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Hydrothermal vent temperatures fluctuate in response to transient magmatic and tectonic activity at the axis of mid-ocean ridges (MORs) and modulate energy fluxes from the deep Earth to the ocean. Such fluctuations have thus far only been documented on time scales of minutes to years, because of the scarcity of long, continuous observations. Here, we assemble a ~35-year-long time series of exit fluid temperatures from five hydrothermal vents on the East Pacific Rise axis, between 9°46’-51’N. This dataset reveals a steady increase in maximum venting temperatures atop the central part of the axial magma lens (AML), from ~350 °C to ~390 °C between the 1991–92 and 2005–06 eruptions. Temperatures decreased back to ~350 °C shortly after the 2005–06 eruption and have been rising ever since. We interpret the temperature increase as a result of a steady decrease in upflow zone permeability caused by the steady inflation of the AML compressing the oceanic upper crust. Using laboratory-determined pressure–permeability relations, we estimate crustal pressurization rates of 0.38 MPa/y (1992–2005) and 0.33 MPa/y (post-2006), consistent with geodetic observations from 2009–2011. Decadal fluctuations in hydrothermal vent temperatures likely mimic the rate of AML pressurization, yielding valuable new constraints on the dynamics of magmatic replenishment and eruptions at MORs. Notably, this temperature time series underpinned our forecast of the April 2025 eruption at the study site. 

Abstract We provide a new algorithm for mass‐balance calculations in petrology and geochemistry based on the log‐ratio approach championed initially by John Aitchison (e.g., Aitchison, 1982,https://doi.org/10.1111/j.2517-6161.1982.tb01195.x; Aitchison, 1984,https://doi.org/10.1007/bf01029316) along with the underlying principles, mathematical frameworks, and data requirements. Log‐ratio Inversion of Mixed End‐members (LIME) is written in MATLAB and calculates phase proportions in an experiment or rock given a bulk composition, the composition of each phase, and the associated compositional uncertainties. An important advantage of LIME is that performing the mass‐balance calculation in inverse log‐ratio space constrains phase proportions to be between 0 and 100 wt.%. Further, the resulting LIME phase proportions provide realistic estimates of uncertainty regardless of data distribution. These two characteristics of LIME improve upon standard multiple linear regression techniques, which may yield negative values for phase proportions if non‐constrained or report oversimplified symmetric errors. Primary applications of LIME include estimating phase abundances, calculating melting and metamorphic reaction stoichiometries, and checking for open system behavior in phase equilibria experiments. The technique presented here covers whole‐rock analysis, mineralogy, and phase abundance, but could be extended to isotopic tracers, trace element modeling, and regolith component un‐mixing. We highlight the importance of uncertainty estimations for phase abundances to the fields of petrology and geochemistry by comparing our results from LIME to previously published mass‐balance calculations. Furthermore, we present case studies that demonstrate the role of mass‐balance calculations in determining magma crystallinity and defining melting reactions. 

Locked areas of subduction megathrusts are increasingly found to coincide with landscape features sculpted over hundreds of thousand years, yet the mechanisms that underlie such correlations remain elusive. We show that interseismic locking gradients induce increments of irreversible strain across the overriding plate manifested predominantly as distributed seismicity. Summing these increments over hundreds of earthquake cycles produces a spatially variable field of uplift representing the unbalance of co-, post-, and interseismic strain. This long-term uplift explains first-order geomorphological features of subduction zones such as the position of the continental erosive shelf break, the distribution of marine terraces and peninsulas, and the profile of forearc rivers. Inelastic yielding of the forearc thus encodes short-term locking patterns in subduction landscapes, hinting that megathrust locking is stable over multiple earthquake cycles and highlighting the role geomorphology can play in constraining Earth’s greatest source of seismic hazard.