On approximations of EASY%Ro solutions to estimate maximum temperature from vitrinite reflectance

Abstract

Vitrinite reflectance R_o is commonly used as a paleotemperature proxy for rocks. Among various models used to reconstruct paleothermal histories, EASY%R_o, a set of ordinary differential equations to describe the maturation of vitrinite, has been widely used since 1990. Approximations of EASY%R_o solutions employing specific paleothermal histories have been used in the field of structural geology to estimate maximum paleotemperatures T_max. However, comparisons of those approximations with results obtained with EASY%R_o have not been reported in scientific literatures, and the errors on the approximations and the limitations of their use to determine T_max remain undocumented. Here, we performed such comparisons and found that the use of those approximations can lead to considerable deviations from the results obtained with EASY%R_o. We then derived new approximations of EASY%R_o solutions for four representative paleothermal histories that provided estimates of T_max within 3 ^°C of those obtained with EASY%R_o. We also describe the Jacobian of EASY%R_o, which can be used to propagate errors from R_o to T_max. We expect that the four approximations provided herein will be useful, although we recommend using EASY%R_o itself if greater precision or particular paleothermal histories other than those assumed in this study are required.