In the 3D view of Arc Sense, several foliation planes were exhibited in Figure 4.2A. And, purple lineaments (Fig 4.2B) were identified and mapped through RRIM in the same area (Fig 3.3). The foliation planes were highlighted by the small dark blue triangle planes in the DEM data (Fig 4.2C). The 3D parallel, planar, triangle faces are characterized as foliation planes in 3D view. Figure 4.2D indicated that the features of planar morphologic geometry of foliation (purple lines) in the ridge where was truncated by fracturing (red and green arrows). Fracture planes with NW-SE strike and west-dipping (red arrows) and ENE-WSW strike fracture planes (green arrows) cut and broke the foliation, and foliation became the discontinuously geological features (Fig 4.2D). Although in detailed observation, the fracture surfaces are gently unsmooth due
40
to the influence of surface process, the fracture plane still is able to be mapping. In summary, the foliation and fracture planes can be observed by using the DEM with GIS relevant applications. Furthermore, their attitudes have the potential to calculate if they are clearly exposed on the surface by one plane. The calculation of foliation attitude was following a similar approach to fracture planes. The results were examined in three representative locations for three domains of this study area. The foliation characteristics in the 3D environment are shaped by parallel triangle faces, and, in comparison, the results of the foliation attitude calculation from DEM were similar to attitudes with field data from the geological map (Fig 4.2E). Therefore, the research methodology of this study is the potential to apply in the calculation of fracture attitudes.
Figure 4.1: Location map of geologic features in the study area.
41
Figure 4.2: Foliation traces and foliation planes in the 3D view. (A) 5m DEM illustrated the regional foliation aspects in schist rock of the NW Heping area. (B) Purple lines were mapped as the foliation traces. (C) Regional foliation planes. (D) Cutting-relationship between foliation system and fracture system. (E) The diagram showed that each stacked triangle reflected the foliation plane and the lower hemisphere projection presents a similar attitude between foliations from DEM-derivation and foliation from fieldwork.
42 4.1.1.1 Domain I
The systematic parallel solid purple lines in NE-SW trending are interpreted as the trace of the foliation plane and have been traced along the gullies of the Dongao greenschist area in the 3D environment of DEM data (Fig 4.3A). Foliations are gently west-dipping with a dip angle of 48○-58○ (Table 4.1). It can continually extend several hundred meters if the surface process does not modify the landform. The attitude of foliation from nearly field data (Table 4.2), which are marked by green dots (Fig 4.3A), was selected to compare with our foliation attitude calculation results. The lower hemisphere projection in Figure 4.2B illustrated that the green great circles presented the foliation attitude derived from field data, whereas the purple great circles described the foliation plane from DEM (Fig 4.2B). It shows a strong similarity of attitude between field mapping and calculation. Also, poles to the plane displayed a similar distribution of foliation in this area between field data and DEM-derivation.
In this domain, the red arrows indicated the traces of NE-SW striking fracture planes that cut the NW-SE purple foliations. According to the cutting-relationship between the fracture traces and foliation, we can distinguish fractures from foliation.
43
Figure 4.3: Comparison of foliation attitude between DTM-derivation and field data at the location 1. (A) The NW- SE purple lines indicated the foliation plane and the green dots referred for the existing foliation at the geological map. (B) Comparison results of foliation attitude between our interpretation from DEM (dark green dots) and field foliation data from Geological map (purple dots) in the lower hemisphere projection.
44
Table 4.1: The foliations attitudes calculated from the DEM data at Domain I.
No. Strike Dip Long Lat R2
13 N 76 W 48 W 331747 2714714 1
14 N 83 W 49 W 331641 2715032 0.99
15 N 78 W 47 W 331747 2715133 1
16 N 84 W 49 W 331904 27213 1
17 N 70 W 52 W 332842 2713772 0.98
18 N 77 W 59 W 332915 2714096 0.99
19 N 74 W 58 W 332944 2714024 0.99
Table 4.2: Foliation attitude from the geological map
No. Dip Direction Dip
783 009 63
785 186 39
786 189 63
820 184 79
789 193 73
787 194 64
45 4.1.1.2 Domain II
In the Heping area, we clearly observed the predominance of W-E striking lineaments. The representative lineament illustrated by purple, parallel lines (Fig 4.4A) supposedly indicates foliation traces located in the west flank of the ridge were cut by three distinctively fracture planes numbered by 1, 2, and 3 (Fig 4.4A). This is these fracture planes also cut across the ridges, and normally explained why we could clearly observe numerous discontinuous lineaments. Therefore, the planes cut the foliation traces, and together cut across the ridges on a large scale can consider as the fracture planes (Fig 4.4A).
Field investigations are often difficult to perceive in highly forested metamorphic terrain. Although, only two field data were documented at two locations near the river area (Fig 4.1) and simply marked by green dots in the 3D scene of Arc Sense (Fig 4.4A).
However, these valuable field data gave us an opportunity in foliation attitude comparisons. The attitudes calculation of foliations from DEM derivation are closely vertical and ranged from 62○ to 72○ (Table 4.3), and in the comparison, they are compatible with the foliation attitudes from field data (Fig 4.4B).
N-S striking and west-dipping fractures numbered by 1, 2, and 3 (Fig 4.4A) were generally used to distinguish the foliation of metamorphic rock.
46
Table 4.3: The distribution of foliation attitudes calculated from DEM data of Domain II.
No. Strike Dip Long Lat R2
1 N 76 E 72 W 323948 2704302 0.84
2 N 72 E 66 W 323890 2704421 0.96
3 N 80 E 60 W 323806 2704525 0.95
4 N 72 E 75 W 323928 2704176 0.99
5 N 81 E 71 W 323784 2704758 0.8
6 N 73 E 62 W 325737 2705467 0.97
47
Figure 4.4: Comparison of foliation attitude between DTM-derivation and field data at the location 2. (A) The NE-SW systematic purple parallel lines were identified as the traces of foliation in the Heping area, and foliation was cut by fracture surfaces numbered by 1, 2, and 3. (B) Stereonet showed the foliation attitude determined from DEM data and field data in the geological map.
4.1.1.3 Domain III
We identified the NE-SW striking and NW dipping foliation system at location 3 where it is greenschist (Fig 2.4) near the lithological transition area between marble and greenschist. The purple lines, which are displayed in the 3D environment of Arc Sense, are illustrated for the foliation traces (Fig 4.5A). The similarity of attitudes is observed in the lower hemisphere (Fig 4.5B).
48
The dip angle of foliation planes with ranged from 41○-52○ was cut by one fracture plane. This fracture plane is composed of three planar surfaces numbered by 1, 2, and 3 and has attitude in W-E striking and south-dipping (Fig 4.5A). The fracture planes with strikes in NW-SE in this area were denoted by yellow arrows (Fig 4.5A). Those fracture planes are considered as the different fracture systems from previous W-E striking fracture planes. It could denote disparate deformation phases with the W-E fracture system due to the evolution of the tectonic setting.
49
Figure 4.5: Comparison of foliation attitude between DTM-derivation and field data at the location 3. (A) The regional foliation with NW – SE striking (purple linear) was cut by a NE-SW trending fracture plane, which was distinguished by three planar planes numbered by 1, 2 and 3. (B) The great circle in stereonet presented a similar strike and dip angle of regional foliation calculated from DEM and the attitude of foliation in geological map.
50
Table 4.4: The distribution of foliation attitudes calculated from DEM data of Domain III.
No. Strike Dip Long Lat R2
1 N 48 E 41 W 308956 2685017 0.99
2 N 49 E 41 W 309033 2684946 0.98
3 N 33 E 52 W 309283 2684879 0.92
4 N 38 E 56 W 309182 2684922 0.98
Table 4.5: The distribution foliation attitudes of field data analyzed from the geological map.
No. Dip Direction Dip Long Lat
386 290 28 308413 2684239
387 310 36 307750 2684787
382 316 30 310948 2686848
383 312 28 310235 2686456
51 4.1.2 Fracture plane mapping
4.1.2.1 Interpretation of fracture plane
The surface fracture set, in combination with the ductile foliation, define the regional morphotectonic lineament pattern. Therefore, Florinsky (2016) dedicated that the mapping morphological lineaments can be used to recognize geologic structures, especially the lineaments located along the straight river bank, across the ridge, etc., are able to present the plane of the fracture. The planes, when breaking the slope or scarp during the action of the tectonic or non-tectonic process supposedly are planar (Fig 4.6A) and exposed on the surface. In a 2D map, lineaments located along the plane supposedly is “traces” (Fig 4.6B). Tracking the “traces” in the 3D environment of Arc Sense can recognize the fracture plane and even evaluate the contribution and development of the fracture system in the 3D model (Figure 4.6C). Along lineaments, because the supposed fractures are represented the sensitive and risky area with the erosional surface process, the topography is easy modification and forms the gullies topography. Therefore, tectonic lineaments along the gullies structure implied the fracture planes. The paths of gullies are significant features to recognize the neotectonics fracture (Chen et al., 2016).
52
Figure 4.6: Characteristics of the fracture plane in the 3D view of Arc Sense. (A) The footprint of the fracture plane on the surface significantly correlates with the distribution of lineaments. (B) Four lineaments (purple lines) along with the fracture footprint. (C) Four fracture planes are mapped based on the fracture trace in 3D view.
53 4.1.2.2 DEM-derived fracture plane
In DEM mapping, 187 fracture planes were identified, mapped, and calculated their attitudes in three different domains. In the Domain I, 50 fracture planes was recognized with the orientation dominated in ENE-WSW striking, and the mean fracture plane was evaluated and displayed by the ENE-WSW striking great black circle in the lower hemisphere projection. 65 & 72 fractures in Domains II and III were recognized, respectively. The attitudes of fracture planes at Domain II were gently clockwise rotated to NE-SW compared with the attitude of N-S striking of fracture in Domain III. The evidence in the lower hemisphere illustrated 30○ differences in the strike of mean fracture attitude of Domain II and III (Fig 4.7).
54
Figure 4.7: Spatial distribution of surface fracture planes in DEM data. 187 fracture planes were identified, mapped, and calculated their attitude in three different domains of NE Taiwan via used the 5m DEM data. 50, 65, and 72 fractures were mapped in Domain I, II, and III, respectively. The lower hemisphere projection represented the distribution of the fracture plane by the contour map. The mean fracture attitude was calculated and displayed by the mean pole (red dot) and the great mean circle (black curve lines) in different domains.
55 4.1.2.3 Restriction of Selected Fracture Plane
The strike and dip of DEM-derived fracture planes are evaluated from each measurement triangle. Triangle selection in the study area is based on the following restrictions for better results of representative fracture plane results.
Reliability of regression calculation
During calculating the fracture attitude, the regression reliability (R2) values of the measured triangle can also be determined. Yeh et al. (2014) indicated that the selected triangles with high R2 have the goodness of fit for the regression plane. Therefore, the fracture planes were classified into ten groups based on different R2 values (Fig 4.8).
The dark green to light green lines represented the fracture plane within lower R2 (0.03-0.4), the yellow to orange line represented fracture planes of middle R2 (0.41-0.8), fracture planes of high R2 (0.81-1) values were indicated by red lines. Totally, in three domains, 120 measurement triangles with R2 > 0.85 based on the above restrictions are used for the instability analysis.
56
Figure 4.8: Classification of the fracture planes based on R2 value. 120 selected fracture planes (red lines) are reasonable for the input database of tendency analysis.
57 Subsurface Rupture Length
Furthermore, we supposed that the fracture patterns in NE Taiwan correlated with earthquakes events. The known magnitude earthquakes events conducted the fault ruptures (Well and Coopersmith., 1994). Therefore, the rupture area of the fracture is an important key to evaluate the correlation of fracture pattern with earthquake events. And, the rupture parameters commonly including rupture length and fracture width that they can be estimated in the spatial.
The observational data from field studies of faults as well as theoretical studies of seismic moment suggest that earthquakes magnitude should correlate with the amount of rupture area along the causative faults (Well and Coopersmith., 1994).
The subsurface source can obtain rupture length and rupture area. The magnitude (M) of earthquake events is positively correlated with the fracture rupture length (Fig 4.9). Well and Coppersmith (1994) concluded that the smallest earthquake events with M=4 could be conducted 1km rupture length along the fault and 600km rupture length can be created by the earthquake events in M > 8.
In our study, the horizontal distance (RLD) of fracture planes were calculated from the first and end vertices of fracture coordinate. The fracture rupture lengths are in the range of 1-9 kilometers (Fig 4.10). The focal mechanism in NE Taiwan (Wu et al., 2008) provides the seismic magnitude (M) is in the range of 2.5-6.5 of different seismic fault types. We categorized seismic fault types from focal mechanism data by rake angles.
Therefore, the distribution of fracture rupture length corresponded with the magnitude size of single EQ events should be in range 1-20km.
58
Finally, we determined 120 fracture planes based on the restriction of R2 and RLD, which are illustrated by the red lines in Fig. 4.11. Those fractures will be used to test the hypothesis that whether the fracture sequences are correlated with the stress evolution in NE Taiwan.
Figure 4.9: Relationship of subsurface rupture length with the magnitude of earthquake events. (A) The regression of average subsurface rupture length with earthquake magnitude (M) for all fault types. (B) There is no distinct difference in the regression line (Well and Coppersmith, 1994).
59
Figure 4.10: Distribution of subsurface rupture length of fracture planes in study area.
60
Figure 4.11: Classification of fracture planes based on the horizontal distance.
61
Analysis result of focal mechanism data
4.2.1 Distribution of focal mechanism.
The distribution of several focal mechanism clusters can be identified and illustrated in the tectonic evolution of NE Taiwan (Fig 4.12). The reverse faulting focal mechanism (1) is dominated by the NNE-SSW trending and is positioned along the coastal line from the Taroko to the Hualien. In the transition area between Ilan and Hualien, two clusters of strike-slip focal mechanisms (3) and (4) were recognized. The NNE-SSW trending strike-slip focal mechanism cluster (3) is inclined ENE-WSW trending cluster near the Heping area (Domain II). ENE-WSW trending the focal mechanism cluster followed the orientation of the Ryukyu volcanic arc. This cluster could represent the transition area between the collision and the subduction system.
Other strike-slip focal mechanism clusters extend NNE-SSW trending from Nanao Plain to southern Ilan Plain (Domain I). The normal faulting focal mechanisms are distributed in two different clusters in this area. A small cluster of normal faulting (5) was represented in the south of Okinawa Trough, whereas NE-SW normal faulting trending (2) was presented in the eastern flank of the Central Range. Two cross-sections (NE-SW trending AA’profile and ENE-WSW trending BB’profiles) are established to analyze the distribution of focal mechanism, and the location of profiles was shown in Figure 4.12. In Figure 4.13, N15○E striking-profile AA ’ presented the clearly various distribution of focal mechanisms not only from south to the north but also from shallower to deeper part of the crust. Three determined focal mechanism clusters are placed along this cross-section (Fig 4.13). In the south, the normal focal mechanism clusters (2) are located at about 5-7.5km and overlapped with thrust faulting clusters (1).
62
The thrust faulting cluster extends farther to the north and becomes deeper, suggesting the seismic belt (Huang et al., 2012). Along this profile, the arbitrary distribution of the strike-slip faulting events and normal faulting events conspicuously developed at a distance of 25 km. The strike-slip focal mechanism events are particularly dominant in comparison with normal faulting events. Especially, one sub-vertical strike-slip focal mechanism cluster (3) was observed as the distancing at 45-50 km, which is considered as mostly left-lateral strike-slip events (Huang et al., 2012). Previous seismic investigation (Ku et al., 2009) examined this cluster may extend further seaward, which is correlated with this event in Figure 4.13.
In Figure 4.15, along with N80○E striking profile BB’, three recognizable focal mechanism clusters were observed. At 20 km distance, the distinct thrust faulting events (6) (Fig.4.14) was regarded under the eastern flank of Central Range (Huang et al., 2012). The other cluster thrust faulting (1) is located primary shallower than 12.5 km deep in the eastern part of this profile. In the western part of this profile, a west-dipping the normal faulting cluster (2) is found in the shallow depth of about 5-10 km.
63
Figure 4.12: Distribution of focal mechanism of NE Taiwan (M>2). Normal, thrust, and strike-slip faulting are categorized by the rake angle (Huang et al., 2012) (thrust, 45○ to 135○; normal, - 45○ to - 135○, others) and presented by blue, red, and green. Lines A-A’
and B-B’are the locations of the cross-section.
64
Figure 4.13: Focal mechanism data distribution along cross-section AA’. In the south, the normal faulting cluster (2) dominated at about 5-10 km and overlapped with the thrust faulting cluster (1). The thrust faulting cluster extends farther to the north and becomes deeper at about 7.5-20 km. The strike-slip faulting cluster (3) is located in the northern area.
65
Figure 4.14: Focal mechanism distribution of B-B’ cross-section. Two distinct clusters of focal mechanism events are composed of a thrust-faulting cluster in the west (6) and thrust faulting cluster in the east (1) at shallow depth. The normal faulting cluster (2) presented the normal stress regime under the western flank of CeR.
4.2.2 Stress inversion
164 focal mechanisms with a magnitude larger than 2.5 are collected to obtain the seismotectonic stress tensor of three domains by solving the inversion solution with code (Vavryčuk, 2014). The focal mechanism data inside each rectangle are applied to evaluate the inversion results of each domain (Fig 4.15). Thus, the result of stress inversion analysis for three different domains was demonstrated in Figure 4.17. and it was conducted shallower than 10 km depth due to the exhumation rate of this area (Liu, 1982; Hsu et al., 2016; Chen et al., 2016) (Fig 4.16). At least four earthquake events are required to calculate four unknown parameters of the stress tensor, including three
66
directions of principal stress and stress ratio (R). The stress regime along NE Taiwan coastline is established from focal mechanism data (Fig 4.17).
Figure 4.15: Map of stress domains in the study. (red, blue, green rectangles are noted for the Domain I, II, III, respectively), the orange polygonal indicated study area. A-A’
and B-B’ are the cross-sections.
Figure 4.16: Exhumation rate of NE Taiwan area 0.00
1.00 2.00 3.00 4.00 5.00
Present- 0.5 0.5-1.5 1.5-2
Thickness (km)
Year (Ma)
EXHUMATION THICKNESS
Depth
67
Figure 4.17: Stress inversion results with different depths. In each Domain, 1, 2, 3 are maximum, intermediate, and minimum principal stress and are presented by red, green, and blue circles, respectively. n is earthquake event.
68
In this figure, at the lower crust, no reliable stress state is available in Domains I, II, and III due to the lack of the focal mechanism data. Only two or three focal mechanisms are obtained from earthquake events at 5 km of Domain I and II, whereas no earthquakes event happened in the domain III. After examining five earthquake events at 5 km depth, the stress inversion results demonstrated a normal faulting stress regime, but the stress state is unstable because 3 and 2 orientation are slightly permutation (Fig 4.17). Hence, only stress states ranged from 7.5-10 km depth of each domain are reasonable for operating fracture instability analysis (Fig 4.18).
In the middle crust at about 7.5-10 km of Domain I and II, the prevailed strike-slip faulting regime was observed. The compression orientation was detected in NE-SW trending, while the tensile orientation is NW-SE. However, at Domain III, the compression turned to NW-SE orientation, and the tensile axis of stress state was NE-SW trending. Especially, the stress state shifted at 7.5 km from the strike-slip faulting with sub-vertical 2 to thrust faulting stress regime at 10 km. The orientation of three principal stress states and the standard deviation was addressed in Table 4.6.
69
Figure 4.18: The reasonable stress state of each domain for fracture instability investigation. And, the evolution and exhumation path of the stress state might be indicated the variation of fracture system from south to north of NE Taiwan.
70
Table 4.6: The principal stress orientation and standard deviation.
Principal stress
Domain
1 Azimuth/Plunge 2 Azimuth/Plunge 3 Azimuth/Plunge
III-D 135.4/3.8 ± 7.9 44.2/14 ±10.8 239.8/75.4 ± 9.6 possessed the instability over 0.8 are mainly distributed at 7.5 km, as well (Fig 4.19A).
Therefore, we supposed that fault planes at Domain III are more unstable if the instability larger or equal to 0.8.
71
Figure 4.19: The threshold of fault instability at Domain III. Morh’s diagram and
Figure 4.19: The threshold of fault instability at Domain III. Morh’s diagram and