# Modeling the co-seismic deformation field of a fault and determining the sensitivity of the geometrical and physical parameters of the model to this deformation field

Authors

1 Graduate Student, Faculty of Geodesy & Geomatics Engineering, K. N. Toosi University of Technology, Tehran, Iran

2 Assistant Professor, Faculty of Geodesy & Geomatics Engineering, K. N. Toosi University of Technology, Tehran, Iran

Abstract

The study of faulting and its resultant earth surface deformations is an essential research field in Iran. The major part of this large country is located in very active seismic zones. Any study in this field can enable us to mitigate the risk of earthquake hazards.
3D modeling of displacement and surface deformation caused by earthquake faulting based on a homogeneous, isotropic, elastic half space model is the main aim of this paper. The paper focuses on the modeling of a 3D co-seismic deformation field caused by stress accumulation and its release along seismogenic faults based on a homogeneous elastic half-space model. The most commonly used analytic models of fault deformations have been based on the dislocation solutions of Okada (1985, 1992). This dislocation model is used to investigate surface deformations which are generated by strike-slip and dip-slip faulting. A method of sensitivity analysis is applied to determine sensitivity of the model and its resultant displacement field with respect to the change of parameters of the model.
During the last decades, powerful new models have been developed and deployed with encouraging results for improving knowledge of fault system behavior and its consequent earthquake hazards. Fault displacement models based on elastic dislocation theory have been used to calculate displacements and strains due to co-seismic slip events. In the elastic dislocation theory, faults are considered as displacement discontinuities or dislocations in an otherwise continuous elastic medium. In this approach, faults are represented as surfaces across which there is a discontinuity in the elastic displacement field.
The elastic dislocation theory is conceptually valid for modeling co-seismic deformations. The elastic dislocation formulation of Okada is used in our models, which expresses the displacement field U(x, y, z) at any given point as a function of fault parameters (slip, dip, strike, length, and width) and the elastic constants within the continuum, for rectangular fault panels with horizontal upper and lower edges. The Okada formulation is mathematically robust and tractable, and these attributes make it suitable for rapid, iterative, forward numerical modeling.
In the first section of the paper, the relationship between surface deformation and dislocation theory will be summarized using representation formula. The dislocation theory can be described as that part of the theory of elasticity dealing with surfaces across which the displacement field is discontinuous, the suggestion seems reasonable. As commonly done in mathematical physics, it is necessary for simplicity to make some assumptions. Here the curvature of the earth, its gravity, temperature, magnetism and non-homogeneity are neglected and a semi-infinite medium which is homogeneous and isotropic is considered. For this modeling, the fault parameters that must be considered, are dislocation amount, length, width, depth and dip angle for fault plane.
This model can calculate displacements at every depth and the free surface specially. Here, the first displacement field is calculated for a simulated fault and sensitivity analysis is carried out for model parameters. The dislocation model provides us with surface deformation fields generated by strike-slip and dip-slip faulting and the vector maps of horizontal and vertical displacement fields can be represented.
In the next step, the sensitivity analysis is done to determine the sensitivity of the model and its deformation behavior with respect to any fault parameters. Then the results of the analysis for both cases of strike and dip-slip faults are compared. The analysis shows that the model has maximum sensitivity to dislocation parameter and minimum sensitivity to lame coefficients.
The numerical results of the analysis show that when the amount of dislocation increases the range and area of the surface deformation are greater. The horizontal displacements are more sensitive to the change of the dislocation amount in comparison with the vertical displacements. The results of the analysis result are summarized in the following table.

Result of sensitivity analysis

No.

Parameters

1

Dislocation (U)

2

Depth of fault (c)

3

Dip Angle (δ)

4

Width of fault (w)

5

Length of fault (L)

6

Lame coefficient (λ , µ)

The model can be applied for simulating co-seismic deformation fields of faulting to prepare a hazard map for the investigated fault in case of any consequent earthquake due to fault motions and for use in any further planning. This knowledge will translate into tangible societal benefits by providing the basis for more effective hazard assessments and mitigation efforts.

Keywords