[Paper Review] Numerical simulation of salt migration -- Large deformation in viscoelastic solid bodies

I-Shih Liu, Rolci Cipolatti+2 more|arXiv (Cornell University)|Aug 10, 2011

Geological formations and processes14 references3 citations

TL;DR

This paper proposes a successive linear approximation method based on updated referential configurations to simulate large deformation in viscoelastic solids, enabling accurate numerical modeling of salt diapirism. The method treats large deformations as a sequence of small incremental steps relative to the current configuration, successfully simulating diapir formation and migration over time with minimal remeshing, even under extreme deformation.

ABSTRACT

We consider instability of a two layered solid body of a denser material on top of a lighter one. This problem is widely known to geoscientist in sediment-salt migration as salt diapirism. In the literature, this problem has often been treated as Raleigh-Taylor instability in viscous fluids instead of solid bodies. In this paper, we propose a successive linear approximation method for large deformation in viscoelastic solids as a model for salt migration.

Motivation & Objective

• To address the challenge of simulating large deformation in viscoelastic solids, particularly in the context of salt migration.
• To overcome limitations of traditional fluid-based models (e.g., Rayleigh-Taylor instability) that fail to capture solid-like behavior in salt diapirism.
• To develop a robust numerical method that enables stable and accurate simulation of diapir formation under realistic viscoelastic material behavior.
• To demonstrate the feasibility of simulating long-term diapir evolution with minimal remeshing despite extreme deformation.

Proposed method

• The method employs a relative-descriptional formulation, where each time step uses the current deformed configuration as the reference for linearization.
• At each step, constitutive functions are evaluated at the current state and linearized for small incremental deformations, transforming the problem into a sequence of linear boundary value problems.
• The finite element method is used to solve the linearized equations at each step, with boundary conditions applied directly on the current configuration.
• The approach avoids the complexity of incremental data in initial configuration formulations by updating the reference state at every time step.
• The method is implemented in both 2D and 3D domains, using a Mooney-Rivlin-type viscoelastic model for salt and elastic parameters for sediments.
• Mesh updates are performed at each step, but remeshing is rarely needed due to the stability of the incremental approach under large deformations.

Experimental results

Research questions

• RQ1 Can a successive linear approximation method effectively simulate large deformation in viscoelastic solids relevant to salt diapirism?
• RQ2 How does the proposed method compare to traditional fluid-based Rayleigh-Taylor instability models in capturing diapir formation?
• RQ3 To what extent can the method simulate long-term diapir evolution with minimal remeshing under extreme deformation?
• RQ4 How do initial perturbations and base rock inclination influence the initiation and morphology of salt structures in a viscoelastic solid model?

Key findings

• The method successfully simulates the formation of salt diapirs over 100 million years, with the diapir reaching maximum height at approximately 20 million years.
• The simulation shows that buoyancy from density inversion drives diapirism, with the diapir becoming mature and stable after 20 million years.
• The deformed mesh at n=300 (30 million years) exhibits large deformation patterns that closely resemble experimental silicone putty models of diapirs.
• When the base rock is gradually inclined by one degree over 10 million years, the model produces a sequence of salt pillows and diapirs forming from right to left, matching geological observations from northern Germany.
• The numerical results qualitatively reproduce the multi-diapir structures observed in the Permian salt complex of northern Germany, validating the model’s geological relevance.
• Despite the use of convenient, non-geologically calibrated material parameters, the method maintains numerical stability and produces physically plausible deformation patterns without frequent remeshing.