Diapirism and topography

SUMMARY A new numerical technique using markers and a deformable Lagrangian mesh is used to study the deformation of the surface above a rising diapir. This method allows modelling of a free‐surface boundary in a self‐consistent way. The method makes it possible to investigate many different problems with non‐regular geometry. The codes were verified through comparison with analytical solutions for the initial stages and with other numerical codes for mature stages. Our simulations led to the following conclusions. (1) The growth rate of the diapir is more strongly influenced by the viscosity contrast than the wavelengths. This is due to the strong growth rate difference during the initial stage. (2) The maximum elevation above the diapir linearly increases with increasing wavelength and is approximately the same for different viscosity contrasts. (3) The elevation will be considerably higher for a low‐viscosity diapir at a given depth than for an isoviscous diapir. Comparisons for different thicknesses of the buoyant layer showed that the highest topography is produced when the two layers have equal thickness. We showed the dependence of the topographic behaviour on the parameter R (the ratio of the density difference between two layers to the density of the upper layer). It was found that topography behaves linearly up to R = 0.15. It indicates that a posteriori estimation of topography for traditional calculations using the free‐slip boundary condition works well within this limit.