Multi-electrode resistivity method is an electrical exploration technique based on resistivity differences between subsurface media. It studies the distribution patterns of conductive currents under artificially applied steady-state electric fields.

The method’s defining feature is deploying tens to hundreds of electrodes along a survey line simultaneously. Automated acquisition systems measure potential values between measurement electrodes and current values in circuits using predefined array configurations (Dong and Wang, 2003).

Electrode spacing is adjustable based on detection requirements. Extensive data acquisition ensures sufficient geoelectric information for inversion imaging. In field operations, current is transmitted between surface electrodes (A, B), while potentials are measured between electrodes (M, N). The apparent resistivity formula (Equation 1) for subsurface media is: ρ s = k ∆ V I (1)

In the formula, ρ s denotes apparent resistivity (unit: Ω·m); ∆ V represents the potential difference between points M and N (unit: V); I indicates the loop current intensity (unit: A); and k , the geometric factor, is defined as k = 2 π 1 A M − 1 A N − 1 B M + 1 B N .

In practical operations, various electrode configurations may be employed. Taking the Wenner array as an example: Electrodes A, M, N, and B are deployed sequentially along the survey line with equal spacing n. After each measurement cycle, all electrodes advance simultaneously to the next station until Electrode B reaches the terminus of the line. The electrode spacing n is then incrementally modified, and the procedure repeats. Systematic increases in n facilitate the mapping of apparent resistivity ( ρ s ) profiles at progressively greater depths beneath the survey line (Figure 1) (Li, 2005).

Field-acquired resistivity data typically represents apparent resistivity, which requires processing to reveal subsurface geology and enable geological interpretation.

(1) Data Transfer and Format Conversion: Field data stored in the instrument console are transferred to a computer and converted into. dat format compatible with processing software using dedicated utilities.

As tabulated in Table 1, compact limestone and dolomite demonstrate resistivities reaching 6,000 Ω m, contrasting markedly with water-saturated silty sands (<100 Ω m) and karstic groundwater (<30 Ω m), while air-filled cavities exhibit near-infinite resistivity values. This pronounced electrical contrast fundamentally enables karst cavity detection ‌through multi-electrode resistivity method.

Illustrating with a multi-electrode resistivity method survey for karst exploration in Hunan, China (Figure 2), three prospective karst zones (A1–A3) were delineated: Zones A1 and A3 exhibiting low-resistivity anomalies indicative of water-filled cavities, while Zone A2 displayed high-resistivity signatures characteristic of air-filled cavities. Subsequent drilling operations comprising eight boreholes confirmed water-filled cavities in Borehole K3 (elev. 314–347 m), K4 (elev. 315–353 m), and K6 (elev. 325–348 m), with an air-filled cavity intercepted in K7 (elev. 298–300 m). No karst features were encountered in other boreholes.

Borehole validation demonstrates that anomalies A1 and A3 accurately predict water-filled cavities, whereas anomaly A2 yields no karst cavity—confirming multi-electrode resistivity method exhibits higher reliability in detecting water-filled cavities. Low-resistivity anomalies serve as robust indicators for filled-karst features. ‌Notably‌, despite the significant resistivity contrast between air (theoretically infinite) and competent bedrock (e.g., limestone/dolomite), multi-electrode resistivity method possesses inherent limitations: its greater sensitivity to conductive targets complicates definitive identification of small air-filled cavities, primarily due to resolution constraints and signal attenuation effects.

The fundamental principle of cross-borehole computed tomography technique lies in reconstructing an object through layer-by-layer tomographic imaging. For a cross-sectional image slice of the object, defined as a function of two spatial variables x , y , this image function is designated as f x , y . When the object is illuminated by incident waves from varying directions, the measured wavefield data—constituted as a function of at least two variables: incident wave direction θ and observation point position ρ —is termed the projection function, denoted u ρ , θ . In 1917, Austrian mathematician Johann Radon rigorously established that knowledge of the projection function u ρ , θ across all incident angles θ permits the unique reconstruction of the image function f x , y . This mathematical theorem, now recognized as the Radon transform, constitutes the theoretical foundation of tomographic imaging methodologies. The attenuation amplitude transfer equation (Equation 2) for electromagnetic waves in lossy media can be expressed as (Yue, 2007; Liu et al., 2014): E = E 0 · e − ∫ R β r d r R · f (2)

In the formula, E 0 is the initial field strength at the transmission point (unit: V/m); R denotes the distance between the transmission and reception points (unit: m); f represents the directionality factor; β stands for the absorption coefficient of the medium in the detection region (unit: Nper/m); and E corresponds to the measured field strength at the reception point (unit: V/m).

(1) Field Data Acquisition: Electromagnetic wave field amplitude values are acquired, with excitation and receiver coordinates for each ray path calculated based on surveyed positional data.

As tabulated in Table 1, compact limestone and dolomite exhibit electromagnetic wave attenuation coefficients below 0.2Nper/m, contrasting markedly with air-filled cavities (0.01Nper/m), water-saturated silty sands (>0.4Nper/m) and karstic groundwater (>0.5Nper/m). This pronounced electromagnetic wave attenuation contrast fundamentally enables karst cavity detection through cross-borehole electromagnetic wave computed tomography.

Figure 3 illustrates the electromagnetic wave tomography results from a karst exploration in Hubei, China, where the profile exhibits strong electromagnetic wave attenuation in the upper section due to overburden effects, contrasting with low-attenuation bedrock zones in the lower section. Within this competent bedrock, three high-attenuation anomalies (B1–B3) were identified as potential karst features. Borehole validation confirmed cavities at all anomaly locations: B1 corresponds to an air-filled cavity, B2 to an argillaceous semi-filled cavity, and B3 to a water-filled cavity. Analysis reveals that anomalies B2 and B3 reflect highly attenuative fill materials, with B3’s elevated absorption coefficient relative to B2 being consistent with the greater electromagnetic wave absorption of karstic groundwater versus water-saturated silty sands. Paradoxically, despite air’s intrinsically low absorption coefficient, anomaly B1 exhibits strong attenuation attributable to multiple internal electromagnetic wave reflections within the air-filled cavity that dissipate wave energy. This case demonstrates that cross-borehole electromagnetic wave tomography effectively discriminates cavities with distinct infill conditions (air/water/sediment) through their characteristic attenuation signatures.

Microtremors represent persistent low-amplitude vibrations of the earth’s surface, generated by natural sources (e.g., wind, oceanic waves, volcanic activity, and tidal forces) and anthropogenic activities (e.g., vehicular traffic and machinery operation). The former, characterized by frequencies typically <1 Hz, are classified as long-period microtremors; the latter, exhibiting frequencies >1 Hz, are termed short-period microtremors. These vibrations constitute a composite wavefield comprising body waves (P- and S-waves) and surface waves (Rayleigh and Love waves), with surface wave energy dominating approximately 70% of the total signal energy.

Microtremor survey entails processing ambient microtremor signals to extract Rayleigh wave dispersion curves via spatial autocorrelation (SPAC) or frequency-wavenumber (F-K) analysis. Through inversion of these dispersion characteristics, subsurface shear-wave velocity (Vs.) structures are reconstructed. Geological features are subsequently delineated by analyzing Vs. contrasts between target formations and surrounding media, thereby addressing critical engineering geological objectives such as bedrock profiling, cavity detection, and stratigraphic interface mapping (Coccia et al., 2010).

(1) Data Extraction Phase: The continuous observation files are segmented based on the precise start/end acquisition timestamps recorded at each field array station, yielding discrete datasets for individual measurement points. This process ensures temporal alignment with actual field deployment configurations while preserving original sampling characteristics.

As tabulated in Table 1, compact limestone and dolomite exhibit shear-wave velocities exceeding 1400 m/s, while shear-wave propagation is physically prohibited in air-filled cavities and karstic groundwater (effectively yielding zero velocity). Water-saturated silty sands typically register velocities below 300 m/s. This pronounced shear-wave velocity contrast between competent bedrock and cavities serves as the physical basis for microtremor survey for karst cavity detection.

Illustrating a microtremor survey for karst exploration in Jiangxi, China (Figure 4), the Vs. section delineates distinct velocity domains: surficial low-velocity layers overlie high-velocity bedrock, with embedded low-velocity anomalies (C1–C4) indicating potential karst development. Subsequent drilling confirmed cavities at all four anomalies: C1 and C3 as fully sediment-filled cavities, and C2 and C4 as partially filled cavities. Critically, microtremor methods accurately detect cavities regardless of fill saturation—since all filled cavities manifest as velocity deficits relative to intact rock—but cannot discriminate fill conditions.

Ground penetrating radar (GPR) operates as an electromagnetic method wherein a transmitting antenna directs high-frequency, short-pulse electromagnetic waves into subsurface interfaces. When encountering boundaries with contrasting electrical properties, these waves undergo partial reflection governed by the Fresnel equations, with reflection coefficients determined by dielectric permittivity contrasts. Reflected waves are captured by a receiving antenna, with propagation paths obeying Snell`s law and reflection amplitudes correlating to dielectric contrasts and interface geometry. Through acquisition of time-domain signals, velocity-based time-depth conversion, and waveform analysis, this technique resolves the depth, lateral position, and geometric attributes of subsurface targets or stratigraphic interfaces (Al-fares et al., 2002; Xu, 2015).

(1) Data Preprocessing: Raw data imports undergo compatibility verification in dedicated software, followed by trace editing and dead-channel removal. Direct current offsets are eliminated to normalize waveform baselines, reflection events are time-aligned, and coherent background noise (e.g., surface metallic objects, fixed interference sources) is suppressed to enhance valid signals.

The dielectric properties of materials govern their polarization capability under electric fields. Table 1 demonstrates that compact limestone and dolomite exhibit relative permittivity values typically below 8, while air-filled cavities register as 1. In contrast, water-saturated silty sands show permittivity ≥23, and karstic groundwater reaches 81. This pronounced dielectric contrast between competent bedrock and cavities, coupled with electrical conductivity differences, serves as the theoretical basis for ground penetrating radar cavity detection by inducing measurable alterations in reflected wave amplitude and frequency.

Illustrating two representative ground penetrating radar surveys for advance geological prediction in a Hunan tunnel (Figures 5a,b), diagnostic subsurface anomalies exhibiting hyperbolic phase axes were identified.

Figure 5a reveals a high-amplitude reflection zone (D1) at 12 m behind the tunnel face, exhibiting near-parabolic waveform phase axes, interpreted as a karst cavity development zone. Subsequent excavation confirmed a clay-filled karst cavity in this location.

Figure 5b delineates two anomalies: a pronounced reflective zone (D2) at 14 m behind the face with parabolic phase axes, indicating a cavity; and a secondary zone 5 m further back (D3) showing weaker-amplitude parabolic reflections, likely attributable to multiple reflections. Excavation validated an air-filled cavity at 13 m depth (D2).

Geophysical analysis establishes that the presence of karst cavities within a ground penetrating radar survey zone invariably modifies radar wave signatures through distinct interfaces: the cavity’s frontal boundary invariably generates high-amplitude reflections accompanied by waveform distortions and discontinuous phase axes, manifesting as intense reflective zones exemplified by areas D1 and D2. Critically, the infill material dictates subsequent signal behavior—cavities saturated with conductive media such as water-saturated silts or karstic groundwater induce severe electromagnetic attenuation, wholly suppressing secondary reflections. Conversely, air-filled cavities permit unimpeded wave transmission with minimal loss, enabling reflections at the rear interface that subsequently transmit through the frontal boundary; these secondary reflections exhibit waveform coherence with the primary wave but display attenuated amplitudes, as empirically documented in Area D3. Collectively, these diagnostic amplitude-phase responses and multi-reflection signatures empower ground penetrating radar to accurately detect and differentiate cavity infill conditions with high geophysical fidelity.