Experimental study on the detection of metal sulfide under seafloor environment using time domain induced polarization

Abstract

The induced polarization (IP) method can play an important role in the exploration of seafloor polymetallic sulfide deposits. Compared to frequency-domain IP, time-domain IP (TDIP) requires a simpler apparatus configuration and can be more widely and economically deployed for operations in seafloor environments. To investigate the effect of the seafloor environment on the TDIP measurement and find suitable parameters to characterize metallic bodies, laboratory experiments on synthetic samples were carried out based on a special electrical experimental system. The time-domain Cole–Cole model and relaxation time distribution (RTD) method were combined to process and interpret the measured data. The results show that the volume content of metallic minerals in ore-bearing rocks can be directly quantified by the total chargeability. The sizes of metallic particles can be approximately determined by the relaxation time defined from the peak of the RTD. The RTD method was used to distinguish multiple polarizable sources, such as sulfide and basalt. TDIP surveying in the marine environment is more efficient than surveying in the terrestrial environment. A short time delay used before starting secondary voltage measurements is more suitable for a successful TDIP survey in a high-salinity environment. In addition, the chargeability is shown to be more sensitive to the variation in the volume content of metallic minerals than the direct current resistivity.

Appendix

Inversion of the relaxation time distribution

The time-domain IP phenomenon of a porous material with metallic particles is a superposition of individual relaxations caused by various polarizable elements. The induced polarization decay can be expressed mathematically as a weighted superposition of a series of exponential decays ${e}^{\frac{-t}{\tau }}$ with different time constants ${\tau }_{i}$ (Tong et al. 2004, 2006). Hence, the measured induced polarization decay curve can be described as follows:

$$m\left( t \right)\; = \;\int_{{\tau_{min} }}^{{\tau_{max} }} {e^{{\frac{ - t}{\tau }}} \;{\text{G}}\left( \tau \right)\;d\tau }$$

(1)

where G(τ) is the nonnegative weight coefficient relating to ${\tau }_{i}$. ${\tau }_{min}$ is the shortest relaxation time. ${\tau }_{max}$ is the largest relaxation time. For the numerical computation of G(τ), Eq. 1 needs to be discretized into a matrix equation.

$$Ax = b,\;A \in R^{(n \times m)} ,\;x \in R^{m} ,\;b \in R^{n}$$

(2)

where

$$A_{n \times m} \; = \;e^{{\frac{{ - t_{n} }}{{\tau_{m} }}}} ,\;b_{n \times 1} \; = \;\left( {V_{1} ,V_{2} , \ldots \ldots \ldots V_{n} } \right)^{T}$$

(3)

$$x_{m \times 1} \; = \;\left( {G_{1} ,\;G_{2} ,\; \ldots \; \ldots \; \ldots \;G_{m} } \right)^{T}$$

(4)

${A}_{n\times m}$ is the dimensional coefficient matrix of kernel ${e}^{\frac{-{t}_{n}}{{\tau }_{m}}}$. ${t}_{n}$ denotes the time moment of recording the secondary voltage. ${b}_{n\times 1}$ is the discrete column vector of the normalized secondary voltage, and ${x}_{m\times 1}$ is the solution column vector, which represents the dimensional amplitude G(τ) of the relaxation time constant ${\tau }_{m}$. ${\tau }_{m}$ (m = 1, 2, 3…, $i$) are relaxation time constant series determined from ${\tau }_{min}$ to ${\tau }_{max}$ in advance. The solution vector $x$ is sensitive to the noise of the TDIP data.

The generalized inverse of Eq. 2 is

$$min:\left\| {b - Ax} \right\|^{2}$$

(5)

However, the solution of this equation is greatly affected by the signal-to-noise ratio, and a small noise effect of the secondary decay curve could lead to a large deviation of the result $x$. This problem can be solved by using a regularized least squares method (Liu et al. 2014a). The new equation can be expressed as:

$$min:\left\| {b - Ax} \right\|^{2} + \lambda^{2} \left\| {Wx} \right\|^{2}$$

(6)

where $\lambda$ is the regularization parameter and $W$ is the regularization operator corresponding to a specific constraint matrix. The regularization operator is the unit matrix in our study, so the optimization problem is solved based on the minimum length model. Then, the solution of Eq. 6 can be expressed as follows:

$$\left( {A^{T} \cdot A + \lambda^{2} \cdot W^{T} \cdot W} \right) \cdot x = A^{T} \cdot b$$

(7)

Then, we solve Eq. (7), and the relaxation distribution (${\tau }_{m}, x$) is computed. The G(τ) calculated in our study is a series of discrete values corresponding to the ${\tau }_{m}$. To present the results visually, a solid line is used to connect these discrete points on the graph.