# Using fuzzy inference system to model the Earth’s displacement field

Document Type : Research Article

Authors

1 Assistant Professor, Department of Geoscience Engineering, Faculty of surveying, Arak University of Technology, Arak, Iran

2 M.Sc. Student, Department of engineering, Faculty of surveying, Azad University, Ahar branch, Ahar, Iran

Abstract

Today, by the expansion of geodetic networks and the creation of base points for geodetic applications, the study of the motion of the earth's crust and the study of the activity of faults are the most important tasks of geodesic. With the establishment of satellite positioning systems, the creation of base points in geodetic networks has been substantial. The basic point in creating base points is the estimation and obtaining the velocity field and the displacement of these points in a reference framework. Determining velocity field with the high precision and the displacement of the base points in geodetic networks is of great importance. With the availability of information on the velocity of GPS stations in a geodetic network, one can model the kinematics and dynamics of the earth's crust in that area. In this regard, extensive research on these problems has been conducted around the world.
The main objective of this paper is the use of Fuzzy Inference System (FIS) for modeling the surface displacement field in Iran. The concept and study of fuzzy logic began in 1920, but the fuzzy logic was first used by Lotfizadeh (1921-2017) in 1965 at Berkeley University. FIS can formulate the behavior of a phenomenon in terms of the use of descriptive and empirical rules without the need for an accurate analytical model. The fuzzy inference system is the tool for formulating a process with the help of rules as if-then. The set of these fuzzy rules is called the fuzzy rules base. Argumentation is done using a fuzzy inference system. The fuzzy inference system is generally made up of the following components:
1. Fuzzy, 2. Base rules, 3. Fuzzy Inference Engine, 4. Diffusion.
The process of converting explicit variables into linguistic variables is called fuziation. The inference engine evaluates and deduces the rules using inference algorithms, and after the rules are combined, the output is converted by the divisible unit into an explicit or numerical value. The most common type of fuzzy inference system is the Tacagi-Sugeno fuzzy system.
In this paper, the FIS is used to model the surface displacement field of the Earth's crust in Iran. A fuzzy inference system is a system that uses the rules of the if-then-fuzzy rules to recognize the properties of the phenomenon. Since this system is capable of modeling nonlinear phenomena, in this paper it is used to model the surface variations. For better and more accurate evaluation, the results of the fuzzy inference system were compared with the results of GPS velocity field observations as well as the results of the artificial neural network (ANNs). To do this, 5 test stations have been considered and observations of these 5 stations have not been used in fuzzy network and neural network training. Based on the analysis, the maximum relative error calculated at the 5 test stations for the fuzzy network and the neural network in the eastern component were calculated to be 20.02% and 29.74%, respectively. The results indicate that the fuzzy network has more accuracy than the artificial neural network in speed field modeling.

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#### References

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