Marine self-potential survey for exploring seafloor hydrothermal ore deposits

We conducted a self-potential survey at an active hydrothermal field, the Izena hole in the mid-Okinawa Trough, southern Japan. This field is known to contain Kuroko-type massive sulphide deposits. This survey measured the self-potential continuously in ambient seawater using a deep-tow array, which comprises an electrode array with a 30-m-long elastic rod and a stand-alone data acquisition unit. We observed negative self-potential signals not only above active hydrothermal vents and visible sulphide mounds but also above the flat seafloor without such structures. Some signals were detectable >50 m above the seafloor. Analysis of the acquired data revealed these signals’ source as below the seafloor, which suggests that the self-potential method can detect hydrothermal ore deposits effectively. The self-potential survey, an easily performed method for initial surveys, can identify individual sulphide deposits from a vast hydrothermal area.


Supplementary figures cited in the manuscript.
Deep-tow altitude (black curves) and depth (blue curves). The notation is identical to that in Fig. S2.  For example, polarisation is -90 degrees for a downward dipole.

Appendix to the Materials and Methods section.
Instruments. Our tool, developed to conduct self-potential surveys in marine environments 1 (Fig. 2), consists of an electrode array and a data acquisition unit installed on a deep-tow apparatus. A fibre-reinforced plastic (FRP) rod (30 m long, 1 cm diameter in this study) bends and recovers elastically to keep the rod straight. Thereby the sensor distance is maintained. Five non-polarised Ag-AgCl electrodes 2 are mounted at equal intervals of 5 m along the rod (Fig. 2). A common electrode is placed between the second and third electrodes. The use of numerous electrodes is important for observing marine environments because of redundant data acquisition, but only two electrodes can measure the self-potential. We placed a sea sinker at the tail of the rod to stabilise it. During surveys, the electrostatic potential of each electrode was recorded using a stand-alone precise (24 bit) voltage meter. The recorder contains a battery and requires no external power supply. We used 1 Hz resampled data extracted from the original 50 Hz data.
Positioning. The deep-tow position (in three dimensions; Fig. 2) was monitored using a super-short baseline (SSBL) ranging between the deep-tow and the vessel. The time interval of ranging is 8 s. The accuracy of the SSBL ranging is within 1% of the slant range. It is ±20 m in the present case with the deep-tow. The deep-tow depth is also monitored using a pre-calibrated depth meter, with a time interval of 1 s. For analysis, the deep-tow depth obtained from the depth meter is used because it is more stable and accurate (< 1 m in specifications) than that obtained from SSBL ranging. To calibrate the depth meter, a one-dimensional profile of sound speed is obtained using a CTD launcher system. The deep-tow altitude is monitored using an acoustic altimeter, with a time interval of 1 s. The sum of the measured depth and altitude is the seafloor depth below the deep-tow apparatus.
The electrode rod tail position is also monitored by SSBL ranging. The relative position of the rod can be estimated using the two SSBL positions by assuming the rod as straight. To obtain a smooth time series of the positions of the deep-tow and the tail of the rod, least-squares spline approximation is applied to the raw data.
Electric field. The electric field in the direction of the rod is calculable using any combination of two electrodes (out of five electrodes) divided by the distance between them, with the position of measurements being defined at its centre. In general, using a long sensor distance gains sensitivity, i.e. the signals become larger, but the positioning becomes inaccurate, whereas taking a short sensor distance improves the positioning accuracy, but the sensitivity worsens. We chose the shortest sensor distance of 5 m because we found that the electric field is not constant along the 30-m-long rod, particularly when the deep-tow altitude is low (e.g. 5 m). This difficulty related to the electric field probably occurs because the electrode rod is not straight. Therefore, it reflects rapid changes in the deep-tow altitude. The electrode cable responds to local self-potential signals near sulphide mounds with spatial scale of approx. 30 m. Results show that these four combinations of 5-m-spacing electrode pairs produce the same electric field if the location of measurements is given properly and if an offset value (assumed to be constant) inherent to each electrode pair is subtracted (Supplementary Fig.   S1). Therefore, we can assume that the self-potential signal is homogeneous with the spatial scale of approx. 5 m. Effective self-potential. As a visual reference, the calculated electric field is integrated along the dive tracks to reveal the self-potential along the dive tracks. The measured electric field is not parallel to the dive track in general. Therefore, we approximate the electric field along the dive track as equal to the observed electric field. The "effective" self-potential is therefore calculated as where θ represents the slope angle of the survey line (i.e. cosθ = 1 / 1+ (dz / dx) 2 ), and subscript 'ref' denotes a reference point that is distant from ore bodies. This integration works well for practical uses because both the initial and final self-potentials are found to be approx. 0 mV (upper panels, Figs. 3 and 4). As described in the Results section, we do not use this "effective" self-potential to detect the location of sources for the observed self-potential signals, but instead use the observed electric field in the direction of the rod (E obs ; Supplementary Fig. S1) for analysis of the probability tomography method. In the present survey, the calculated effective self-potential is zero both before and after passing sulphide mounds, indicating that the data obtained with an error in the rod angle are sufficiently accurate for our purposes.
Method of detecting self-potential signals. The probability tomography method 3-6 is a kind of cross-correlation method to produce images of the source locations of the self-potential signals in a probabilistic manner. The method was first limited to an electric current monopole source below a flat surface 3 . Then the effects of topography 4 and dipole sources 5 were included. Assuming an electric current dipole as a first approximation to represent an ore body 5,7 , we obtain the expression for cases in which the direction of the measured electric field is not parallel to the survey line 6 ( Fig. 2 shows the geometric configuration.).
The occurrence probability of a unit-strength electrical current dipole (η i ; i = V for a vertical dipole and i = H for a horizontal dipole) located at (x q , z q ) is calculated by taking cross-correlation between the observed electrical field in the direction of the rod (E obs ) and the synthetic electric field induced by a unit-strength dipole ( where θ(x, z(x)) is the slope angle of the dive track, ϕ(x, z(x)) is the slope angle of the electrode array, and with S i (i = V, H) is the self-potential field induced by an electric current dipole. Here we assume for simplicity that the survey line is along the x direction (north-south). The use of E obs instead of V eff produces accurate results because we can equate the direction of the electric field induced by the synthetic electric current dipole ( ℑ i ) to the direction of E obs .
If the effect of electrical conductivity contrast is ignored, then S i has the following form 5,6 : This simplification gives no effect for the case of a flat seafloor with a layered electrical conductivity structure. Considering the seafloor topography, this simplification might also be justified at a first order, even though the electrical conductivity in shallow sediment might vary by approximately five times within the uppermost few tens of 20 metres. Synthetic tests show that contrasts in electrical conductivity of the one-order of magnitude can be ignored in the present analysis when the required accuracy is approx.
10 m (Supplementary document 2). For more precise estimations, S i should be calculated numerically or an inversion should be performed 8 .
Scanning the location of an electric current dipole (x q , z q ) calculates the occurrence probability of a dipole. In the present study, the spacing is 10 m in the is the overall probability of an electric current dipole. The polarisation direction is defined as the following unit vector: (S6) Effects of electrical conductivity contrast on estimating the electric dipole source depth.
Herein, we demonstrate that the contrast of electric conductivity can be ignored in analyses when the source location is emphasized.
Numerical Model. We calculate the electric potential field induced by a dipolar electric current source below the seafloor in the presence of seafloor topography and electrical conductivity contrast. We resolve this difficulty using three-dimensional finite element method. An electric dipole is represented as a spatial derivative of the delta function 9 . The equation to be solved is given as where φ stands for the electric potential (self-potential in our case), σ signifies electrical conductivity, I 0 denotes the source intensity, δ denotes the delta function, r 0 represents the location of an electric dipole, and n is the direction of polarisation. For simplicity, the Dirichlet boundary condition with zero potential is applied for all outer boundaries. An electric dipole is represented as a spatial derivative of a discrete delta function 9 .
The calculation area is a cube of 1000 m with the upper half and lower half respectively including the ocean and sediment (Fig. S7a). This area is discretized by 100 unevenly sized (approx. 1.25 m from the seafloor) tri-linear hexahedron elements in each dimension. We restrict ourselves to performing calculations corresponding to the largest mound encountered in the present study (the south site). The seafloor topography (Fig.   S7b) is approximated as shown below. We estimate the source location using probabilistic tomography described in the main text. The spacing is 1 m in both the horizontal and vertical directions. We monitor the electric potential 5 m above the seafloor and at 50 m high relative to the topographic low (dashed curves in Fig. S7).
Numerical results. With constant electrical conductivity, the resultant electric field ( Fig.   S8a; a 50-m-deep source is imaged using a 5-m-height survey line) is fundamentally the same as the analytical solution in an infinite space 10 , as This equation shows the effect of the Dirichlet boundary condition because φ is inversely proportional to the square of the distance from the source. We confirmed that the probabilistic tomography can estimate the source depth exactly (Table S3).
With piecewise-constant electrical conductivity in which electrical conductivity of the sediment is 0.1 times that of seawater, the resultant electric field is increased significantly (with the same source intensity; see equation (S7)). In this case, probabilistic tomography that ignores electric conductivity contrast produces almost true source location (Table S3). Similar results are obtainable for cases with a more realistic electric conductivity profile (Fig. S8b and Table S3).
In these examples, the estimation error is within 10% or 5 m for most cases. Therefore, information related to electric conductivity is unimportant to estimate the source location, but the electric conductivity is of particular importance when the source intensity is considered.   As an example for the worst case, we set this angle to 0. Furthermore, the cable angle (ϕ) was set to zero. Both cases produce almost identical results to those obtained in the original case (cf. Fig. S9a and Fig. 6a for Track 2 of the western survey line, and Fig. S9b and Fig. 6d for Track 4 of the eastern survey line).
Deep-tow depth. However, when the deep-tow depth is set as constant (1600 m), the result becomes worse when the deep-tow altitude changes with time (cf. Fig. S9c and Fig.   6c for Track 2 of the western survey line, and Fig. S9d and Fig. 6d for Track 4 of the eastern survey line). The distance between the source and the observed points is important for analysis because a dipole has strong dependence on the distance (inverse-square relation). The deep-tow depth is obtained very accurately (approx. 1 m). The test described above is unrealistic. However, if the depth meter is broken, then imaging cannot be performed very well.