Illite-Age-Analysis (IAA) for the Dating of Shallow Faults: Prerequisites and Procedures for Improvement

Abstract

Fault age determination using the illite-age-analysis (IAA) method for fault gouges has played a key role in providing absolute age information in tectonic evolution studies for the last 20 years. The accuracy and precision of the IAA method depend on (1) how to reasonably quantify the relative content of 1M/1M_d illite generated from fault activity compared to detrital 2M₁ illite in the size fractions of the fault gouge, and (2) how to minimize the error factors in K-Ar or Ar-Ar dating analysis. XRD-based quantitative analysis of illite polytype has made great progress in accuracy by generating a simulated XRD pattern of 1M/1M_d polytype using WILDFIRE© and full-pattern-fitting it with the XRD pattern measured from size fractions of the fault gauge. Nevertheless, the results of quantitative analysis of illite polytypes may vary depending on the sample state of the size fractions for XRD analysis, especially the preferred orientation due to the layered crystal structure of illite. In addition, the radiometric dating results may be distorted depending on the error factor of the dating method itself and on the mineral composition of the size fractions, that is, the presence of K-containing minerals such as biotite and K-feldspar other than illite. In this study, we reviewed previous studies that determined fault activity ages by applying IAA to fault gouges. From this, the prerequisites and recommendations for each of the five steps (particle size separation process, XRD analysis process, polytype quantification, radiometric dating, IAA plot) for improving the IAA method are summarized and presented. The continuous application of the improved IAA is expected to greatly contribute to the study of tectonic evolution through geological time.

1. Introduction

The Illite-Age-Analysis (IAA) method was first proposed by Pevear (1992, 1999) [1,2] for the catalytic dating of sedimentary basins. After van der Pluijm et al. (2001) discovered a new application for defining the age of fault-thrust development with the IAA method [3], it has been applied to the shallow faults of various tectonic environments by a number of researchers for the past 20 years, and has played a decisive role in the study of tectonic evolution and understanding of seismic phenomena. In particular, the development of the WILDFIRE© program by Reynolds (1994) [4] has made great strides in the quantitative analysis of illite polytype by simulating the 1M/1M_d polytype patterns. Moreover, the incorporation of micro-encapsulation in the ⁴⁰Ar-³⁹Ar method [3] and the improvement of the K-Ar method with a small amount of sample have greatly enhanced the reliability of the IAA method.

The relative content of illite polytype is a key variable that determines the reliability of the IAA method. Most researchers have applied X-ray diffraction (XRD) analysis and the illite quantification method based on the WILDFIRE© program, but there are some differences in the XRD analysis conditions and the method of using the simulated pattern generated by WILDFIRE©. For example, since the XRD pattern of illite has a layer structure, the relative intensity of peaks may be distorted due to the preferred orientation of the particles. However, the back-/side-packing method applied in most studies to minimize this effect is difficult to consistently guarantee the state of the analyzed sample for each researcher, so it may become an error factor in the quantitative analysis value. This will be discussed further in Section 4. As another example, in the WILDFIRE©-based quantitative analysis method used in most IAA studies, there is a difference depending on the researcher in the method of using the simulated XRD pattern. This will be discussed further in Section 5.

Furthermore, there may be some error factors in the process of determining the absolute age of each particle size. Both the radiometric K-Ar or Ar-Ar methods have advantages and disadvantages, and this problem is still debated. This will be discussed further in Section 6. In addition, the state of each fraction, such as the presence of K-containing minerals other than illite, and the presence of K⁺ in the exchangeable site of layer silicates, can also be an important factor that can affect the dating results.

Although there are fault activity dating methods such as U-Pb dating and Rb-Sr dating for carbonate minerals, the IAA method, which has a wider application range, is still a highly useful method for determining the absolute age of a shallow fault activity. Therefore, in order to obtain reasonable and consistent dating results by applying it, a systematic process should be established in consideration of the aforementioned influencing factors (i.e., mineralogy of sample, error factors in the particle size separation process, preferred orientation of the sample, polytype quantification method, selection of dating method, etc.). In this paper, we summarize the studies on fault dating using the IAA method, and review the differences in the applied quantification method in detail and their results. Based on this, we would like to suggest a direction for improvement and a systematic IAA application procedure to minimize the error and error range of the IAA chronology and to obtain reliable results.

2. Basic Concept of IAA and Previous Studies

Fault gouges, a product of fault activity, generally appear as a mixture of 1M/1M_d illite generated due to fault activity and detrital 2M₁ illite derived from surrounding rocks [3]. This is a factor that makes it difficult to determine the age of fault activity using fault gouges. IAA is a method proposed to solve this problem, and to determine the generation age of only 1M/1M_d illite generated by fault activity. The basic concept of IAA is to obtain the y-axis intercept of 0% detrital 2M₁ illite from linear extrapolation through a graphical plot of the dating data (y-axis) of three or more size fractions separated from one fault gouge, versus the relative content of 2M₁ illite of each fraction (x-axis) in the binary system between 1M/1M_d − 2M₁ illite.

When the K-Ar dating formula is arranged, the linear relationship formula is obtained between the term of the dating (e^λt − 1) and the mixing rate (x) of detrital mica as seen in the following equation. This is only possible under conditions where K-concentrations of 1M/1M_d and 2M₁ illite are equal.

−e^λt − 1 = (λ_e + λ_β)Ar/λ_e K
       = (λ_e + λ_β)(Ar_a(1 − x) + Ar^d·x)/λ_e·K
       = (λ_e + λ_β)(Ar^a + (Ar^d − Ar^a)x)/λ_e·K

Ar(a): Radiogenic argon content of mica clay minerals formed by fault activity.

Ar(d): Radiogenic argon content of detrital mica Argon content.

The y-axis intercept is determined as the generation age of 1M/1M_d illite, that is, a fault activity age. A conceptual diagram of the IAA method is presented in Figure 1.

Therefore, the accuracy and precision of the IAA method depend on (1) how to reasonably quantify the relative content of 1M/1M_d illite generated from fault activity compared to detrital 2M₁ illite in the size fractions of the fault gouge, and (2) how to minimize the error factors in K-Ar or Ar-Ar radiometric dating analysis. In the 20 years since it was first applied to shallow faults by van der Pluijm et al. (2001) [3], many fault-dating studies have been conducted.

Table 1. Summary of fault dating researches using IAA for last 20 years, in which fault names, selected size fractions, type of XRD equipment and holder, illite polytype quantification method, and raiometric dating method to each study result.

No.	Fault Name	Size Fractions (µm)	XRD Equipment with Sample Holder	Illute Polytype Quantification	Radiometric Dating	Year	Ref. No
1	Lewis thrust	<0.02, 0.02–0.2, 0.2–2	Conventional	Grathoff and Moore (1996) method using WILDFIRE	40Ar/39Ar	2001	3
2	Moab Fault, Utah	<0.05, 0.05–0.5, 0.5–2	Conventional	Grathoff and Moore (1996) method using WILDFIRE	40Ar/39Ar	2005	5
3	Faults in Canadian Rocky Mountains	<0.02, 0.02–0.2, 0.2–2	Conventional	Grathoff and Moore (1996) method using WILDFIRE	40Ar/39Ar	2006	6
4	Anatolian Fault	<0.2, 0.2–0.5, 0.5–1, 1–2, >2	Conventional	Grathoff and Moore (1996) method using WILDFIRE	K-Ar	2006	7
5	Sierra Mazatan detachment fault	<0.05, 0.05–0.1, 0.1–0.5, 0.5–1, 1–2	Conventional	Lowest-variance approach using WILDFIRE	40Ar/39Ar	2008	8
6	Fault of the Ruby Mountains	<0.05, 0.05–0.4, 0.4–2	Conventional	Lowest-variance approach using WILDFIRE	40Ar/39Ar	2009	9
7	San Andreas fault, Parkfield, Califonia	<0.02, 0.02–0.2, 0.2–2	Conventional	Lowest-variance approach using WILDFIRE	40Ar/39Ar	2010	10
8	Faults in AlpTransit deep tunnel site	<0.1, 0.1–0.4, 0.4–2, 2–6, 6–10	Conventional	SIROQUANT from Sietronics Pty Ltd.	K-Ar	2010	28
9	West Qinling fault	<0.05, 0.05–0.2, 0.2–2	Conventional	Lowest-variance approach using WILDFIRE	40Ar/39Ar	2011	11
10	Pyrenean thrusts	<0.05, 0.05–0.4, 0.4–2	Conventional	Lowest-variance approach using WILDFIRE	40Ar/39Ar	2011	12
11	Deokpori Thrust	<0.1, 0.1–0.4, 0.4–2, 2–6, 6–10	Conventional	not mentioned in detail	K-Ar	2011	29
12	Chugaryeong fault zone, Korea	<0.1, 0.1–0.4, 0.4–1, 1–2	Micro-focused with capillary, 2D detector	Iterative full-pattern-fitting with the WILDFIRE	K-Ar	2014	13
13	Daegwangri fault, Korea	<0.1, 0.1–0.4, 0.4–1, 1–2	Micro-focused with capillary, 2D detector	Iterative full-pattern-fitting with the WILDFIRE	K-Ar	2014	14
14	Inje fault, Korea	<0.1, 0.1–0.4, 0.4–1, 1–2	Micro-focused with capillary, 2D detector	Iterative full-pattern-fitting with the WILDFIRE	K-Ar	2015	15
15	Red River Fault, Vietnam	<0.1, 0.1–0.4, 0.4–1, 1–2	Micro-focused with capillary, 2D detector	Iterative full-pattern-fitting with the WILDFIRE	K-Ar	2016	16
16	Mexican Fold-Thrust Belt	<0.05, 0.05–0.2, 0.2–1, 1–2	Conventional	Lowest-variance approach using WILDFIRE	40Ar/39Ar	2016	17
17	Faults in Death Valley and Panamint Valley	<0.05, 0.05–0.2, 0.2–2	Conventional	Lowest-variance approach using WILDFIRE	40Ar/39Ar	2016	18
18	Yangsan Fault in the Sangcheon-ri, Korea	<0.1, 0.1–0.4, 0.4–1, 1–2	Micro-focused with capillary, 2D detector	Iterative full-pattern-fitting with the WILDFIRE	K-Ar	2016	19
19	Minami-Awa Fault	<0.2, 0.2–0.5, 0.5–1, 1–2, 2–4	X’Pert Pro Multi-purpose with capillary	Iterative full-pattern-fitting with the WILDFIRE	K-Ar	2016	30
20	Dien Bien Phu Fault, Vietnam	<0.1, 0.1–0.4, 0.4–1, 1–2	Micro-focused with capillary, 2D detector	Iterative full-pattern-fitting with the WILDFIRE	K-Ar	2017	20
21	Alpine Fault, New Zealand	<0.1, 0.1–0.2, 0.2–0.5, 0.5–1	Conventional	Grathoff and Moore (1996) method using WILDFIRE	40Ar/39Ar	2017	21
22	Yangsan Fault in the Pohang Area, Korea	<0.1, 0.1–0.4, 0.4–1, 1–2	Micro-focused with capillary, 2D detector	Iterative full-pattern-fitting with the WILDFIRE	K-Ar	2017	22
23	Faults in Yeongwol are, Korea	<0.1, 0.1–0.4, 0.4–1, 1–2	Micro-focused with capillary, 2D detector	Iterative full-pattern-fitting with the WILDFIRE	K-Ar	2018	23
24	Río Grío, Vallès-Penedès Faults	<0.1, 0.1–0.4, 0.4–2, 2–6, 6–10	Conventional	Integrated peak areas, using calibration constant for standard	40Ar/39Ar	2019	31
25	Faults within Shimanto accretionary complex	<0.2, 0.2–0.5, 0.5–1, 1–2, 2–4	X’Pert Pro Multi-purpose with capillary	Iterative full-pattern-fitting with the WILDFIRE	K-Ar	2019	32
26	Sronlairig Fault	<0.05, 0.05–0.1, 0.1–0.2, 0.2–2	X’Pert Pro Multi-purpose with capillary	corrected peak-area-measurement, Dalla Torre et al. (1994)	K-Ar	2019	24
27	Sevier fold–thrust	<0.05, 0.05–0.1, 0.1–0.5, 0.5–1, 1–2	Conventional	Lowest-variance approach using WILDFIRE	40Ar/39Ar	2019	25
28	Faults in Chungnam Basin, Korea	<0.1, 0.1–0.4, 0.4–1, 1–2	Micro-focused with capillary, 2D detector	Iterative full-pattern-fitting with the WILDFIRE	K-Ar	2019	26
29	Faults in West Sarawak, Borneo	<0.2–0.5, 0.5–1, 1–2	Conventional	Iterative full-pattern-fitting with the WILDFIRE	K-Ar	2021	27

lists previous studies using IAA and the respective experimental and methodological setup, including selected size fractions, XRD conditions (type of equipment, aluminum holder/capillary tube, detector type, etc.), illite polytype quantification method, and dating method for each study result.

In most studies, <2 μm particle size was separated into 3 to 4 particle size fractions [3,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27], but in some studies, >2 μm fraction was also separated [28,29,30,31,32]. The particle size range for each fraction is slightly different depending on the research (Table 1). The XRD equipment used in most studies is the conventional powder diffractometry, and it seems to have been loaded by back/side-packing the powder sample in an aluminum holder and measured [3,5,6,7,8,9,10,11,12,17,18,21,25,27,28,29,31]. Contrary to this, some studies used capillary tubes as sample holders to minimize the preferred orientation effect of grains [13,14,15,16,19,20,22,23,24,26,30,32]. Illite polytype quantification is the most important factor in determining the reliability of IAA results, but there are differences among researchers in the experimental set-ups of quantitative analysis. Therefore, each experimental set-up applied in the IAA process will be discussed in more detail below. Several methods have been proposed so far, and most are based on simulated XRD patterns generated with WILDFIRE© [3,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,25,26,27,30,31,32]. Both K-Ar and Ar-Ar methods were used as radiometric dating methods (Table 1).

3. Selection of Size Fractions and Its Interval

The key to particle size separation for IAA application is to make the interval with difference in the relative content of illite polytypes for each particle size fraction, and to separate finer fractions with a higher 1M/1M_d illite content as much as possible. In some studies, even the extremely fine fraction of <0.02 or <0.05 was separated [3,5,6,8,9,10,11,12,17,18,24,25]. In this case, it contains almost pure 1M/1M_d illite, so it may show a value close to the fault activity age, and the error can be reduced when applying IAA. In order to secure the amount of sample required for polytype quantification and dating of the extremely fine fraction, it takes a lot of time for particle size separation using a high-speed centrifuge (SIGMA 4-16S, SIGMA, Darmstadt, Germany).

If micro-focused XRD and thin capillary tubes are used in XRD analysis, only a few mg of sample is required, and the time required for particle size separation can be greatly saved because only the amount of sample required for radiometric dating is secured. In addition, in previous studies, it has been reported that the mineral composition of <0.1 μm particle size is more than 90% 1M/1M_d illite [13,14,15,16,19,23,26]. The time required for separation of the <0.1 μm particle size fraction using the centrifuge method is much shorter than that of the <0.02 and <0.05 μm particle size fractions. Therefore, considering the amount of sample required for XRD analysis, the time required for particle size separation, and the 1M/1M_d illite content, it seems appropriate to set the smallest particle size fraction to <0.1 μm.

In some studies, a particle size range of >2 μm is analyzed [28,29,30,31,32], but a particle size of >2 μm contains a large amount of other minerals, which becomes an error factor in quantitative analysis of illite polytype. In particular, at a particle size of >2 μm, K-containing minerals such as K-feldspar and biotite are included in some cases [28,29,30,31,32], which may affect the dating value, thereby reducing the reliability of IAA. Therefore, it would be appropriate to select three or more fractions at a particle size of <2 μm for IAA.

4. X-ray Diffractometry Procedure for IAA

The key to XRD analysis of size fractions is how to obtain all (hkl) reflections of the illite polytype with an ideal peak-intensity ratio. This indicates that XRD analysis should be performed by minimizing the inevitable preferred orientation effect in the layer crystal structure. Therefore, samples for XRD analysis should be loaded as randomly as possible.

The back-/side-packing method using the aluminum holder increases randomness rather than the simple top-packing method. However, because of the difference in the amount of sample per unit volume used and the packing strength for each case, there is an inevitable difference in the degree of randomness for each case.

On the other hand, the capillary tube can maximize randomness and reduce the difference between researchers. In addition, the capillary tube can be analyzed with only a small amount of sample, so it is more useful for fine-size fractions where it is difficult to secure a sufficient amount of sample.

Although the type of XRD equipment is less important, micro-focused XRD equipment with a 2D-detector (image plate) can obtain an XRD pattern with good peak-selectivity, targeting a microscopic area of a thin capillary tube even with an extremely small amount of sample. Therefore, the micro-focused XRD equipment is optimized for XRD analysis for IAA, and the accuracy and precision of illite polytype quantification results can be enhanced. Indeed, Song et al. (2014) [14] successfully obtained high-resolution (hkl) reflections in a random state for the first time using micro-focused XRD equipment with a 2D-image plate attached to an extremely small amount of sample loaded into a thin capillary tube (0.6 mm in diameter). This method has been applied recently in several studies [13,14,15,16,20,22,23,26].

5. WILDFIRE©-Based Polytype Quantification

5.1. Simulation of Polytype XRD Patterns Using WILDFIRE©

The randomly-mounted measured XRD pattern is a mixture of reflections of 1M/1M_d and 2M₁ illite polytypes. For this pattern, the relative content of each polytype must be determined before IAA can be applied. Illite, a layer silicate, has many factors that affect the relative peak intensity of (hkl) reflections, such as crystallinity, stacking ordering of layers, and interlayer expandability, etc., as well as the preferred orientation due to the layer structure [4]. For this reason, it is difficult to accurately determine the relative content of illite polytypes by applying a general XRD-based quantitative analysis method.

To overcome this problem, in most previous studies, polytype simulated XRD patterns were created using WILDFIRE© developed by Reynolds (1994) [4] and used for the quantitative analysis of clay minerals. WILDFIRE©, a forward model algorithm, can create various types of 3-dimensional simulated patterns by using crystallographic parameters affecting the XRD pattern of illite polytype as variables. In the WILDFIRE©-based quantitative analysis method, an appropriate pattern is selected and used through iteration that repeats the process of creating a pattern with different variables.

WILDFIRE© is very useful for creating simulated patterns of 1M_d polytypes, especially with low crystallinity and poor regularity in the stacking type of layer structure. Since the simulated patterns of 1M and 2M₁ consider only a few parameters, such as crystallinity and trans/cis octahedral sheet, it is not difficult to determine a representative simulated pattern. On the other hand, in the case of 1M_d polytype, there are many crystallographic parameters that affect the simulated pattern. WILDFIRE© is designed to reflect these parameters and create simulated patterns for various combinations of each parameter variable. The parameters considered as variables to create a simulated pattern of 1M_d polytype in WILDFIRE© are as follows.

-

probability of zero rotation (P0)

-

probability of 120 rotation (P120)

-

fraction of n.60 degree rotation (F60)

-

proportion of cis-vacant layers (Pcis)

-

mean defect-free (Coherence) distance (MDFD)

-

water in expandable interlayers

-

crystallite thickness (% expandability)

-

no. of unit cells along X (N1)

-

no. of unit cells along Y (N2)

-

no. of unit cells along Z (N3)

-

K and Fe fraction in the structure

-

Randomness of sample (Dollase factor)

-

ordering of the illite/smectite (Reichweite), etc.

2M₁ and 1M_d illite simulated patterns under various conditions created by WILDFIRE© using the above parameters as variables provide core basic data for the developed illite polytype quantification method [8,19,33,34], etc. Boles et al. (2018) [35] suggested a WILDFIRE© Model End-member library by creating 20 patterns for 2M₁ illite and 695 patterns for 1M_d illite using these parameters as variables, respectively.

5.2. Illite Polytype Quantification

For Illite polytype quantification, the previously introduced WILDFIRE©-based quantification method is most commonly used. In addition, there are polytype end-member standards methods [24,31] and methods based on Rietveld refinement [28].

Two main types of quantitative analysis of illite polytype based on WILDFIRE© has been developed as follows; (1) A method using the area ratio of polytype-specific peaks in simulated patterns of 2M₁ and 1M/1M_d polytypes made by WILDFIRE© modeling [33], and (2) quantification method through graphically best-fitting ratio between mixed pattern made with simulated patterns of illite polytypes and measured pattern [14,33,34]. The first method proposed by Grathoff and Moore (1996) [33] is that in the simulated patterns created with WILDFIRE©, the relative area ratio is calculated for each of the five unique peaks of 2M₁ illite against the area of the 2.58 Å/35° 2θ (Cu Kα) peak, which is the common peak of 2M₁ and 1M_d illite. A linear equation between the 2M₁ content and the area ratios is then derived, and then the 2M₁ content in a natural sample is determined by substituting the value of the area ratio for each peak obtained in the same way from the measured pattern in this equation. In addition, a primary formula for determining the 1M illite content by the same method for two 1M unique peaks was also proposed [33]. This method was applied to the study of the determination of fault dating just after the study of van der Pluijm et al. (2001), applying IAA (Table 1 [3,5,6,7,21]). However, the quantitative values for each of the five peaks presented in this 2M₁ polytype quantification method show significant differences. In particular, the hump appearing in the fine-size fraction with a high 1M_d polytype content affects the setting of the intensity and width of other 2M₁ and 1M peaks, which causes the error that the quantitative value is underestimated or overestimated.

The second method is a full-pattern-fitting method of simulated and measured patterns generated by WILDFIRE©. Ylagan et al. (2002) [34] developed a new code called PolyQuant, which is a quantification program automating the iterative matching process to find a ‘best fit’ between the mixed pattern of simulated 1M_d and 2M₁ patterns created in the forward modeling of WILDFIRE© and the measured pattern obtained from the size fractions. In particular, the optimal 1M_d polytype simulated pattern selection process was automated by changing the crystallographic parameters. In this method, full-pattern-fitting was applied for the first time, and the difference was quantitatively presented by defining the objective function (J). In this respect, significant improvements have been made that are different from previous quantitative methods. Haines and van der Pluijm (2008) [8] proposed a least-squares lowest-variance approach based on WILDFIRE©, which is also essentially a full-pattern-fitting method, to find the best match between simulated and measured patterns (Table 1).

This WILDFIRE©-based polytype quantification method through full-pattern-fitting may seem to be theoretically the most proper quantification method that is likely to yield accurate results among the methods presented so far. Nevertheless, in the studies to which this method is applied, the error range of quantitative analysis values is significantly large (for example, [8,9,10,27,28,29]). The most fundamental cause for this is, above all, considered to be the limitation of the measured XRD pattern quality of the target sample obtained in the back-/side-packing state with conventional XRD equipment. In other words, it will be difficult to maintain consistency for each researcher in the randomness of the sample and the background correction in the XRD analysis procedure.

In order to overcome this problem, it is required to obtain (hkl) reflections by loading the sample into a capillary tube rather than back-/side-packing loading into an aluminum holder, and to perform background correction by measuring the empty tube. Minerals such as I-S (illite-smectite interstratified mineral) components may be contained in the sample, which may also be a hindrance to the process of finding the best-fit. The existence of I-S can be confirmed from the oriented XRD pattern in the low-angle 2θ range. Considering the fundamental particle concept, I-S can be viewed as 1 M_d illite. Therefore, among the crystallographic parameters of WILDFIRE©, variables such as percentage of interlayered smectite and its hydration state, ordering of the illite/smectite (Reichweite), and K fraction in the structure can be used to reflect the effect of I-S in the simulated pattern [4].

Song et al. (2014) [14] obtained the measured pattern of the target sample obtained under optimized conditions such as using Micro-focused XRD equipment with a 2D-image plate attached and thin capillary tube (0.6 mm in diameter) for the first time. Reliable quantitative analysis results were obtained by iterative full-pattern-fitting this pattern with mixed patterns of 2M₁ and 1M_d illite based on WILDFIRE© made at various mixing ratios [14]. In addition, by presenting the R% value ((Σ|(simulated−measured)/simulated)|/n × 100) [36] similar to the objective function (J) suggested by Ylagan et al. (2002) [34], the degree of full-pattern-fitting was presented quantitatively. Since then [14,34], the R% value, or objective function (J) has been applied in a number of studies [13,14,15,16,19,20,22,23,26]. Figure 2 shows an example of polytype quantitative analysis of WILDFIRE©-based full-pattern-fitting.

In addition, methods using natural polytype end-member standards as synthetic mixtures without using WILDFIRE© [24,31] and methods such as BGMN^®, Topas, Profex, AutoQuan, SIROQUANT, etc., based on Rietveld refinement [28] are also used. The Rietveld refinement method is basically a function of domain size, strain, and instrumental factors. Therefore, it does not consider the structural characteristics of clay crystallites, which is a factor of quantitative analysis error. Boles et al. (2018) [35] analyzed the results of evaluation experiments of WILDFIRE©-based full-pattern-fitting, End-member Standards Matching (STD) and Rietveld whole-pattern matching (BGMN^®) quantitative analysis methods for synthetic samples. As a result, it was suggested that the WILDFIRE©-based full-pattern-fitting method is useful for samples with high 1M_d illite content, in that it can utilize a data library of simulated patterns generated under various conditions of 1M_d polytype [35].

6. Radiometric Dating Method

K-Ar and Ar-Ar methods have been applied as dating methods for size fractions separated from the fault gouge. Clauer et al. (2012) [37] discussed the limitations of the two methods through a comparative study. K-Ar dating requires a relatively large amount of sample (ca. 10–20 mg), although the amount required has reduced due to technological advancement, and since K content determination and Ar isotope analysis are separated in the analysis process, the analytical uncertainty is higher than that of Ar-Ar dating [37]. Therefore, duplicate or triplicate experiments are required in the K-content analysis process.

For fine size fraction, it is difficult to secure sufficient sample amount required for IAA application. Therefore, if dating is performed on a small sample, such as a fine fraction, Ar-Ar dating with low uncertainty of the result may be more appropriate. However, since the potential loss of Ar due to the recoil effect occurs in fine particles, there is a problem in that the encapsulation technique, which still requires technical verification, must be used to obtain reasonable results [3,5,6,8,9,10,11,12,17,18,21,25,31]. Therefore, for the fine size fraction, K-Ar dating may be more appropriate if the amount of size-separated sample is sufficient [37]. For this reason, in spite of recent developments in Ar-Ar dating, the conventional K-Ar method is still a valuable tool, because it is convenient and straightforward to use, with a high level of technical perfection and standardization. Therefore, the two dating methods can be used complementary to each other [37].

An additional point to be considered in dating is the presence of K-containing minerals, such as K-feldspar and biotite, that affect the dating results. In particular, the content of these minerals may be high at a relatively coarse particle size. In this case, it can be solved through Ar-release spectra analysis of Ar-Ar dating, but in most cases, it becomes an error factor in the dating result.

7. IAA (Illite-Age-Analysis) for Fault Dating

In the IAA (Illite-Age-Analysis) method, the first step is to graphically plot the dating data (y-axis) of three or more size fractions versus the relative content of 2M₁ illite in each fraction (x-axis). From the simple linear extrapolation of the plots, the y-intercept value with a detrital 2M₁ illite content of 0% is calculated. This y-intercept value is the generation age of 1M/1M_d illite, that is, the fault activity age. Here, as the y-axis data, the value of exp(λt) − 1, which is a linear relationship with the radiogenic ⁴⁰Ar/K ratio, rather than the age value, should be plotted against the relative content of 2M₁ illite in each size fraction [1,2,3,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32].

The error of the fault dating result can be calculated from the value indicating the degree of fitting between the simulated pattern and the measured pattern in the polytype quantitative analysis process. The J value of Ylagan et al. (2002) [34] and the R% value of Song et al. (2014) [14] are values showing the degree of full-pattern-fitting. Song et al. (2014) [14] treated the R% value as the error range of the quantitative value determined for each fraction, and calculated the y-intercept value determined through its extrapolation as the error range of the 1M_d illite generation age. In Figure 3, the IAA plot published in Song et al. (2014) [14] are presented as an example.

In addition, it is possible to confirm the reliability of the fault dating value by plotting the apparent K–Ar age value of each fraction against the illite crystallinity index (or Kübler index, defined as the half-height width (°∆2θ) of the illite (001) reflection of about 10 Å) [38], and by whether it is fitted with hyperbolic curves of negative correlations. In Figure 4, the K-Ar age value versus illite crystallinity index of each fraction published in Song et al. (2014) [14] are presented as examples.

8. Prerequisites and Procedures for Improvement of IAA

While reviewing the research results so far on fault dating by applying IAA, we introduced the details of the applied methods step by step, discussed the advantages and disadvantages, and suggested the prerequisites and process for obtaining reliable dating results.

Table 2. Summary of key prerequisites and suggestions for IAA method.

Step	Descriptions of Procedures	Prerequisites and Recommendations
1	Particle size separation using high-speed centrifuge	- Removal of exchangeable K+ ion by using dilute NaHCO3 for dispersion should be needed. - Flocculation by adding NaCl for extremely fine fraction should be required. - Removal of excess Na+ ions by using dialysis and freeze-drying should be required. - For particle sizes < 2 µm, 3 or more size fractions are required. - As the smallest size fraction, <0.1 µm size is recommended (ex. <0.02, <0.05, <0.1 µm).
2	X-ray diffraction analysis for size fractions	- Randomness of size fractions should be required for minimizing preferred orientation. - Using Micro-focused XRD with capillary tube is strongly recommended. - XRD pattern of empty capillary tube is required as background for capillary tube method
3	WILDFIRE©-based polytype quantification	- For conventional XRD and back/side-packing method, Grathoff and Moore (1996) [33] and internal standard method [35] seem to be appropriate. - For Micro-focused XRD with capillary tube, full-pattern-fitting method should be proper. - For quantification using full-pattern-fitting method, R% value can be determined as accuracy.
4	Radiometric dating for size fractions	- Both K-Ar and Ar-Ar methods are available. - For the Ar-Ar method, the vacuum-encapsulation method should be applied to prevent recoiling of 39Ar in the fine-size fraction. - Presence of K-containing minerals, such as K-feldspar, biotite, etc. should be checked.
5	Illite-Age-Analysis (IAA) for dating fault age	- Data should be plot exp(λt) − 1 vs. relative 2M1 content. - Plotting the age vs. illite crystallinity index (Kübler index) can be suggested for verification.

summarizes the key prerequisites and suggestions mentioned above for each IAA step.

To summarize the important parts of the IAA, in step 1 of particle size separation, a pre-treatment process for exchangeable K⁺ removal and an appropriate particle size fraction were proposed. In the XRD analysis in step 2, the key is to obtain a measured XRD pattern including polytype (hkl) reflections by minimizing the preferred orientation for each fraction. For this purpose, the use of micro-focused XRD equipment with capillary tubes is strongly suggested. In the WILDFIRE©-based polytype quantification in step 3, full-pattern-fitting between an appropriate WILDFIRE©-based simulated and measured pattern is used as the most appropriate quantification method, but the quality of the measured pattern obtained in step 2 must be premised for reliability. High quantitative values can be obtained.

In the radiometric dating of step 4, both K-Ar and Ar-Ar methods are available, but it is a prerequisite to check whether K-containing minerals that can affect the age value are included. In the IAA of step 5, the value of exp(λt) − 1 should be plotted against the value of the relative content of 2M₁ illite in each size fraction.

9. Concluding Remarks

The IAA method is a highly useful method to determine fault age, and there has been great progress in detailed methods for the last 20 years. In order to enhance the reliability of the IAA results, sub-processes should be performed in five steps.

Through a review of IAA applied studies, the prerequisites for each of the five steps (particle size separation process, XRD analysis process, polytype quantification, radiometric dating, IAA plot) and recommendations for improvement by detailed experimental content, etc., are summarized and presented. In particular, the application of micro-focused XRD with capillary tubes and improvement of the WILDFIRE©-based full-pattern-fitting method were strongly suggested as key to develop the reliability of IAA.

If the IAA method is improved as suggested in this study, it will be possible to determine the date of fault activity more reliably, and it will be an important tool for tectonic evolution research.