Application of fold style elements for estimation of strain parameters (Case study: Asmari horizon of Karanj oil field)

Introduction
Strain analysis in natural deformed rocks is very important for understanding the strain states in different parts of the earth's crust. Using data that can be collected in the field, and applying different methods in strain studies, geologists will be able to measure quantitative amounts of strain in various geological structures. Since geologists are always dealing with the latest deformed products in the earth's crust, they will be able to perform finite strain analysis in structural features or deformed rocks (Ramsay and Hubber, 1983). If geologists need to investigate the changes of incremental strain values at any moment of time in different parts of a structure, the use of laboratory and numerical modeling will be inevitable. In carrying out numerical analysis of strain, it is very important to find elements that can be used as indicators in strain measurement. Several methods have been presented by different researchers to estimate strain values in metamorphic rocks. Methods such as Rf/Φ method (Ramsay and Hubber, 1983), Fry method (Fry, 1979), Bridin method, Wellman method, and the method of preparing balanced cross sections (Ferhner and Grasemann, 2012; Lopez-Mir, 2019) are the most common methods of strain studies, which are used by Structural geologist in different natural deformed areas. Usually, two-dimensional strain studies can help to understand the characteristics of strain ellipsoid in three dimensions. There are several mathematical methods that help to structural geologist for understand the 3D nature of strain from 2D studies. Using of graphical functions is very common in many strain studies. In recent decades, the use of graphical functions (Nomograms) as a quick and simple method in strain analysis is used by many researchers (Ramsay and Hubber, 1983; Imber et al, 2012; Fossen, 2016; Sarkarinrjad et al, 2017, Keshavarz and Faghih, 2020). In this research, the amounts of strain ratio and shortening value in deferent parts of Karanj anticline oil field have been calculated with application of seismic profiles and using fold style elements.
 
Materials and Methods
In this research, using interpreted seismic sections, some parameters of the fold style elements in the Karanj anticline oil field have been investigated. Interlimb angle, folding angle, geometry of the axial surface, bluntness and fold aspect ratio were determined. Also the Ramsay and Fourier classification were made for deferent part of anticline. By applying the interlimb angle value and by using graphical functions, the fold aspect ratio of Karanj anticline was calculated in different parts. Also, using the fold aspect ratio-shortening and shortening-strain ratio nomograms, the values of shortening and strain ratio were estimated for different parts of anticline.




Application of fold style elements for estimation of strain parameters                                                                                     Samani et al, / 20




Results and Discussion
The analyzes based on the value of the curvature of the folded surfaces between the hinge and inflection points of the fold show that the Karanj anticline is located in the range of sinusoidal to parabolic folds based on the Fourier division and according to the almost equal curvature of the folded surfaces and uniformity The real thickness of the folded layer is placed in the class 1B group of folds. The fold bluntness parameter is measured based on the ratio of the radius of curvature at the fold closure to the radius of curvature tangent to the edges of the fold at the inflection points of the fold. According to the results, the Karanj anticline with the value of b=0.22 to b=0.64 is sub-angular to sub-rounded folds. The measurement of the interlimb angle in different parts of the Asmara horizon shows a gentle to open fold. Using the interlimb angle values and application of interlimb angle-fold aspect ratio nomogram, the values of the fold aspect ratio of the Karanj anticline were determined in the range of 0.15 to 0.44. Based on this amounts, the general geometry of the Karanj anticline is placed in the group of broad to wide folds. In order to determine the amount of shortening and the strain ratio in Asmari folded layer, various mathematical relationships and graphical functions have been presented (Ramsay and Hubber, 1983; Bastida et al., 2005, 2007; Ghassemi et al., 2010). It is possible to measure the shortening values by using the fold aspect ratio and using equation 1.
Eq. 1)
 P = 0.5(1/(1+e)²-1)^0.5                                        
Also, by using shear strain and determining the values of the square of elongation (Equation, 2), it is possible to determine the values of the strain ratio (Equation, 3).
Eq. 2)
 λ1 or λ3 = 1/2 (γ²+2±γ(γ²+4)^1/2)                     
Eq 3)
R²= λ1/ λ3                                                       
In order to determine the values of the strain ratio using equation 4, it is also possible to use the values of the fold aspect ratios (Ghassemi et al, 2010).
Eq 4)
P= 0.5(R-1)^0.5     or    R= 4P²+1                         
Also, by using the equation 5, it is possible to establish a relationship between the shortening values and the strain ratio.
Eq 5)
e = (1/R^0.5)-1                                                    
In this research, using graphical functions, the values of shortening and strain ratio were determined along the seismic profiles in different parts of the Asmari horizon for the Karanj anticline. The results of this research show that the Karanj oil field anticline is an asymmetric fold with different amounts of interlimb angel along the anticline. Based on the analysis, the values of interlimb angle are not the same throughout the Karanj anticline and it shows lower values in the central parts than in the northern and southern parts of the anticline. Based on the amounts of interlimb angles in different parts, the Karanj anticline is mainly can be categorized in the gentle to open folds. Based on the amounts of bluntness the Karanj anticline is placed in the sub-angular to sub-rounded folds. According to the dip isogon patterns (Ramzay method) and Fourier analysis the Karanj anticline is categorized in the 1B and Sinusoidal to parabolic folds. Based on the strain analyses the values of the strain ratio and shortening percentage in the central parts of the anticline show higher values than the northern and southern parts.
 
Conclusion
Based on the fold style elements and strain analyses of the Karanj anticline oil field, the following results were obtained:
- The interlimb angles along the Karanj anticline are varying between 74 to 140 degrees.
- The bluntness values of the Karanj anticline oil field is 0.22<b<0.64 and shows the geometry of sub-angular to sub-rounded fold. 
- The fold aspect ratio for the Karanj anticline is between (0.15 to 0.44) and based on these amounts shows the geometry of broad to wide folds.    
- Also, the results show the shortening values between 7.5% to 32% and strain ratio values in the range of 1.25 to 1.45 in different parts of the anticline.