Petrology as an ill-posed inverse problem

Rocks found at the Earth’s surface typically undergo long and complex transformations within the Earth’s crust. In response to varying pressures and temperatures deep in the crust, rocks undergo recrystallization, involving the formation or dissolution of minerals and changes in the equilibrium composition of existing phases. The underlying processes, such as inter-crystalline chemical diffusion and recrystallization, are irreversible, as they continually modify the properties of evolving rocks. While such processes can preserve evidence of past geological conditions, they can also erase earlier equilibration stages. Understanding these processes is challenging because the inverse problem of reconstructing past conditions is inherently non-unique (ill-posed).

This presentation showcases different modeled examples of re-equilibration, revealing that interpretations of past equilibria can sometimes be misleading. In addition, inverse diffusion modeling can estimate the duration of geological processes, although it remains prone to ambiguity. Forward modeling of physical processes helps to identify sources of non-uniqueness and provides regularization, which reduces the model-parameter space. Therefore, integrating geophysical, geodynamic, and petrological inversion methods offers distinct advantages by providing a more robust framework for testing hypotheses and reducing uncertainty.