Reply to discussion on numerical validation of Gassmann’s equations (Yury Alkhimenkov, 2023, Geophysics, 88, no. 4, A25–A29) by Leon Thomsen

Abstract

Gassmann’s equations have been known for several decades and are widely used in geophysics. These equations are treated as exact if all the assumptions used in their derivation are fulfilled. However, a recent theoretical study claimed that Gassmann’s equations contain an error. Shortly after that, I performed a three-dimensional numerical calculation on a simple pore geometry that verifies the validity of Gassmann’s equations. This pore geometry was simpler than those in real rocks but arbitrary. Furthermore, the employed pore geometry did not contain any special features (among all possible geometries) that were tailored to make it consistent with Gassmann’s equations. In other recent studies, I also performed numerical calculations on several other more complex pore geometries that supported the validity of Gassmann’s equations. To further support the validity of these equations, I provide here one more convergence study using a more realistic geometry of the pore space. Given that there are several studies that rederive Gassmann’s equations using different methods and numerical studies that verify them for different pore geometries, it can be concluded that Gassmann’s equations can be used in geophysics without concern if their assumptions are fulfilled. MATLAB routines to reproduce the presented results are provided.