Abstract
In order to understand the formation history and mechanism of volcanoes and their related structures, including calderas, their subsurface structures play an important role. In recent years, gravity gradiometry survey has been introduced, and new analyses techniques for gravity gradient tensors obtained by the survey have been developed. In this chapter, we first describe the gravity gradient tensor and its characteristics, and the method for obtaining the tensor from the gravity anomaly. Next, we review the semiautomatic interpretation methods for extracting information on subsurface structures, and apply some of the techniques to the volcanic zone of central Kyushu, Japan. The results showed that the horizontal and vertical gravity gradient methods, and the CLP method were useful for extracting outlines of important volcanic and tectonic structures in this region. Using the maximum eigenvector of the gravity gradient tensor, the caldera wall dip of the Aso caldera was successfully estimated to be in the range of 50–70°, and the dip of the Median Tectonic Line which was the largest tectonic line in the southwest Japan was consistent with seismic reflection surveys. In addition, a large circular structure surrounding the Shishimuta caldera with a diameter of 35 km was distinguished in some analyses.
Keywords
- caldera
- gravity gradient tensor
- subsurface structure
- semi-automatic interpretation method
- edge emphasis
- dip estimation
- curvature of the potential field
- Hohi Volcanic Zone
- Shishimuta caldera
- Aso caldera
1. Introduction
Subsurface structures reveal the current form of the static basement and crust and may also indicate the result of past crustal deformation. Consequently, subsurface structures are essentially fossil evidence of crustal movement, such as faulting, dyke emplacement, and/or volcanic activity, and the restoration of these subsurface structures provides important information on the tectonic and/or volcanic history of a region.
In volcanic areas, large eruptions produce widespread volcanic ejecta at the Earth’s surface, such as ash and lava flows, as well as volcanic depressions in the Earth’s crust. And, there are fossil magma chambers, that is, plutons. These are frequently recorded as gravity and magnetic anomalies, and especially collapse calderas formed by partial or total collapse of a magma chamber roof (e.g., [1–3]) have low gravity anomalies and it is a roughly concentric circular shape. Large eruption forming calderas occur with a very low frequency, however, since much smaller calderas such as the Miyake-jima caldera (e.g., [4]) form more frequently (e.g., [5]), understanding the mechanisms behind caldera formation is very important not only for advancing scientific knowledge but also for social purposes such as the construction of hazard maps.
Thus, studies on caldera formation have been conducted not only by geological surveys in the field but with analogue experiments, numerical simulations, and theoretical approaches (e.g., [6–21]). Although results obtained by these experiments have been compared with surface topography and ring-fault distributions, they have not been compared with subsurface structures or gravity anomalies reflecting subsurface structures. This is a result of the difficulty inherent in estimating caldera subsurface structures and in transforming analogue experiment results into gravity anomalies. Nevertheless, many researchers have recognized the importance of caldera subsurface structures and observed significant relationships between the dip of the caldera wall, the radius of the magma chamber, processes of caldera formation, and the type of caldera (e.g., [14, 19–21]).
Geoelectromagnetic and gravity surveys are popular geophysical techniques used in volcanic areas and have been employed frequently to estimate shallow to medium depth subsurface structures. In recent years, gravity gradiometry has been introduced. This measures the gravity gradient tensor generated by a source body, which consists of six components of three-dimensional (3D) gravity gradients. Gravity gradiometry survey has higher sensitivity than gravity surveys. Various analysis techniques for gravity gradient tensors have been developed and have given excellent results in subsurface structure estimation and edge detection, for example (e.g., [22–25]).
In this chapter, we first describe the gravity gradient tensor and its characteristics. Generally, the gravity gradient tensor is obtained by gravity gradiometry. However, surveys of this type have been made in only a few areas, so that tensor data are rarely available. Therefore, in Section 2.2, we present a method based on the work of Mickus and Hinojosa [26] that is used to obtain the tensor from the gravity anomaly. We then review the semiautomatic interpretation methods used to extract information on subsurface structures without additional geological and geophysical information, and apply some of these techniques to the volcanic zone of central Kyushu in Japan.
2. Gravity gradient tensor
2.1. Characteristics of gravity gradient tensor
The gravity gradient tensor Γ is defined by the differential coefficients of the gravitational potential
Defining
Here,
Here, we set a point mass model under the surface (Figure 1). In this case, the gravitational potential
where
and
These are
Taking the second derivatives of the potential
and
These are six independent components of the gravity gradient tensor. The other three second derivatives can be obtained using the symmetry characteristics of the second derivative. And, since the sum of Eqs. (8), (11), and (13) is zero, namely
diagonal components satisfy Laplace's equation (Δ
We show a numerical example for the point mass model in Figure 2. In the numerical example, we set the point mass model with a depth of 4 km and a mass anomaly of –5.7 × 104 kg. Here, negative mass anomaly means lack of mass caused by negative density contrast such as hole in the crust, and the mass anomaly of –5.7 × 104 kg is equivalent to a sphere having radius of 3 km and density contrast of –500 kg/m3. The vertical component,
In the gravity gradient tensor, Γ, we first find the triplet pattern, negative-positive-negative, in the
2.2. Derivation of gravity gradient tensor from gravity anomaly
In general, the gravity gradient tensor is measured with gravity gradiometry (e.g., [29–31]). However, we can obtain the tensor from gravity anomaly data using calculations shown in [26], even if the gravity gradiometry surveys have not yet been undertaken.
As a technique for calculating the gravity gradient tensor from the gravity anomaly data, Mickus and Hinojosa [26] used the following procedure: (1) application of a Fourier transformation to the gravity anomaly, (2) estimation of the gravitational potential by integration of the gravity anomaly in the Fourier domain, (3) calculation of the gravity gradient components from second-order derivatives of the potential in each direction, and (4) application of a Fourier inverse transformation to finally obtain all components of the tensor in the spatial domain.
When the Fourier transformation of a function
The Fourier inverse transformation of the function
where
and we use the notation
Integration of the function in the Fourier domain is given by division of the wavenumber. From these and relationships between gravity and gravitational potential, we derive the following equations on gravitational vector components:
where
and Eqs. (19) and (20) are rewritten as follows:
Therefore, we can obtain
In a similar manner, we derive equations to obtain each component of the gravity gradient tensor:
and
From these equations, as summarized in [26], we can obtain all components of the gravity gradient tensor from the gravity anomaly as follows:
3. Semiautomatic interpretation techniques
3.1. Edge emphasis
Edge emphasis techniques are extraction techniques used to find locations (namely, edge) where the gravity anomaly changes abruptly due to density variations, and these techniques play an important role in interpretation of potential field data (e.g., [33–35]).
In these techniques, the horizontal and vertical gravity gradient methods have frequently been employed to find structural boundaries such as faults or contacts between different materials (e.g., [36–39]). The vertical gravity gradient (
In addition to these gravity gradients, the second vertical derivative, ∂2
Miller and Singh [44] proposed the
This emphasis technique does not extract extremely large amplitude signals in the short wavelength range and is known as a balanced method. However, it is noted that the
Wijns et al. [47] proposed the
and Cooper and Cowan [44] proposed the
Li et al. [48] conducted a numerical test of these emphasis techniques for structural boundary extraction. As a result, they found that (1) the
Based on these discussions, Li et al. [48] suggested the
where
In recent years, specialized edge emphasis techniques have been developed to find the edges of potential field data related to multi subsurface structures. For example, Ma [46] suggested the Improved Local Phase method (
And, Ferreira et al. [49] have suggested the
Using numerical tests, Zhang et al. [50] showed that the
Kusumoto [51] pointed out that because the
3.2. Curvature of the potential field
Curvatures of potential field data vary in response to density changes in the subsurface structure, and these curvatures are described by the
Pedersen and Rasmussen [52] defined the invariant ratio,
Here,
The invariant ratio
Cevallos et al. [54] and Cevallos [55] pointed out that the shape index (e.g., [56, 57]) is useful for determining the characteristics of potential fields and is defined by
The shape index,
Studies on the curvature of the potential field have recently been developed as new interpretation techniques because they use a lot of the characteristics of the gravity gradient tensor (e.g., [58–62]). However, some problems relating to its practical usage remain unsolved. In fact, Li [63] conducted numerical tests for 13 well-known semiautomatic interpretation methods based on the curvature of the potential field and concluded that the shape of the potential does not always correspond to the subsurface structure, and therefore care should be taken when interpreting these results.
3.3. Euler deconvolution
Euler deconvolution is a semiautomatic interpretation method based on Euler’s homogeneity equation and is often employed to estimate locations and/or outlines of causative bodies. Because the Euler deconvolution technique can provide rapid interpretations of any potential field data in terms of depth and geological structures, it has been used by several researchers for analyzing both magnetic anomalies (e.g., [64–66]) and gravity anomalies (e.g., [67]).
The Euler deconvolution based on the three orthogonal gradient components of the potential field is simply called Euler deconvolution or conventional Euler deconvolution. For the gravity anomaly
In Eq. (44),
Rewriting Eq. (44), we obtain the following equation in which we can separate unknown parameters from known parameters:
There are four unknown parameters in Eq. (45). If we have enough data, namely
Zhang et al. [68] suggested the Tensor Euler deconvolution, designed to consider the full gravity gradient tensor (Eq. (2)) and all components (
Here,
3.4. Dip estimation of a fault or structural boundary
In recent years, a technique estimating the dip of structures such as dikes, faults, or other geological structure boundaries has been developed and produced good results as a semiautomatic interpretation method using the gravity gradient tensor.
Beiki [69] suggested that the dip,
where
4. Application of semiautomatic interpretation method
Here, we apply the semiautomatic interpretation methods shown in the previous section to a volcanic area located in central Kyushu, Japan. This area consists of the Aso caldera and the Hohi Volcanic Zone containing a buried caldera, the Shishimuta caldera, where many previous geological and geophysical studies have been conducted. In addition, a database of the Bouguer gravity anomaly is available for use (e.g., [71]), although a gravity gradiometory survey covering this area has not yet been carried out. Since this gravity anomaly database employed in this study gives users 1 km × 1 km mesh data, we discussed structures larger than several kilometers in this study. If we would like to discuss fine structures, it would be possible by employing denser mesh data.
4.1. Background of Hohi Volcanic Zone and Aso caldera
4.1.1. Hohi Volcanic Zone and Shishimuta caldera
The Hohi Volcanic Zone (e.g., [73]) is located in the eastern part of central Kyushu (Figure 4) and is characterized by a wedge-shaped low gravity anomaly area, which becomes narrow toward the east (Figure 5). In the Hohi Volcanic Zone, there are four conspicuous low anomaly areas toward the west-southwest from Beppu Bay, which correspond to the Beppu Bay, Shonai Basin, Shishimuta caldera, and Kuju basin, respectively. The Beppu Bay has the lowest gravity anomaly, which reaches –50 mGal.
Subsurface structures in this region have been estimated by gravity anomaly data, drill core data, reflection survey, and surface geology data (e.g., [74, 75]). Kusumoto et al. [75] showed that, although the average depth of the basement was estimated to be approximately 1.2 km in the Hohi Volcanic Zone, the small basins (the Shonai basin and the Kuju basin) along the Oita-Kumamoto Tectonic Line (the tectonic line suggested by a steep gravity gradient (e.g., [76])) are deeper than 2 km. In addition, it was shown that the basement depth in Beppu Bay reaches to approximately 4 km. Detailed geological surveys have shown that this volcanic zone consists of half-grabens detailing volcanic activity that began 6 Ma (e.g., [73]) and pull-apart basins that formed after the half-graben formation (e.g., [77]).
During formation of the Hohi Volcanic Zone, it is known that eruption of more than 5000 km3 of material occurred in the last six million years, and that eruption rate gradually decreased. The volcanic zone erupted 2900 km3/Ma in its initial stage of activity from 5 to 4 Ma. After that, the zone erupted approximately 1300, 900, 400, and 200 km3 between 4–3, 3–2, 2–1, and 1–0 Ma, respectively [73]. The formation of the pull-apart basin began 1.5 Ma; this tectonic change occurred due to a counter-clockwise shift of the subducting Philippine Sea Plate (e.g., [77]).
Kusumoto et al. [78] attempted to restore the tectonic structures by numerical simulations based on the dislocation theory (e.g., [79]). They showed that tectonic structures such as half-grabens and pull-apart basins can be restored by obeying the tectonics suggested by Itoh et al. [77]. Kusumoto et al. [80] assumed a simple two-layer structure model, which consisted of the basement and the sediment, and estimated the gravity anomaly field from the vertical displacement field of the basement obtained by tectonic modeling [78]. As a result, it was shown that a gravity anomaly of volcanic origin cannot be restored. In this model, the unrestored gravity anomaly was that relating to the Shishimuta caldera.
The Shishimuta caldera is a buried caldera and is the origin of the Yabakei and Imaichi pyroclastic flows that are widely distributed throughout central Kyushu (e.g., [81, 82]). The volumes of these flows have been estimated as 40 km3 (e.g., [81]) and 90 km3 (e.g., [82]), respectively, based on detailed surface geological surveys. The red circle shown in Figure 4 indicates the caldera wall at 1 km depth with a diameter of approximately 8–10 km, estimated from drilling core data and gravity anomalies (e.g., [81]). Density contrast between basement and sedimentary layers is estimated to be in the range of 300–700 kg/m3 by Kusumoto et al. [75]. As shown in Figure 5, this Shishimuta caldera does not have the concentrically circular low gravity anomaly found in many calderas; rather, this caldera has a triangular low gravity anomaly.
The subsurface structure of the Shishimuta caldera was estimated from a geological perspective, and the structure shallower than 3 km depth was revealed by drill core data and gravity anomalies. On the basis of drill core data, gravity anomalies, active fault distribution, microearthquake activity, and geological surveys in and near the Shishimuta caldera, Kamata [81] estimated that the shape of this caldera is a funnel type. In addition, Kamata [81] estimated a magma chamber depth of the Shishimuta caldera would be 7–12 km depth. This was estimated by assuming that the original depth of the Yabakei pyroclastic flow is equal to the source depth of the Ito pyroclastic flow of Aira caldera, Kagoshima (e.g., [83]).
4.1.2. Aso caldera
The Aso caldera, like the Shishimuta caldera, is located in central Kyushu (Figure 4). However, it extends approximately 25 km in the south-north direction and about 18 km in the east-west direction and is thus elliptical in plan view, and is one of the largest calderas in the world.
It is known that the Aso caldera was formed by four eruptions with large-scale pyroclastic flows. The first large pyroclastic flow is called Aso-1 and flowed out from the present Aso caldera prior to 0.27 Ma. The second is called Aso-2 and was erupted before 0.14 Ma. The Aso-2 was the smallest pyroclastic flow and its volume is estimated at approximately 25 km3. The third pyroclastic flow is called Aso-3 and is dated at 0.12 Ma. The fourth pyroclastic flow is called Aso-4 and is the largest pyroclastic flow with a volume of more than 80 km3. From detailed geological surveys, it has been found that Aso-4 would have flown over the sea (the Seto inland sea and Tachibana Bay) and reached Yamaguchi Prefecture and Shimabara Peninsula. In the Aso caldera, there is also a central group of volcanic cones, which are currently active (e.g., [84]).
Gravity surveys of this region have been initiated by Tsuboi et al. [76] and Kubotera et al. [85]. Yokoyama [86] estimated that the subterranean caldera structure is similar to a funnel-shape. Komazawa [87] accumulated gravity data and conducted high accuracy, high-resolution analyses for the compiled gravity data. As a result, they found that the Aso caldera has a piston-cylinder type structure rather than a funnel-shaped structure with a single low anomaly. In addition, five minor local gravity lows exist in the caldera, which make up the major low gravity zone of the Aso caldera. The major gravity low has a steep gradient inside the caldera rim, and the central area of the minor gravity anomalies has a relatively flat bottom.
4.2. Gravity gradient tensor in central Kyushu
In Figure 6, we show all components of the gravitation vector and gravity gradient tensor. Since the gravity gradiometry survey covering this region has not been conducted, the gravitation vector and gravity gradient tensor were calculated from the Bouguer gravity anomaly data shown in Figure 5.
Although all components of the gravity gradient tensor were theoretically estimated by the method of Mickus and Hinojosa [26], we also obtained components of the gravity gradient tensor by numerical differentiation of
5. Results and discussion
5.1. Edge emphasis
In this section, we applied the 10 edge emphasis techniques shown in Section 3.1 to the field data. The results obtained by each method are shown in Figures 7–16.
The maps of the horizontal gravity gradient (
The vertical gravity gradient extracts the boundaries of the low gravity and high gravity areas, and emphasizes areas of low density (Figure 8). In particular, the caldera rim of the Aso caldera and boundaries of the tectonic lines and sedimentary basins are clearly extracted. In addition, areas of low-density material such as ash, pyroclastic flows, and sediments are accurately predicted and emphasized, and correspond to the inner areas of the Aso caldera, Shishimuta caldera, Kuju basin, Shonai basin, and Beppu Bay. The
The maps of the
The
The maps of the
5.2. Curvature analysis
Figures 17 and 18 are the dimensionality index map and the shape index map. The dimensionality index map indicates whether the subsurface structure in the region is 2D, such as a vertical or subvertical dike or fault, or 3D, such as a dome structure. If the subsurface structure is 2D, the dimensionality index,
The shape index in the Shishimuta caldera rim reaches –1 (Figure 18). This indicates that the potential shape of the low-density material is either bowl-like, a downward convex structure, or both. In fact, since Kamata [81] predicted that the Shishimuta caldera would be a funnel type caldera, the obtained results are considered suitable. Furthermore, these results are compatible with the result shown in Figure 17; the inner structure of the Shishimuta caldera would be 3D. In addition, locally low shape index areas are distributed around the Shishimuta caldera.
In the Aso caldera, the shape index is in the range of –1 to +1. This indicates that the subsurface structures would be complex since the Aso caldera has experienced four caldera formations. Moreover, areas of locally low shape index less than –0.75 correspond to the five local minor gravity lows found by Komazawa [87].
5.3. Euler deconvolution
We employed here the Tensor Euler deconvolution [68] to obtain information on the subsurface structures. In the calculation, we set a 24 km width window (the required amount of data to solve Eq. (9) is 576) with a structure index of 0.001. Generally, a structure index of 0 is employed for sills, dikes, and faults (e.g., [88]), but calculations with this value did not give solutions in our study field. The value of 0.001 was obtained through trail and error.
In Figure 19, we show the solution clouds given by the Tensor Euler deconvolution. We identify a deep and flat structure like a sedimentary basin at the east of the Aso caldera. There are large structural gaps between this structure and the Hohi Volcanic Zone, and the gaps appear to resemble a cliff (Figure 19b). In the Aso caldera, structural boundaries within the caldera are extracted as a void area of the solutions. However, these inner boundaries were not extracted in the Shishimuta caldera. In addition, we detect a large circular wall structure surrounding the Shishimuta caldera. Although partially observable in map view (Figure 19a), the structure is more clearly distinguished in bird’s-eye view (Figure 19b).
5.4. Dip estimation
Dips of faults and/or structural boundaries were estimated in the areas that satisfied the conditions
In the Aso caldera, dip of its caldera wall are in the range of 50–70° (inward dipping), as shown in Figure 20. Dips become gradually lower toward the caldera center, which is almost flat. These subsurface structural characteristics in the inner area of the Aso caldera have already been observed by detailed gravity analysis [87], and our results and Komazawa's results support to each other. However, this is the first time that caldera wall dips have been explicitly determined. In the Shishimuta caldera, because the condition of the dimensionality index was not satisfied, the distribution of caldera wall dips could not be estimated. Since the dip of the caldera wall leads to a discussion of the radius of the magma chamber, the process of caldera formation, and the type of caldera (e.g., [9, 14, 19–20]), the dip of the wall is thought to be as important as the fault dip.
The dips of the large circular wall structure surrounding the Shishimuta caldera are in the range of approximately 45–60° (inward dipping). This large structure appears in
6. Conclusions
By obtaining the gravity gradient tensor from the gravity anomaly, we can use a variety of techniques to extract subsurface structures. In this study, we reviewed semiautomatic interpretation methods using the gravity gradient tensor, and applied some of the techniques to the volcanic zone of central Kyushu, Japan. This area consists of the Aso caldera and the Hohi Volcanic Zone containing a buried caldera, the Shishimuta caldera, and has large tectonic lines such as the Median Tectonic Line and the Oita-Kumamoto Tectonic Line, and tectonic sedimentary basins such as the Beppu Bay, the Kuju basin, and the Shonai basin.
Most edge detection methods extracted the outlines of these structures, and some of them indicated density structures. In spite of classical methods, the horizontal gravity gradient method and the vertical gravity gradient method were excellent edge detection methods. As for recent methods, the
In the curvature analysis, we obtained useful information from the shape index and the dimensionality index that indicated caldera shape. In the estimation of the dip of structural boundaries using the eigenvector of the gravity gradient tensor, we obtained the fault dip of the Median Tectonic Line, which is consistent with seismic reflection surveys, and estimated the caldera wall dip of the Aso caldera, which corresponds to that obtained by detailed gravity analysis.
Through these data analyses, we distinguished a large circular structure with a diameter of 35 km surrounding the Shishimuta caldera. This structure appeared also in solution clouds obtained by the Tensor Euler deconvolution. However, we cannot confidently judge what this structure represents using only the gravity gradient tensor. More detailed surveys and studies are required to further discuss this issue.
Acknowledgments
This work was supported partially by JSPS (Japan Society for the Promotion of Science) KAKENHI Grant Number 15K14274. The author is grateful to the agency. The author is also most grateful to Agust Gudmundsson for very useful comments that have considerably improved the manuscript. In addition, the author is most grateful to Karoly Nemeth and Dajana Pemac for their editorial advices and cooperation.
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