This work proposes a new processing method based on orthonormal basis functions (OBFs) for two-dimensional (2D) magnetic anomaly data, which is an innovative extension of one-dimensional (1D) OBFs. In most surveys, ferromagnetic targets are usually regarded as magnetic dipoles. The magnetic anomaly field of a dipole in a horizontal plane is essentially a linear combination of linearly independent basis functions, which are then transformed into a set of 2D orthonormal basis functions (2D-OBFs) using the Gram–Schmidt algorithm. On the basis of the 2D-OBFs, a processing procedure for 2D magnetic anomaly data is established and named the 2D-OBF method. This method converts magnetic anomaly maps to energy maps, in which there is only one positive peak corresponding to the horizontal location of a magnetic dipole. As a consequence, the detection and localization are significantly simplified. To verify this new method, a total of 3000 Monte Carlo simulations were carried out, and the synthetic data were also processed using the traditional 1D-OBF method. The statistics of the 2D-OBF results showed that the localization accuracy and false alarm rate are 0.34 m and 1.9 %, respectively, at a data noise level of 10 nT, which was much better than the 1D-OBF method. Another synthetic data experiment verified the reliability of the 2D method for handling multiple targets simultaneously, even when the magnetic anomalies of adjacent targets are severely superimposed. For the measured aeromagnetic data, the 2D-OBF method also works well. Additionally, this method exhibits outstanding noise immunity in all tests. The signal-to-noise ratios (SNR) of the energy data are improved by approximately 14 dB compared to that of the magnetic anomaly data within the signal bandwidth. Developed from rigorous mathematical physics definitions, the 2D-OBF method is more conducive to the implementation of automatic data processing programs and has considerable practical promise.

The resistivity method and time-domain-induced polarization (TDIP) are two branches of electric exploration that are used to solve problems in mineral exploration, hydrogeology and engineering geology. In recent years, integrating different physical parameters for joint inversion to improve the accuracy of inversion results has been extensively examined; however, three-dimensional joint inversion of the two methods above has not been realized. To further address this issue, in this research, we used the limited-memory BFGS (L-BFGS) method to develop a three-dimensional joint inversion algorithm of the resistivity method and TDIP based on the cross-gradient constraints. In the new algorithm, the resistivity method and TDIP inversion were iteratively updated alternately to ensure that the inversion results can simultaneously meet the two conditions of obtaining minimum data misfits and finding structural similarity. The three-dimensional synthetic dataset inversion results showed that the models obtained by joint inversion are more accurate in the recovery of both the boundaries and the values of the anomalies. Especially in the background of high noise, joint inversion has higher resolution for the target body. The joint inversion algorithm was also successfully applied to a groundwater detection practice in Beijing, China, in which the practicability of the algorithm was confirmed.

Seismic interferometry is widely used to image and monitor earth structures at different scales by extracting an empirical Green’s function (EGF) from the crosscorrelation of ambient noise under the assumption of diffuse wavefields or energy equipartitioning. However, EGFs may be incorrectly estimated and lead to a misunderstanding of subsurface structures because the distribution of ambient noise sources is neither isotropic nor stationary. To extract reliable EGFs from the nonideal ambient noise data, we develop a polarization-based azimuth filter (PAF) to attenuate the ambient noise energy of nonstationary sources to improve the quality of crosscorrelation functions. The PAF is a time-frequency domain azimuth filter for 3C seismic data, which uses time-frequency polarization analysis to measure the azimuths of ambient noise signals and then filters the 3C data to obtain the signals from desired directions. Based on the stationary-phase theory, we use the PAF to extract the ambient noise signals from stationary-phase zones, which improves the quality of the crosscorrelation function and eliminates the requirement for long observations. A synthetic test and two short-time engineering examples demonstrate that uneven source distributions might cause serious spurious signals in EGFs, and we demonstrate the improvement in EGFs using our method. In addition, the PAF may allow for the complete separation of the fundamental and higher modes of Rayleigh waves, which uncovers more information implicit in the ambient noise data.

Different electromagnetic (EM) techniques have distinct resolutions for the exploration of natural resources. Integrating independent information from different EM datasets in a joint inversion results in a more precise and reliable resistivity model. To conduct an efficient joint inversion, it is crucial to understand the resolution characteristics of each EM technique and configuration. To enhance the interpretation using 1-D joint inversion of multiple EM datasets in a former mining area in eastern Thuringia (Germany), we developed a novel workflow for systematic resolution studies. Rather than focusing on limited resistivity models, our approach provides a broader perspective on the resolution characteristics of specific EM methods. The workflow is applied to helicopter-borne EM (HEM), semi-airborne EM (Semi-AEM), and long-offset transient EM datasets. Resolution studies reveal not only the advantages and limitations of each method but also demonstrate scenarios where joint inversion benefits. These insights are useful to optimally design multimethod applications. A synthetic 1-D joint inversion example successfully reconstructs the true model, while each individual method fails. This example demonstrates the added value of our presented resolution study workflow with respect to experimental design and acquiring optimal data in terms of resolution capabilities. We provide a toolkit for resolution analysis that serves as a roadmap for multimethod studies. Subsequently, we demonstrate that the accurate determination of shallow layers improves the resolution for deep targets. This is significant for designing deep exploration prospects. In the last step, our novel triple-method joint inversion scheme is validated through the application of field data.