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Subseafloor resistivity sensing using a vertical electrode configuration
Earth, Planets and Space volume 66, Article number: 31 (2014)
Abstract
There is growing interest in marine direct current (DC) resistivity methods for subseafloor exploration of a broad range of geophysical and geological targets. To address this, we have developed a new marine DC method with a vertical electrode configuration (VEC). Compared to conventional marine DC methods that use a horizontal electrode configuration, the shape and position of our VEC cable can be controlled relatively easily. Therefore, the VEC is suitable for operations in regions of steep bathymetry and for expeditious subseafloor resistivity exploration. In this study, we introduce a waterresistant electrode array cable and an onshore multichannel DC measurement system for stable and rapid data acquisition. To evaluate the performance and efficiency of the new system, we conducted field experiments in the shallow water zone at Shimizu Port, Suruga Bay, Japan. In order to quantitatively analyze the VECDC data, we adopt a 1D numerical modeling code that computes the electric potential and apparent resistivity generated by a point and dipole current source used in the VECDC measurement. These can be placed at any position with an arbitrary electrode configuration in a multilayered space, including seawater and subseafloor layers. We also develop an inversion code for the VECDC data based on a simulated annealing (SA) optimization and applied this to the field data. The observed data is of sufficiently good quality to be used for inversion, and the SA result demonstrates that the proposed VECDC system is able to estimate the subseafloor resistivity structure.
Findings
Introduction
The use of marine (offshore) and underwater electromagnetic (EM) and direct current (DC) exploration methods for various geological and engineering targets has generated considerable interest in recent years (e.g., Constable2010; Edwards et al.1985; Goto et al.2008; Holten et al.2009; Loke and Lane2004; Orlando2013). Typical targets for marine EM and DC methods include port facilities, active fault structures, groundwater conditions, nuclear waste depository sites, carbon dioxide capture and storage, hydrocarbon reservoirs, and seafloor hydrothermal deposits beneath coastal and deepwater areas. To address these social demands, it is important to develop appropriate survey methods according to the local conditions, such as the depth of the targets and seawater.
In this study, we develop a new marine DC method with a vertical electrode configuration (VEC) (e.g., Baumgartner1996; Barsukov et al.2007; Holten et al.2009). The basic theory and concept of our marine VECDC method are based on standard onshore (e.g., Reynolds1997; Zhdanov and Keller1994) and offshore/underwater (e.g., Chave et al.1991) DC methods. The difference between conventional onshore and marine DC methods is that the proposed VECDC method measures electric potentials using vertically deployed electrodes. Compared to the conventional horizontal electrode configuration, the shape and position of the electrode cable in the VEC can be controlled relatively easily, without the need for positioning equipment such as an acoustic pinger. Therefore, the VECDC is suitable for exploration in regions of steep bathymetry and could become the preferred method for surveying shallow subseafloor targets in both coastal and deep water areas. In this study, we focus on the instrumentation required for data acquisition and the numerical analysis of VECDC data. In terms of instrumentation, we have introduced a waterresistant electrode array cable and an onshore multichannel DC survey system. These will improve the data quality compared to that collected during preliminary feasibility experiments.
A series of field tests were conducted using our new system in the shallow water zone at Shimizu Port, Suruga Bay, Japan. To evaluate and interpret the field data, the computation of theoretical responses (forward modeling) is essential, as is data inversion for a layered earth including seawater layers. We apply theoretical formulas presented in Mitsuhata and Ueda (2010) and Ueda et al. (2010) using the process of recursive relations introduced by Sato (2000) to calculate the electric potential generated by a point and/or dipole current source placed at any position in a multilayered space. Based on these theoretical formulas, we implement a numerical calculation tool to compute the electric potentials in Ueda et al. (2010). Moreover, we develop an inversion method for the VECDC data using simulated annealing (SA) optimization (e.g., Sen et al.1993; Sharma2012). Finally, we perform a numerical analysis of the observed data based on the electric potential calculation and SA inversion.
Instruments and field experiment
To evaluate the performance and efficiency of the proposed VECDC system, we carried out field experiments at the Shimizu Port in Suruga Bay, Japan (Figure1). For VECDC data acquisition in the field, we developed a new measurement system that operates in seawater to depths of 30 to 100 m. The new VECDC system consists of four primary components: (a) a DC transmitter and datalogger, (b) an electrode array cable for potential measurement, (c) two singleconductor cables for the current injection, and (d) two waterdepth meters (Figures2 and3). The potential electrode array cable consists of 32 single conductor cables with stainless steel electrodes (P_{1} to P_{32}, Figure3). This is deployed vertically from the rear deck of the survey boat with a single current electrode (C_{1}) cable, two depth meters, and a sea anchor attached with rope (Figure2). Another current electrode (C_{2}) is deployed at sea level with a buoy, which is kept 30 to 50 m away from the front of the survey boat (Figure2). For the transmitter and receiver mounted on the survey boat, we adopted a commercial onshore DC resistivity survey system (McOHM Profiler4 by OYO) to yield transmitting currents and measure electric potentials. The specification of each component is shown in Table1. Measurements were conducted at two sites around the Shimizu Port in Suruga Bay. These are denoted as # 01 and # 02 (sea depths of approximately 45 and 60 m, respectively) in Figure1. At the measurement sites, the electrode array cable of potential measurement (P_{1} to P_{32}) and singleconductor cable for the seafloor current electrode (C_{1}) were deployed from the survey boat. Two small depth meters (MDSMkV/D, JFE Advantec, Kobe, Hyogo Prefecture, Japan) were attached to the rope. One was fixed to the end that was lowered to the seafloor, and the other was fixed 10 m above the first one to estimate the depth of the electrodes and the tilt angle of the cables during the measurements. We used 0.5 and 1.0 m electrode spacings at the two measurement sites. Each measurement recorded 31 pairs (channels) of potential differences ΔV, given by
using 32 potential electrodes. The current electrodes were fixed at the seafloor (C_{1}) and at sea level (C_{2}). The data acquisition time depends on the choice of data stacking number of the McOHM Profiler4; it generally took 1 to 10 min to measure 31 potential differences. After several data acquisition runs with different stacking numbers, the rope, current electrode cable, and electrode array cable were retrieved. Figure4a,b shows the observed electric potential difference ΔV using the VECDC system at test sites #01 and #02, respectively. Each data set contains a total of 31 voltages (ΔV_{ i },i = 1,2,…,31) measured at 32 potential electrodes for the two fixed current electrodes described above. The results show that highquality data were obtained at both sites, down to approximately 1 × 10^{4} V (0.1 mV). This implies that the VECDC system and survey configuration of this experiment has a noise level of approximately 0.1 mV. The maximum tilt angle of the electrode cables, estimated from the two depth meter logs, was less than 1.5°, so we assume that the cables retained their vertical position during data acquisition.
Numerical analysis
Electric potential and apparent resistivity
In this study, we perform onedimensional (1D) numerical analysis with a multilayered space including seawater and subseafloor layers. We begin by formulating the electric potential and introducing an apparent resistivity for the marine VECDC method. We then develop a 1D inversion method using simulated annealing (SA) for the VECDC data and finally apply this inversion method to the field data.
The formula for the electric potential generated by a point current source placed at any position (except layer interfaces) in a multilayered space has been given using cylindrical coordinates by Mitsuhata and Ueda (2010), as shown in Figure5. In this section, we present a summary of the formula given in Mitsuhata and Ueda (2010). In the cylindrical coordinate system, the governing equation for the electric potential ϕ_{ i } given by the source (0,z_{ c }) at receiver (r,z) in the i th layer is described as
where r is the horizontal distance between the source and the receiver. The general solution ϕ_{ i } of (2) is given by a Hankel transform using the coefficients D, U, and Bessel’s function (e.g., Koefoed1979; Zhdanov and Keller1994).
The potential ϕ_{ i } is determined by coefficients U_{ i } and D_{ i }. Details of the solution of (3) are shown in Mitsuhata and Ueda (2010) and Ueda et al. (2010). A digital filter is generally used to compute the Hankel transforms in (3) (e.g., Anderson1979; Guptasarma and Singh1997; Rijo and Almeida2003). In our calculation code (Ueda et al.2010), we adopt the digital filters provided by Rijo and Almeida (2003). It is common to introduce the apparent resistivity instead of the electric potential for the initial estimation of subsurface resistivity distribution (e.g., Koefoed1979; Zhdanov and Keller1994). In marine/underwater electrical methods, the apparent resistivity can be defined as, for example, (1) ρ_{ a } for the whole space model, and (2) ρ_{ s } in the double halfspace with a seawater resistivity of ρ_{ w } (e.g., Francis1985; Jones1999, p. 255). For the whole space with resistivity ρ_{ a }, the electric potential difference (ΔV) of a fourelectrode configuration (Figure6a) is given by
where r is a function of the distance between current and potential electrodes, defined as{r}^{1}={r}_{11}^{1}+{r}_{22}^{1}{r}_{21}^{1}{r}_{12}^{1}. For the double halfspace (e.g., seawater ρ_{ w } and seafloor ρ_{ s }, shown in panel b of Figure6), ΔV for a fourelectrode configuration is obtained by the method of images (e.g., Reynolds1997):
where k is an electrical reflection coefficient defined as
and{{r}^{\prime}}^{1}={{r}^{\prime}}_{11}^{1}+{{r}^{\prime}}_{22}^{1}+{{r}^{\prime}}_{21}^{1}+{{r}^{\prime}}_{12}^{1}. Therefore, by solving for ΔV using (4) and (5), ρ_{ s } is obtained as
For multilayered and/or multidimensional subseafloor regions, ρ_{ s } represents the apparent resistivity of the entire subseafloor domain.
Very fast simulated annealing for VECDC data
For the data inversion, we adopt a very fast simulated annealing (VFSA, e.g., Sharma2012) optimization, which is based on the simulated annealing (SA) algorithm (e.g., Sen et al.1993). In this study, we simply follow the VFSA algorithm presented by Sharma (2012) and implement the onedimensional inversion computer code for VECDC data in MATLAB. The unknown model parameters of the VFSA inversion are represented by model P and include ρ and h, the resistivity and thickness of subseafloor layers, respectively. Observed electric potentials are converted to the seafloor apparent resistivity ρ_{ s } using ρ_{ w }, (4), and (7). Model parameter P and data ρ_{ s } are transformed into the log domain. Then, following Sharma (2012), the objective function ε is defined as
where{\rho}_{\mathit{\text{sj}}}^{\text{Obs}} and{\rho}_{\mathit{\text{sj}}}^{\text{Prd}}\left(P\right) are the j th observed and predicted (computed with estimated model P) data, respectively. N is the number of data (a total of 31 data points for the current VECDC system). During the VFSA inversion, model parameters{P}_{i}^{m} for the m th iteration are updated to{P}_{i}^{m+1} according to
where{P}_{i}^{\text{max}} and{P}_{i}^{\text{min}} are upper and lower bounds of the i th model parameter P_{ i } and y_{ i } is the updating factor computed as
Here, u_{ i } ∈ [0,1] is a random number, and T_{ m } is the temperature,
which controls the convergence behavior of the VFSA inversion. The variable m is the iteration number, c and α are constant parameters, and T_{0} is the initial temperature. In this study, we use c = 1 and α = 0.5. The number of temperature cooling steps is fixed to 100, and at each temperature, the update calculation (9) is repeated (20 × number of unknown model parameters) times to yield a better solution. Therefore, the total number of SA iterations (model evaluation) is 100 × 20 × (number of unknown model parameters) (e.g., a total of 6,000 iterations for two layers with three unknown parameters). Details of the VFSA inversion algorithm and parameters used in this study are available in Sharma (2012). We have developed the VFSA inversion code based on the VFSA algorithm described above. This was applied to the synthetic data generated by a test model to verify that appropriate results had been obtained. Figure7 shows the VFSA convergence behavior for the synthetic VECDC data. Figure8 presents the synthetic data and predicted apparent resistivity obtained by the VFSA inversion as a function of the distance of the electrodes from the seafloor. In this verification, a subseafloor model consists of two layers, and the unknown model parameters are (ρ_{1},h_{1}, and ρ_{2}). The synthetic true model has ρ_{1} = 0.5 Ω· m, h_{1} = 5.0 m, and ρ_{2} = 5.0 Ω·m, while the SA inversion results are ρ_{1} = 0.49 Ω·m, h_{1} = 3.2 m, and ρ_{2} = 4.3 Ω·m.
The difference between (synthetic) observed and predicted data is defined as the residual δ (%),
The fit between observed and predicted data appears to be good, and the resulting residual of the inversion is 1.47%. Thus, we can apply the developed SA inversion technique to the VECDC data.
Field data inversion
Next, we applied the proposed SA inversion to the real VECDC data collected at Shimizu Port. In this inversion, we assume a model consisting of a uniform seawater layer and (a) a uniform subseafloor and (b) two subseafloor layers. The unknown model parameters for the VFSA optimization are the subseafloor resistivity ρ_{1} for the uniform subseafloor model, the subseafloor resistivities ρ_{1},ρ_{2}, and the first subseafloor layer’s thickness h_{1}, for the two subseafloor layer model. The seawater layer resistivity and thickness are fixed to 0.3 Ω·m and 60 m, respectively, during the VFSA procedure. The resulting two subseafloor layer model at site #01 has ρ_{1} = 0.11 Ω·m, ρ_{2} = 0.89 Ω·m, and h_{1} = 0.55 m, while that for site #02 gives ρ_{1} = 0.13 Ω·m, ρ_{2} = 0.78 Ω·m, and h_{1} = 0.8 m. Figure9 presents the VFSA convergence behavior for the field VECDC data. Figure10 plots the observed data and predicted apparent resistivity obtained by the VFSA inversion depending on the heights of the electrodes from the seafloor. In Figure10, the predicted data obtained by the VFSA inversion for a uniform subseafloor model with resistivity of 0.44 and 0.40 Ω·m for sites #01 and #02 are also presented. At site #01, the VFSA iteration converged with minimum residuals δ of 10.7% and 28.2% for the twolayer and uniform model, respectively. At site #02, the results gave 8.0% and 23.4% for the twolayer and uniform model, respectively. It can be clearly seen that the predicted data for the two subseafloor layer model fits the observed data better than those for the uniform subseafloor model at both sites. These results indicate that both subseafloor resistivity mapping and sounding information could be obtained by the VECDC measurements. Considering the noise level (0.1 mV) and transmitting current (1 A) of the proposed VECDC system, it is necessary to increase the transmitting current for deep resistivity sensing.
Conclusion
We have developed a vertical electrode configuration DC measurement method and reported the results of field experiments in a shallow water coastal zone. We conducted field experiments to evaluate the performance and efficiency of the proposed system in the shallow water zone around Shimizu Port, Suruga Bay, Japan. To interpret the VECDC data, we adopted theoretical formulas and computed the electric potential generated by a point current source placed at any position within an arbitrary electrode configuration in a multilayered space including seawater and subseafloor regions. An inversion method for VECDC data was also developed. This is based on VFSA optimization and was applied to the synthetic and actual data obtained from the field experiments. The observed data were of good quality, except for those below the system noise level. A resistivity model with two subseafloor layers was estimated by the VFSA inversion. The results confirm that the VECDC method can be applied to subseafloor resistivity mapping as well as for vertical resistivity sounding.
The positions and locations of vertically deployed electrodes can be determined with two small depth meters, meaning there is no need for largescale underwater positioning systems, such as an acoustic pinger and GPS buoy. This makes the VECDC field operation simple and the system compact, easily handled with a small boat. It would be suitable for efficient nearseafloor resistivity mapping in rugged seafloor environments where it would be difficult to measure the exact positions and locations of individual electrodes in a horizontal electrode configuration (HEC) without any sophisticated positioning devices. It is important to understand the advantages and disadvantages of both VEC and HEC and to choose the right method depending on individual targets and situations.
In future studies, we will focus on improving our VECDC method for deeper resistivity sounding and applying it to the exploration of various targets.
Abbreviations
 DC:

direct current
 HEC:

horizontal electrode configuration
 VEC:

vertical electrode configuration.
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Acknowledgements
The authors would like to thank the survey crew of MinamiJuuji for their assistance with VECDC data acquisition. We also acknowledge Mr. M. Inoue for his advice and suggestions regarding marine/underwater DC resistivity measurements, including field surveys and data interpretation. We would also like to thank the two anonymous reviewers for their valuable comments and contributions to this letter.
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Authors’ contributions
TU designed the study and instrumentation, developed the numerical methods, participated in the field experiment, conducted the numerical analysis and interpretation, and drafted the manuscript. YM carried out the theoretical formulation, participated in the numerical analysis and interpretation, and helped to draft the manuscript. MJ participated in the survey design and the field experiment. HB organized the field experiment and participated in the field measurements. All authors read and approved the final manuscript.
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Ueda, T., Mitsuhata, Y., Jinguji, M. et al. Subseafloor resistivity sensing using a vertical electrode configuration. Earth Planet Sp 66, 31 (2014). https://doi.org/10.1186/188059816631
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DOI: https://doi.org/10.1186/188059816631