Development of an NB-IoT-Based Measurement and Control System for Frequency Division Multiplexing Electrical Resistivity Tomography (FDM-ERT) Instruments

Abstract

Urban geophysical exploration faces significant hurdles due to strong electromagnetic interference and limited operational space, which restrict the efficiency and depth of traditional Electrical Resistivity Tomography (ERT). To overcome these limitations, this paper presents a novel ERT measurement and control system based on the Frequency Division Multiplexing (FDM) principle. Unlike conventional time-domain methods, this instrument synchronously transmits three independent AC signals at distinct frequencies. The acquisition station utilizes Fast Fourier Transform (FFT) to isolate specific frequency responses, enabling the simultaneous retrieval of apparent resistivity data for three different electrode spacings from a single transmission. The system architecture integrates low-power STM32 microcontrollers with an Android-based control terminal via Bluetooth, Wi-Fi, and NB-IoT technologies. This wireless design supports real-time current monitoring and cloud-based data synchronization. Experimental results demonstrate that the FDM operating mode significantly enhances data acquisition efficiency and anti-interference capability through frequency-domain separation. Controlled indoor and preliminary field tests indicate that FDM mode substantially improves acquisition efficiency through concurrent multi-channel measurement while effectively resolving target signals from noise. This study demonstrates the system’s technical feasibility and provides a practical foundation for future geophysical detection in time-constrained urban environments.

1. Introduction

Electrical Resistivity Tomography (ERT) is a geophysical exploration technique that relies on the electrical resistivity variations in subsurface materials [1,2]. This technique has evolved from traditional resistivity methods and operates by injecting current into the ground through electrodes while concurrently measuring the potential difference between them to deduce the apparent resistivity distribution of the subsurface target area. ERT presents considerable advantages over conventional resistivity methods, including robust anti-interference capabilities, intuitive imaging results, operational convenience, cost-effectiveness, and high efficiency [3,4]. Currently, ERT is widely utilized in near-surface exploration domains such as engineering geology [5,6,7], archaeology [8,9,10,11], hydrogeology [12,13,14], environmental engineering [15,16,17], and contaminated site remediation [18,19,20]. It has emerged as one of the most widely employed methods in near-surface engineering geophysics, showcasing exceptional practical effectiveness.

The technical development of ERT instruments began in the 1970s with the introduction of the electrical sounding system by Dr. Johansen [21,22,23]. In the 1980s, the OYO Corporation in Japan achieved a preliminary realization of field data acquisition for high-density resistivity methods through the utilization of an electrode switching board [24]. Since then, researchers globally have engaged in extensive and in-depth studies on this technology.

With the increasing complexity of geophysical exploration demands, ERT instruments are rapidly evolving towards multi-channel, intelligent, and networked systems [25,26]. Modern mainstream commercial instruments have achieved high levels of system integration [27,28]. For example, the RESECS system developed by DMT (Essen, Germany) supports large-scale 3D exploration with up to 960 electrode channels [29]. Concurrently, the convergence of the Internet of Things (IoT) and wireless communication technologies has emerged as a key trend. Both the SuperSting R8/IP by AGI (Austin, TX, USA) and the McOHM Profiler-8i by OYO (Tokyo, Japan) have incorporated Wi-Fi and IoT technologies, enabling real-time monitoring and cloud-based data processing [30,31]. Furthermore, the Terrameter LS by ABEM (Sundbyberg, Sweden) utilizes an open communication platform and remote diagnostic functions to optimize field exploration workflows [32,33]. Significant technological advancements have also been made in distributed architecture. Instruments such as the DUK-3/4 series employ embedded Linux systems to measure parameters like apparent resistivity and chargeability, thereby enhancing the diversity of observational parameters [34,35]. Meanwhile, distributed systems exemplified by the GeoPen E60DN achieve flexible parallel acquisition and real-time data transmission [36,37,38]. Collectively, these technologies have facilitated the expansion of ERT applications in complex environments.

Despite substantial advancements in the integration and networking capabilities of existing ERT instruments, most devices continue to rely on the principle of Time Division Multiplexing (TDM). In urban environments characterized by complex interference sources, this traditional approach encounters challenges such as low operational efficiency and inadequate anti-interference capabilities. To address these challenges, this paper proposes the development of an ERT instrument based on the Frequency Division Multiplexing (FDM) principle. Unlike the traditional TDM mode, the proposed instrument can simultaneously transmit multiple mutually isolated, frequency-orthogonal signals to current electrodes positioned at different locations. This process is equivalent to multi-electrode synchronous acquisition, thereby significantly enhancing field exploration efficiency. By separating and processing data at different frequencies, the system can effectively identify and eliminate frequency interference. Furthermore, it adapts to the flexible requirements for electrode configurations in urban exploration and supports rapid exploration deployment [39,40].

With the rapid development of IoT and edge-cloud collaborative technologies, data routing and coordination in dynamic network environments have become a core challenge in distributed system design. For example, in dynamic scenarios such as Ambient Assisted Living (AAL), recent work has emphasized edge preprocessing, data prioritization, and bandwidth-efficient routing to address node mobility and intermittent connectivity [41]. These mechanisms provide important references for adaptive data-flow management in resource-constrained environments. Drawing inspiration from such approaches, this paper leverages a commercial IoT platform and implements asynchronous message routing through a cloud-based rule engine and AMQP, thereby achieving multi-node collaboration and cross-device parameter synchronization tailored to the specific scenarios of geophysical field exploration.

In light of the limitations of existing instruments concerning portability, intelligence, and operational efficiency, this study proposes a measurement and control system specifically designed for an FDM-ERT instrument. The architecture of the system consists of two primary components: the Main Measurement and Control Unit and the Current Station Measurement and Control Unit. An Android smart mobile terminal serves as the core control interface, facilitating short-range command interaction and data transmission through Bluetooth and Wi-Fi, while utilizing NB-IoT for the synchronization of current data and the cloud-based uploading of measurement results. Additionally, the system implements real-time demodulation and amplitude extraction of multi-frequency data on the Android terminal. By integrating the synchronized current data, real-time processing and imaging are executed directly within the mobile application, thereby significantly enhancing the system’s portability and the instrument’s level of intelligence.

2. Materials and Methods: Measurement Principle and Working Configuration

The conventional apparent resistivity method typically employs a four-electrode configuration. In this setup, current is injected into the ground through two current electrodes (A and B) to establish an artificial electric field, while the potential difference arising from resistivity variations in the subsurface media is measured using two potential electrodes (M and N) [42,43]. The exploration depth is primarily influenced by factors such as the spacing between current electrodes AB (or AO, where O denotes the midpoint of the potential electrodes MN), the magnitude of the injected current, and the sensitivity of the receiving instrument [44,45]. To acquire resistivity information at varying spatial positions and depths, the current electrodes (AB) and potential electrodes (MN) must be repositioned after each measurement. This discrete, point-by-point operational mode suffers from low efficiency and high operational costs, thereby complicating the fulfillment of demands for rapid, high-precision exploration over large areas.

To address the efficiency limitations of traditional apparent resistivity methods, researchers have proposed a multi-frequency resistivity exploration technique based on Frequency Division Multiplexing (FDM) technology. The essence of this method is rooted in parallel transmission and synchronous acquisition.

An electrical transmitter capable of generating n mutually independent and frequency-orthogonal current signals is utilized to inject distinct frequency currents into the ground through n pairs of grounded current electrodes. In the target area, the receiver synchronously acquires the composite electric field signal, which encompasses n distinct frequency components, between two potential electrodes. Utilizing signal demodulation and separation techniques, the potential difference data corresponding to each individual frequency is extracted. By integrating the 3D coordinates of the electrodes, apparent resistivity data at varying depths are computed. Subsequently, inversion processing is conducted to derive the true resistivity distribution characteristics, thereby facilitating the inference of the geological structure of the target area.

In contrast to traditional apparent resistivity methods, the FDM-ERT technique achieves ‘single deployment, multi-frequency acquisition,’ as shown in Figure 1. This approach facilitates the simultaneous collection of geoelectrical data at varying depths by employing multiple pairs of current electrodes and allows for the automatic switching of potential electrodes (MN), thus eliminating the necessity for manual electrode relocation. Furthermore, the transmitted alternating current (AC) signals are independent and vary in frequency, endowing the system with strong anti-interference capabilities and effectively reducing environmental noise. This enhancement significantly improves exploration efficiency and data quality, particularly in environments characterized by intense electromagnetic interference and constrained operational space [46,47,48].

The measurement configuration utilizes the Multiple Gradient Array, an innovative setup derived from the traditional intermediate gradient method. This configuration incorporates modern multi-channel acquisition technologies [49,50] retaining high sensitivity to vertical structures while achieving depth scanning through the variation in current electrode spacing. As a result, it possesses true tomographic imaging capabilities [51,52].

In the practical operation of the FDM-ERT instrument, an electrical transmitter is employed that can simultaneously emit three mutually independent current signals, each with distinct frequencies. These signals are injected into the ground concurrently through three pairs of current electrodes, which are positioned at varying spacings to establish an artificial electric field. Within the target area located between the current electrodes, n acquisition stations of FDM-ERT, each equipped with 24-channel distributed acquisition systems, are utilized to measure the composite electric field signal between adjacent potential electrodes. This signal is subsequently demodulated and separated to extract the potential difference data corresponding to each frequency ($∆U_1, ∆U_2, ∆U_3$). The apparent resistivity is then calculated based on the standard formula for the Direct Current (DC) resistivity method:

$${\rho }_{si}=K_i{\displaystyle \frac{{∆U}_i}{I_i}}\left(i=\mathrm{1,2},3\right),$$

(1)

$∆U_i$ denotes the potential difference in each separated frequency component, measured in Volts (V). $I_i$ represents the current intensity at the corresponding frequency, measured in Amperes (A). The apparent resistivity value for each separated frequency is denoted as ${\rho }_{si}$, expressed in Ohm-meters ($\Omega ·\mathrm{m}$). K refers to the geometric factor, also known as the array coefficient. The general calculation formula for the geometric factor K is as follows:

$$K_i={\displaystyle \frac{2\pi }{\left|\frac{1}{A_{i}M}-\frac{1}{B_{i}M}-\frac{1}{A_{i}N}+\frac{1}{B_{i}N}\right|}},$$

(2)

In this equation,

$$A_{i}M=\sqrt{{\left(x_{Ai}-x_M\right)}^2+{\left(y_{Ai}-y_M\right)}^2+{\left(z_{Ai}-z_M\right)}^2}\left(i=\mathrm{1,2},3\right),$$

(3)

$$A_{i}N=\sqrt{{\left(x_{Ai}-x_N\right)}^2+{\left(y_{Ai}-y_N\right)}^2+{\left(z_{Ai}-z_N\right)}^2}\left(i=\mathrm{1,2},3\right),$$

(4)

$$B_{i}M=\sqrt{{\left(x_{Bi}-x_M\right)}^2+{\left(y_{Bi}-y_M\right)}^2+{\left(z_{Bi}-z_M\right)}^2}\left(i=\mathrm{1,2},3\right),$$

(5)

$$B_{i}N=\sqrt{{\left(x_{Bi}-x_N\right)}^2+{\left(y_{Bi}-y_N\right)}^2+{\left(z_{Bi}-z_N\right)}^2}\left(i=\mathrm{1,2},3\right),$$

(6)

In this equation, the variables ($x_{Ai}, y_{Ai}, z_{Ai}$) denote the 3D geodetic coordinates of the current electrode $A_i$, while ($x_{Bi}, y_{Bi}, z_{Bi}$) represent the 3D geodetic coordinates of the current electrode $B_i$. Additionally, ($x_M, y_M, z_M$) indicate the 3D geodetic coordinates of the potential electrode M, and ($x_N, y_N,z_N$) represent the 3D geodetic coordinates of the potential electrode N.

Upon obtaining the apparent resistivity data for the target area, inversion processing is conducted to recover the true resistivity distribution characteristics. Subsequently, geological interpretation is performed based on these true resistivity results to finalize the exploration survey.

3. System Design and Implementation

3.1. Overall System Architecture

As illustrated in Figure 2, the system of the FDM-ERT instrument comprises two primary subsystems: the transmission system and the acquisition system. The transmission system employs a 220 V AC generator as its power source, which supplies power to three independent channels of the FDM-ERT transmitter through three AC-DC rectifier modules. The transmitter interfaces with the PC host terminal via an RS232 connection, allowing for control over the frequency, synchronization mechanism, and the start-stop status of the three transmission signals.

The acquisition system comprises the Current Station of FDM-ERT and the Acquisition Station of FDM-ERT. Hall sensors are utilized for current monitoring, converting high-magnitude ACs in the supply lines into proportional voltage signals, which are then accurately acquired by the Current Station. Subsequently, the Android-based software computes the effective current values for each frequency ($I_1, I_2, I_3$) using built-in conversion coefficients. In the survey area, the Android software manages the Acquisition Station to measure the potential difference between electrodes. Finally, apparent resistivity is computed directly from the measured current, potential difference, and 3D coordinates of the electrodes.

This paper focuses on the research and implementation of FDM-ERT instrument and control scheme specifically designed for the acquisition system of the instrument.

As illustrated in Figure 3, this paper presents the design of a measurement and control system for the FDM-ERT instrument based on an Internet of Things (IoT) architecture. The system employs a hierarchical structure consisting of an “Embedded Control Terminal + Android Control Terminal + Cloud Platform.” The embedded measurement and control system, centered around the STM32F429 processor, is deployed at both the acquisition station of FDM-ERT and the current station of FDM-ERT, facilitating information exchange with the Android terminal through integrated wireless communication modules. The system design effectively addresses the requirements for local control, remote control, and inter-device communication. In local control mode, users directly operate the mobile application, transmitting control commands to the instruments via Bluetooth and receiving uploaded acquisition data through Wi-Fi. By integrating the current station data forwarded through the cloud platform, data processing and real-time imaging are achieved on the Android terminal of the acquisition station. In remote control mode, the acquisition station connects to the Huawei IoT Cloud Platform via an NB-IoT module. Users can access the cloud platform through the Android terminal over 5G/4G networks, facilitating remote command transmission and data retrieval.

3.2. Embedded Software and Firmware Design

Given the complex characteristics of the FDM-ERT instrument—such as distributed acquisition, concurrent multi-frequency operation, and real-time imaging—the embedded system faces significant challenges. These challenges include high-concurrency multi-task scheduling, the coexistence of heterogeneous communication protocol stacks (Bluetooth, Wi-Fi, NB-IoT), and the maintenance of data integrity under low-bandwidth IoT conditions. To address these issues, a modular hierarchical design scheme has been adopted. Furthermore, due to the high degree of similarity in the underlying control logic between the acquisition station and the current station, their embedded software architectures are described in a unified manner.

The system software is organized into three layers, arranged from bottom to top: the Hardware Driver Layer, the Real-Time Operating System (RTOS) Layer, and the Application Task Layer. At its core, the system utilizes the STM32 series microcontroller. The underlying drivers are developed using the Standard Peripheral Library, which facilitates hardware abstraction for the multi-mode communication modules and peripherals. This strategy provides unified and robust API interfaces for the higher layers. Additionally, the system integrates the μC/OS-III real-time operating system. By leveraging its preemptive kernel and efficient multi-task scheduling mechanism, the system effectively addresses the stringent requirements of the FDM-ERT instrument for synchronous data acquisition and rapid command response [53].

The Application Layer assigns task priorities according to functional modules and utilizes semaphore and message queue mechanisms to enable inter-task synchronization and communication. It primarily consists of the following five core tasks:

• System Initialization Task: This task serves as the primary stage of system startup, responsible for establishing both software and hardware environments. Specific operations include loading drivers, mounting the file system, registering the NB-IoT network, and configuring Bluetooth/Wi-Fi communication modes (Slave/Access Point modes). These actions ensure that the system transitions into a ready state.
• Command Parsing and Control Task: This task is responsible for managing multi-source heterogeneous instructions. It receives and parses control commands from Bluetooth or NB-IoT interfaces, subsequently transmitting the parsed binary commands to the hardware acquisition system through the SPI bus. To meet the requirement for 24-channel synchronous acquisition, the task automatically controls the relay array by interpreting grouping protocols, thereby facilitating automated channel switching and data acquisition.
• Data Storage and Backup Task: This task, based on the FatFs file system, implements local data persistence. The acquired raw full-waveform data are written to the SD card in real-time. Simultaneously, current data are preserved not only at the Current Station but also synchronously stored at the Acquisition Station to ensure data security.
• Communication and Concurrency Task: This task enables the transmission of raw data via Wi-Fi and employs NB-IoT to transfer processed current data between the Current Station and the Acquisition Station, as well as to upload the acquisition results to the cloud platform. Furthermore, a Mutex (Mutual Exclusion) mechanism is implemented to effectively address resource contention for the file system and communication interfaces within the multi-tasking environment, thereby ensuring the stability of data transmission.
• Edge Computing and Data Processing Task: To address the bandwidth constraints of NB-IoT, the system adopts an edge computing strategy to perform data processing locally on the embedded device. By leveraging the CMSIS-DSP library, the system executes Fast Fourier Transform (FFT) transformation, filtering, and normalization locally to directly extract the potential amplitude at specific frequency points. For the calculation of apparent resistivity, current data from the Current Station is transmitted via the cloud platform to the Acquisition Station. In local communication, the mobile application conducts real-time calculations and imaging based on user configurations. In remote communication, geometric factors are downloaded from the cloud, after which the embedded system performs calculations locally and uploads the results back to the cloud.

3.3. Cloud Platform and IoT Data Synchronization

This study constructs a cloud-based data center utilizing the Huawei Cloud Internet of Things Device Access (IoTDA) platform. The architecture is designed to address the challenges associated with centralized management of distributed heterogeneous devices and cross-regional data routing. The core design emphasizes the adaptation of low-power protocols and the collaborative transmission of data between cloud and edge.

3.3.1. Heterogeneous Protocol Adaptation and Product Modeling

Considering the bandwidth constraints and power sensitivity of the NB-IoT network, a heterogeneous protocol conversion mechanism termed “Binary-to-JSON” has been designed. On the device side, the FDM-ERT instrument utilizes binary streams for transmission to minimize communication overhead. On the cloud side, Node.js message codec plugins are deployed through FunctionGraph (Serverless function computing) to facilitate the mutual conversion between binary data and the standard JSON format. This approach not only ensures transmission efficiency at the underlying level but also promotes standardized data interaction for upper-layer applications. Based on this mechanism, an FDM-ERT Product Model (Profile) has been created, defining core attributes such as Current and Apparent Resistivity, as well as control commands like FDM-ERT-Start/Stop, as illustrated in

Table 1. Definition of cloud platform service functions.

Service Type	Name	Description	Data Type	Example Value
Property	Electricity	Current Data	String	{“Electricity”: 0.85}
Property	Resistivity	Apparent Resistivity	String	{“Resistivity”: 256.78}
Property	NumID	Group ID	String	{“NumID”: 1}
Command	FDM-ERT-Start	Start Acquisition	String	{“FDM-ERT-Start”: “START”}
Command	FDM-ERT-Stop	Stop Acquisition	String	{“FDM-ERT-Stop”: “STOP”}
Command	FDM-ERT-State	Status	String	{“FDM-ERT-State”: “NORMAL”}
Command	FDM-ERT-Config	Send Configuration	String	{“FDM-ERT-Config”: {“sampling_rate”: [250]}}

All properties are reported as String types in the Huawei Cloud IoTDA platform to accommodate the Binary-to-JSON codec. Numeric values (current and apparent resistivity) are formatted as decimal strings with units A and Ω·m, respectively. Typical ranges: electricity “0.001”–“5.000” A; resistivity “0”–“10,000” Ω·m. Commands are transmitted as predefined strings or JSON strings. For FDM-ERT-Config, the payload is a JSON object string containing structured parameters (e.g., sampling_rate as array of frequencies in Hz).

.

3.3.2. Rule-Engine-Based Data Routing

Building upon recent advances in dynamic IoT data-flow management and coordination, this subsection describes an adaptive message routing architecture based on a cloud-based rule engine and AMQP. This design enables flexible multi-node collaboration and compatibility across diverse working scenarios by dynamically adjusting data flow paths according to data types and operational modes.

To facilitate multi-node collaboration and ensure compatibility with diverse working scenarios, an adaptive message routing architecture based on a rule engine and AMQP has been constructed. This architecture dynamically adjusts data flow paths according to data types and working modes:

Cross-device Current Parameter Synchronization: To meet the demand for real-time sharing of current data, the system employs SQL filtering statements within the cloud-based rule engine. This mechanism accurately identifies specific topic messages reported by the Current Station and automatically forwards them to the embedded terminal of the Acquisition Station. Consequently, the Acquisition Station can obtain synchronized current parameters in real time, enabling it to perform apparent resistivity calculations even during distributed operations.

Differentiated Apparent Resistivity Data Distribution: A differentiated distribution scheme has been developed to satisfy the visualization requirements of the final imaging data (apparent resistivity). In local mode, current data is transmitted via the cloud to the Acquisition Station, where it is involved in the real-time processing of apparent resistivity using the Android application. The computed resistivity can subsequently be uploaded to the cloud for storage. In remote mode, the system utilizes AMQP message queues. The apparent resistivity data stored in the cloud is sent to these queues, and the Android client subscribes to the queue to retrieve data in real-time for remote monitoring.

3.4. Mobile Application and Control Terminal Design

To meet the requirements for portable measurement and control of the FDM-ERT instrument in complex field environments, a visualization host software based on the Android platform was developed [54]. The software employs a modular hierarchical architecture, serving as the core control interface that integrates command interaction, multi-source data fusion, and real-time imaging functionalities. It facilitates collaborative management of the transmitter source at the Current Station and the receiver end at the Acquisition Station.

3.4.1. Software Architecture and Collaborative Logic

Based on the functional differences in the instruments, the system constructs distinct software modules for both the Current Station and the Acquisition Station, thereby achieving a logically closed loop through the cloud platform.

• Software of Current Station: This module is dedicated to the high-precision monitoring of the transmission source current. It parses current data uploaded by Hall sensors in real-time. By analyzing the spectrum of the transmission waveform through FFT transformation, the software ensures the stability of the transmission source during concurrent multi-frequency operations.
• Software of Acquisition Station: The Software of Acquisition Station functions as the intelligent control hub of the system, facilitating seamless transitions between local and remote operational modes. Designed specifically for a six-channel distributed acquisition architecture, this software employs a multi-channel grouping scan algorithm that automatically coordinates time-division acquisition and stitching of data from 24 channels. Moreover, by integrating local potential difference data with current data synchronized from the cloud, along with electrode geometric factors, it enables real-time calculation and imaging of apparent resistivity directly on the mobile terminal.

3.4.2. Dual-Mode Heterogeneous Communication Architecture

To meet the requirements for data transmission capacity and broad coverage control in field operations, the system adopts a hybrid communication architecture integrating a “dual-mode direct connection + cloud collaboration” strategy. In the local direct-connection mode, a control–data separation scheme is implemented. Classic Bluetooth is employed to establish a low-latency command channel based on an acknowledgment-oriented mechanism to enhance transmission reliability. During continuous testing sessions lasting approximately 3 h, this channel exhibited a typical latency ranging from 50 to 200 ms and maintained stable command transmission. Meanwhile, Wi-Fi operating in access point (AP) mode maintains a persistent TCP socket connection for transmitting large volumes of raw waveform data. This Wi-Fi link also maintained a typical packet latency of 50–200 ms and demonstrated stable data transmission throughout the ~3-h testing periods. Furthermore, heartbeat monitoring and breakpoint-resumption mechanisms are incorporated to enhance data continuity during transmission interruptions.

In the remote cross-domain collaboration mode, remote measurement and control are enabled through NB-IoT connectivity and cloud platform APIs. Control commands are transmitted via HTTPS, while data streams are delivered through an AMQP-based message queuing mechanism. During the ~3-h testing sessions, the end-to-end data upload latency was typically observed to be around 5–8 s, with data being transmitted stably throughout the test period. On the Android client, a foreground service is adopted to continuously monitor the message queue, thereby reducing the risk of unintended background process termination by the operating system. The communication architecture is designed to enhance the reliability and stability of control commands and data transmission under field operating conditions.

3.4.3. Signal Processing and Visual Interaction

As a core functional module, the data-processing unit aims to extract high-precision frequency-domain features from strong noise backgrounds. The sampling rate of both instruments was fixed at 250 Hz. For each acquisition window, the Current Station processed 500 samples (corresponding to a 2 s time window), while the Acquisition Station processed 1000 samples (corresponding to a 4 s time window). The FFT window length was equal to the acquisition window length. Accordingly, the frequency resolutions were 0.5 Hz and 0.25 Hz, respectively. To suppress power-frequency interference, a digital low-pass filter with a cutoff frequency of 20 Hz was applied prior to spectral analysis. This effectively attenuates 50 Hz interference and its higher-order harmonics in the time domain. Subsequently, the JTransforms library was employed to perform a Fast Fourier Transform (FFT) on the filtered data. A Hann window was applied before FFT computation to mitigate spectral leakage. Moreover, the acquisition window lengths were deliberately selected to contain integer multiples of the fundamental operating frequencies (1–4 Hz), thereby further reducing leakage effects and improving amplitude estimation accuracy. The amplitude at each principal frequency was extracted from the corresponding spectral bin. By integrating the extracted voltage amplitude with synchronized current data, the apparent resistivity was calculated in real time. To ensure data reliability, an adaptive quality-control mechanism based on the Relative Root Mean Square Error (RRMSE) was incorporated. The RRMSE between the measured waveform and the fitted sinusoidal model was computed as:

$$RRMSE=\sqrt{{\displaystyle \frac{{\sum \left(x_i-\widehat{x_i}\right)}^2}{{\sum x_i}^2}}},$$

(7)

A threshold of 5% was adopted as the quality-control criterion. When the RRMSE exceeded this threshold, the acquisition window was discarded and re-sampling was automatically triggered. Up to 3 re-sampling attempts were permitted for each flagged window. If the RRMSE remained above the threshold after 3 attempts, the measurement point was flagged as anomalous and excluded from further processing.

To quantify inter-channel cross-talk, a leakage ratio (in dB) was defined as the amplitude ratio between non-target and target frequency components:

$$Leakage Ratio=20 {\log }_{10}\left({\displaystyle \frac{A_{non-target}}{A_{target}}}\right),$$

(8)

where A_target and A_non-target denote the amplitudes at the principal and selected non-target frequencies, respectively. This ratio was calculated from the post-processed FFT spectra in both laboratory and field settings.

In terms of interaction design, the software interface deeply integrates the requirements of on-site data quality monitoring by adopting a split-screen rendering strategy, as shown in Figure 4. The upper time-domain monitoring panel dynamically plots the raw waveforms of six acquisition channels, assisting technicians in evaluating the signal-to-noise ratio (SNR). Meanwhile, the lower frequency-domain visualization panel continuously updates the calculated current results, along with the apparent resistivity curves at different frequency points and the corresponding relative error tables in real time. This joint time–frequency real-time visualization mechanism effectively converts low-level data streams into intuitive graphical representations, thereby providing a reliable basis for rapid field configuration adjustments and on-site data quality assessment.

To further clarify the methodological novelty and technical positioning of the proposed FDM-ERT system, a comparison with representative commercial instruments is provided below.

Table 2. Comparison of key technical features between the proposed ERT system and FDM-ERT.

Feature	FDM-ERT	ABEM Terrameter LS	IRIS Syscal Pro
Concurrent Frequencies	Up to 3	Single-frequency	Single-frequency
Data Communication	Wi-Fi, NB-IoT	Wi-Fi, Ethernet, USB	USB, Wi-Fi
Control Platform	Mobile App via Wireless Connection (Wi-Fi/Bluetooth)	Embedded Industrial PC (Touchscreen)	On-board Microprocessor Console

contrasts the key technical features of the developed system with the ABEM Terrameter LS and IRIS Syscal Pro, highlighting the shift from traditional single-frequency acquisition to frequency-division multiplexing. Furthermore,

Table 3. Comparison of key electrical parameters between the proposed ERT system and FDM-ERT.

Parameter	FDM-ERT	ABEM Terrameter LS	IRIS Syscal Pro
Injected Current Magnitude Range (A)	0.001–5	Up to 2.5	0–2.5
Voltage Compliance/Withstand (V)	2500 VAC@50 Hz &1 min	Up to ± 600	800 V (switch mode)/1000 V (manual mode);
Receiver Noise Floor (equivalent input-referred RMS)	Average 0.563 μV	3 nV (theoretical @ 1 s)	Not explicitly stated; resolution 1 μV, accuracy 0.2%
Dynamic Range (dB)	Average 129.4	Not explicitly specified (24-bit ADC)	Not explicitly specified (24-bit ADC)

Data are sourced from publicly available manufacturer datasheets [32,55].

summarizes the key electrical performance metrics of the FDM-ERT system, using the ABEM Terrameter LS and IRIS Syscal Pro as benchmarks. While the primary objective of this work is to validate the feasibility of the frequency-division multiplexing approach, these comparisons demonstrate that the developed instrument maintains high internal consistency and competitive performance in core parameters such as dynamic range and noise floor. It should be noted that certain high-power operation metrics may differ from dedicated commercial systems as the current design focuses on the validation of the FDM architecture

4. Performance Evaluation and Field Experiments

4.1. Laboratory Testing and Functional Verification

To validate the practical performance of the system, a simulation test platform was established in the laboratory. Tests were conducted to assess the transmission monitoring accuracy of the Current Station, the multi-channel consistency of the Acquisition Station, and the reliability of cloud data transmission.

4.1.1. Current Station Signal Monitoring

A high-precision signal generator was utilized to simulate the transmission source, producing sine wave signals with varying frequencies (1 Hz–4 Hz) and amplitudes (1 Vpp–3 Vpp), which were subsequently fed into the input terminal of the Current Station (as illustrated in Figure 5). The test results are depicted in Figure 6 and

Table 4. Error table of Current Station signal test results.

Figure No.	Measured Value (mV)	Theoretical Value (mV)	Error (%)
a	1494.09	1500	0.39
	1493.03	1500	0.46
	1494.56	1500	0.36
b	995.46	1000	0.46
	994.74	1000	0.53
	995.36	1000	0.46
c	499.93	500	0.014
	499.57	500	0.086
	500.08	500	0.016

(sampling rate: 250 Hz). Taking the 1 Hz signal as an example, the waveform generated by the software displays continuous phase with zero packet loss, while the FFT spectrum analysis accurately identifies the dominant frequency component. These tests demonstrate that the software can respond swiftly to dynamically changing input signals and accurately demodulate both amplitude and frequency information, thereby fulfilling the requirements for real-time high-precision monitoring of the transmission source.

To further evaluate the robustness of the proposed system under practical interference conditions, controlled interference experiments were conducted. In addition to the fundamental sinusoidal signal, either a 50 Hz sinusoidal interference or broadband noise with specified amplitudes was injected at the input terminal. The system performance was quantitatively assessed in the demodulation domain using the Signal-to-Noise Ratio (SNR), defined as the ratio of the root-mean-square (RMS) amplitude of the signal component extracted at the target frequency to that of the residual noise:

$${SNR}_{dB}=20 {\log }_{10}\left({\displaystyle \frac{A_{signal,rms}}{A_{noise,rms}}}\right),$$

(9)

where $A_{signal,rms}$ is the RMS amplitude extracted directly from the spectral peak at the operating frequency $f_0$. $A_{noise,rms}$ is calculated as the RMS value of the residual sequence, which is obtained by subtracting the extracted signal component (a sinusoid generated using the measured amplitude and phase at $f_0$) from the data record. Performance was evaluated both before and after the 20 Hz low-pass filter to determine the $SNR$ improvement ($∆SNR$). Furthermore, the leakage ratio was evaluated to verify the system’s frequency selectivity, ensuring that the signal amplitude at $f_0$ is accurately resolved without being biased by out-of-band interference. Each condition was repeated over 10 independent acquisition windows, and the results are reported as mean ± 95% confidence intervals. The results of the interference experiments are summarized in

Table 5. Quantitative controlled-interference validation for the Current Station (n = 10 windows per condition). Values are mean ± 95% CI.

Frequency (Hz)	Level (Vpp)	Interference Type	Level (Vpp)	SNR_Before (dB)	SNR_After (dB)	ΔSNR (dB)	Error (%)
1	2	50 Hz	0.5	12.08 ± 0.00	42.77 ± 2.08	30.69 ± 0.78	0.27 ± 0.01
			1.0	5.94 ± 0.00	35.82 ± 1.98	29.88 ± 1.98	0.65 ± 0.01
			1.5	2.46 ± 0.00	31.36 ± 1.89	28.90 ± 1.89	0.64 ± 0.01
2	2	50 Hz	0.5	12.07 ± 0.00	38.50 ± 0.30	26.43 ± 0.30	1.77 ± 0.01
			1.0	5.94 ± 0.00	34.78 ± 1.52	28.84 ± 1.52	2.18 ± 0.00
			1.5	2.46 ± 0.00	31.26 ± 1.66	28.80 ± 1.66	2.20 ± 0.00
4	2	50 Hz	0.5	12.07 ± 0.00	39.96 ± 1.27	27.89 ± 1.27	1.86 ± 0.00
			1.0	5.94 ± 0.00	35.30 ± 1.85	29.36 ± 1.85	2.25 ± 0.00
			1.5	2.45 ± 0.00	33.20 ± 1.95	30.75 ± 1.95	2.16 ± 0.01
1	2	Noise	0.5	43.71 ± 0.03	43.73 ± 0.04	0.02 ± 0.01	0.27 ± 0.01
			1.0	39.89 ± 0.03	39.92 ± 0.03	0.03 ± 0.04	0.65 ± 0.00
			1.5	38.52 ± 0.06	38.58 ± 0.06	0.06 ± 0.00	0.65 ± 0.01
2	2	Noise	0.5	46.47 ± 0.04	46.45 ± 0.05	−0.02 ± 0.07	0.28 ± 0.00
			1.0	40.09 ± 0.04	40.12 ± 0.04	0.03 ± 0.00	0.66 ± 0.00
			1.5	39.71 ± 0.05	39.78 ± 0.05	0.07 ± 0.00	0.66 ± 0.01
4	2	Noise	0.5	47.91 ± 0.04	47.58 ± 0.12	−0.32 ± 0.08	0.30 ± 0.00
			1.0	41.38 ± 0.05	41.34 ± 0.06	−0.04 ± 0.01	0.63 ± 0.00
			1.5	41.28 ± 0.06	41.31 ± 0.05	0.03 ± 0.00	0.65 ± 0.00

SNR is computed in the demodulation domain. $A_{signal,rms}$ is the amplitude extracted from the spectral peak at $f_0$, while the noise component $A_{noise,rms}$ is derived from the residual sequence after subtracting the extracted signal component from the time-domain record. $∆SNR$ denotes the difference in $SNR$ values obtained after and before the 20 Hz filtering. Demodulation error represents the relative amplitude deviation referenced to the no-interference baseline.

and

Table 6. Leakage ratio and amplitude stability in controlled indoor interference tests for the Current Station (sine-wave excitation, representative values for 4 Hz, 2 Vpp excitation).

Parameter	Before Filtering (Mean ± 95% CI)	After Filtering (Mean ± 95% CI)
Amplitude at principal frequency (4 Hz, V)	0.9784 ± 0.0001	0.9784 ± 0.0001
Leakage ratio at 1 Hz (dB)	−84.49 ± 1.32	−84.53 ± 1.39
Leakage ratio at 2 Hz (dB)	−77.28 ± 0.36	−77.28 ± 0.40
Leakage ratio at 50 Hz (dB)	−2.45 ± 0.00	−74.76 ± 0.01
Leakage ratio at 100 Hz (dB)	−79.05 ± 0.12	−148.70 ± 5.83
Average leakage (non-principal bins, dB)	−44.11 ± 0.00	−78.15 ± 0.06

All values are derived from the post-processed FFT spectra (Hann window applied). Leakage ratio = 20 log₁₀ (A_non-target/A_target), where A_target is the amplitude at 4 Hz and A_non-target is at selected non-target frequencies. Average leakage excludes ±1 bin around the principal frequency. Sine-wave excitation was employed in these controlled indoor interference tests, with an additional 1.5 Vpp 50 Hz sine-wave interference signal superimposed at the input to isolate and evaluate the system’s robustness against monochromatic power-frequency noise.

.

4.1.2. Multi-Channel Acquisition Accuracy

To validate the consistency of the 24-channel acquisition system and the accuracy of the apparent resistivity calculations, a simulated geoelectric model was constructed using six 1 KΩ resistors with 0.1% precision. A signal generator was employed to inject sinusoidal excitation, and the electrode positions were systematically rotated in groups to complete a full-channel scan, as illustrated in Figure 7.

The test interface (Figure 8) employs a split-screen display, with the upper panel presenting raw waveforms and the lower panel showcasing real-time calculated apparent resistivity. Taking Figure 8a (1 Hz, 2 Vpp input) as an example, the software-measured single-channel voltage amplitude is approximately 167 mV, which aligns closely with the theoretical value derived from the voltage divider principle (

Table 7. Error table of Acquisition Station signal test results.

Figure No.	Measured Voltage (mV)	Theoretical Voltage (mV)	Error (%)	Measured Apparent Resistivity (Ω·m)	Theoretical Apparent Resistivity (Ω·m)	Error (%)
a	166.22	166.67	0.27	524,069.4	527,787.6	0.70
	164.80	166.67	1.12	501,320.6	509,268.7	1.56
	165.23	166.67	0.86	467,767.7	473,931.7	1.30
	165.38	166.67	0.77	419,721.3	424,896.1	1.21
	165.33	166.67	0.80	361,638.1	366,219.9	1.25
	165.96	166.67	0.42	299,704.7	302,350.7	0.88
b	330.43	333.33	0.87	236,596.5	237,629.5	0.43
	327.58	333.33	1.73	173,653.2	175,929.2	1.29
	328.46	333.33	1.46	119,206.1	120,449.4	1.03
	328.73	333.33	1.38	72,952.2	73,651.5	0.95
	328.62	333.33	1.41	36,927.1	37,293.7	0.98
	329.87	333.33	1.04	12,448.6	12,524.6	0.61
c	410.29	416.67	1.53	523,100.2	527,787.6	0.89
	406.75	416.67	2.38	500,394.4	509,268.7	1.74
	407.83	416.67	2.12	466,905.4	473,931.7	1.48
	408.18	416.67	2.03	418,947.3	424,896.1	1.40
	408.04	416.67	2.07	360,964.5	366,219.9	1.43
	409.60	416.67	1.70	299,152.8	302,350.7	1.06
d	490.94	500	1.81	235,335.5	237,629.5	0.96
	486.71	500	2.66	172,727.0	175,929.2	1.82
	488.01	500	2.40	118,570.2	120,449.4	1.56
	488.41	500	2.32	72,563.2	73,651.5	1.47
	488.25	500	2.35	36,729.2	37,293.7	1.51
	490.14	500	1.97	12,382.5	12,524.6	1.13

). In terms of apparent resistivity calculation, the equivalent grounding resistance, back-calculated from the apparent resistivity ρ_s (obtained using the preset geometric factor K and the specified current value), corresponds to the actual resistance of 1 KΩ. By integrating test results across various frequency points, the relative errors of measurement data for all channels are maintained within an acceptable range, thereby confirming the high Signal-to-Noise Ratio (SNR) of the underlying hardware acquisition and the accuracy of the upper-layer software calculation logic.

Similarly, the acquisition station was subjected to the same controlled interference experiments. At each operating frequency (1–4 Hz), the fundamental sinusoidal signal was combined with either a 50 Hz sinusoidal interference or broadband noise of specified amplitudes. The instrument performance was quantitatively evaluated in terms of the demodulation-domain signal-to-noise ratio (SNR) before and after the 20 Hz low-pass filter, as well as the corresponding relative demodulation error. Furthermore, the leakage ratio was characterized to verify the system’s frequency selectivity, ensuring that the resolved signal amplitude at $f_0$ remains immune to out-of-band interference. Each condition was repeated over 10 independent acquisition windows, and the results are presented as mean ± 95% confidence intervals. The results of the interference experiments are summarized in

Table 8. Quantitative controlled-interference validation for the Acquisition Station (n = 10 windows per condition). Values are mean ± 95% CI.

Frequency (Hz)	Level (Vpp)	Interference Type	Level (Vpp)	SNR_Before (dB)	SNR_After (dB)	ΔSNR (dB)	Error (%)
1	2	50 Hz	0.5	12.54 ± 0.00	46.56 ± 0.95	34.02 ± 0.95	0.32 ± 0.04
			1.0	5.04 ± 0.00	37.16 ± 0.69	32.12 ± 0.69	0.82 ± 0.08
			1.5	1.56 ± 0.00	35.77 ± 1.00	34.21 ± 1.00	0.82 ± 0.08
2	2	50 Hz	0.5	12.53 ± 0.00	46.42 ± 1.01	33.89 ± 1.01	1.59 ± 0.08
			1.0	5.04 ± 0.00	38.60 ± 0.78	33.56 ± 0.78	1.77 ± 0.08
			1.5	1.56 ± 0.00	34.56 ± 0.95	33.00 ± 0.25	1.77 ± 0.08
4	2	50 Hz	0.5	12.53 ± 0.00	45.65 ± 1.04	33.11 ± 1.04	2.08 ± 0.08
			1.0	5.04 ± 0.00	38.95 ± 0.58	33.92 ± 0.58	2.26 ± 0.08
			1.5	1.55 ± 0.00	35.65 ± 0.92	34.10 ± 0.92	2.26 ± 0.08
1	2	Noise	0.5	60.84 ± 0.27	61.92 ± 0.33	1.08 ± 0.07	0.32 ± 0.04
			1.0	42.73 ± 0.04	42.82 ± 0.04	0.09 ± 0.00	0.41 ± 0.06
			1.5	43.46 ± 0.05	43.70 ± 0.05	0.23 ± 0.00	0.41 ± 0.06
2	2	Noise	0.5	51.13 ± 0.50	51.19 ± 0.50	0.06 ± 0.02	0.29 ± 0.04
			1.0	41.82 ± 0.04	41.88 ± 0.04	0.06 ± 0.01	0.39 ± 0.06
			1.5	42.95 ± 0.05	43.16 ± 0.05	0.20 ± 0.01	0.41 ± 0.06
4	2	Noise	0.5	33.78 ± 0.08	33.76 ± 0.08	−0.01 ± 0.01	0.33 ± 0.05
			1.0	42.59 ± 0.04	42.61 ± 0.04	0.02 ± 0.01	0.42 ± 0.06
			1.5	43.35 ± 0.04	43.48 ± 0.05	0.13 ± 0.01	0.43 ± 0.06

Values are reported as mean ± 95% confidence intervals (n = 10). The definitions of SNR and demodulation error are identical to those described in Table 5.

and

Table 9. Leakage ratio and amplitude stability in controlled indoor interference tests for the Acquisition Station (sine-wave excitation, representative values for 4 Hz, 2 Vpp excitation).

Parameter	Before Filtering (Mean ± 95% CI)	After Filtering (Mean ± 95% CI)
Amplitude at principal frequency (4 Hz, V)	0.1660 ± 0.0005	0.1660 ± 0.0005
Leakage ratio at 1 Hz (dB)	−104.5 ± 2.0	−104.5 ± 2.0
Leakage ratio at 2 Hz (dB)	−96.0 ± 1.5	−96.0 ± 1.5
Leakage ratio at 50 Hz (dB)	−1.55 ± 0.01	−73.84 ± 0.01
Leakage ratio at 100 Hz (dB)	−83.0 ± 0.5	−170.0 ± 10.0
Average leakage (non-principal bins, dB)	−49.37 ± 0.01	−89.80 ± 0.30

Values derived from the same dataset and processing method as Table 6.

.

Although controlled laboratory experiments provide quantitative evidence for the system’s signal separation capabilities, applying these results to complex field environments is necessary to demonstrate the real-world robustness of the proposed methodology.

First, regarding heterogeneous subsurface structures, complex geological conditions significantly attenuate signals and alter phases; however, they essentially act only as a passive resistor–capacitor (RC) network and do not generate new frequency components. Although hardware limitations and polarization effects may introduce harmonics, our selected operating frequencies (1 Hz, 2 Hz, and 4 Hz) ensure that their fundamental harmonics do not overlap. While some low-frequency harmonics may pass through the 20 Hz low-pass filter, the subsequent Fast Fourier Transform (FFT) algorithm can mathematically isolate them into orthogonal frequency bins.

Second, field environments inevitably introduce unpredictable, non-stationary noise sources (e.g., industrial stray currents). The system’s 20 Hz low-pass filter suppresses high-frequency interference (such as typical 50 Hz power-line interference). Furthermore, the narrow-band FFT extraction method also acts as a highly selective filter, rejecting the vast majority of broadband non-stationary noise energy that falls outside our narrow target frequency ranges. In practical field operations, when encountering elevated environmental noise, the signal-to-noise ratio (SNR) can be effectively improved by appropriately increasing the transmission power within the system’s hardware limits, thereby helping to maintain data reliability.

4.1.3. Cloud Collaboration and Data Flow Verification

End-to-end testing was conducted on the core component of “cross-device current data synchronization” (refer to Figure 9). The results of the tests indicate that the system successfully executed data transmission. Raw data, sampled at the full rate, is transmitted in real-time to the Current Station App via Wi-Fi. After the Current Station App completes its calculations, key current parameters (frequency and amplitude) are uploaded to Huawei Cloud using NB-IoT, effectively triggering the rule engine and accurately forwarding the data to the embedded system of the target Acquisition Station. Figure 9c demonstrates that the Acquisition Station successfully received and parsed the current packets forwarded from the cloud, established a local parameter buffer, and ensured that precise current data was matched during the apparent resistivity calculation, thereby validating the reliability of data flow within the distributed architecture.

4.2. Field Experiments and Validation

To further validate the operational stability of the measurement and control system in real geological environments and to quantitatively evaluate the effectiveness of the FDM-ERT in actual exploration, field experiments were conducted in a forested area along the Xiangjiang River in Changsha, Hunan Province. This site, characterized by dense vegetation coverage and relatively complex surface grounding conditions, is located adjacent to an urban trail with nearby river embankment infrastructure, street lighting, and residential buildings approximately 200 m away. This semi-urban fringe setting introduces some level of cultural electromagnetic noise and spatial considerations, although not as severe as in fully urbanized areas with dense buried utilities or high-voltage power infrastructure. The experiments effectively assessed the system’s signal acquisition performance, environmental adaptability, and internal consistency between operating modes under these representative non-ideal conditions.

4.2.1. Experimental Setup and Device Deployment

To assess the system’s suitability for long-term field deployment, power consumption was measured using a regulated 5 V DC supply (see Figure 10). The Current Station consumes approximately 2.07 W (5 V × 0.414 A) during active acquisition, while each Acquisition Station consumes 1.61 W (5 V × 0.322 A). Each module is independently powered by a 10000 mAh portable power bank with a rated energy of 34.49 Wh. Accounting for typical DC-DC conversion efficiency (~85%), a single power bank can support the Current Station for approximately 14–15 h and the Acquisition Station for approximately 18–19 h. These power consumption levels basically meet the requirements for medium-term field geophysical exploration using portable power banks.

A multiple middle gradient observation system was utilized for this experiment. By leveraging the transmitter’s capability for simultaneous emission across three mutually independent channels, the setup incorporated three pairs of supply electrodes, spaced 20 m apart between ipsilateral supply electrodes. Each of the three signal channels of the transmitter was powered by independent AC-DC rectifier power supplies. The spacing between the measurement electrodes was established at 1 m. Figure 11 illustrates the schematic diagram of the field experimental observation system.

Despite the constraints imposed by site conditions, a minimum test unit was constructed by deploying one Current Station and two Acquisition Station, as illustrated in Figure 12. During the testing period, the system established a stable wireless communication link, and the Current Station operated seamlessly in conjunction with the Acquisition Station. In the complex electromagnetic environment of the woodland, the instrument successfully executed the concurrent emission of multi-frequency square wave signals, data transmission, and real-time imaging. This performance underscores the system’s adaptability and stability during prolonged operation.

4.2.2. Multi-Mode Comparison and Data Consistency Analysis

This experiment focuses on validating the data consistency between the ‘multi-frequency concurrent’ and ‘single-frequency time-division’ acquisition modes. The aim is to demonstrate that the FDM-ERT enhances efficiency without compromising measurement accuracy.

In single-frequency time-division, only the AC-DC rectified power supply for the corresponding channel needs to be turned on. Subsequently, parameters including the transmitter electrode coordinates, receiver electrode coordinates, and sampling rate are set in the application on the acquisition station and current station, after which data acquisition can commence. In multi-frequency concurrent mode, the AC-DC rectified power supplies for all three channels are activated simultaneously, with the remaining parameter settings following the same procedure.

To robustly evaluate the acquisition efficiency, multiple repeated tests were conducted under strictly identical field conditions for both the multi-frequency concurrent mode and the single-frequency time-division mode of the FDM-ERT system. These conditions included the same electrode array configurations, equivalent grounding resistances, consistent network environment, and unchanged AC-DC power supply currents. Working times were manually recorded for each test (with precise timestamps also available from the saved data files), starting immediately upon issuance of the acquisition command via the application software and ending upon successful receipt of the complete dataset. Aggregating data from 10 independent runs for single-frequency time-division and 10 runs for multi-frequency concurrent modes, the average duration of a single measurement operation was 5 min, with an observed fluctuation range of 1–2 min. This minor variability was primarily attributable to occasional resampling events.

As shown in

Table 10. Comparison of Work Efficiency between Single-Frequency Time-Division and Multi-Frequency Concurrent Modes.

Acquisition Modes	Work Frequency (Hz)	Number of Emissions (Times)	Number of Electrode Reconfigurations (Times)	Average Working Time (min)	Notes
single-frequency time-division	1, 2, 4	3	3	15–18	Based on 10 independent runs; actual per-frequency ≈ 5–6 min, total range ≈ 15–18 min
multi-frequency concurrent	1, 2, 4	1	1	5–6	Based on 10 independent runs; actual range 5–6 min

Table values represent average working times derived from multiple tests under identical conditions.

, in the single-frequency time-division mode, the typical working time to complete measurements for the three frequencies (1, 2, and 4 Hz) is 15–18 min (approximately 5–6 min per frequency). In contrast, the multi-frequency concurrent mode enables simultaneous probing of the three frequencies within 5–6 min, yielding apparent resistivity data corresponding to three different exploration depths and thereby substantially improving work efficiency. These working times are derived from statistical analysis of 10 independent runs per mode under identical field conditions, with an average single-operation duration of approximately 5 min and an observed fluctuation range of 1–2 min. This minor variability is primarily attributable to occasional resampling events. Overall, the multi-frequency concurrent mode achieves an efficiency improvement of approximately 2.5–3.6× (approaching 3× in optimal cases).

Apparent resistivity consistency analysis: The experiment collected three-frequency mixed waveform data (1 Hz, 2 Hz, and 4 Hz) in FDM-ERT mode, as well as single-frequency waveform data at the corresponding frequency points in single-frequency time-division mode. The statistical results are illustrated in Figure 13. A comparison of the apparent resistivity curves obtained from the two modes indicates that, at the 1 Hz, 2 Hz, and 4 Hz frequency points, the relative errors between the apparent resistivity measured in multi-frequency concurrent mode and the single-frequency benchmark values remain strictly within 5%. The shapes of the curves exhibit a high degree of coincidence, with no significant spectral aliasing or intermodulation interference detected. This observation demonstrates that the system maintains excellent spectral isolation between frequency channels, and the embedded FFT algorithm effectively extracts dominant frequency components from mixed signals.

To further verify the impact of harmonics on the amplitude of principal frequencies under multi-frequency square-wave excitation and to evaluate the filtering effect, we calculated the leakage ratio as a metric for cross-talk interference.

Table 11. Leakage ratio and amplitude stability in field tests for the Current Station (multi-frequency square-wave excitation, representative values for 4 Hz component).

Parameter	Before Filtering (Mean ± 95% CI)	After Filtering (Mean ± 95% CI)
Amplitude at principal frequency (4 Hz, V)	0.0045 ± 0.0016	0.0045 ± 0.0016
Leakage ratio at 50 Hz (dB)	−43.93 ± 4.66	−115.87 ± 5.71
Leakage ratio at 100 Hz (dB)	−50.14 ± 3.45	−144.58 ± 2.49
Average leakage (non-principal bins, dB)	−35.09 ± 1.48	−39.89 ± 2.06

Values derived from the same dataset and processing method as previous tables. Multi-frequency square-wave excitation (1 Hz + 2 Hz + 4 Hz simultaneous) in field conditions with strong low-frequency environmental noise. Amplitude and leakage values reported for the 4 Hz component only.

and

Table 12. Leakage ratio and amplitude stability in field tests for the Acquisition Station (multi-frequency square-wave excitation, representative values for 4 Hz component).

Parameter	Before Filtering (Mean ± 95% CI)	After Filtering (Mean ± 95% CI)
Amplitude at principal frequency (4 Hz, V)	0.0042 ± 0.0004	0.0042 ± 0.0004
Leakage ratio at 50 Hz (dB)	−29.22 ± 3.92	−101.46 ± 3.91
Leakage ratio at 100 Hz (dB)	−37.29 ± 2.44	−165.39 ± 2.77
Average leakage (non-principal bins, dB)	−38.39 ± 1.15	−42.07 ± 1.53

Values derived from the same dataset and processing method as Table 11.

present the amplitude stability at the 4 Hz component and the leakage ratios before and after filtering for the Current Station and Acquisition Station, respectively, based on field tests with simultaneous 1 + 2 + 4 Hz emission. The results show no significant change in the 4 Hz amplitude before and after filtering, indicating that harmonics do not produce measurable influence on the target frequencies. Meanwhile, interference at 50 Hz and 100 Hz was effectively suppressed, confirming the effectiveness of the filter.

Verification of inversion imaging results: To further validate the consistency of geological interpretation, the ZondRes2D software (version 6.1) was employed to conduct inversion processing on the apparent resistivity data from both modes [56,57], resulting in inversion RMS errors of 1.3% and 1.4%, respectively. The final inversion results were visualized using Surfer software (version 21.1.158), as illustrated in Figure 14. A comparison of Figure 14a,b demonstrates that the geoelectric structure morphology derived from multi-frequency data closely aligns with that obtained from single-frequency data, effectively delineating the electrical distribution characteristics of the subsurface media.

4.2.3. Experimental Conclusions

Field test results indicate that the FDM-ERT technical approach adopted by this system is practically feasible. The instrument can simultaneously acquire apparent resistivity information at various depths through a single current emission, with measurement results demonstrating high consistency with those obtained from the single-frequency time-division mode. This suggests that, while maintaining exploration accuracy, the proposed method significantly reduces the necessity for repetitive electrodes deployment and the number of emissions, thereby greatly enhancing the efficiency of field data acquisition.

5. Conclusions

To address challenges such as low efficiency, weak anti-interference capability in ERT exploration within complex urban environments, this paper develops a distributed FDM-ERT measurement and control system based on the NB-IoT architecture. This study thoroughly integrates embedded control (STM32), mobile computing (Android), and heterogeneous wireless communication technologies, achieving a seamless link from bottom-layer data acquisition to top-layer collaborative imaging. The main research results and conclusions are as follows:

• We developed a collaborative distributed architecture termed ‘Device-Edge-Cloud’. The innovative integration of NB-IoT technology establishes a wide-area data link between current stations and acquisition stations, facilitating cross-device transmission and fusion of emission current data. This approach effectively addresses critical limitations of traditional distributed instruments, specifically cumbersome wiring, synchronization challenges, and inaccuracies in current calculations, thereby significantly enhancing the system’s deployment flexibility and operational coverage.
• We implemented an efficient strategy for FDM-ERT acquisition and real-time imaging. By leveraging STM32-based control logic and Android-based FFT signal processing algorithms, we successfully achieved the concurrent acquisition and demodulation of multi-channel orthogonal frequency signals. The system is characterized by its ‘single layout, multi-depth detection’ capability, which significantly enhances the efficiency of field data acquisition.
• The reliability and field applicability of the system have been thoroughly verified. Laboratory tests and field experiments confirmed the system’s stability under both Bluetooth/Wi-Fi near-field control and cloud-based modes. A comparative analysis revealed that the apparent resistivity measurement results obtained from the multi-frequency concurrent mode were highly consistent with those from the single-frequency time-division mode, with relative errors meticulously controlled within 5%. Furthermore, the inversion process achieved a high fitting precision (RMS = 1.3%), resulting in clear and reliable apparent resistivity imaging. By significantly enhancing acquisition efficiency while maintaining necessary precision, this portable system provides a practical and intelligent foundation for future urban shallow geophysical exploration.

Based on the aforementioned research findings, future work can focus on optimizing and expanding the instrument system from the following aspects. Firstly, regarding acquisition capability, the number of concurrent frequencies in the acquisition stations can be further increased by expanding the channel count to six. This will enable the capture of richer multi-frequency geoelectric field information, thereby enhancing the resolution capability for complex geological structures. Secondly, in terms of exploration efficiency, plans involve deploying multiple additional acquisition stations for collaborative network acquisition. By arranging these stations in a dense array, the coverage area of a single deployment can be expanded, significantly improving the efficiency of field data collection. Thirdly, concerning data transmission, to overcome the narrow bandwidth constraints of NB-IoT, the system will adopt an edge computing architecture. Only pre-processed characteristic data (compressed to the order of Kb) will be transmitted, ensuring the feasibility of data backhaul for a massive number of nodes over Low-Power Wide-Area Networks (LPWANs). Finally, with regard to time synchronization, future instrument improvements will integrate high-precision GPS/BeiDou timing modules. This will resolve the sub-microsecond-level time synchronization challenges among distributed multi-station setups, laying the foundation for subsequent high-resolution array data processing. Building upon the preliminary validation results presented in this paper, subsequent research will involve field trials in urban exploration environments to progressively evaluate and refine the system’s adaptability and performance under complex real-world conditions.