Surveys in Geophysics

This review paper addresses the development of numerical modeling of electromagnetic fields in geophysics with a focus on recent finite element simulation. It discusses ways of estimating errors of our solutions for a perfectly matched modeling domain and the problems that arise from its insufficient representation. After a brief outline of early methods and modeling approaches, the paper mainly discusses the capabilities of the finite element method formulated on unstructured grids and the advantages of local h-refinement allowing for both a flexible and largely accurate representation of the geometries of the multi-scale geomaterial and an accurate evaluation of the underlying functions representing the physical fields. In summary, the accuracy of the solution depends on the geometric mapping, the choice of the mathematical model, and the spatial discretization. Although the available error estimators do not necessarily provide reliable error bounds for our complex geomodels, they are still useful to guide grid refinement. Therefore, an overview of the most common a posteriori error estimators is given. It will be shown that the sensitivity is the most important function in both guiding the geometric mapping and the local refinement.

The significant role of nonlinear wave–particle interactions in the macrodynamics and microdynamics of the Earth’s outer radiation belt has long been recognised. Electron dropouts during magnetic storms, microbursts in atmospheric electron precipitation, and pulsating auroras are all associated with the rapid scattering of energetic electrons by the whistler-mode chorus, a structured electromagnetic emission known to reach amplitudes of about \(1\%\) of the ambient magnetic field. Despite the decades of experimental and theoretical investigations of chorus and the recent progress achieved through numerical simulations, there is no definitive theory of the chorus formation mechanism, not even in the simple case of parallel (one-dimensional) propagation. Here we follow the evolution of these theories from their beginnings in the 1960s to the current state, including newly emerging self-consistent excitation models. A critical review of the unique features of each approach is provided, taking into account the most recent spacecraft observations of the fine structure of chorus. Conflicting interpretations of the role of resonant electron current and magnetic field inhomogeneity are discussed. We also discuss the interplay between nonlinear growth and microscale propagation effects and identify future theoretical and observational challenges stemming from the two-dimensional aspects of chorus propagation.

This review presents the progress made in the last decade in the field of large-scale electromagnetic (EM) induction with natural sources, which fluctuate at periods from seconds to years and originate in oceans, ionosphere and magnetosphere. These mechanisms produce field variations that can be used to image subsurface electrical structure of Earth and planets across scales and depths from the shallow crust to the lower mantle. In the last decade, we have seen a substantial progress made in different areas related to methods, observations and 3-D numerical modelling of EM phenomena at crustal and mantle scales. Specifically, new methods for handling complex ionospheric and magnetospheric sources were proposed, accompanied by more efficient forward and inverse modelling tools that allowed us to combine several broadband sources and constrain electrical conductivity on multiple scales simultaneously. Magnetic signals due to oceanic tides were established as a new source to probe conductivity of the sub-oceanic upper mantle. Further, the launch of ESA Swarm satellites in 2013 and their successful ongoing operation have marked a new era in the field of large-scale EM induction, unlocking a set of new opportunities, but also posing new challenges. These developments were backed by new lab measurements of electrical conductivity for mantle minerals at temperatures and pressures that are getting closer to the relevant pressure and temperature conditions in the mantle, alleviating the need for inaccurate extrapolations. The latter enabled more plausible quantitative estimates of water content, melt fractions and temperature in the mantle. In parallel, crust and mantle conductivity models along with developed modelling techniques have become an integral part of geomagnetic field and geomagnetically induced currents (GICs) modelling workflows, establishing new inter-disciplinary knowledge domains.

Globally, unconventional hydrocarbons, known for the symbiosis of their hydrocarbon source and reservoir, pose significant seismic exploration challenges due to their confined target regions, extensive burial depth, minimal acoustic impedance variation, marked heterogeneity, and strong anisotropy. Over the past decade, electromagnetic (EM) exploration has evolved markedly, improving resolution and reliability, thus becoming indispensable in unconventional hydrocarbon exploration. Focusing on China's application of the controlled source electromagnetic method (CSEM), this review examines the geological and electrical attributes of these reservoirs, notably the low resistivity, high polarization and strong electrical anisotropy of shale gas reservoirs. Despite the demonstrated positive correlation between induced polarization (IP) parameters and reservoir parameters, current methodologies emphasize the IP effect, inadvertently neglecting electrical anisotropy, which affects data precision. Moreover, single-source CSEM methodologies limit the observational components, acquisition density, and exploration area, impacting the accuracy and efficacy of data interpretation. Recently developed CSEM techniques in China, namely wide-frequency electromagnetic method (WFEM), time–frequency electromagnetic method (TFEM), long offset transient electromagnetic method (LOTEM), and wireless electromagnetic method (WEM), harness high-power pseudo-random binary sequence (PRBS) waveforms, reference observation and processing technology, hybrid inversion, and enhancing operational efficiency and adaptability despite the pressing need for multi-functional software for data acquisition. Case studies detail these methods' applications in shale gas sweet spot detection and continuous hydraulic fracturing monitoring, highlighting the immense potential of EM methods in unconventional hydrocarbon sweet spot detection and total organic content (TOC) predication. However, challenges persist in suppressing EM noise, streamlining 3D inversion processes, and improving the detection and evaluation of sweet spots.

The occurrence of subsurface karst caves can cause the development of superficial depressions which, in turn, may pose a construction hazard. Identifying such a substratum requires integrated non-invasive measurement methods. The main objective of the study was to demonstrate the effectiveness of the non-invasive ERT, TLS, and GPR survey techniques in identifying the karst floor and determining the direction of discontinuities around the cave. The paper analyzes the limitations of the methods used in the study of heterogeneous media. These limitations are related to the methodology and measurement conditions, data processing, and interpretation in the context of the resolution and depth range. The study was conducted using the example of the Jaskinia pod Świecami cave, formed in the Sarmatianal calcarenites in Poland. The research confirmed its complex karst-anthropogenic genesis. The cave was formed as a result of the infiltration of rainwater and the dissolution of limestone by groundwater, while the paleokarst forms that are characteristic of it and of the surrounding caves and occur in their vicinity, i.e., narrow ridges called "karst candles", were formed as a result of water circulation during the local permafrost degradation in the middle Pleistocene. However, these forms were modified in the Upper Pleistocene and Holocene, as indicated by ERT images.

Two-dimensional dense seismic ambient noise array techniques have been widely used to image and monitor subsurface structure characterization in complex urban environments. It does not have limitations in the layout under the limitation of urban space, which is more suitable for 3D S-velocity imaging. In traditional ambient seismic noise tomography, the narrowband filtering (NBF) method has many possible dispersion branches. Aliases would appear in the dispersive image, and the dispersion curve inversion also depends on the initial model. To obtain high-accuracy 3D S-velocity imaging in urban seismology, we developed a robust workflow of data processing and S-velocity tomography for 2D dense ambient noise arrays. Firstly, differing from the NBF method, we adopt the continuous wavelet transform (CWT) as an alternative method to measure the phase velocity from the interstation noise cross-correlation function (NCF) without 2π ambiguity. Then, we proposed the sequential dispersion curve inversion (DCI) strategy, which combines the Dix linear inversion and preconditioned fast descent (PFD) method to invert the S-velocity structure without prior information. Finally, the 3D S-velocity model is generated by the 3D spatial interpolation. The proposed workflow is applied to the 2D dense ambient seismic array dataset in Changchun City. The quality evaluation methods include residual iteration error, horizontal-to-vertical spectral ratio (HVSR) map, and electrical resistivity tomography (ERT). All tests indicate that the developed workflow provides a reliable 3D S-velocity model, which offers a reference for urban subsurface space exploration.

The estimation of elastic properties of thin-bed formations from sonic logging is challenging. Standard slowness processing of sonic logging waveforms typically yields an average slowness log profile over the span of the receiver array, obscuring thin-layer features smaller than the array aperture. In order to enhance vertical resolution of the slowness logs, the subarray processing techniques have been developed. However, for the subarrays with smaller aperture, the semblance from subarray waveforms becomes susceptible to noise, which results in a low signal-to-noise (S/N) ratio for the processing slowness logs. To overcome the above drawbacks, we propose a slowness estimation method with the enhanced resolution ranging from the conventional array aperture resolution to the inter-receiver spacing based on the reconstruction of neighboring virtual traces (RNVTs). The method utilizes super-virtual interferometry to reconstruct a large number of waveforms for slowness extraction using redundant information from overlapping receiver subarrays. We validate the feasibility and effectiveness of the proposed method using synthetic numerical experiments. By adding different levels of noise to synthetic data, we conclude that the new method has better noise robustness. Finally, we apply this method to field data, and the estimated high-resolution slowness logs show good agreement in interbedded sand-shale sequences. Both numerical tests and examples of field data show that, the slowness logs estimated by the new method can be obtained with a high resolution as well as with a high S/N ratio, providing an effective method for assessing slowness properties from a borehole.