Pressure‐to‐Depth Conversion Models for Metamorphic Rocks: Derivation and Applications

Pressure‐to‐depth conversion is a crucial step toward geodynamic reconstruction. The most commonly used pressure‐to‐depth conversion method assumes that pressure corresponds to the lithostatic pressure. However, deviatoric stresses can cause pressure to deviate from the lithostatic case strongly, thus adding considerable uncertainty to pressure to‐depth conversion. First, we rederive formulas of pressure‐to‐depth conversion that take into account deviatoric stresses. Then, we estimate the range of possible depth independently for each point in a data set containing peak and retrograde metamorphic pressure data (one‐point method). In a second time, we use both the peak and retrograde pressure of a rock sample together, assuming that both pressures were recorded at the same depth (two‐point method). We explore different cases to explain the transition from peak to retrograde pressure by varying the direction and magnitude of stresses. This alternative model is consistent with all data points but for a more restricted range of stress state and depth than the one‐point model. Our results show that (1) even small deviatoric stresses have a significant impact on depth estimates, (2) the second principal stress component σ 2 plays an essential role, (3) several models can explain the pressure evolution of the data but lead to different depth estimates, and (4) strain data offer a mean to falsify our proposed two‐point pressure‐to‐depth conversion. The maximum predicted depth at peak pressure is 170 km using the assumption that pressure is lithostatic, compared to <75 km for our two‐point model, which could correspond to the crustal root Moho's depth.