4.1. Design of Key Parameters for New Kind Circular Permutation Electrode
The ring electrode measurement method is one of the penetration measurement methods, which can directly deploy the electrode array to marine sediments. As shown in
Figure 9, the ring electrode installed at a certain distance is embedded on the surface of the vertical rod. After the probe is installed, it can be measured by selecting four continuous electrodes.
Similar to the horizontal array four-electrode resistivity measurement technology, the ring-electrode resistivity measurement technology adopts the principle of the electric field of the uniform isotropic medium half-space point power supply [
7]. The principle of electric field distribution is shown in
Figure 10.
It can be understood that a cylinder with radius of and infinite length is embedded in a homogeneous isotropic medium. The resistivity of the medium is . The current source connected to the annular electrode A2 injects uniform current in its radial direction. Assuming that A1 is at infinity, the current source will form an equipotential surface with the insulating probe rod as the boundary.
The current density at any point
on the equipotential surface is:
In the formula
is the area of the circular equipotential surface,
R is the distance from point
P to the ring electrode, then:
Formula (1) satisfies the boundary condition:
at infinity. The current intensity on the cylinder surface is 0, according to Ohm law:
where
V is the
P-point potential, the Formula (1) is combined with the Formula (3) to obtain:
is the electric potential of point source.
The Wenner ring electrode arrangement is the four electrodes arranged according to Wenner, namely equidistant vertical installation on the insulation probe surface.
According to Wenner configuration of four electrodes, external A1 and A2 are current source electrodes, and internal V1 and V2 are potential difference measurement electrodes. All electrodes are arranged in equal spacing, and the spacing is a.
According to the Formulas (5)–(7), the potential difference between
V1 and
V2 is:
The electrode geometry configuration factor
G of the vertical four-ring Wenner arrangement is:
After calculating the electrode geometry configuration factor, the resistivity can be calculated.
The traditional Wiener ring electrode method only uses four electrodes, which is not conducive to obtaining accurate values. Therefore, we propose a new kind circular permutation electrode measurement method, and the developed probe is shown in
Figure 11.
At present, there are three methods of resistivity measurement using the C1C2C3C4, C2C3C4C5, C3C4C5C6 electrode combination. The advantage of this method is to increase the number of measurements and make the calculated value more accurate, but this will also make the probe length too long, which is not conducive to the later design. Therefore, considering the measurement times and the length of the probe, we designed a circular permutation electrode probe, that is, we can use the similar measurement of C1C2C5C6, that is, the current is injected into C1 and C6 to measure the potential difference between C2 and C5. If we design x (x > = 4) electrodes, according to the traditional method, we only have the x−3 group measurement method. If we use the new kind ring circuit measurement method, we can have kinds of measurement method, which reduces the length of the probe, saves cost, and facilitates subsequent calculation.
For example, for
C1,
C2,
C3,
C5 four electrodes have:
According to Formulas (5), (11), and (12), the potential difference between
C1 and
C2 is:
For
C1,
C2,
C3,
C6 four electrodes have:
According to Formulas (5), (14), and (15), the potential difference between
C1 and
C2 is:
The electrode geometry configuration factor
G of the vertical four-ring Wenner arrangement is:
After calculating the electrode geometry configuration factor, the resistivity can be calculated.
After calculating the resistivity of each electrode combination, the average value is:
In this way, more accurate resistivity value can be obtained, and the length of the probe can be appropriately reduced to facilitate the subsequent design.
4.2. Key Parameter Design of the Filter and Amplification Module
Because DDS [
13] adopts an all-digital structure, spurious is inevitably introduced. There are three main sources of error: spurious caused by phase round-off error of phase accumulator, spurious caused by amplitude quantization error as a result of limited word length of memory, and spurious caused by non-ideal characteristics of a D/A converter. Therefore, in order to obtain a better quality output signal, a low-pass filter is added to the signal output end. The main function of the filter is to filter out the high frequency noise in the output spectrum. Common types of low-pass filters include the Butterworth filter, Chebyshev filter, and elliptical filter. Among them, the transition bands of the Butterworth filter and Chebyshev filter are relatively flat, while the elliptical filter has a steep transition band, which is more suitable for filtering the noise near the passband frequency. Therefore, the elliptical filter is selected in this paper. Considering the chip output signal cut-off frequency of 70 MHZ, a low-pass elliptic filter with cut-off frequency of 70 MHZ is designed.
The order of the elliptic filter is calculated according to Matlab [
14], and the calling format is as follows:
where
n is the minimum order of elliptic filter,
Wp is the cut-off angular frequency of the elliptic filter,
Ws is the stopband starting angular frequency of the elliptic filter,
Rp is the passband ripple, and
Rs is the minimum stopband attenuation. The Filter Solution software is used to calculate the parameters of the internal components of the filter, and a 7-order elliptic low-pass filter with a cut-off frequency of 70 MHz is obtained. At the same time, due to the small output signal of AD9851 [
15], the signal is amplified to the required range through the amplitude, and the amplification factor is (
R8 +
R9)/
R7. Here, OPA454 is used as the amplification chip. OPA454 is a high-voltage operational amplifier produced by TI company. Its dynamic range is 100 V, and the maximum output current is 50 mA. The filter and amplification circuit are shown in
Figure 12.
4.4. System Software Design
The system software design is mainly divided into the lower machine program design and the upper machine program design; the lower machine software design flow chart is shown in
Figure 14, mainly through the Stm32Cube to build the corresponding framework, and the initialization configuration, the use of multi-threaded processing method in the system of DDS driver module, analog-to-digital conversion module, temperature acquisition module and communication module processing; at the same time, the collected voltage and temperature values are stored in the SD card after the initial Kalman filter processing and the communication module uses the serial port to receive an idle interrupt way to monitor the data sent by the upper machine and respond according to the analysis. The upper machine selects the integrated environment Visual Studio 2019 [
16], based on NET Framework 4.8, and uses multi-threaded processing to process the communication module, data analysis module, and data display module in the system.
The software design flow chart of the upper machine is shown in
Figure 15. After the system is initialized, the man–machine interface instruction waits to be received, and the inquiry instruction is sent to the lower machine after receiving the inquiry instruction. The data is received by the serial port in real time and judges whether it enters the interrupt function. The correct data are preprocessed, displayed, and stored, and the wrong data are discarded.
The upper machine software interface of the marine sediment resistivity measuring instrument is shown in
Figure 16. After the software is opened, the circuit is connected and the serial port is set to the corresponding port number, and then clicked to start; the resistivity value of the resistivity measuring instrument can be directly measured.