Three-dimensional numerical analysis of magma transport through a pre-existing fracture in the crust

• Magma transport in a pre-existing vertical fracture is studied.
• A 3D numerical approach combining FEM, FDM and DDA is developed.
• Dyke opening and the crust surface deformation in both 2D and 3D are determined.
• Minimum magma chamber overpressure for magma transport to the surface is predicted.
• Magma chamber depth significantly influences the minimum overpressure.

Magmas are transported through pre-existing fractures in many repeatedly erupting volcanoes. The study of this special process of magma transport is fundamentally important to understand the mechanisms and conditions of volcanic eruptions. In this paper, we numerically simulate the magma propagation process through a pre-existing vertical fracture in the crust by using the combined finite difference method (FDM), finite element method (FEM) and discontinuous deformation analysis (DDA) approach. FDM is used to analyze magma flow in the pre-existing fracture, FEM is used to calculate the opening of the fracture during magma intrusion, and DDA is used to deal with the contact of the closed fracture surfaces. Both two-dimensional (2D) and three-dimensional (3D) examples are presented. Parametric studies are carried out to investigate the influence of various physical and geometric parameters on the magma transport in the pre-existing fracture. We have considered magma chamber depth ranging from 7 km to 10 km under the crust surface, magma viscosity ranging from 2 × 10−2 to 2 × 10−7 MPa s, and the density difference between the magma and host rock ranging from 300 to 700 kg/m3. The numerical results indicate that (1) the fluid pressure p varies gradually along the depth, (2) the shape of the magma body during propagation is like a torch bar and its width ranges from 2 m to 4 m approximately in the 3D case and 10 m to 50 m in the 2D case for the same physical parameters used, (3) the crust surface around the pre-existing fracture begins to increase on both sides of the fracture, forms a trough between them, then gradually uplifts during the transport of the magma, and finally takes the shape of a crater when the magma reaches the surface. We have also examined the influence of physical and geometric parameters on the minimum overpressure for magma transport in the 3D case. The numerical results show that our numerical technique presented in this paper is an effective tool for simulating magma transport process through pre-existing fractures in the crust.