Enhanced MT Responses from Deep Underground Observations

1. Introduction

Magnetotelluric (MT) sounding is one of the most widely adopted geophysical methods for investigating the deep structure of the Earth. Owing to electromagnetic (EM) attenuation and the skin effect, MT transfer functions are primarily controlled by subsurface conductive structures [1,2]. As a result, water-bearing porous media within the sedimentary cover can effectively shield the responses of underlying targets, thereby hindering their detection and inversion and giving rise to the so-called “conductive overburden” effect [2,3,4]. The inversion of conventional surface MT data is further affected by the following three factors: (1) shallow sedimentary cover significantly suppresses the EM responses of deep high-resistivity bodies, producing only minor perturbations in apparent resistivity and phase and consequently increasing inversion uncertainty [3,5]. (2) the generally strong EM noise environment encountered in surface MT observations degrades the signal-to-noise ratio of the data, thereby reducing inversion accuracy [6,7,8,9]. (3) electrical heterogeneities within near-surface sediments can induce current distortion and static-shift effects, thereby directly compromising inversion reliability [10,11].

It has been demonstrated that underground environments generally exhibit significantly lower EM background noise than surface environments [12,13,14,15]. This low-noise environment is beneficial for acquiring EM data with high signal-to-noise ratios and for capturing weak EM signals associated with deep geological processes [16]. In this study, we primarily address the question of what advantages underground observations offer over conventional surface MT observations and inversions in areas with sedimentary sequences. We employed both synthetic and field data to evaluate the potential of underground observations for improving the inversion accuracy of deep electrical structures by comparing EM responses at surface and underground stations under different sedimentary thicknesses and resistivity-anomaly configurations. In addition, for a sedimentary basin scenario, we discuss the weak EM responses of deeply buried anomalies at surface stations and the signal-detection capabilities of typical EM sensors.

2. Plane waves within Layered Model

To provide a realistic reference for the subsequent comparison and inversion of simulated and observed EM fields, we used the geological and geophysical setting of the Huainan Underground Laboratory (HNLab) to construct the synthetic model, where surface and underground EM channels were recorded synchronously. HNLab is located on the margin of the Hefei Basin in the southern North China Craton (Figure 1) and was constructed within the tunnels of the Huainan coal mine. The surface observation site is located at an elevation of +22 m, whereas the underground laboratory is situated at an elevation of −848 m. A 300–400 m thick sequence of Neogene and Quaternary sediments forms the shallow cover and unconformably overlies Mesozoic and Paleozoic coal-bearing successions composed of sandstone, mudstone, and interbedded coal seams deposited in continental and transitional marine–continental facies. The underground laboratory is hosted within the Carboniferous–Permian coal measures, with both the roof and floor strata dominated by mudstone, sandstone, and mud shale. The underlying strata comprise karstified and weathered marine Ordovician carbonates and Cambrian limestones. The logging data indicate that the overlying unconsolidated sediments have a bulk resistivity of approximately 2.2 Ω·m [16]. Wide-angle seismic data suggest that the upper-crustal cover sequence in the Hefei Basin is 4–7 km thick [17]. In addition, a broadband MT profile reveals the presence of a conductive sedimentary layer with a thickness of approximately 3–6 km [18].

2.1. Synthetic Model and Numerical Simulation

We employed a simplified one-dimensional (1D) layered resistivity model (Figure 2a) based on the stratigraphic structure and logging data shown in Figure 1. The model consists of two layers, with the upper layer represented by a conductive cover having a resistivity of 2.2 Ω·m, as constrained by the logging data [16]. Two cover thicknesses, 870 m and 5000 m, were used in the simulations. A two-dimensional resistivity model indicates that the upper crust of the Hefei Basin is characterized by resistivities of approximately 50–500 Ω·m, whereas the middle and lower crust contain large scale conductive bodies with resistivities of 10–20 Ω·m [18]. The underlying formation in our synthetic model was set as a homogeneous half space with a resistivity of 50 Ω·m.

We conducted three-dimensional (3D) forward simulations using the AC/DC Module of COMSOL Multiphysics, a finite-element-based multiphysics simulation platform [19]. The numerical model covered a computational domain of 70 km $\times$ 70 km $\times$ 70 km (length $\times$ width $\times$ height). Two orthogonal background magnetic field vectors, ${\mathrm{H}}_0=(0,1000,0)$ and $(1000,0,0)$, were prescribed under the plane wave assumption. The relative magnetic permeability and relative permittivity were both set to unity, and a free tetrahedral mesh was employed for spatial discretization. To minimize the effects of frequency-dependent mesh resolution and finite-domain boundary conditions, only the effective frequency range of the simulated data was considered in the following analysis. In addition, the resistivity of the underlying layer in Figure 2a was assigned values of 2.2, 50, and 500 Ω·m. The ratios between the EM fields at the surface and those at depth were then calculated using a recursion formulation based on 1D layered earth theory [4,20]. Stations were placed at the surface and at the base of the sedimentary layer, and the corresponding ratios of surface to underground EM fields are presented in Figure 2b and Figure 2c.

2.2. Results and Analysis

A comparison of the surface and underground EM fields obtained from different simulation methods and field measurements, as shown in Figure 2, reveals the following:

(1)

The 3D forward modeling results agree well with those derived from the recursion method at frequencies below 10 Hz for the 870 m thick sedimentary layer and below 3 Hz for the 5000 m thick sedimentary layer. Notably, the 3D simulated responses become distorted in higher-frequency bands because of frequency-dependent mesh-resolution limitations. The measured magnetic field at a depth of 870 m shows good agreement with the simulated results, whereas the attenuation coefficient of the measured electric field is lower than that predicted by the simulations. This discrepancy is probably attributable to the fact that the study area deviates from an ideal 1D layered earth model. In addition, the difficulty of positioning electrodes at underground stations is likely an important factor contributing to the differences between the measured and simulated results.

(2)

The electric and magnetic fields exhibit different attenuation coefficients. For example, when ${\rho }_{inf}=$ 50 Ω·m, the electric field attenuation coefficients for sedimentary-layer thicknesses of 5000 m and 870 m are approximately 0.002 and 0.5 at 1 Hz, 0.2 and 1 at 0.1 Hz, and both approach unity at 0.01 Hz, respectively. In contrast, the corresponding magnetic field attenuation coefficients are approximately 0.001 and 0.1 at 1 Hz, 0.04 and 0.3 at 0.1 Hz, and 0.2 and 0.6 at 0.01 Hz, respectively. These results indicate that: (i) for a given sedimentary layer thickness, the magnetic field is more strongly attenuated than the electric field; and (ii) increasing sedimentary layer thickness enhances electric field attenuation more markedly in the high frequency band, whereas its influence on magnetic field attenuation persists over a broader low frequency band.

(3)

The electric field attenuation curves for different values of ${\rho }_{inf}$ are relatively similar, whereas the magnetic field attenuation curves exhibit more pronounced differences. This indicates that, under the influence of shallow sedimentary layers, the magnetic field response is more sensitive to resistivity perturbations in the background medium.

3. Inversion of Layered Models

To further investigate the effects of shallow sedimentary cover on the apparent resistivity, impedance phase, and inversion results of surface and underground MT observations, we performed 1D MT inversion for both synthetic and field data using the trans-dimensional Markov chain Monte Carlo (RJMCMC) algorithm [21]. This method does not require the number of model layers to be specified a priori, and statistical analysis of the probability distributions of the inversion results provides a better characterization of the non-uniqueness and uncertainty associated with different datasets.

3.1. Synthetic Data

Figure 3a and Figure 3b present the apparent resistivity and impedance phase curves of the layered model shown in Figure 2(a) for observations at the surface and at a depth of 870 m, respectively. For the surface station, the apparent resistivity remains approximately 2.2 Ω·m over the frequency range of 10,000–1 Hz, while the impedance phase is close to 45°. At longer periods of T > 1 s, the apparent resistivity gradually increases, reaching approximately 20 Ω·m at T = 100 s, while the corresponding impedance phase gradually decreases. In contrast, at the underground station, the apparent resistivity remains approximately 50 Ω·m and the impedance phase remains close to 45° over the entire frequency range. The sounding data from the underground station better characterize the resistivity properties of the underlying basement. It should be noted that, owing to frequency-dependent mesh-resolution limitations in our AC/DC Module simulations, extrapolation was used to supplement the high frequency data for both surface and underground stations. Specifically, for the surface data, the skin depths associated with the supplemented high frequency responses are smaller than the thickness of the sedimentary layer; therefore, these responses have a negligible influence on the delineation of resistivity interfaces. For the underground data, because the basement is assumed to be a homogeneous medium with uniform resistivity, the supplemented high-frequency data likewise do not introduce spurious interface anomalies. Therefore, extrapolation of the high-frequency data has no significant influence on the inversion results.

The 1D inversion results for the surface and underground data are presented in Figure 3c and Figure 3d, respectively. Both inversions achieve good data fits (Figure 3a and Figure 3b) and recover the subsurface resistivity structure. The results for the surface station indicate that the posterior probability distribution of shallow resistivity is highly concentrated, suggesting that the inversion provides strong constraints on the shallow sedimentary layer. However, the estimated thickness of the sedimentary layer shows a certain deviation from the true value. In addition, although the mode and median models are broadly consistent with the true resistivity at greater depths, the mean model yields resistivities higher than the true values. Moreover, the interval between the 10th and 90th percentile models spans several orders of magnitude, ranging from 50 Ω·m to several tens of thousands of Ω·m, reflecting the uncertainty in the inversion results. In contrast, all probabilistic models obtained from the underground station are tightly clustered around the true values, demonstrating good inversion reliability and accuracy.

We further added Gaussian noise to the sounding data shown in Figure 3 to assess the robustness of the inversions. The mean of the Gaussian noise was set to zero for both apparent resistivity and impedance phase, while the standard deviations were set to 10 Ω·m and 5°, respectively. Because of the dominant influence of the shallow conductive sedimentary layer on bulk resistivity, the apparent resistivity at the surface station is generally low in the high-frequency band. As a result, even minor noise perturbations may lead to substantial deviations in apparent-resistivity amplitudes. By comparison, the apparent resistivity at the underground station is less sensitive to the same level of noise.

Figure 4 shows the noisy data and corresponding inversion results. Although the apparent resistivity curves of the surface data differ considerably before and after noise contamination, the model responses remain close to the noise free data (Figure 4a). By comparison, the phase data are less affected by noise, resulting in a better data fit (Figure 4b). For the underground station, the apparent-resistivity response fitted to the noisy data is generally consistent with the noise free data, except for slightly higher amplitudes in the low frequency band. The phase data also exhibit an excellent fit. The inversion results for the surface station exhibit highly dispersed posterior probability distributions at depths of approximately 700–3000 m, indicating a high degree of uncertainty in the inverted models. Furthermore, the resistivities of both the mode and median models exceed 1000 Ω·m, representing a substantial departure from the true model. In contrast, despite the relatively large interval between the 10th and 90th percentile models, the results from the underground station are considerably more concentrated. The mode model agrees well with the true model, while the median and mean models also reproduce the true structure reasonably well, with the main deviations confined to depths between 1000 and 1500 m. These results further demonstrate that, for noise contaminated data, inversion based on underground observations provides higher reliability and lower uncertainty than inversion based on surface observations.

3.2. Field Data

We further conducted 1D inversion using synchronously observed surface and underground MT data from HNLab. A total of 24 hours data were selected for impedance tensor estimation. During the observations, HNLab was still undergoing planning, design, and renovation. Therefore, both surface and underground data were affected by EM noise to varying degrees, including noise from high voltage transmission facilities, power supply systems, ventilation and drainage equipment, railway transport systems, mine hoists, and densely distributed pumping pipelines. Figure 5 shows a comparison of the apparent resistivity and phase data obtained from the surface and underground stations.

(1)

In the frequency band of > 10 Hz, both apparent resistivity and phase curves of the ground station exhibit considerable outlier (Figure 5a, blue shaded region). Although the underground apparent resistivity curves are relatively continuous, the phase data exhibit out-of-quadrant behavior, and the YX-mode phase curve is distorted (Figure 5b, blue shaded region). This indicates strong attenuation of high frequency EM fields by the overlying conductive layer, resulting in significant distortions in impedance estimation when conventional MT processing approaches are used.

(2)

In the 10–1000 s period band, the overall quality of the surface data improves; however, the YX-mode data still exhibit obvious outliers. By contrast, the underground data are smoother and more continuous. However, in the 10–100 s period band, the underground phase curve transitions from out-of-quadrant behavior toward values close to 45° or −135°, indicating that attenuation by the shallow sedimentary layer still affects the data in this band and leads to biased transfer functions.

(3)

At periods longer than 1000 s, the surface apparent resistivity curve exhibits an upward trend with an approximately 45° slope, suggesting that the data are significantly affected by near-field effects (Figure 5a, orange-shaded region). In contrast, the underground data appear to be free from surface near-field sources. The data quality remains generally good up to a period of 10,000 s, except for some outliers at low frequencies (Figure 5b, orange-shaded region).

Figure 6 shows the 1D inversion results for the surface and underground observations. Considering the effects of high frequency noise and low frequency near-field effects, data in the period range of 1–3000 s were used. In addition, attenuation by the shallow sedimentary layer causes distortion of the underground transfer functions in the high frequency range. Therefore, inversion results obtained with and without retaining the out-of-quadrant period range of 1–200 s were further compared. The results suggest the following:

(1)

The results derived from the surface data indicate a low resistivity layer (~1 Ω·m) at depths shallower than 1 km, consistent with the characteristics of the shallow sedimentary layer. However, the resistivity increases sharply to ~10,000 Ω·m below 1 km, resulting in a complete loss of resolution for deeper structures (Figure 6c).

(2)

The interval between the 10th and 90th percentile models derived from the underground data is relatively wide, indicating low model certainty. The phase fit is poor when the distorted high-frequency band is included (Figure 6b). The results indicate resistivities of ~1000 Ω·m at depths of 1–5 km, decreasing to ~10 Ω·m at 5–12 km and increasing again to ~1000 Ω·m at 12–22 km. The subsurface is characterized by a low-resistivity feature of approximately 10 Ω·m below a depth of ~22 km (Figure 6d). We suggest that the out-of-quadrant distortions in the high frequency band are responsible for the two high resistivity layers imaged in the inversion models.

(3)

The results obtained using only the low frequency underground data (Figure 6e) indicate that the probabilistic models are dispersed at depths shallower than ~8 km. This is likely due to the lack of high frequency data constraints. Model uncertainty is relatively reduced below 8 km. The mode and median models indicate a simple subsurface structure with a resistivity of approximately 10 Ω·m. The mean model shows a decrease in resistivity from several tens of Ω·m at depths of 8–15 km to ~20 Ω·m at depths of 15–40 km, followed by a further decrease to ~10 Ω·m below a depth of ~40 km. This result is broadly consistent with previous evidence for a large scale mid- to lower-crustal conductive layer [18].

Overall, in contrast to the severely distorted results derived from the surface data, the underground data still provide effective constraints on deep resistivity structures to some extent, although both surface and underground data were affected by strong and complex EM noise. This demonstrates that underground observations have advantages in improving inversion results by mitigating the influence of shallow sediments.

4. Surface Electromagnetic Response Controlled by Sedimentary Cover

Identifying and extracting the weak responses of deep high resistivity targets remain challenging in terms of observation configuration, instrumentation, and data processing, particularly because of the shielding effect of a conductive cover layer. Figure 7 shows a 3D resistivity model consisting of a shallow conductive overburden (2.2 Ω·m) overlying a 50 Ω·m basement. A 3D high resistivity body was embedded in the model, with its top located at a depth of 30 km and dimensions of 30 km $\times$ 30 km $\times$ 20 km (length $\times$ width $\times$ height). An MT profile was deployed at the center of the model surface. 3D forward simulations were performed using the COMSOL AC/DC Module to investigate the EM response characteristics of the resistive anomaly at surface and underground stations.

Figure 8 shows the variations in electric-field response along the profile deployed at the surface. The amplitudes at the center of the profile indicate the following:

(1)

For a sedimentary layer thickness of 870 m, the response induced by the 1000 Ω·m anomaly exceeds 200 mV/km at T = 10,000 s, whereas that induced by the 55 Ω·m anomaly is close to 20 mV/km (Figure 8a). The response induced by the 55 Ω·m anomaly still reaches several tens of mV/km at T = 10 s (Figure 8d). However, the electric-field response induced by the 1000 Ω·m anomaly is only 0.016 mV/km at T = 1 s (Figure 8e), whereas the self-noise level of conventional non-polarizable electrodes is 0.01 mV/km/√Hz at 1 Hz [22]. This indicates that conventional non-polarizable electrodes may have difficulty for reliably detecting such weak signals.

(2)

For a sedimentary layer thickness of 5000 m, the 1000 Ω·m anomaly induces a response exceeding 50 mV/km at T = 10,000 s, whereas the response induced by the 55 Ω·m anomaly is approximately 5 mV/km (Figure 8a). Compared with the self-noise level of conventional non-polarizable electrodes, which is approximately 1 mV/km/$\sqrt{Hz}$ at 1 mHz [22], the electric-field response induced by the 55 Ω·m anomaly at the surface is relatively weak. For T < 100 s, the results show negative amplitudes (Figure 8c–e), probably because the skin depth is smaller than the depth to the top of the target.

Compared with the electric-field response, the magnetic-field response is weaker because induced eddy currents are suppressed within high resistivity anomalies. Figure 9 shows the variations in magnetic-field response along the profile, indicating the following:

(1)

The magnetic-field responses for sedimentary-layer thicknesses of 870 m and 5000 m are nearly identical at T = 10,000 s (Figure 9a), indicating that variations in sedimentary-layer thickness have only a limited influence on long period magnetic-field induction. When the anomaly resistivity is 1000 Ω·m, the amplitude difference between the profile center and the profile boundary exceeds 0.1 nT, whereas for the 55 Ω·m anomaly, it is less than 0.01 nT. The self-noise level of typical magnetic sensors > 1 nT/$\sqrt{Hz}$ at T = 10,000 s [22] is insufficient for resolving the response characteristics described above.

(2)

At T = 1000 s and T = 100 s, the magnetic-field responses along the profile show significant differences for different sedimentary layer thicknesses (Figure 9b and Figure 9c).

(3)

At T = 1 s, the response difference between the profile center and boundary for the 1000 Ω·m anomaly is only 1.4 pT and 5 aT for sedimentary layer thicknesses of 870 m and 5000 m, respectively (Figure 9e). The former is already close to the theoretical noise level of conventional induction coils, which is approximately 1 pT/$\sqrt{Hz}$at 1 Hz [22]. The latter is far below the noise level of low temperature superconducting magnetometers, which is approximately 1 fT/$\sqrt{Hz}$ at 1 Hz [23].

The results indicate that the magnetic-field response is relatively insensitive to high resistivity medium. Under the influence of a conductive sedimentary cover, the surface magnetic-field response of subsurface structures is further attenuated, imposing stricter requirements on background noise levels and the sensitivity of magnetic sensors.

The apparent resistivity responses (Figure 10) and electric-field responses (Figure 8) exhibit consistent curve characteristics, indicating that the apparent resistivity response of the deep high resistivity anomaly is primarily controlled by the electric-field response.

(1)

For a sedimentary layer thickness of 870 m, the relative apparent resistivity response of the 1000 Ω·m anomaly is approximately 0.03 Ω·m at T = 10,000 s, 0.6 Ω·m at T = 1000 s, and 0.3 Ω·m at T = 100 s (Figure 10a–c).

(2)

For a sedimentary layer thickness of 5000 m, the relative apparent-resistivity response remains very weak across the entire period range.

Overall, the responses of deep high-resistivity anomalies in surface MT observations are relatively weak, indicating that surface observation configurations generally have difficulty on constraining the geometric boundaries of deep 3D high resistivity bodies beneath a conductive sedimentary cover. On the other hand, how to use inversion algorithms to retrieve the electrical structure implied by the responses, and how to improve the determinacy, uniqueness, and reliability of anomaly resistivity values and boundary information in inversion results, are beyond the scope of this study.

5. Discussion

Figure 11 shows the electric-field, magnetic-flux-density, and apparent resistivity curves for surface and underground stations deployed at different depths, as well as the response differences in these physical quantities for different anomalies. The results show that the EM responses at observation sites with different depths exhibit significant differences, as indicated by the curves of different colors in Figure 11a1, Figure 11b1, and Figure 11c1. In contrast, for anomalies with different resistivities, the EM field and apparent resistivity response curves at the same depth are nearly identical, as indicated by the solid and long-dashed lines in Figure 11a1, Figure 11b1, and Figure 11c1. This suggests that the resistivity contrasts of deep anomalies, such as 60 Ω·m and 1000 Ω·m, produce only very weak perturbations at the observation sites. The comparison between surface and underground EM fields indicates the following:

(1)

High frequency EM signals recorded at underground stations are significantly attenuated and converge with the surface data at low frequencies. In addition, the electric and magnetic fields differ in their attenuation behavior and attenuation coefficients (Figure 11a1 and Figure 11b1).

(2)

The electric-field differences at the surface and at a depth of −870 m are relatively similar, as indicated by the black and blue short-dashed lines in Figure 11a2, whereas both differ significantly from those at a depth of −5000 m, as indicated by the yellow short-dashed line in Figure 11a2.

(3)

The magnetic-field differences at the surface are very weak (<1 nT), whereas the maximum amplitude approaches 2000 nT at 0.004 Hz at a depth of −870 m. The maximum amplitude further increases to 8000 nT at 0.006 Hz at a depth of −5000 m (Figure 11b2).

(4)

Compared with the results from the surface and a depth of −870 m, the apparent-resistivity response at a depth of −5000 m better reflects the characteristics of the deep high-resistivity medium (Figure 11c1). In addition, the apparent-resistivity differences are only approximately 0.2 Ω·m at the surface and at a depth of −870 m, whereas the difference increases to 5 Ω·m at a depth of −5000 m (Figure 11c2). Clearly, the perturbation signatures associated with resistivity contrasts in high resistivity bodies are more pronounced in deeper underground observations, particularly at −5000 m.

6. Conclusions

Our study focuses on the EM response behavior under the influence of shallow sedimentary cover. Using both synthetic and field data, we compare the attenuation characteristics of EM fields and the corresponding 1D probabilistic inversion models. We discuss the controlling effect of sedimentary cover on the EM responses of underlying high-resistivity anomalies in surface and underground observations.

(1)

The electric and magnetic fields differ in their attenuation behavior and attenuation coefficients during propagation through shallow sediments, with the conductive layer exerting a more pronounced attenuation effect on the magnetic field. In contrast, electric field perturbations are more sensitive to variations in sedimentary layer thickness. The 1D probabilistic inversion results for both synthetic and field data indicate that models derived from underground observations exhibit higher certainty and reliability.

(2)

Under the influence of a shallow conductive layer, the EM field and transfer function responses associated with deep high resistivity anomalies are relatively weak in surface data. The limited sensitivity of conventional EM sensors makes it difficult to identify high frequency perturbation features and further constrain the boundaries of high resistivity targets.

(3)

Variations in the resistivity of resistive anomalies produce only weak response perturbations in surface and shallow underground observations, whereas the responses are enhanced in deeper underground data. We suggest that deep underground observations have potential advantages for improving the accuracy and reliability of modeling deep high resistivity bodies.

(4)

For underground observations, transfer functions in the high frequency band derived using conventional data processing methods are distorted and should be excluded from data analysis and inversion. Alternatively, inversion approaches based on integrated surface–underground full space observation systems should be developed.