Determination of slippage field of strike-slip faults using inverse solution methods

In this paper, a theoretical approach is proposed, in which spatial distribution of the strength of interplate coupling between two faces of strike-slip faults is investigated in detail through the inverse analysis of synthesized geodetic data. Synthesized (or available) geodetic data representing free surface movements is implemented to determine the solution of undertaken inverse problem that computes slippage vectors’ rates. Analytical approaches for treatment of faults in crustal deformation analysis involve some limitations. One important limitation of these methods is idealization of uniform dislocation on a rectangular fault plane in a uniform medium or half space. In fact, the real source is more complex than that supposed in these models and thus only the first-order aspects of the source characteristics can be evaluated from a uniform dislocation model. Isotropic and homogeneous material properties are the main assumptions of these methods. The Finite Element Method (FEM) on the other hand, allows easy treatment of complex boundary shape (interface zone) and internal variations of material properties. The FEM can simulate source geometry flexibly, and is also able to regard geological regimes and various layered structures. The standard equations of inverse problems offer a straightforward way for finding slippage vectors at two faces of the considered fault. One of the new aspects of the current study is evaluation of Green’s Operator Matrix (GOM) by means of FEM. This concept enables us to overcome all limitations of traditional inverse methods. In other words, the Green’s functions are not only functions of interface’s geometry, but are also functions of some other parameters like far-field boundary conditions, and geological structures (various material properties) which are not regarded in the traditional analytical inversion analysis. To implement fault sliding in a continuum-based FEM program, Split Node Technique (SNT) as a simple and efficient method is applied. This method does not increase the number of Degree Of Freedom (DOF) and the global stiffness matrix of system remains unchanged, which is the major advantage of this method. Furthermore, no net forces or moments are induced on the finite element mesh. This method is a direct approach and does not need any iteration, which is a common feature of other methods (e.g., contact problem techniques, or interface/joint elements). The initial idea of SNT for simple one-dimensional element is developed to 2D and 3D domains in the present research. How to find the Green’s functions by the FEM? By applying unit slippage vectors in each DOF of the interface nodes, we can determine corresponding component of the GOM. As other common inversion problems, singularity of coefficient matrix is the main problem. This problem particularly emerges if the number of DOFs is too large. The numerical procedure does not fail algorithmically, however it returns a set of slippage vectors that are wrong, even though direct substitution back into the original equations results in acceptable free-surface deformations. Singular Value Decomposition (SVD) diagnoses precisely what the problem is. In some cases, SVD will not only diagnose the problem, it will also solve it. The approach in current research is based on kinematic modeling of seismological problem. In other words, we only investigate fault movement, not causes of the occurred movement. In this research, both forward and inverse steps are considered to completely solve the problem. The forward step is performed by applying the slip along the fault’s faces and determining the displacement at the ground surface. This step is done using the FEM, whose results are compared with the analytical ones to verify the forward step. In the inverse solution on the other hand, our goal is to reach fault slip field using of surface displacement obtained from the first step as input data. Here, using this technique, 2D and 3D models of different types of strike-slip faults are presented in elastic mode for splitting purposes. The final step is to verify the inverse solution obtained for all models, from which the coupled zones of the considered faults are determined with acceptable accuracies.