Simulation of the seismoelectric effect serves as a useful tool to capture the observed seismoelectric conversion phenomenon in porous media, thus offering promising potential in underground exploration activities to detect pore fluids such as water, oil, and gas. The static electromagnetic (EM) approximation is among the most widely used methods for numerical simulation of the seismoelectric responses. However, the static approximation ignores the accompanying electric field generated by the shear wave, resulting in considerable errors when compared to analytical results, particularly under high-salinity conditions. To mitigate this problem, we have adopted a spatial high-order finite-difference time-domain method based on Maxwell’s full equations of time-varying EM fields to simulate the seismoelectric response in 2D mode. To improve the computational efficiency influenced by the velocity differences between seismic and EM waves, different time steps are set according to the stability conditions, and the seismic feedback values of EM time nodes are obtained by linear approximation within the seismic unit time step. To improve the simulation accuracy of the seismoelectric response with the time-varying EM calculation method, finite-difference coefficients are obtained by solving the spatial high-order difference approximation based on the Taylor expansion. Our method yields consistent simulation results compared to those obtained from the analytical method under different salinity conditions, thus indicating its validity for simulating seismoelectric responses in porous media. We further apply our method to layered and anomalous body models and extend our algorithm to three dimensions. Results indicate that the time-varying EM calculation method can effectively capture the reflection and transmission phenomena of the seismic and EM wavefields at the interfaces of contrasting media. This may allow for the identification of abnormal locations, thus highlighting the capability of seismoelectric response simulation to detect subsurface properties.

The induced polarization effects magnetic field measurement method based on the superconductive quantum interfere device (SQUID) and transient electromagnetic (TEM) system can improve the exploration accuracy of metal minerals. As the core component of the SQUID-TEM system based on magnetic source, the current transmitter should reach consensus in three key aspects: high power, controllable turn-off time and combined current waveforms. In order to solve the problem of single transmitting current waveform and uncontrollable turn-off time in traditional current transmitter, a topology structure of current transmitter with multiple waveform combinations in time domain is proposed in this paper. By using the passive multi-group clamp technology and RLC series resonance technology, the falling edge turn-off time of trapezoidal and triangular transmitting current can be controlled, and the pulse width of semi-sinusoidal transmitting current can be adjusted. The laboratory and field experiments are implemented to test the performance of the current transmitter. Compared with the commercial PROTEM67 transmitter, the test results show that it can successfully transmit three current waveforms and their combination waveforms, the current amplitude is more than 100A, and the transmitting current turn-off time is controllable. The field measurement response results show that the combined multi-waveform transmit system can effectively measure the induction field and the polarization field generated by the Cole-Cole polarization ring, which provides technical support for the high-precision detection of induction-polarization effects based on the SQUID-TEM system.

The small-loop time-domain electromagnetic (TDEM) method has been widely used in urban underground space detection in recent years due to the small workspace requirements. Due to the small side length of the transmitting coil of the small-loop electromagnetic method, more difficulties have been introduced in modeling and instrument development. The traditional modeling method cannot include source calculation, and the error becomes significantly large when calculating the initial field of the small-loop, and the cross iteration of electric and magnetic fields also increases the modeling error of the small-loop. Therefore, a high-precision 3-D small-loop source TDEM modeling method need to be proposed to provide the theoretical basis for feature analysis, inversion, and instrument parameter design. In this article, the electromagnetic wave equations are adopted as the controlling equations and discretized based on the Crank–Nicolson finite-difference time-domain (CN-FDTD) method. The entire computational space, including air and ground, is subdivided into sources to support 3-D small-loop TDEM modeling for shallow anomalous body conditions. Furthermore, the iterative formulas of the electromagnetic wave equations in the complex frequency-shifted perfect match layer (CFS-PML) are derived, the reflection errors are largely suppressed, and the modeling accuracy is significantly improved. Finally, the effectiveness of the improved method is verified by homogeneous models, layered models, and complex anomaly models. In addition, analyzing the propagation characteristics of the small-loop can guide the setting of the receiver sampling rate and improve the accuracy of detection. The results show that the improved method can achieve stable, low-memory, and high-precision 3-D small-loop source TDEM modeling, which can provide theoretical support for the application of the TDEM method in urban and shallow detection.

With the improvement in the accuracy of time-domain electromagnetic method (TDEM) observations for geophysical exploration, abnormal diffusion phenomena have become a more salient focus of research. In particular, the induced polarization (IP) effect and magnetic viscosity (MV) effect are often observed in the exploration of polymetallic ore, with IP effect leading to a negative TDEM response, and MV effect generating a power-law decay of -0.6 to 1.4 in the late stage response. Ignoring these effects can lead to incorrect data interpretation. Therefore, to model and analyze both IP effect and MV effect accurately, a three-dimensional (3D) numerical modeling method for induced polarization and magnetic viscosity (IP-MV) effect is proposed. The Cole-Cole conductivity and Cole-Cole susceptibility models are approximated in the time domain using the Multiple-Zero-Pole (MZP) method. Then the diffusion equations for the electric and magnetization intensity fields are derived as control equations, while the 3D modeling of the IP-MV effect with full-waveform is realized based on the improved recursive convolution technique and finite-difference time-domain (FDTD) method. The effectiveness is verified by comparing with the one-dimensional (1D) numerical integration solutions. The response characteristics of IP effect and MV effect are analyzed with full trapezoidal waveform, and a complex model including IP-MV effect is discussed. It is demonstrated that IP-MV effect can be better observed at the on-time stage. The proposed method can effectively model the diffusion process of IP-MV effect with the full-waveform, which can be helpful for improving the inversion accuracy and detection precision for complex geological formations.

Superparamagnetic (SPM) effects lead to 1/t power-law delay approximately during the middle and late periods of transient electromagnetic responses. Ignoring SPM effects can produce large errors and cause incorrect data interpretation. Furthermore, because of the non-linearity of the Chikazumi magnetic susceptibility model, it is difficult to discretize the model in the time domain. Therefore, developing an algorithm for 3-D modelling of SPM effects in the time domain directly is difficult. In view of the above problems, we propose a 3-D modelling method of SPM effects for airborne transient electromagnetic (ATEM) data. We also introduce the widely used Chikazumi magnetic susceptibility model into the finite-difference frequency-domain (FDFD) method. According to the mapping relations between the magnetic field intensity and the magnetic permeability on the grid after discretization, we re-establish the scientific matrix of the magnetic permeability. And we adopt arithmetic averaging of the two adjacent cubes’ magnetic permeability as the magnetic permeability in boundary, which is a different setting method with the electrical conductivity. The 3-D modelling of SPM effects is successfully realized, and its maximum relative error is less than 7 per cent. We subsequently analyse the intrinsic properties of the abnormal magnetic medium, as well as the effect of the SPM unit's parameters, such as the depth, thickness, electrical conductivity, zero-frequency magnetic susceptibility, and the height of the receiver, on the response. Then, we calculate the SPM responses of 3-D magnetic bodies and analyse the influence of magnetic susceptibility and electrical conductivity on magnetite responses. The present study can provide theoretical guidance for ATEM detection in magnetic media and lay a foundation for 3-D inversion of SPM effects.

Recently, the electromagnetic (EM) anomalous diffusion phenomenon has been observed in time-domain electromagnetic (TDEM) surveys. Furthermore, the data interpretation accuracy has been reduced by adopting the traditional EM theory and methods. A number of models, such as random medium and roughness electrical conductivity theory, have been adopted to model the EM anomalous diffusion. However, problems such as modeling difficulty and massive discretization exist regarding characterizing the long-range correlation of EM anomalous diffusion. The space-fractional derivative has been proven to preferably describe the long-range correlation characteristic. Only a handful of studies on TDEM anomalous diffusion with space-fractional derivative have been conducted due to the difficulties in computational engineering problems. Therefore, we performed a series of studies about 2D TDEM anomalous diffusion with space-fractional derivative. The 2D TDEM space-fractional diffusion equation was constructed based on the space-fractional Ohm’s law model. Furthermore, the discretization and iteration forms of the control equation were derived based on the finite element method by introducing the Riemann-Liouville-type Riesz fractional derivatives. The 2D mountain-shaped function and partial integration method were combined to convert the fractional derivative into the primitive function form. Hence, the 2D modeling of the space-fractional EM diffusion was realized. The effectiveness of our method was verified by the function construction method and wavenumber-domain analytical solution. The spatial and temporal characteristics of the space-fractional EM diffusion were analyzed by different geological models. Furthermore, we discuss the differences with the classical EM diffusion. Our method can effectively model the space-fractional EM diffusion in TDEM surveys and provide theoretical bases for improving the TDEM interpretation accuracy with complex geological conditions.