2.1 AMT surveys
2.1.1 Electromagnetic studies at the TVG
The magnetotellurics (MT) principle (e.g., Cagniard [1953]; Vozoff [1991]; Simpson and Bahr [2005]) is based on electromagnetic induction and has been widely used at hydrothermal and volcanic areas for estimating the crustal electric resistivity structures associated with their activity. MT was first used by Chen et al. ([1998]) and Chen [2009] in the TVG to provide preliminary 1-D and 2-D structures, respectively. In addition, Kagiyama et al. ([2010]) conducted extensive and dense VLF-MT surveys to investigate resistivity features near the surface using a singular electromagnetic frequency of 22.1 kHz. They found low resistivity anomalies (less than 30 Ωm) corresponding to the fumarole and hot spring areas. Their NE-SW trending distributions suggested that the hydrothermal activity might be controlled by polarized permeable paths developed in response to the regional stress field (Chang et al. [2003]; Shyu et al. [2005]; Chen et al. [2010]). Utsugi et al. ([2012]) conducted dense audio magnetotellurics (AMT) surveys around Mt. Chishinshan to reveal a resistivity structure down to depths of 2-3 km using multiple frequencies of 1 Hz to 10 kHz. This study extended the AMT observation points to the Matsao and Da-you-keng areas to the north, where there are also active fumaroles and hot springs (Figure 1). The present study will show the shallow crustal resistivity structure associated with the intense hydrothermal activity in the TVG in northern Taiwan. Incorporating the data from Utsugi et al. ([2012]), we will propose an integrated model of detailed crustal resistivity structures, particularly beneath Mt. Chishinshan, and the Matsao hot spring and Da-you-keng fumarolic areas.
It is notable that in the late 1960s to early 1970s, the Mining Research and Service Organization (MRSO [1969], [1970], [1971], [1973]) conducted extensive electrical resistivity surveys (DC surveys) to obtain the spatial distribution of apparent resistivity in the TVG for the purpose of commercial use of its geothermal energy. Unfortunately, at that time, the detailed resistivity structure could not be revealed because of a lack of inversion techniques and insufficient sounding depths.
2.1.2 Data acquisition and processing
AMT surveys were conducted in October 2011 by Utsugi et al. ([2012]), and in December 2012 for the present study, using two Phoenix Geophysics MTU-5 systems. AMT pre-surveys began in 2010. There was no significant change in volcanic activity in the TVG during the time (e.g., Murase et al. [2013]; Wen et al. [2013]). Figure 1 shows the observation points. Those used in 2011 and 2012 were configured to intersect Mt. Chishinshan and the Matsao hot spring and Da-you-keng fumarolic areas. Four Pb- PbCl2 electrodes were used to measure two orthogonal components (N-S and E-W) of the electric field, and one additional electrode was used for grounding. Three orthogonal components (N-S, E-W, and vertical) of the magnetic field were measured using three induction coils. Each consisted of a coil of copper wire wound on a core with high magnetic permeability. At each observation point, continuous data acquisition was carried out for about 4 h. To remove contamination in the data due to local noise, we used Gamble et al.’s ([1979]) remote reference processing method for mutual referencing within the survey area. Actually, there are noise sources like power lines and inhabited areas around the study area that seriously affected the data even after removing the noise as described above. For this study, we removed any data whose electric and magnetic fields had a coherence of less than 0.7 to maintain high quality.
2.1.3 Dimensionality
To examine the regional dimensionality of this study area, impedance phase tensors and skew angles (β) were calculated using the method of Caldwell et al. ([2004]); this method has the merit of removing distortions from original impedances due to near-surface heterogeneities. Figure 2a shows the impedance phase tensors, skew angles, and induction arrows for representative frequencies.
Skew angle β is a proxy for three-dimensional (3-D) heterogeneity in the media structure, where larger β values mean stronger effects. The β value tends to gradually increase with decreasing frequencies. In particular, relatively larger average β values were estimated at observation points near Mt. Chishinshan. Uncertainties were less than 0.1° for 100 to 10,800 Hz and less than a few degrees for 1 to 100 Hz. The resulting values were a few degrees in the range of several hertz to several hundred hertz, suggesting a relatively minor 3-D effect. In addition, the average β at the same frequencies is as small as 0.5° to 2° at the observation points off Mt. Chishinshan, so it is reasonable to infer that 3-D heterogeneity has a minor effect on a regional scale. It is also notable that the average λ values calculated using the magnitudes of the principal axes of phase tensor ellipses, which are the proxy for the one-dimensional (1-D) structure (Bibby et al. [2005]), were found to be as small as 0.2 to 0.3, suggesting a relatively simple structure beneath the observation sites.
2.1.4 Strike estimation
The direction of the main axes of the phase tensor ellipses reflect a two-dimensional (2-D) strike ([Caldwell et al. 2004]). In order to estimate the regional strike, we focused on the data at lower frequencies. The tensor ellipses at frequencies of 18.8 and 8.1 Hz, shown in Figure 2a, have the following features. Most have main axes trending NW-SE at observation points around Mt. Chishinshan (sites 001, 002, 004, 102, 007) and in the Matsao area (sites 111, 104, 105). Those in the Da-you-keng area (sites 108, 109, 110, 008), however, have main axes in the N-S direction. Thus, we defined three areas, referred to as the Chishinshan, Matsao, and Da-you-keng areas, to estimate the respective direction of the major axes. Note that point 102 was at the intersect and was used in both the Chishinshan and Matsao areas.
Figure 2b shows the rose diagrams of the main axes of the phase tensor ellipses for each area. Uncertainties were lower than a few degrees for 100 to 10,800 Hz, and up to 10° for 1 to 100 Hz. The rose diagrams are rendered in discrete frequencies; this is because there are insufficient data at 530 Hz to 3.6 kHz and 40 to 79 Hz (460 Hz to 3.6 kHz, 16.2 to 116 Hz, and 1 to 6.9 Hz for the Chishinshan area). According to Caldwell et al. ([2004]), the dominant direction of the main axes of the phase tensor ellipses reflects the direction of either a regional strike or a conductivity discontinuity. They note that the obtained direction has a 90° ambiguity. The dominant directions of the main axes were estimated primarily from their modes in each area. The rose diagrams at several to several hundred hertz show that there are two rough types of dominant directions: NW-SE (or NE-SW) in the Chishinshan area and N-S (or E-W) at the Da-you-keng area, with the Matsao area having an intermediate direction.
As described above, northern Taiwan has regional NE-SW trending faults (approximately N60° E). Correspondingly, a NE-SW volcanic trend has developed along the Chinshan fault (e.g., Belousov et al. [2010]). The TVG also has an E-W volcanic trend from Mt. Huangzuei to Mt. Tatunshan (Belousov et al. [2010]), suggesting a weak extra E-W trending structure. The structural features noted above are consistent with the dominant directions of the main axes of the phase tensor ellipses. The induction vectors also trend roughly NW-SE and N-S in the Mt. Chishinshan and Da-you-keng areas, respectively, which suggests that the regional strike is perpendicular to the induction vector in each area. Based on these factors, the regional strike was estimated using the dominant directions at low- to middle-frequency ranges (below several hundred Hz) as follows: N57° E for the Chishinshan area, N65° E for the Matsao area, and and N85° W for the Da-you-keng area. This means that the 2-D cross sections are along N33° W for the Chishinshan area (line A-A’ in Figure 1), N25° W for the Matsao Matsao area, and N5° E for the Da-you-keng area. The 2-D cross section of the Matsao area is close to that of the Da-you-keng area, so we combined the Matsao and Da-you-keng areas into one and assumed its 2-D cross section as N10° W (Line B-B’ in Figure 1).
Accordingly, we rotated the impedance tensors to correspond to 2-D strikes oriented to N57° E for the Chishinshan area and N80° E for the Matsao-Da-you-keng area. We then performed a distortion analysis following the method of Bibby et al. ([2005]). This procedure estimates a distortion tensor, produced by surface heterogeneity, considering the ellipticity of a phase tensor and β angle. The effect of the distortion was removed from the rotated impedance tensor by multiplying the inversion matrix of the distortion tensor with the impedance tensor.
2.1.5 Soundings
Figure 3 shows the sounding curves of the apparent resistivity and phase, with open circles representing the TE mode and open rhombi for the TM mode, calculated from the impedance tensors as described above. The apparent resistivity and phase of the TM mode were calculated using electric fields perpendicular to the strike and magnetic fields parallel to the strike and the opposite for the TE-mode. For both modes, apparent resistivities have high values at high frequencies throughout and decrease with decreasing frequencies. In general, the apparent resistivity decreases with decreasing frequency for both modes.
Sounding observations at Chishinshan area, shown in Figure 3a, have the following features. Site 001 has phases less than 45° in high-frequency ranges, suggesting a high-resistivity region near the surface. At sites 001 and 002, the phase significantly decreases with decreasing frequency from a few tens of hertz to 1 Hz. On the other hand, the phase at site 004 gradually decreases compared to sites 001 and 002. This feature suggests a relatively high-resistivity body at a deeper part beneath sites 001 and 002. At site 005, the phases are greater than 60° through frequencies from 10 kHz to 10 Hz for both the TE and TM modes, and the apparent resistivities of both modes decrease to 1 to 2 Ω m at 10 Hz, a feature quite different from the other sites. This suggests that there is a significant change in the resistivity structure around site 005.
Figure 3b shows the same features for the Matsao-Da-you-keng area. At sites 111 and 105, the phase increases from 45° to 50° to 60° as frequency decreases from 10 kHz to 10 to 20 Hz for both the TE and TM modes, although their phase change patterns differ slightly. Site 108 also phase change pattern similar to sites 111 and 105. At these three sites, the phase significantly decreases to approcimately 30° as frequency decreases from 10 to 20 to 1 Hz. These features suggest a shallow conductive body and a resistive body deeper beneath the sites. At sites 109 and 110, the phase begins decreasing from a few hundred hertz, suggesting that the resistive body mentioned above could rise toward a shallower level beneath sites 109 and 110. At site 008, the phase stays higher than 60° through frequencies from 1 kHz to several hertz, suggesting a conductive body underneath.
2.1.6 2-D analysis
2-D resistivity structure analyses were performed using the inversion code developed by Ogawa and Uchida ([1996]). This code performs smoothness-constrained 2-D inversion based on the ABIC minimization method, where trade-off parameters between data misfit, model roughness, and static shift are estimated to minimize the misfit functional, assuming that static shifts follow Gaussian distributions. Error floors for apparent resistivity and phase were set to be 10% and 7% for the Chishinshan and Matsao-Da-you-keng areas, respectively. The resistivity structures were projected to lines A-A’ and B-B’ for the two areas, as shown in Figure 1. To represent the overall topographic change at each observation area, we defined the topography by averaging within 2 km of line A-A’ for the Chishinshan area and within 1.3 km of line B-B’ for the Matsao–Da-you-keng area. Note that the results thus obtained for the average topography do not differ much from those using the actual topography along A-A’ and B-B’.
Figure 4 shows the best-fit models obtained after 42 iterations for the Chishinshan area and 31 for the Matsao-Da-you-keng area, starting from an initial model with a uniform resistivity of 100 Ωm, with both RMS misfits of 1.02. Figure 3 shows the calculated soundings for the TE mode (red line) and TM mode (blue line). The inferred models reproduce most of the apparent resistivity and phase distributions. In the Chishinshan area, there seems to be no relation between the amount of static shift and the topographic change. The TE mode at site 004 has a relatively large static shift. Fumarolic activities do sporadically occur around site 004 in the area called Siao-you-keng. This is characterized by a surface resistivity less than 30 Ωm from the VLF-MT survey (Kagiyama et al. [2010]). This suggests that site 004 could have relatively strong 3-D heterogeneity near the surface, leading to the relatively large static shift. The Matsao-Da-you-keng area has a larger static shift than the Chishinshan area, presumably because most of its sites are situated amid sharp cliffs, resulting in a static shift due to the local topography (e.g., Jiracek [1990]).
2.1.7 Sensitivity tests
Before making any interpretations on the basis of our analyses, we performed the following series of sensitivity tests:
-
(i)
Linear sensitivity analyses based on the method of Schwalenberg et al. ([2002]). According to that study’s authors, model sensitivity can be described as:
(1)
where S
j
is the sensitivity of grid element j of size Δ
j
, f
i
(m) is the forward solution of model m, m
j
is the resistivity change of grid element j, σ
i
is the standard deviation of the data, and N is the number of elements = number of observation sites × number of frequencies × data types. This equation states that model resolution is the sum of the gradient of the forward solution to the resistivity change of a given grid element, which we normalize with regard to the standard deviation of the data, weighted by the size of each grid element. There are four types of data and forward solutions, the apparent resistivities and phases of the TE and TM modes.
Figure 5a shows the resultant model sensitivity, which decreases with depth, corresponding to the limit of the sounding frequency. The high-resistivity body situated below 1 to 1.5 km beneath sites 001 and 002 in the Chishinshan area has a variety of sensitivities ranging from 10−3 to 10−6, as do the resistive bodies situated below 1 km beneath sites 111, 105, 108, and 109 in the Matsao–Da-you-keng area. The MT method is generally less sensitive to resistive bodies because of the properties of electromagnetic waves, which can be easily absorbed by a conductor (e.g., Cagniard [1953]; Vozoff [1991]; Simpson and Bahr [2005]). For this reason, evaluating the reliability of the resistive body was necessary.
As shown in Figure 4, a low-resistivity, column-shaped body was found below a depth of 1 km at sites 102 and 005 in the Chishinshan area. This structural feature is represented by the low-frequency range soundings at sites 004, 102, and 005 (Figure 3). However, many data are missing because of their low quality, suggesting that such inverted deeper structures are not unique. It is also known that low-quality data or 2-D analysis of a 3-D situation may introduce inversion artifacts.
In order to confirm these regions with reliable sensitivity, the deeper resistive or conductive bodies shown by regions X1 to X4 and Y in Figures 4 and 5a were submitted to the following further sensitivity analysis.
-
(ii)
Examination of changes in the sounding curves by making distinctive changes in the model.
Case 1: region X1 to X4
Regions X1, X2, and X4 have high resistivities with values more than 100 Ωm. For these cases, changes in RMS misfits were examined by replacing the data for the regions with a conductive body. Region X3, which has low resistivities with values less than 10 Ωm, was replaced with a resistive body. Figure 5b shows the RMS misfits when a 10- Ωm body was substituted for X1, X2, and X4 and a 100- Ωm body was substituted for X3. The horizontal axis indicates the altitude of the uppermost part of the replacing body. The RMS misfits increase with the elevation of the substitute bodies, except in region X4 where there was no significant increase of the RMS misfit, suggesting that region X4 has little sensitivity. The change of TM phase at site 001 (Figure 5c) shows that the calculated sounding curve does not fit well within 3 to 7 Hz at an altitude of -0.54 km, as the RMS misfit is approximately 1.06. This is indicated by the dotted and dashed line in Figure 5b. Thus, RMS misfits greater than 1.06 indicate significant discrepancies from the best-fit model. We thus concluded that computational blocks with sensitivities of at least 10−4.5 can be supported by the observed data.
Region X3 has relatively high sensitivities at deeper depths compared to the other regions (Figure 5a). Its RMS misfit increased significantly when the block was replaced at the same altitude as the other cases (−0.27 km; Figure 5b). This occurred because of the unstable soundings at low frequencies at site 102. Figure 5d shows the change in the TM phase at site 102 that occurs when region X3 is replaced with a 100- Ωm body. Although the modified soundings show rough changes over the range of the uncertainty of the data for altitudes between −0.87 km and −0.57 km, they are still unstable. Taking into account the changes in RMS misfits, we consider the structure beneath the shallow conductive layer at sites 004, 102, and 005 to be valid for the computational block at altitudes from −0.27 to −0.57 km.
Case 2: region Y
Region Y’s resistivity is high, being more than 100 Ωm. Figures 5b and c show the changes in RMS misfit and the phase sensitivities of the phase when region Y is replaced with a 10 Ωm body. As the elevation of the replacing body increases, the RMS misfit increases significantly, and the fit of the calculated to observed soundings worsens at 1 to 3 Hz, as described in case 1. Given this information, we consider that computational blocks with sensitivities of at least 10−4.5 can be supported.
2.1.8 2-D resistivity structure
Figure 6 shows the resistivity structures of the Chishinshan area (line A-A’) and the Matsao–Da-you-keng area (line B-B’) after removing the low-sensitivity regions defined in the previous section.
The northern half of line A-A’ has a resistive surface of several hundred to one thousand ohm meters with a thickness of one hundred to several hundreds of meters. The southern half has a surface with a resistivity of 10 to 30 Ωm, except at its southern end, where the resistivity is greater than 100 Ωm. These features are consistent with the results from previous electrical resistivity surveys (DC surveys) by the MRSO ([1969], [1970], [1971], [1973]) and VLF-MT surveys by Kagiyama et al. ([2010]). Two discrete conductive regions with resistivities less than 3 Ω m are present at depths of several hundred meters beneath Mt. Chishinshan (C1 in Figure 6). These were also suggested by the apparent resistivity distribution obtained from the MRSO DC surveys ([1969], [1970], [1971], [1973]).
Figure 7a shows the resistivities along borehole E203, shown in Figure 6, one of the MRSO drilling sites ([1970]). Red lines represent the resistivities obtained in the present study, while black represent those from well logging (MRSO [1970]). The latter shows resistivities of a few Ωm at depths from 200 to 670 m with some fluctuations, increasing to several tens of ohm meters at depths of 670 to 1,000 m. The inferred resistivities around the borehole can reproduce the low resistivities from well logging quite well, although the inferred values for the resistive section of 670 to 1,000 m in depth are slightly lower than those from well logging. From these results, we determined that our method produces a reliable resistivity structure for the Chishinshan area from the surface to a depth of approximately 1 km.
Line B-B’, shown in Figure 6, has a surface with a resistivity of generally less than a few tens of ohm meters. In particular, the surface at site 110 has a resistivity of less than 3 Ωm, corresponding to the Da-you-keng fumarolic area. There are two conductive regions at depths of a few hundred meters to 1 km beneath the Matsao hot spring area (C3 in Figure 6) and Cing-tian-gang (C2). They are connected to the conductive surface around the Da-you-keng fumarolic area, overlying a resistive body of about a few hundred ohm meters. Two separate conductive regions are suggested by the distribution of apparent resistivity from the MRSO DC survey ([1969], [1970], [1971], [1973]). Thus, by comparing the inferred results with previous work, the resistivity structure obtained along line B-B’ is likewise believed to be reliable.