Magnetotelluric images of deep crustal structure of the Rehai geothermal field near Tengchong, southern China

Transcription

1 Geophys. J. Int. (2001) 147, Magnetotelluric images of deep crustal structure of the Rehai geothermal field near Tengchong, southern China Denghai Bai, 1, * Maxwell A. Meju 1 and Zhijie Liao 2 1 Department of Geology, University of Leicester, Leicester LE1 7RH, UK. mxw@le.ac.uk 2 Department of Geology, Peking University, Beijing , China Accepted 2001 July 25. Received 2001 July 23; in original form 1999 November 3 ABSTRACT Broadband ( s) magnetotelluric (MT) soundings have been applied to the determination of the deep structure across the Rehai geothermal field in a Quaternary volcanic area near the Indo-Eurasian collisional margin. Tensorial analysis of the data show evidence of weak to strong 3-D effects but for approximate 2-D imaging, we obtained dual-mode MT responses for an assumed strike direction coincident with the trend of the regional-scale faults and with the principal impedance azimuth at long periods. The data were subsequently inverted using different approaches. The rapid relaxation inversion models are comparable to the sections constructed from depthconverted invariant impedance phase data. The results from full-domain 2-D conjugategradient inversion with different initial models are concordant and evoke a picture of a dome-like structure consisting of a conductive (<10 Vm) core zone, c. 2 km wide, and a resistive (> Vm) cap which is about 5 6 km thick in the central part of the known geothermal field and thickens outwards to about km. The anomalous structure rests on a mid-crustal zone of Vm resistivity extending down to about 25 km depth where there appears to be a moderately resistive (>30 Vm) substratum. The MT images are shown to be in accord with published geological, isotopic and geochemical results that suggested the presence of a magma body underneath the area of study. Key words: geothermal field, magma chamber, magnetotelluric imaging, volcanism. 1 INTRODUCTION The Tengchong area (Fig. 1) is geologically unique. It is the only part of the Himalayan geothermal belt extending from south-west Tibet to the western part of Yunnan in China along the Indo-Eurasian suture zone that is affected by Quaternary volcanism. Volcanism started at Tengchong during the Pliocene or Miocene and continued throughout the Pleistocene period, reaching its peak in Early Pleistocene (Liao & Guo 1986). Granite and gneiss are the basement rocks in the area. The crustal thickness in the Tengchong area is about km (Xu et al. 1994), and the structure is dominated by roughly north south trending, regional-scale, strike-slip faults (Fig. 1). Important geothermal fields are located within a circular topographic feature (see Fig. 1) south-west of Tengchong. The Rehai (Hot Sea) and Reshuitang (Hot Pool) fields (Fig. 2) are part of these geothermal fields and are, respectively, situated about 13 and 20 km south-west of Tengchong. The Rehai field is structurally controlled with the main faults running roughly * on leave from State Seismological Bureau, Beijing , China. NNE SSW (c. N20uE) locally and the cross-cutting faults trending NW SE as shown in Fig. 2. There are surface manifestations of geothermal activity (in the form of hot springs and fumaroles) in the area. The reservoir rock in the Rehai field is a 69 Myr granite in the north and Precambrian gneiss in the south which are overlain by Miocene sandstone and conglomerates (Liao et al. 1991; Bai et al. 1994). A Lower Pleistocene andesite cover sequence occurs in the northern and western parts of the Rehai field while Middle Pleistocene basalt abounds in the eastern part (Fig. 2). There is a recent effort to re-evaluate the thermal resources in this volcanic area. Previous geophysical, geological, isotopic and geochemical studies suggest the presence of a magma body underneath the area (Liao & Guo 1986; Liu et al. 1989; Bai et al. 1994; Xu et al. 1994). In the early 1980s, Liu et al. (1989) carried out microseismic measurements around the Rehai field. They inferred the presence of a thin (7 km thick) upper crustal layer over the central portion of this field and which thickens gradually away from the centre forming an umbrella-shaped cap for the geothermal system. Preliminary magnetotelluric (MT) soundings were performed in the mid 1980s at Tengchong by the # 2001 RAS 677

2 678 D. Bai, M. A. Meju & Z. Liao Figure 1. Map showing the general characteristics of the Tengchong volcanic area and the position of the MT line in the Rehai geothermal field. The main results of an isotopic study (Xu et al. 1994) are also shown. The inset map shows the location of the Tengchong area (cross-hatched box) with respect to the regional tectonic setting (Tapponnier et al. 1982). State Seismological Bureau (SSB) of China and 1-D data interpretation suggested the presence of a 5-km thick conductive (6 10 Vm) layer at a depth of 9 10 km (Inst. of Geology, Beijing Unpubl. report, 1990). A follow-up project was initiated by the SSB in the early 1990s to study the Tengchong volcanic area (focusing on its deep structure and heat source potential). Bai et al. (1994) conducted MT soundings between the main Rehai (Liuhuangtang Huangguaqing) and Reshuitang fields (Fig. 2) as part of an effort to establish whether both fields have a common geothermal heat source. Based on a simple 1-D resistivity-depth transformation (Bostick 1977) of the recorded rotationally invariant apparent resistivities, these workers inferred the presence of a confined conductive (<10 Vm) zone, about 20 km thick, at a depth of about 6 km below the Rehai field and interpreted it as a cooling magma chamber. In this paper, the full tensorial MT data set from Rehai (Bai et al. 1994) are re-processed and then inverted using 2-D regularized inversion schemes (Smith & Booker 1991; Mackie et al. 1997) to provide better constraints on the conductivity structure of the Rehai field than previously available. 2 MT DATA ANALYSES Tensorial MT soundings over a broad range of periodicities ( s) were made in 1993 along a 13-km traverse across the Rehai field with an average station interval of c. 1km (Bai et al. 1994). The topography is basically a peneplain with step-wise raised volcanic terraces. The distribution of the MT stations is shown in Fig. 2. Stations T10 to T12 are located on the lowest terrace; T03 to T09 are on another terrace about 500 m higher up (where the main thermal field is found); and T02 is located on another volcanic plain about 500 m further up, near the centre of the main circular topographic feature. Horizontal electric and magnetic field components were recorded simultaneously in the magnetic north south and east west directions at each station. The vertical component of the magnetic field was also recorded. The magnetic declination is about 6u west of geographical north in the area. The data have been reprocessed using standard tensorial techniques (Swift 1967; Egbert & Booker 1986; Bahr 1988) to yield the apparent resistivity, phase and other interpretative response functions. 2.1 Dimensionality analysis We have used the tensor decomposition methods (Swift 1967; Bahr 1988) to gauge the dimensionality of the field data and to ascertain whether the geoelectrical regional strike is in accord with the main geological trend (c. N20uE, geographical) in this area. The computed azimuths and skew parameters define three sectors along the MT profile (coincident with the three raised terraces) each having a somewhat consistent response pattern; sample data from the respective sectors are presented

3 MT images of Rehai geothermal field 679 Figure 2. Map showing the local geological details of the Rehai field and the distribution of MT stations (MT line of Fig. 1). The area where TEM results are available for MT static shift assessment is shown. Electrical resistivity well log was also available for borehole zk201 in the TEM study area. Inset map shows the location of the Tengchong volcanic area in China. in Fig 3(a c). Station T02 is located about 500 m from an old volcanic crater and lies to the east of the accepted limits of the Rehai thermal field. For this station, the value of the Swift (1967) skew is less than 0.2 but remained greater than the Bahr phase sensitive skew at all frequencies; the phase sensitive skew has a value of about 0.1 at periods shorter than 40 s (Fig. 3a). The Swift (1967) azimuth shows a change at 4 s from about 70u at shorter periods to 20u at longer periods while the Bahr decomposed telluric vector defines two azimuths (approximately x20u and 20u) as shown in Fig. 3(a). For those stations within the thermal field (i.e. T03 to T109), the phase sensitive skew parameters have values of about 0.1 at short periods but they increase to 0.2 at periods longer than 0.1 s as in the example shown in Fig. 3(b) for a typical station (T05). Notice that the Swift skew parameters are roughly equal to the Bahr phase sensitive skew at periods shorter than 2 s but are over 0.2 at longer periods suggesting 3-D effects. The computed Bahr azimuths for station T05 suggest two trends: (1) a NNW SSE (x6u to 5u, magnetic) strike for periods shorter than 0.01 s and for periods longer than 40 s, and (2) a NW SE trend (x20u)at intermediate periods (see Fig. 3b). The skew and azimuthal variations with period point to the presence of a 3-D structure over the thermal field. Stations T10 to T12 (lower terrace) are outside the known thermal field and the response pattern is typified by T11. The Swift skew (<0.1) at T11 is smaller than the Bahr phase sensitive skew ( ) at all frequencies (Fig. 3c). The Swift method yielded azimuths of 30u 55u. Bahr s technique yielded azimuths of x10u at the shortest periods (<0.03 s), changing to about x20u to x45u at intermediate periods ( s), and 20u 30u at periods longer than 50 s (see Fig. 3c) suggesting a 3-D environment. Overall, the dimensionality analysis would appear to suggest an approximately NE SW geoelectrical strike (c. 20u) at long periods (and at s for T02) which is in accord with the trend of the regional-scale structures (see Figs 1 and 2), but a strong discordant trend (x10u to x45u) is present at intermediate and short periods depending on the site location. The Groom & Bailey (1989) decomposition was also applied to data from selected sites to gain further insights into structural dimensionality. For station T02, the apparent resistivities and phases from the unrotated estimates of 2-D impedances clearly cross at about 5 6 s while those from the Swift (1967) impedances are decoupled (Fig. 4a,b), requiring variation in strike angle under free rotation (see Fig. 3a) to achieve this. Analysis of results of 3-D Groom-Bailey (GB) decomposition of T02 impedances suggests that: (a) there is no clear evidence of a regional strike angle for periods less than 4 s, but a regional trend with a strike of about 20 degrees is evident at periods longer than 4 5 s, and (b) there are weak 3-D effects at short periods but these are not fully developed until about 0.1 s and they appear to be frequency-independent. The unrotated and Swift decomposition data for stations T05 and T11 are presented in Fig. 4(a,b) and show evidence of static shift. From GB decomposition analysis, T05 showed evidence of 3-D effects

4 680 D. Bai, M. A. Meju & Z. Liao (a) (b) and only at long periods do there appear to be evidence of a regional geoelectric strike of about 15 degrees. It is obvious that 3-D modelling would be appropriate for detailed interpretation of the Rehai data set. However, we have elected to use a 2-D approximation to image the gross features of the geothermal field especially given that conventional 3-D trial-and-error forward modelling of our limited soundings on a single survey line may not lead to a less unequivocal model in the absence of accurate quantified a priori information about the Rehai field. For the purposes of 2-D imaging, we have selected a strike direction coincident with the main regional geological strike (N20uE, geographical) which agrees somewhat with the long period geoelectric strike (c. N20uE, magnetic) but not with the second trend (c. N20uW, magnetic) furnished by Bahr s method (cf. Fig. 3a c). This assumed principal axis is reasonably perpendicular to our MT profile and we proceeded to obtain the apparent resistivity and phase responses (together with their associated observational errors) along this axis, and another one perpendicular to it, as required for 2-D imaging. For convenience, these responses are, respectively, dubbed the transverse electric (TE) and transverse magnetic (TM) mode data despite the associated 3-D signatures. We also obtained the effective MT responses from the determinant of the impedance tensor (Ranganayaki 1984) for each station for initial 1-D imaging. (c) 2.2 Static shift analysis Some of the data sets (T03, T05, T10, T11) have been identified as showing evidence of static shift caused by small-scale surficial heterogeneities (Berdichevsky & Dmitriev 1976). There is available some a priori information about the subsurface resistivity distribution that might be used for static shift correction, viz: (1) proprietary fixed-loop transient electromagnetic (TEM) resistivity map of the western portion of the MT profile (see Fig. 2 for location), and (2) resistivity well log (Fig. 5) for a deep exploratory borehole (zk201 in Fig. 2) in an area of thermal anomaly. The borehole resistivity log only covered the depth interval m but showed that this interval has an average resistivity of about 100 Vm. The proprietary TEM resistivity map (not presented here) suggests variable resistivity ( Vm) for the near-surface. The information from TEM and the resistivity well log were used to assess the level of the apparent resistivity sounding curves at stations T09 and T10; it was only deemed necessary to shift the TE curve at station T10 down such that the highest frequency datum attains a value of 30 Vm. The assumed TE mode sounding curve for station T05 was shifted upward by comparison with the data from T04. Stations T03 and T11 showed small parallel shifts and the TM mode curves were adjusted to the level of the TE curves by comparison with the responses from neighbouring stations. Figure 3. Comparison of some dimensionality indicators for three representative stations. The diamond symbols are the skew and rotation angle parameters from Bahr s (1988) method while the round symbols are those from the Swift (1967) method for stations (a) T02 (b) T05 and (c) T11. The principal axis is for a clockwise rotation from the magnetic north (y6u west of geographical north). 3 EFFECTIVE (INVARIANT) TRANSFORM MODELS Ranganayaki (1984) demonstrated the usefulness of the effective or determinant impedance phase pseudosections for interpretative structural analysis in 2-D environments. The determinant phase pseudosection for our MT line is given in Fig. 6 (top diagram) and shows an almost layered or banded structure. Note the relatively high phase angles (90u 125u) at periods less than 0.1 s and between 1 and 10 s. Very high phase

5 MT images of Rehai geothermal field 681 Figure 4. Sample response curves from selected stations. Shown are the results from (a) unrotated impedance, and (b) Swift impedance for several periods. The xy and yx polarizations are denoted by circular and square symbols, respectively. angles (>125u) are seen at periods of s. Low phases (<90u) are found at periods longer than 100 s and between 0.1 and 1 s. For comparison, we also plotted the determinant phase for each frequency at the corresponding approximate depth of probe (Bostick 1977) as shown in Fig. 6 (bottom diagram). This phase section shows a banded aspect but also suggests the presence of a domed structure with the upper horizon being about km thick at both ends of the MT line and only 5 6 km thick underneath stations T03 to T09 (coincident with the known geothermal field). The underlying high phase (conductive?) horizon appears to have been disrupted between stations T11 and T10 (coincident with the trend of a line of volcanic craters in Fig. 2), between stations T06 and T05 (where there is an old volcanic edifice), and near T02 (which is close to a 0.5-Ma crater to the east). It would thus appear that the zone of doming in the effective phase section corresponds to the belt affected by volcanism in the study area. The invariant resistivity section (see Bai et al. 1994) shows a major conductive body at a depth of 6 20 km between stations T10 and T04 with bordering resistive blocks. Figure 5. Resistivity well log for borehole zk APPROXIMATE 2-D INVERSION Examination of the dual-mode data showed that the data quality (in terms of continuity of data points and magnitude of associated errors) was highest in the interval s. Data in this sounding bandwidth was therefore selected for 2D

6 682 D. Bai, M. A. Meju & Z. Liao Figure 6. Determinant phase sections for the Rehai MT line. (a) A conventional phase pseudosection; (b) the depth-converted phase section. inversion. We also adopted the practical strategy that when inverting a scanty set of noisy field data, it is better to seek the smoothest model that can reproduce the main features of the data (see, e.g. Constable et al. 1987; degroot-hedlin & Constable 1990). We first applied the rapid relaxation inversion code (RRI2D) of Smith & Booker (1991) to our data and one example of the optimal models derived from joint inversion of the TE and TM data is shown in Fig. 7. The fit of the computed model response to the observed data is good but is not presented here. This model suggests the presence of: (1) an upper resistive cap which is about 5 7 km thick between stations T10 and T08 but thickens westward (8 km) and eastwards (12 km) of these stations; (2) a low resistivity (<10 Vm) intermediate horizon occurring at a depth of 7 14 km underneath stations T10 to T08 and flanked by slightly less conductive (c. 20 Vm) zones extending down to km; and (3) a moderately resistive (>30 Vm) substratum. The projected surface position of the western flank of the main conductor

7 MT images of Rehai geothermal field 683 Figure 7. Sample RRI2D inversion model for the Rehai MT line. coincides geographically with a major fault on the geological map. This model is somewhat in accord with the determinant phase transform model shown previously (cf. bottom diagram in Fig. 6). The non-linear conjugate-gradient (NLCG), finite-difference based, inversion program of Mackie et al. (1988, 1997) was also applied to our data. Operationally, the subsurface is discretized into a large number (49r45) of rectangular blocks of constant resistivity and we iteratively re-construct an optimal model with minimized differences between the resistivities of adjacent blocks in both the vertical and horizontal directions using the Twomey Tikhonov (Twomey 1963; Tikhonov 1963) derivative regularization measures. For consistency or non-uniqueness checks, the inversion of the Rehai data was initiated with several half-space models; and only those reconstructed features that are common to all the models may be considered necessary to fit the observed data. The assumed TE and TM mode data were inverted simultaneously with a specified threshold misfit (1.2 rms error). Similar optimal NLCG models were obtained for different starting models as can be seen in the sample results presented in Fig. 8(a,d) for the 50, 100, 300 and 500 Vm half-space initial models. Although statistically equivalent to the rest, the model from the 100 Vm half-space is preferred since the resistivity well log for borehole zk201 south of stations T10 and T09 showed that the top 2 km of the crust has an average resistivity of c. 100 Vm (see Fig. 5). The computed responses of the model constructed from the 100 Vm half-space are superimposed on the observed data (apparent resistivity, phase and associated standard errors) in Fig. 9 to show the typical match obtained. Overall, caution should be exercised when appraising the features present in these models which are approximate 2-D images of a complex 3-D terrain, sensu stricto. The models show a more heterogeneous resistivity structure in the upper 5 12 km of the crust than the RRI2D model. Note the anomalous, c. 2km wide, carrot-shaped, steep zone of low-resistivity (5 8 Vm) confined to the 5 17 km depth range beneath stations T08 and T07, and the possibly connected deeper-lying conductive feature located about 7 km further east near station T02 (all the models independently generated in this study retained both these features which may thus be significant). The sequence overlying these conductors is resistive ( Vm) and varies in thickness from about km west of T10 and from about 6 15 km east of station T04. The resistive upper crustal sequence appears to have been breached by steeply dipping structures that appear to root into the conductive zones at depth. Beyond about 25 km depth, the subsurface resistivity appears to rise above 30 Vm. However, note that a careful analysis of a total of 59 2-D NLCG inversion models constructed from this particular data set suggested that the inverted data bandwidth ( s) was only sufficient to constrain the top 25 km of the crust. Longer period data of good quality are necessary for imaging beyond 25 km depth (cf. Fig. 6). 5 DISCUSSION AND CONCLUSIONS The gross features of our MT models appear to be in accord with published geological, microseismic, isotopic and geochemical results for the area. Microseismic observations (Liu et al. 1989) in the same area suggested an umbrella-shaped structure with the upper crust being about 7 km thick at the centre and thickening outwards. The projected surface position of the lowresistivity feature found between stations T08 and T07 lies within the known confines of the Rehai geothermal field but there appears to be a possibly connected deeper-lying conductive zone located about 4 km east of the currently accepted eastern limit of the Rehai Field. A magmatic origin has been suggested for the heat source beneath the Rehai field (Bai et al. 1994; Xu

8 684 D. Bai, M. A. Meju & Z. Liao Figure 8. Equivalent 2-D NLCG models for the Rehai MT line. The initial half-space models were assigned resistivities of (a) 50 (b) 100 (c) 300 and (d) 500 Vm. et al. 1994). Based on geochemical and isotopic data, Xu et al. (1994) suggested that leakage of mantle 3 He through hydrothermal degassing is greater in the central part than towards the margin of the circular topographic feature (possibly developed over intersecting lineaments responsible for the two apparent geoelectrical strikes?) in the area (Fig. 1). The deep low resistivity zones in our 2-D models may thus be images of possible cooling magma chambers in accord with the existing geological and geophysical wisdom but more MT field measurements and 3-D modelling are required to confirm this hypothesis. However, we remark that it is also possible that these conductors are simply deep-reaching, fluid-saturated, fault-zones.

9 MT images of Rehai geothermal field 685 Figure 8. (Continued.) Chemical analysis of samples of the discharged water (of sodium-chloride-bicarbonate type) from the hot springs in the Rehai field shows the total dissolved solids (TDS) to be about 2800 mg Lx1 (Bai et al. 1994). Using a practical relationship between bulk resistivity and TDS in saline aquifers suggested by Meju (2000; Eq. 4), this would predict a bulk resistivity of about 8 Vm for the potential source reservoir # 2001 RAS, GJI 147, which is fortuitously comparable to the resistivity of the anomalous zone underneath the thermal area in our 2-D models. We conclude that the MT method is useful for subsurface mapping in this terrain and that the reconstructed approximate 2-D images have provided some insights into the possible deep structure of the Rehai field. However, we recommend that a

10 686 D. Bai, M. A. Meju & Z. Liao Figure 9. Fit of 2-D model responses to observed apparent resistivity and phase data for the model of Figure 8 (b). The solid line and circles represent the TE mode synthetic and field data, respectively. The dashed line and triangles correspond, respectively, to the TM mode synthetic and field data. The error bars show the standard errors associated with the field observations. much more detailed, grid-type, 3D survey should be conducted across the geothermal field and that data interpretation be carried out using a full-domain 3-D inverse modelling scheme; only such an approach may unravel the exact structure of the Rehai geothermal field. ACKNOWLEDGMENTS D.B. acknowledges a one-year fellowship award from the Royal Society, London. The MT fieldwork was part of the Eight Five scientific and technological research project of the State Science

11 MT images of Rehai geothermal field 687 and Technology Commission of China. We are extremely grateful to Ross Groom for the very thorough review of the original manuscript and for validating the tensor decompositions for one of the MT stations. The reviewers comments and those of the Editor helped improve the clarity of the paper. We acknowledge the stimulating geological discussions with D. Cunningham of Leicester University. REFERENCES Bahr, K., Interpretation of the magnetotelluric impedance tensor: regional induction and local telluric distortion, J. Geophys, 62, Bai, D., Liao, Z., Zhao, G. & Wang, X., The inference of magmatic heat source beneath the Rehai (Hot Sea) Field of Tengchong from the results of magnetotelluric sounding, Chinese Sci. Bull., 39, Berdichevsky, M.N. & Dmitriev, V.I., Distortion of magnetic and electrical fields by surface lateral inhomogeneities, Acta Geod., Geophys. Et Mont. Acad. Sci. Hung., 11, Bostick, F.X., A simple almost exact method of MT analysis, Workshop on, Electromagnetic Methods in Geothermal Exploration, Snowbird, Utah (U.S, Geol, Surv., Contract no, ). Constable, S.C., Parker, R.L. & Constable, C.G., Occam s inversion: a practical algorithm for generating smooth models from electromagnetic sounding data, Geophysics, 52, Egbert, G.D. & Booker, J.R., Robust estimation of geomagnetic transfer functions, Geophys. J.R. astr. Soc., 87, degroot-hedlin, C. & Constable, S., Occam s inversion to generate smooth two- dimensional models from magnetotelluric data, Geophysics, 55, Groom, R.W. & Bailey, R.C., Decomposition of magnetotelluric impedance tensors in the presence of local three-dimensional galvanic distortion, J. Geophys. Res., 94, Liao, Z. & Guo, G., Geology of the Tengchong geothermal field and surrounding area, west Yunnan, China, Geothermics, 15, Liao, Z., Shen, M. & Guo, G., Characteristics of the reservoir of the Rehai geothermal field in Tengchong, Yunnan, China, Acta Geologica Sinica, 4, (in Chinese). Liu, B.C., Zhang, L.M., Zhang, Z.X., Zhang, B.S. & Tong, W., Field observations of the seismicity in Tengchong volcanogeothermal region. In: Tengchong Geothermics, eds Tong, W. & Zhang, M., pp , Science Press, Beijing (in Chinese). Mackie, R.L., Bennett, B.R. & Madden, T.R., Long period magnetotelluric measurements near the central California coast: a land-locked view of the conductivity structure under the Pacific Ocean, Geophys. J. R. astr. Soc., 95, Mackie, R.L., Rieven, S. & Rodi, W., User s manual and software documentation for two-dimensional inversion of magnetotelluric data, Earth Resources Laboratory Rpt., Massachusetts Institute of Technology, Cambridge, MA. Meju, M.A., 2000, Geoelectrical, investigation, of, old /abandoned, landfill, sites, in urban, area: model development with a genetic diagnosis approach, J. Appl. Geophys., 44, Ranganayaki, R.P An interpretative analysis of magnetotelluric data. Geophysics, 49, Smith, J.T. & Booker, J.R., Rapid inversion of twoand three-dimensional magnetotelluric data, J. geophys. Res., 96, Swift, C.M., A magnetotelluric investigation of electrical conductivity anomaly in the southwestern United States, PhD Thesis Massachusetts Institute of Technology, Cambridge, MA. Tapponnier, P., Peltzer, G., Le Dain, A.P. & Armijo, R., Propagating extrusion tectonics in Asia: new insights from simple experiments with plasticine, Geology, 10, Tikhonov, A.N., Regularization of ill-posed problems, Dokl, Akad, Nauk SSSR, 153, 1 6. Twomey, S., On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature, J. Assoc. Comput. Man., 10, Xu, S., Nakai, S., Wakita, H. & Wang, X., Helium isotopic compositions in Quaternary volcanic geothermal area near Indo- Eurasian collisional margin at Tengchong, China, in, Noble Gas Geochemistry and Cosmochemistry, ed. Matsuda, J., pp , Terra Scientific Publications Co, Tokyo.