Flow systems of the Earth’s viscous subsurface: A complement to groundwater flow systems

Abstract

Assessment of the long term possibilities and risks related to geological storage requires insight in the deep groundwater flow systems. The objective of this paper is to show the relevance of the deep creep flow of the earth’s viscous upper mantle and crust as a complement to the groundwater flow. The paper presents an approach based on Fourier decomposition of the topography. The creep flow equations are solved analytically, which results in simple indices like penetration depth and relaxation time characterizing the gravity-driven creep flow. Thanks to the very high effective viscosity of the Earth’s subsurface a Darcy-like equation is obtained in which the ‘creep conductivity’ is Fourier mode dependent, which allows for simple comparison with the hydraulic conductivity for groundwater flow. Order of magnitude calculations indicate that for horizontal length scales of 100–1000 km the subsurface creep velocities are 0.3–30 mm/year, respectively, which shows that creep velocities in the deep subsurface are significant with respect to deep groundwater velocities.

Keywords

• Creep flow
• Crust and upper mantle
• Darcy’s law
• Deep geological storage
• Effective viscosity
• Groundwater flow