Geochemically discriminating between magmatism in different tectonic settings remains a fundamental part of understanding the processes of magma generation within the Earth's mantle. Here we present an approach where machine learning (ML) methods are used for quantitative tectonic discrimination and feature selection using global geochemical data sets containing data for volcanic rocks generated in eight different tectonic settings. This study uses support vector machine, random forest, and sparse multinomial regression (SMR) approaches. All these ML methods with data for 24 elements and five isotopic ratios allowed the successful geochemical discrimination between igneous rocks formed in eight different tectonic settings with a discriminant ratio better than 83% for all settings barring oceanic plateaus and back‐arc basins. SMR is a particularly powerful and interpretable ML method because it quantitatively identifies geochemical signatures that characterize the tectonic settings of interest and the characteristics of each sample as a probability of the membership of the sample for each setting. We also present the most representative basalt composition for each tectonic setting. The new data provide reference points for future geochemical discussions. Our results indicate that at least 17 elements and isotopic ratios are required to characterize each tectonic setting, suggesting that geochemical tectonic discrimination cannot be achieved using only a small number of elemental compositions and/or isotopic ratios. The results show that volcanic rocks formed in different tectonic settings have unique geochemical signatures, indicating that both volcanic rock geochemistry and magma generation processes are closely connected to the tectonic setting.

Identifying the data structure including trends and groups/clusters in geochemical problems is essential to discuss the origin of sources and processes from the observed variability of data. An increasing number and high dimensionality of recent geochemical data require efficient and accurate multivariate statistical analysis methods. In this paper, we show the relationship and complementary roles of k‐means cluster analysis (KCA), principal component analysis (PCA), and independent component analysis (ICA) to capture the true data structure. When the data are preprocessed by primary standardization (i.e., with the zero mean and normalized by the standard deviation), KCA and PCA provide essentially the same results, although the former returns the solution in a discretized space. When the data are preprocessed by whitening (i.e., normalized by eigenvalues along the principal components), KCA and ICA may identify a set of independent trends and groups, irrespective of the amplitude (power) of variance. As an example, basalt isotopic compositions have been analyzed with KCA on the whitened data, demonstrating clear rock type/tectonic occurrence/mantle end‐member discrimination. Therefore, the combination of these methods, particularly KCA on whitened data, is useful to capture and discuss the data structure of various geochemical systems, for which an Excel program is provided.

Monitoring of seismic signals generated by slow deformation at convergent and transform plate boundaries worldwide, known as tectonic tremor, might provide insights into deformation processes in the source regions of megathrust earthquakes. Tremor signals occur dominantly in the 2–8 Hz frequency band and can last for tens of seconds to several minutes, in contrast to typical earthquakes that produce seismic signals at frequencies up to several tens of hertz and last less than a minute. Because tremor is caused by stochastic processes, the resultant waveforms are represented by a stochastic function and construction of deterministic measures to discriminate tremor signals from earthquakes is very difficult. In this study, we used a convolutional neural network (CNN) to discriminate the signals of tectonic tremor from those of local earthquakes in running spectral images of these signals. We developed a method (seismic running spectra‐CNN [SRSpec‐CNN]) that is sensitive to the absolute frequency of signal appearance, which reflects the physical properties of the signal source, but is insensitive to the time of signal onset. SRSpec‐CNN has 130,211 parameters that were trained by 17,213 images of $64×64pixels$⁠. Based on simultaneous analyses of the frequency contents and durations of the signals, we achieved 99.5% accuracy for our identifications of signals from tectonic tremor, local earthquakes, and noise. Because running spectra clearly differentiate the characteristic features of these signals, we were able to achieve this high accuracy by using a CNN of simple architecture.

Detrital monazite geochronology has been used in provenance studies. However, there are complexities in the interpretation of age spectra due to their wide occurrence in both igneous and metamorphic rocks. We use the multinomial logistic regression (MLR) and cross-validation (CV) techniques to establish a geochemical discrimination of monazite source rocks. The elemental abundance-based geochemical discrimination was tested by selecting 16 elements from granitic and metamorphic rocks. The MLR technique revealed that light rare earth elements (REEs), Eu, and some heavy REEs are important discriminators that reflect elemental fractionation during magmatism and/or metamorphism. The best model yielded a discrimination rate of ~97%, and the CV method validated this approach. We applied the discrimination model to detrital monazites from African rivers. The detrital monazites were mostly classified as granitic and of garnet-bearing metamorphic origins; however, their proportion of metamorphic origin was smaller than the proportion that was obtained by using the elemental-ratio-based discrimination proposed by Itano et al. in Chemical Geology (2018). Considering the occurrence of metamorphic rocks in the hinterlands and the different age spectra between monazite and zircon in the same rivers, a ratio-based discrimination would be more reliable. Nevertheless, our study demonstrates the advantages of machine-learning-based approaches for the quantitative discrimination of monazite.

This study presents a forward model to quantify the P‐wave velocity (V_P), S‐wave velocity (V_S), and electrical conductivity (σ) of the solid‐liquid mixtures for a given set of pressure, temperature, lithology, liquid phase (aqueous fluid or melt), liquid fraction, and geometrical parameters in relation to the aspect ratio and connectivity of the liquid phase. This is based on previous experimental and theoretical studies on seismic velocity and electrical conductivity of solid rocks and liquid phases. A total of 78 lithologies, an aqueous fluid with NaCl (∼0–10 wt.%), and mafic to felsic melt appropriate for the crust and the uppermost mantle conditions were described in terms of V_P, V_S, and σ, as per previous experimental measurements and molecular dynamics simulation. This forward model is provided as a Windows executable program, and generates synthetic V_P, V_S, and σ, referring to the seismic velocities and electrical conductivity observed in the northeast Japan arc. After generation of the synthetic V_P, V_S, and σ, the original lithology and liquid parameters (phase, fraction, aspect ratio, and connectivity) were searched by implementing the grid search algorithm to map the misfit over the broad parameter space. The mapping shows the presence of a global misfit minimum around the optimized solution and the possibility of resolving the lithology and the liquid phase parameters based on the observed V_P, V_S, and σ by using the forward model presented in this study.