Stability of Melt Lineaments in Plume-Ridge Interaction Settings: Insights from Two-Phase Flow Models and Wavelet Analysis of the Galápagos Platform

The interaction between mid-ocean ridges and mantle plumes (~1000 km scale) is a fundamental geodynamic process, generating complex spatio-temporal patterns of volcanism exemplified by the Galápagos platform and the prominent, en-echelon Wolf-Darwin lineaments. Unlike axial volcanism driven by pure extension, these off-axis features form in a regime where plate motion and deep plume flow create a dominant shear component. While such lineaments are characteristic of plume-ridge interaction (PRI) settings, the physical mechanisms governing their distinct spacing, orientation, and longevity remain enigmatic. Understanding these mechanisms is critical, as the resulting topographic heterogeneity governs seamount formation, which in turn profoundly influences ocean circulation and the distribution of deep-sea benthic habitats.

Here, we test the hypothesis that these lineaments result from melt localization instabilities driven by asthenospheric shear. We employ numerical models of viscous two-phase flow¹ to simulate the deformation of pre-existing melt heterogeneities embedded in a porous background, treating the system as a localized shear box. We systematically vary the background porosity (φ_back= 0.01 - 0.05) and the melt pocket porosity (φ_mp = 0.04 - 0.08) to determine the conditions under which melt patches remain distinct—forming separate features like the Wolf-Darwin lineaments—versus coalescing into background flow channels.

Our results identify a hierarchy of length scales controlling melt structure evolution. Consistent with linear stability analysis and laboratory experiments, we observe an intrinsic background instability scale of λ_inst ≈ 0.1· δ_c (where δ_c is the compaction length). We find that the survival of pre-existing melt pockets follows a gradient dependent on the porosity contrast (φ_mp/φ_back): generally, pockets must exceed λ_inst by a factor of 2–4 to survive shear as intact features. Furthermore, we constrain the critical separation distance for maintaining distinct lineaments. Simulation results demonstrate that a minimum edge-to-edge separation of ≈ 1· δ_c is required to prevent hydraulic connectivity; below this threshold, pressure gradients drive adjacent patches to connect via background melt channels and coalesce.

To validate these scaling laws against natural systems, we apply a quantitative 2D continuous wavelet analysis² to both simulation porosity fields and high-resolution bathymetry of the Galápagos Archipelago. This comparative spectral approach allows us to objectively quantify the dominant wavelengths and anisotropy of the observed lineaments without bias. By mapping the modeled stability regimes to the observed lineament spacing, we place constraints on the effective mantle viscosity and permeability structure required to preserve the Wolf-Darwin lineaments. These findings provide a mechanical framework for interpreting off-axis volcanism and define specific targets for future seafloor magnetotelluric and seismic anisotropy campaigns aimed at resolving lateral melt transport in PRI system.

¹Zhongtian Zhang, & Jacob S. Jordan. (2021). Zenodo. https://doi.org/10.5281/zenodo.4460676
²Ungermann, J. (2025). JuWavelet (v01.03.00). Zenodo. https://doi.org/10.5281/zenodo.16962346