Pecube: A new finite-element code to solve the 3D heat transport equation including the effects of a time-varying, finite amplitude surface topography

A robust finite-element code (Pecube) has been developed to solve the three-dimensional heat transport equation in a crustal/lithospheric block undergoing uplift and surface erosion, and characterized by an evolving, finite-amplitude surface topography. The time derivative of the temperature field is approximated by a second-order accurate, mid-point, implicit scheme that takes into account the changing geometry of the problem. The method is based on a mixed Eulerian-Lagrangian approach that requires frequent re-interpolation of the temperature field in the vertical direction to ensure accuracy. From the computed crustal thermal structure, the temperature history of rock particles that, following an imposed tectonic scenario, are exhumed at the Earth's surface, is derived. These T-t paths can then be used to compute apparent isotopic ages for a range of geochronometers. The usefulness of the code is demonstrated by computing the predicted distribution of (U-Th)/He apatite ages in a high relief area of the Sierra Nevada, California, for a range of tectonic scenarios and comparing them to existing data.