizontal components, and this phenomenon is consistent with the results in section 3. Because the underwater electric field in coastal water are more easily affected by human factors [20], some line spectrum signals in the 0.5 ∼ 30 Hz range are found as shown in figure 12(b). And most of these line spectrum signals are generated by moving ships and port activities. In other times of the day, similar line spectrum signals also occur many times. While line spectrum signals are rarely found in high seas when the depth is more than 50 m.
Comparing the electric field measured at the bottom of coastal water with that measured at 20 m depth of high seas, we can find that they have the same level of peak-to-peak values in the 0.01 ∼ 0.5 Hz range, but the peak-to-peak value of the former is nearly twice larger than the latter in the 0.5 ∼ 30 Hz range. This is because the electric field in the 0.5 ∼ 30 Hz range in coastal water is more easily affected by human factors, such as ships and port activities. The ship's shaft-rate electric field (mainly in the 0.5 ∼ 30 Hz range) can be measured within several kilometers and the port activities (including welding operations, fishing, etc.) will also generate electric field around this frequency range. While the electric field in the 0.01 ∼ 0.5 Hz range is mainly caused by sea waves.

Conclusions
The natural electric field in the depth range of 0 ∼ 1500 m in South China Sea is obtained by a new electric field measuring device. The results show that the natural electric field in the 0.01 ∼ 0.5 Hz range is obviously affected by the surface waves at the depth less than 50 m, but basically not affected by the surface waves at the depth more than 100 m.
For the natural electric field in the 0.5 ∼ 30 Hz range, its peak-to-peak value gradually decreases with the depth increases from 50 m to 200 m. At the depth of 200 m, the peak-to-peak value of the natural electric field is about 0.1 μV/m. But the peak-to-peak value remains as a small value when the depth continues to go deeper.
At the end of the paper, we measured the natural electric field of coastal area in Sanya City. By comparing the natural electric field between coastal water and high seas, we find that the peakto-peak value of natural electric field in the 0.5 ∼ 30 Hz range in coastal water is twice larger than that measured at 20 m depth of high seas, and nearly 20 times larger than that of deeper depths (> 100 m) in high seas. Line spectrum signals are rarely found in high seas at the water depth more than 50 m, while artificial line spectrum signals are often seen in one day of coastal water. However, the peak-to-peak value of natural electric field in the 0.01 ∼ 0.5 Hz range is the same between coastal water and high seas when they have the same surface wave strength.