Solving 3D boundary element problems using constrained iterative approach

Some major challenges for geophysicists and structural geologists using three-dimensional boundary element method codes (3D-BEM) are: (1) reducing the amount of memory required to solve large and dense systems and (2) incorporation of inequality constraints such as traction inequality constraints (TIC) and displacement inequality constraints (DIC). The latter serves two purposes. First, for example, inequality constraints can be used to simulate frictional slip (using TIC). Second, these constraints can prevent element interpenetration while allowing opening mode (using DIC). We have developed a method that simultaneously incorporates both types of functionality of the inequality constraints. We show that the use of an appropriate iterative solver not only avoids the allocation of significant memory for solving the system (allowing very large model computation and simplifying parallelization on multi-core processors), but also admits interesting features such as natural incorporation of TICs and DICs. Compared to other techniques of contact management (e.g., Lagrange multipliers, penalty method, or complementarity problem), this new simple methodology, which does not use any incremental trial-and-error procedures, brings more flexibility, while making the system more stable and less subject to round-off errors without any computational overhead. We provide validations and comparisons of the inequality constraints implementation using 2D analytical and numerical solutions.     

Implicit Structural Modeling by Minimization of the Bending Energy with Moving Least Squares Functions

Mathematical Geosciences - In this paper, an implicit structural modeling method using locally defined moving least squares shape functions is proposed. The continuous bending energy is minimized...     

Multiple mechanisms driving detachment folding as deduced from 3D reconstruction and geomechanical restoration: the Pico del Águila anticline (External Sierras,Southern Pyrenees)

Three‐dimensional (3D) modelling allows observation of geological features that may not be evident by classical two‐dimensional approaches. This is particularly important in the Pico del Águila anticline (Central External Sierras, Southern Pyrenees, Spain), a structure characterized by important geometrical variability in 3D. The Pico del Águila is a N–S‐trending fold, transverse to the E–W‐trending South‐Pyrenean thrust front, with well‐exposed growth strata that record the evolution of the structure and the influence of the South‐Pyrenean thrust front. Fold kinematics is complex and not precisely quantified. It is characterized by multiple folding mechanisms acting simultaneously in a heterogeneous stratigraphic sequence. To better understand the fold's structural evolution, 3D reconstruction and geomechanical restoration of the structure were performed. The restoration takes into account rock mechanical properties without assuming a specific kinematic model. Our work suggests that the growth of the structure was characterized by variable uplift/sedimentation rates through time and between fold limbs. The restoration also reveals that a combination of multiple folding mechanisms operated simultaneously in different units and structural domains during anti‐clinal growth. This has major implications in the understanding of detachment folds with associated growth strata, as such structures are described in many settings as potential traps for hydrocarbons and natural resources.