Curie Point Depth from Spectral Analysis of Magnetic Data in the Southeast Tibet

The satellite magnetic anomalies are used to calculate the Curie point depth of the Southeast Tibet by spectral analysis method in the study. The relationship between the Curie point depth and the regional faults or heat flow will be discussed. The results show that the Curie point depth of the study area ranges from 15 km to 36 km and the average depth is 26.3 km. The Curie point depth is cluster-like on the north of the Ailaoshan-Red River Fault, while it is strip-like distribution on the north side. The Curie point depth in the Xiaojiang Fault zone, the Xiaojinhe Fault zone, the Dien Bien Phu Fault zone and the Gaoligong Fault zone are shallow. It could be related to their strong frictional heat induced by these faults. The Curie point depth in the middle Sukhothai Block is shallow, which it is not only related to the Phayao Fault, the Mae Chan Fault and the Nam Ma Fault, but also to the subduction of the Palaeo-Tethys into the Indochina Block. There is a negative but nonlinearly correlation between the heat flow and the Curie point depth in this study area. The areas of low heat flow value correspond to the areas of deep Curie point depth. However, both the high and low heat flow values can be found in the areas of shallow Curie point depth. The possible reason is thought to be related to the low thermal conductivity of the rock.


Introduction
The Curie point depth (CPD, also called Curie isothermal surface) refers to the thermal surface for the ferromagnetic crustal rocks transforming to paramagnetic rocks when the temperature reach the Curie point [1]. It is the bottom of the magnetic layer in the lithosphere. The CPD reflects the thermal state of the lithosphere rather than the geologic tectonic surface, so that it is not appropriate to be measured by the geological markers.
As a crustal thermal boundary, the CPD reflects the thermodynamic structure of the crust. Many scientists demonstrated the CPD distributed characteristics of different areas due to its meaningful reflection of tectonic settings, geothermal distribution and volcanic activity. Tanaka et al. [2] calculated the CPD in East Asia and found that the CPD distribution varied greatly according to the geological context. The CPD are shallower than 10 km at volcanic and geothermal areas, about 15-25 km at island arcs and ridges and deeper than about 20 km at plateaus, respectively. In the west part of Anatolian, Turkey, the study on the CPD showed a geothermal anomaly area, which the length is 350 km and the width is 100 km. It is considered that the asthenosphere upwelling caused by the lithosphere extension formed the anomaly area [3]. The CPD in Sinai Peninsula, Egypt showed that seismicity generally occurred in shallow CPD locations and the Suez Bay is developed about the prospect of geothermal resources [4]. Kasidi and Nur [5] studied the CPD distribution in northeast part of Nigeria and found that the CPD is negatively correlated with the heat flow. The CPD ranged from 30-40 km in the central Brazil, which induced that three magnetic layers were existed in this region [6]. Comparison the CPD in Taiwan with the measured heat flow, the results showed that the CPD is negatively correlated with the measured heat flow with correlation coefficient 0.62 [7].
As a lateral collision zone and material escape zone induced by the Indian and the Eurasian plate, the southeast Tibet consists of various blocks and faults, which is developed in different stages. The complex geological structure has been attracting the attention of numerous scholars. Part of them tried to reveal the tectonic structure and fault activity characteristics based on the study of the CPD. According to the calculation of the CPD in Kang-Dian continental paleo-rift zone using aeromagnetic data, the authors concluded that the CPD in rigid block is deep, whereas the edge of the block is shallow [8]. Using satellite magnetic data, Gao et al. [9] studied the CPD in southeast Tibet in China. They found that the CPD uplift zones near large deep faults correspond to the faults and the distribution of the magnetic anomaly reflects the escape flow from east Tibet.
The study area is in the intersection of multiple blocks as well as the complexity of the geological structure. The deep and comprehensive discussions about the CPD distributed characteristics and the influence of the geological structure on the CPD distribution is rare. In this paper, the CPD of the study area is calculated by using satellite magnetic anomaly data with spectral analysis method. And then, the causes of the distribution of the CPD from the perspective of geological structure are discussed. Additionally, the relationship between the CPD and the heat flow is also discussed.

Geological Settings
The study area is located in the southeast Tibet, which is composed by eight blocks (Figure 1): the Northwest Sichuan Block, the Central Yunnan Block, the Eastern Yunnan Block, the Sibumasu Block, the Sukhothai Block, the Lanping-Simao Block，the Indochina Block and the Song Da Block. Major faults (e.g., the Ailaoshan-Red River Fault (RRF), the Xiaojinhe Fault (XJHF), the Xiaojiang Fault (XJF), the Gaoligong Fault (GLGF) and the Dien Bien Phu Fault (DBPF)) can be identified in southeast Tibet [9][10]. The RRF is an important transition zone among the blocks in study area. Its formation is caused by the collision between Indian and Eurasian plate. The tectonic movement of the fault is left lateral strike slip ductile shearing at early stage, while it is the right lateral strike slip at late stage. The average slip rate of the RRF since Quaternary is about 4-5 mm/y [11]. The RRF is a large deep fault in the Himalayan orogeny. The fault was formed during the end of Paleozoic and Mesozoic caused by the collision between the Gondwana and Eurasian Plate. The Yangtze Block is located in the north of the RRF, while the adjoining region between the East Tethys tectonic domain and the western Pacific tectonic domain is located in the south of the RRF [12][13][14][15][16]. The Chuan-Dian rhombic block (CDRB) located in the southwest Yangtze plate consists of the Northwest Sichuan Block and the Central Yunnan Block. The western boundary of CDRB is the RRF while the eastern boundary is the XJF.   [9]; Metcalfe [10]; Tun et al. [17]; Noisagool et al. [18]).
The crustal material in the southeast Tibet moves eastward due to the collision between the Indian plate and the Eurasian plate. Previous studies show a southward displacement of the CDRB during the last 12 m. y [19][20][21][22]. Lv et al. [23] suggested the relatively stable South China block blocked the eastward movement of CDRB, and the direction of the CDRB motion changed from east to south along the XJF zone. The XJF zone as the eastern boundary of the CDRB is a left lateral strike slip active fault with intense internal heat action and high frequent earthquakes [24]. The major geological structures in the south of the RRF are the GLGF zone, the Sukhothai Block and the DBPF zone. The GLGF zone is derived from the northward subduction of the Indian plate beneath the Eurasian plate. The Tengchong volcano area is characterized as strong shear deformation and frequent magmatic activity. Therefore, the Tengchong volcano area is one of the most abundant geothermal resources in China. The Sukhothai Arc is located in the Sukhothai Block. Its formation can be traced back to the subduction of Paleo-Tethys to the Indochina Block in the Latest Carboniferous or very Early Permian. The Sibumasu Block collided with the Sukhothai Arc in the early Late Triassic, which formed the extensive accretionary prism of the Paleo-Tethys Suture Zone (CRL). The magmatism of the Sukhothai Arc ceased at the end of the Triassic [16,25]. The Phayao Fault (PF), the Mae Chan Fault (MCF) and the Nam Ma Fault (NMF) are the three major faults in the Sukhothai Block. The DBPF located in the east of the Sukhothai Block is an important left lateral strike slip fault in the Indochina region [26][27]. The average slip rate of the fault is 2.5 mm/y since the early Pliocene [28]. Six strong earthquakes (Ms≥5.0) occurred at the fault since 1900 which indicates the DBPF is an active fault.

Data and Methods
A total number of 73 heat flow data (Appendix, Table 1) is compiled from the Global Heat Flow Database of the International Heat Flow Commission [29] last updated in 2011 and the published papers [30][31][32]. The magnetic anomaly data used in this study is based on the Earth Magnetic Anomaly Grid [33][34], which is a 3 arc-minute resolution data set compiled from satellite, ship and airborne magnetic measurements. Comparison between the CPD estimated from the satellite magnetic data and the CPD estimated from the aeromagnetic data show that they are comparable [9,[35][36]37]. The total intensity anomaly is 5 km above WGS84 ellipsoid. The measured magnetic anomaly consists of the anomalies generated by the shallow and deep magnetic bodies. The presence of the shallow magnetic bodies may reduce the accuracy of the data. Upward continuation of two-dimensional magnetic anomalies can effectively suppress the effect from the shallow bodies, thus highlighting the effect from the deep bodies [38]. The magnetic anomaly data used in this paper is 15 km above mean sea level after upward continuation for 10km, because the magnetic anomaly in this height effectively removes the anomalies generated by shallow magnetic bodies. The magnetic anomaly in the study area varies from -89 nT to 75 nT ( Figure 2). Some researchers [39][40][41] confirmed that it is not necessary to reduce the spectrum to the pole (RTP). This is advantageous for calculating CPD at low magnetic latitudes where a RTP is difficult [39], because RTP is a phase operation which theoretically has no effects on estimated CPD, though there may exist a small spatial shift in CPD with RTP [42].
The method used in this paper to estimate the Curie surface depth is based on the spectral analysis method. Tanaka et al. [2] assumed that the layer extends infinitely far in all horizontal directions. The depth to the top bound of a magnetic source is small compared with the horizontal scale of a magnetic source, and that magnetization ( , ) is a random function of x and y. Blakely [41] introduced the power-density spectra of the total-field anomaly (P): where is the power-density spectra of the magnetization, is a proportionality constant, and are factors for magnetization direction and geomagnetic field direction. Besides, % & and % ' are top and basal depth of magnetic source, respectively, and are the wavenumbers from the 2D Fourier expansion of the magnetic anomaly field in frequency domain, = ( + . The above equation can be simplified by noting that all terms, except | | and are radially symmetric. Moreover, the radial average of and are constant. If ( , ) is completely random and uncorrelated, * , is a constant. Hence, the radial average of ∆ can be simplified as [7]: where A is a constant. By taking natural logarithm on both sides of eq. On the other hand, eq. (2) can be simplifies to where 2 7 is the depth to the central point of the magnetic source. At low wavenumber band, | |( ! 6 ) = | |( $ 6 ) ≈ | |(2 ' − 2 7 ), thus eq.(5) can be rewritten as where B is a constant and 2d is the thickness of the total magnetic source. Now by taking logarithms on both sides of eq. (6), where C is a constant. Thus the central depth 2 7 is estimated by fitting a straight line through the high wavenumbers of the power spectrum of ln [ + ∆ (| |) ; < /| |]. Once 2 & and 2 7 are calculated, the depth to the bottom of the magnetic source can be derived [2,40] as The obtained basal depth of the magnetic source is assumed to be the Curie point depth.
Previous studies show that the size of the optimal square window is about 4-6 times the estimated depth [43][44]. This paper divides the study area into a window of 150km×150km, and two neighboring windows have an overlapping of 50%.
The relationship between CPD (2 ' ) and heat flow (= > ) can be described as [45]: (9) where ? represents the coefficient of thermal conductivity, J & , J ' is the temperature of the top and bottom of magnetic layer, @ 7 is the heat production rate at the surface, ℎB is the characteristic drop off of @ 7 . It is assume that J ' − J & = 580K, 2 & =0, @ 7 =3.0×10 -6 W/m 3 , ℎB=10 km [46], then the theoretical curves of geothermal heat flow for different k are plotted.

Results
Results ( Figure 4) show that the CPD ranges from 15 km to 36 km and the average depth is 26.33 km. The distributed characteristic of CPD on the north and south sides of the RRF are different. The CPD the south side is strip-like distribution, while the north side is cluster-like distribution. There are three parts with shallow CPD on the south side of the RRF (F1): the GLGF (F7) zone, the middle part of the Sukhothai Block (IV) and the DBPF (F13) zone, while two parts with deep CPD: the Lanping-Simao Block (V-1) and the middle part of the Sibumasu Block (III). On the north side of the RRF, CPD in the Eastern Yunnan Block (II), the middle XJF (F3) zone and the XJHF (F2) are shallow, while the northwest Sichuan Block (I-1), the central Yunnan Block (I-2) and the north and south part of the XJF are deep. In the study area, the shallowest CPD is 15.5 km, which is located in the Chiang Rai zone belongs to the middle of the Sukhothai block (IV). The average CPD is less than 20 km in this region. The deepest CPD is 35.2 km, which is located in the south part of the Northwest Sichuan Block zone where the average CPD is more than 30 km.

CPD Versus Geological Structure
The Chuan-Dian rhombic block (CDRB, Figure 4, I) located in the north part to the RRF (Figure 4, F1) was divided by XJHF (F2) into the north part and the south part (I-1 and I-2). The fault cutting might induce the shallow CPD in the XJHF (F2) zone, while the north and south sides are deep. At the same time, as the eruption channel of the Emeishan basalt, the extension of the large deep fault which was caused by the Emeishan large igneous province in Late Paleozoic made the extensive eruption of the basalt along the fault [47], resulting in elevating the Curie point surface in this area. As the eastern boundary of the CDRB, the XJF (F3) plays an important role in the SE direction movement process of the block. The CPD in the central XJF zone is shallow. The average depth is about 23 km. However, the CPD in the northern and southern parts are more than 30 km. Previous tomography study in this area showed that the middle and lower crust beneath the XJF zone were characterized by low velocity anomaly, whereas the north and south crust are characterized by high velocity anomaly [48]. It is implied that the CPD distribution corresponds to the tomography velocity anomaly. There is a high velocity anomaly body in the southern XJF (F3) zone and it has a blocking effect on the southward movement of the CDRB. This phenomenon leads to strong deformations and strong earthquakes in the upper and middle crust. Therefore, the CPD of the southern XJF is deep, while strong earthquakes happen frequently.
The CPD distribution characteristics on the west and east sides of the XJF (F3) are different. The CPD in the Central Yunnan Block (I-2) is deep, whereas in the Eastern Yunnan Block (II) is especially shallow that is even shallower than 19 km. Tomographic results showed that a high velocity anomaly area beneath the Central Yunnan Block and a large low velocity anomaly area beneath the middle part of the Eastern Yunnan Block in the depth of 40 km [48]. Furthermore, the low velocity anomaly area decreased with the decrease of the depth and disappeared at 20 km depth. It is believed that the underplating process happened in the deep lower crust beneath the Eastern Yunnan Block might cause this phenomenon. The underplating process changes the geothermal field of deep crust, therefore, which leads to the increase of the temperature of the lower crust. It not only causes the generation of the large low velocity anomaly area, but also elevates the Curie point surface. Besides, it makes the CPD shallower in this region than that of the surrounding areas.
The Gaoligong CPD uplift zone in the Sibumasu Block (III) is characterized by GLGF (F7) and Nanting Fault (F8). The elevated CPD is caused by the underplating process. The process is that the Indian plate collided with the Eurasian plate, resulting in that the bottom of asthenosphere in this region partially upwelled since the Cenozoic period. The original basaltic magma originated from decompression melting induced underplating [49][50]. Seismic tomographic result shows that a low velocity anomaly area exists in the middle and lower of the crust in this region [51][52]. Previous studies in Tengchong zone showed that magma chambers in the crust were found [53][54][55][56][57][58]. The existence of the magma chambers changed the geothermal field, making the magnetic layer become thinner with the increased temperature. Consequently, the CPD is shallow.
The CPD in the Sukhothai Block (IV) presented strip-like shape. The shallowest CPD in the central part of Sukhothai Block is about 16 km. This block was characterized by PF (F11), MCF (F10) and NMF (F9). These faults were formed by the subduction between the Indian plate and the Eurasian plate [59]. The average left lateral slip rate of the MCF since the late Pleistocene was about 12 mm/y [60]. The average slip rate of the NMF was 0.6-2.4 mm/y [61]. Strong earthquakes above Ms.5 have occurred for several times around these faults [18,62], indicating a strong tectonic movement in this region. The shallow CPD is probably caused by the strike slip movement of these faults. The frictional heat induced by the fault shearing movement induced the partial melting, and the anomalous heat sources within the crust formed [63]. The distribution of abundant hot springs in northern Thailand might possibly be related to these faults [59]. On the other hand, the formation of the Sukhothai Arc may have an effect on the geothermal field in the area. The volcanic arc system, Sukhothai Arc [10,16,[64][65][66][67], was constructed in the late Carboniferous-early Permian on the margin of the Indochina Block (V) by northwards subduction of the Palaeo-Tethys. However, it is unlikely that the arc magmatism could influence the CPD distribution due to the age-old magmatism.
The DBPF CPD uplift zone is located in the DBPF (F13) zone. The regional crustal extension induced the upwelling of the deep mantle, making the basaltic magma in the DBPF zone quickly move to the surface in the Pliocene period [68]. The frictional heat induced by the fault and the upwelling of the deep mantle caused the shallow CPD in the DBPF zone.

CPD Versus Heat Flow
The heat flow is the energy that is transmitted from the interior of the earth to the surface in the unit area over the earth's surface per unit time and then distributed to the space of the universe. It can reflect the characteristics of a geothermal field [69]. A total number of 73 heat flow points are plotted on CPD distribution map ( Figure 5). These measured heat flow points are mainly distributed in Yunnan, China and northern Thailand. The mean heat flow in study area is 70.48 mW/m 2 , it is higher than the mean overall continental flow of China, 63 mW/m 2 [31]. Previous studies showed that the heat flow corresponds with the CPD [7,36,[70][71]. The heat flow in the Central Yunnan Block (I-2) is low, while the CPD is deep. The heat flow in Tengchong is more than 118 mW/m 2 and the shallowest CPD is 21.7 km. The maximum heat flow in the northern Chiang Rai area reached 104 mW/m 2 and the CPD is shallower than perimeter, the shallowest point is only 20.4 km. However, heat flow in the Eastern Yunnan Block (II) is low with the average value 60 mW/m 2 [72], whereas the average CPD is as shallow as 20 km. Actually, measured heat flow is nonlinearly correlated with the calculated CPD [73]. Theoretical curves of heat flow for different thermal conductivities (?) are plotted on Figure 6 based on Eq. (9). Most of the heat flow points are located between the theoretical curves of ?= 1 W (m°C) to ?= 5 W (m°C). This phenomenon indicates that the thermal conductivity varies greatly in different area in study area. According to Eq. (9), if ? changes 1W (m°C) in one heat flow point, the heat flow various ranges from 16.5 to 37.5 mW/m 2 . It indicates that the heat flows are likely more influenced by thermal conductivity. Previous studies on the eastern and southeastern Asia, the north Atlantic and the South China Sea show that the low thermal conductivity of crustal rocks may induce a delay between the changed thermal field and the effect of heat flow [47,[73][74]. It is supposed that the low thermal conductivity might probably cause the low CPD with low heat flow in the Eastern Yunnan Block.

Conclusions
In the study area, the CPD ranges between 15 km and 36 km. The CPD distribution characteristics present cluster-like in the northern part and trip-like in the southern part, which are related to the geological and tectonic activities in the deep and shallow crust. The thermal disturbances caused by the tectonic activities in middle-lower crust, such as the subduction between the Eurasian plate and the Indian plate as well as the underplating beneath the Eastern Yunnan Block, could change the distribution of the underground geothermal field, resulting in influencing the distribution of the CPD. At the same time, the geological activities caused by the Xiaojinhe Fault, the Xiaojiang Fault, the Dien Bien Phu Fault, the Phayao Fault and the Mae Chan Fault also can result in shallow CPD. The thermal conductivities of the distinguishable zones in the study area are different. The low heat flow is probably related to the low thermal conductivity in the Eastern Yunnan Block.