Summary To investigate the effects of slope geometric parameters and soil stratigraphic properties on the topographic amplification of ground motions, a large number of 2D horizontally layered slope models are constructed. Firstly, the linear and nonlinear seismic responses of a slope model are compared, and the result shows that the nonlinear characteristics of soils should be considered when studying the amplifying effect of slope topography on ground motions. Then, the nonlinear seismic responses of these slope models are analyzed from four aspects: the maximum shear strain in the slopes, the effects of geometry and stratigraphy on the seismic response, the distance between the maximum topographic amplification indicators and the slope crest, and the influence range of slope topography behind the slope crest. The results indicate that the amplifying effect of slope topography on ground motions increases with increasing slope height or decreasing average shear-wave velocity of the overlying soil layers. Besides, the variation of the topographic amplification effect with slope gradient is significantly influenced by soil stratigraphic properties. The distance between the maximum topographic amplification indicators and the slope crest is mainly in the range of 0 ∼ 60 m, and the influence range of slope topography behind the slope crest is mainly in the range of 0 ∼ 150 m. Subsequently, approximate relations are derived based on regression analyses of simulation results, which can provide meaningful references for the seismic design and seismic retrofitting of engineering structures behind the slope crest. Finally, the effects of slope geometric parameters and soil stratigraphic properties on ground motion modifications are further evaluated according to the prediction curves provided by the approximate relations.

Summary An accurate magnitude estimation is necessary to properly evaluate seismic hazard, especially in low to moderate seismicity areas such as Metropolitan France. However, magnitudes of small earthquakes are subject to large uncertainties caused by major high-frequency propagation effects which are generally not properly considered. To address this issue, we developed a method to separate source, attenuation and site parameters from the elastic radiative transfer modeling of the full energy envelopes of seismograms. The key feature of our approach is the treatment of attenuation -both scattering and absorption- in a simple but realistic velocity model of the Earth’s lithosphere, including a velocity discontinuity at the Moho. To reach this goal, we developed a 2-step inversion procedure, allowing first to extract attenuation parameters for each source-station path from the whole observed energy envelope using the Levenberg-Marquardt and grid-search algorithms, then to determine site amplification and the source displacement spectrum from which the moment magnitude Mw is extracted. In the first step, we use the forward modeling procedure of Heller et al. (2022) in order to simulate energy envelopes by taking into account the full treatment of wave polarization, the focal mechanism of the source and the scattering anisotropy. The inversion procedure is then applied to the 2019 ML 5.2 Le Teil and 2014 ML 4.5 Lourdes earthquakes which both occurred in southern France. Data from 6 stations are selected for each event. The inversion results confirm a significant variability in the attenuation parameters (scattering and absorption) at regional scale and a strong frequency dependence. Scattering appears to be stronger towards the French Alps and Western Pyrenees. Absorption is stronger as frequency increases. Although not very resolvable, the mechanism of scattering appears to be forward or very forward. By inverting the source spectrum, we determine moment magnitudes Mw of 5.02 ± 0.17 for the Le Teil earthquake and 4.17 ± 0.15 for the Lourdes earthquake.

Summary As deep-seated ore deposits become increasingly relevant for mineral exploration, the demand for time-efficient and powerful deep-sounding exploration methods rises. A suitable method for efficiently sensing ores at great depth is airborne electromagnetics (EM) using natural signal of atmospheric origin. The method relates airborne magnetic field recordings in the audio-frequency range to reference magnetic field recordings measured at a ground-based site and can achieve greater penetration depths when compared to controlled source airborne EM techniques. However, airborne natural source EM data are prone to noise caused by platform vibrations especially deteriorating data quality at low frequencies and thus narrowing the depth of investigation. Motional noise manifests as coherent noise on all airborne magnetic field components demanding for a powerful processing tool to remove such kind of noise. Unlike the bivariate approach, which is widely used in natural source EM, the multivariate approach is capable of detecting and reducing the effect of coherent noise. We introduce a robust multivariate processing for airborne natural source EM data and present the code implementation. The code was applied to a large-scale data set from the Kalahari-Copper-Belt in Namibia covering over 1, 000 km2. We obtained spatially consistent and smooth sounding curves in a frequency range of 10 to 1, 000 Hz including frequencies with prominent motional noise. Transfer functions are in good agreement with other geophysical and geological information.

Summary Gravity gradient data can show the structural features of geological bodies in the shallow lithosphere with higher sensitivity and resolution than conventional gravity data. Gravity gradient inversion can be applied to obtain the lithospheric density structures of geological bodies. However, as with gravity data, gravity gradient data have no inherent depth resolution. The methods of gravity gradient depth imaging and gravity gradient inversion are integrated in this study. The depth imaging method is effective for calculations without prior information and iterative computations. As the parameters in the depth weighting function should be chosen from a set of values used in inversion tests of synthetic data, which brings some uncertainties, the depth imaging results of gravity gradient are introduced into the depth weighting function. Several synthetic models are tested to demonstrate the advantages and features of the effective integrated method. Finally, the integrated method is applied to the interpretation of the GOCE satellite gravity gradient tensors over the northeastern margin of the Qinghai-Tibet Plateau. The results reveal that in the crust of the study area, the distribution of density anomalies is more in line with the mechanism of the crustal flow model, in the upper mantle of the study area, the density anomalies are mainly influenced by the high heat flow environment.

Summary A three-dimensional finite-difference solver has been developed and implemented for Boussinesq convection in a spherical shell. The solver transforms any complex curvilinear domain into an equivalent Cartesian domain using Jacobi transformation and solves the governing equations in the latter. This feature enables the solver to account for the effects of the non-spherical shape of the convective regions of planets and stars. Apart from parallelization using MPI, implicit treatment of the viscous terms using a pipeline alternating direction implicit scheme and HYPRE multigrid accelerator for pressure correction makes the solver efficient for high-fidelity direct numerical simulations. We have performed simulations of Rayleigh-Bénard convection at two Rayleigh numbers Ra = 105 and 107 while keeping the Prandtl number fixed at unity (Pr = 1). The average radial temperature profile and the Nusselt number match very well, both qualitatively and quantitatively, with the existing literature. Closure of the turbulent kinetic energy budget, apart from the relative magnitude of the grid spacing compared to the local Kolmogorov scales, ensures sufficient spatial resolution.

Summary Ambient noise source localization is of great significance for estimating seismic noise source distribution, understanding source mechanisms and imaging subsurface structures. The commonly used methods for source localization, such as the matched field processing and the full-waveform inversion, are time-consuming and not applicable for time-lapse monitoring of the noise source distribution. We propose an efficient alternative of using deep learning for noise source localization. In the neural network, the input data are noise cross-correlation functions and the output are matrices containing the information of noise source distribution. It is assumed that the subsurface structure is a horizontally layered earth model and the model parameters are known. A wavefield superposition method is employed to efficiently simulate ambient noise data with quantities of local noise sources labelled as training datasets. We use a weighted binary cross-entropy loss function to address the prediction inaccuracy caused by a sparse label matrix during training. The proposed deep learning framework is validated by synthetic tests and two field data examples. The successful applications to locate an anthropogenic noise source and a carbon dioxide (CO2) degassing area demonstrate the accuracy and efficiency of the proposed deep learning method for noise source localization, which has great potential for monitoring the changes of the noise source distribution in a survey area.

Summary In this article, we use a new workflow to substantiate the characterization of a prominent, deep sediment conductor in the hyper-extended Bjørnøya Basin (SW Barents Sea) previously identified in smooth resistivity models from 3D deterministic inversion of magnetotelluric data. In low dimensionality environments like layered sedimentary basin, 1D Bayesian inversion can be advantageous for a thorough exploration of the solution space but the violation of the 1D assumption has to be efficiently handled. The primary geological objectives of this work is therefore preceded by a secondary task: the application of a new machine learning approach for handling the 1D violation assumption for 21 MT field stations in the Barents Sea. We find that a decision tree can adequately learn the relationship between MT dimensionality parameters and the 1D-3D residual response for a training set of synthetic models, mimicking typical resistivity structures of the SW Barents Sea. The machine learning model is then used to predict the dimensionality compensation error for MT signal periods ranging of 1 to 3000 s for 21 receivers located over the Bjørnøya Basin and Veslemøy High. After running 1D Bayesian inversion, we generated a posterior resistivity distribution for an ensemble of 6000 1D models fitting the compensated MT data for each 21 field stations. The proportion of 1D models showing ρ < 1 Ω.m is consistently beyond 80% and systemically reaches a maximum of 100% in the Early Aptian - Albian interval in the Bjørnøya Basin. In hyper-extended basins of the SW Barents Sea, the dimensionality compensation workflow has permitted to refine the characterization of the deep basin conductor by leveraging the increased vertical resolution and optimal used of MT data. In comparison, the smooth 3D deterministic models only poorly constrained depth and lateral extent of the basin anomaly. The highest probability of finding ρ < 1 Ω.m is robustly assigned to the syn-tectonic Early Aptian - Albian marine shales, now buried at 6 to 8 km depth. Based on a theoretical two phase fluid-rock model, we show that the pore fluid of these marine shales must have a higher salinity than seawater to explain the anomaly ρ < 1 Ω.m. Therefore, the primary pore fluid underwent mixing with a secondary brine during rifting. Using analogue rift systems in paleomargins, we argue that two possible secondary brine reservoir may contribute to deep saline fluid circulation in the hyper-extended basin: (1) Permian salt-derived fluid and, (2) mantle-reacted fluid from serpentinization.

Summary To address complex subsurface structures, a high-resolution velocity model must be constructed. Conventionally, algorithms such as full waveform inversion (FWI) have been used to derive accurate high-resolution velocity structures, but obstacles such as high computational costs remain. Therefore, we propose a high-resolution U-NET (HR U-NET) machine learning model to derive a high-resolution velocity model from a low-resolution velocity model. The low-resolution velocity model and migration data obtained through the corresponding velocity information were used as input data for training. In addition, we tried to improve the accuracy of the high-resolution velocity model by using prior information containing accurate velocity values. A prior model generated through geophysical logging data and a weight model including the reliability information of the prior model were also utilized. Therefore, the HR U-NET model was trained using the low-resolution velocity model, the migration data, the prior model, and the weight model. Numerical experiments conducted using synthetic and field data demonstrated that the proposed model could accurately construct a high-resolution velocity model and verified that the prior model and weight model play important roles in the training process. Additionally, we confirmed that the proposed method derived almost similar results using only 8.2 per cent of the computational cost of the conventional inversion method. In other words, there is an advantage that it is possible to predict high-resolution velocity information more efficiently in terms of computational cost.

Summary The determination of seismic event locations with sparse networks or single-borehole systems remains a significant challenge in observational seismology. Leveraging the advantages of the location approach HADES (eartHquake locAtion via Distance gEometry Solvers), which was initially developed for locating clustered seismicity recorded at two stations, through the solution of a Distance Geometry Problem, we present here an improved version of the methodology: HADES-R (HADES-Relative). Where HADES previously needed a minimum of 4 absolutely located master events, HADES-R solves a least-squares problem to find the relative inter-event distances in the cluster, and uses only a single master event to find the locations of all events, and subsequently applies rotational optimizer to find the cluster orientation. It can leverage iterative station combinations if multiple receivers are available, to describe the cluster shape and orientation uncertainty with a bootstrap approach. The improved method requires P- and S-phase arrival picks, a homogeneous velocity model, a single master event with a known location, and an estimate of the cluster width. The approach is benchmarked on the 2019 Ridgecrest sequence recorded at two stations, and applied to two seismic clusters at the FORGE geothermal test site in Utah, USA, with a microseismic monitoring scenario with a DAS in a vertical borehole. Traditional procedures struggle in these settings due to the ill-posed network configuration. The azimuthal ambiguity in such a scenario is partially overcome by the assumption that all events belong to the same cluster around the master event and a cluster width estimate. We are able to find the cluster shape in both cases, although the orientation remains uncertain. HADES-R contributes to an efficient way to locate multiple events simultaneously with minimal prior information. The method’s ability to constrain the cluster shape and location with only one well-located event offers promising implications, especially for environments where limited or specialised instrumentation is in use.

Summary Observations of large-scale seismic anisotropy can be used as a marker for past and current deformation in the Earth’s mantle. Nonetheless, global features such as the decrease of the strength of anisotropy between ∼150–410 km in the upper mantle and weaker anisotropy observations in the transition zone remain ill-understood. Here, we report a proof of concept method that can help understand anisotropy observations by integrating pressure-dependent microscopic flow properties in mantle minerals particularly olivine and wadsleyite into geodynamic simulations. The model is built against a plate-driven semi-analytical corner flow solution underneath the oceanic plate in a subduction setting spanning down to 660 km depth with a non-Newtonian n = 3 rheology. We then compute the crystallographic preferred orientation (CPO) of olivine aggregates in the upper mantle (UM), and wadsleyite aggregates in the upper transition zone (UTZ) using a viscoplastic self-consistent (VPSC) method, with the lower transition zone (LTZ, below 520 km) assumed isotropic. Finally, we apply a tomographic filter that accounts for finite-frequency seismic data using a fast-Fourier homogenization algorithm, with the aim of providing mantle models comparable with seismic tomography observations. Our results show that anisotropy observations in the UM can be well understood by introducing gradual shifts in strain accommodation mechanism with increasing depths induced by a pressure-dependent plasticity model in olivine, in contrast with simple A-type olivine fabric that fails to reproduce the decrease in anisotropy strength observed in the UM. Across the UTZ, recent mineral physics studies highlight the strong effect of water content on both wadsleyite plastic and elastic properties. Both dry and hydrous wadsleyite models predict reasonably low anisotropy in the UTZ, in agreement with observations, with a slightly better match for the dry wadsleyite models. Our calculations show that, despite the relatively primitive geodynamic setup, models of plate-driven corner flows can be sufficient in explaining first-order observations of mantle seismic anisotropy. This requires, however, incorporating the effect of pressure on mineralogy and mineral plasticity models.