# Dip distribution of Oita–Kumamoto Tectonic Line located in central Kyushu, Japan, estimated by eigenvectors of gravity gradient tensor

- Shigekazu Kusumoto
^{1}Email authorView ORCID ID profile

**Received: **17 June 2016

**Accepted: **27 August 2016

**Published: **6 September 2016

### Abstract

*M*= 7.3. Because a gravity gradiometry survey has not been conducted in the study area, we calculated the gravity gradient tensor from the Bouguer gravity anomaly and employed it to the analysis. The general dip distribution of the Oita–Kumamoto Tectonic Line was found to be about 65° and tends to be higher towards its eastern end. In addition, we estimated the dip around the largest earthquake to be about 60° from the gravity gradient tensor. This result agrees with the dip of the earthquake source fault obtained by Global Navigation Satellite System data analysis.

## Keywords

## Introduction

The central Kyushu area is well known for its active volcanoes and calderas such as the Aso and Shishimuta calderas (e.g. Yokoyama 1963; Kubotera et al. 1969; Komazawa 1995; Kamata 1989). This area also includes the Beppu–Shimabara Graben (Matsumoto 1979) in addition to brisk seismic activities with focal mechanisms of lateral faulting, normal faulting or both (e.g. Shimizu et al. 1993; Sudo 1993). The strain field in Kyushu during the last 100 years, which was obtained by geodetic survey, indicates N–S extension (Tada 1984). Matsumoto et al. (2015) reported that the stress condition determined by focal mechanisms in the seismogenic layer, shallower than 30 km, has compressive and tensile axes of WSW–ENE and NNW–SSE directions. They also reported that the seismicity around the shear zone at the southern edge of the Beppu–Shimabara Graben is strike-slip faulting and that in the graben is normal faulting.

In general, subsurface structures play important roles in the understanding and discussion of tectonics of active areas. Frequently employed geophysical survey methods in these volcanic areas include geoelectromagnetic and gravity surveys (e.g. Mogi and Nakama 1993; Komazawa 1995; Kusumoto et al. 1996; Handa 2005). In recent years, gravity gradiometry has been introduced (e.g. Jekeli 1988; Dransfield 2010; Chowdhury and Cevallos 2013; Braga et al. 2014).

This type of survey observes a gravity gradient tensor consisting of six components of three-dimensional (3-D) gradients of gravitation by a causative body and has higher sensitivity than gravity surveys. Various analysis techniques using gravity gradient tensors have been developed and have given excellent results in subsurface structure estimations and edge detections (e.g. Zhang et al. 2000; Beiki 2010; Martinez et al. 2013; Cevallos 2014; Li 2015). In the recent years, techniques estimating the dip of a geological structure boundary by using the gradient tensor of the potential fields have been developed and have shown good results (e.g. Beiki 2013; Kusumoto 2015, 2016; Itoh et al. 2016). The dip of the structure plays an important role in numerical simulations that quantitatively examine tectonics (e.g. Finch et al. 2004; Itoh et al. 2014; Kusumoto et al. 2015).

In this paper, as a quick report, we show the dip distribution of the Oita–Kumamoto Tectonic Line estimated by the technique suggested by Beiki (2013) and Kusumoto (2015). With the exception of some geothermal areas, gravity gradiometry survey has not been conducted thus far in central Kyushu. Therefore, we estimated the gravity gradient tensor by using calculations based on Mickus and Hinojosa (2001) to obtain the tensor from the gravity anomaly, which was used for this study.

## Gravity anomaly and gravity gradient tensor

^{3}was employed here. In this study, the gravity anomaly database by Komazawa (2004) was employed. Because this database provides mesh data with intervals of 1 km × 1 km, we discuss structures larger than several kilometres.

The figure indicates negative gravity anomalies caused by the Shishimuta and Aso calderas and some tectonic sedimentary basins such as Beppu Bay. In addition, high horizontal gravity gradient belts caused by the Median Tectonic Line and the Oita–Kumamoto Tectonic Line are shown. The Beppu–Shimabara Graben shown in Fig. 1 corresponds to the negative gravity anomaly area in the north-east and to a gravity low area less than about 20 mGal in the south-west.

*Γ*is defined on the basis of differential coefficients of the gravity potential (e.g. Torge 1989; Hofmann-Wellenhof and Moritz 2005). Defining

*g*

_{ x },

*g*

_{ y },

*g*

_{ z }as the first derivative of the gravity potential along the

*x*-,

*y*-, and

*z*-directions, the gravity gradient tensor Γ is shown as

Here, *g*
_{
z
} is the gravity anomaly, and *g*
_{
zz
} is the vertical gradient of the gravity anomaly. The gravity gradient tensor is symmetric (e.g. Torge 1989), and the sum of its diagonal components is zero because the gravity potential satisfies the Laplace equation.

Although the gravity gradient tensor is generally measured by gravity gradiometry (e.g. Lee 2001; Barnes and Lumley 2011; Dransfield and Christensen 2013), the tensor can be obtained from the gravity anomaly data by using calculations shown in Mickus and Hinojosa (2001). Mickus and Hinojosa (2001) showed the following procedures: (1) apply a 2-D Fourier transformation to the gravity anomaly; (2) estimate the gravity potential by integration of the gravity anomaly in the Fourier domain; (3) calculate the gravity gradient components by second-order derivatives of the potential in each direction; and (4) apply a 2-D Fourier inverse transformation to finally obtain all components of the tensor in the spatial domain. Integration and differentiation of a function in the Fourier domain are equivalent to division and multiplication by powers of wave number (e.g. Blakely 1996).

This method is excellent and mathematically sound. However, because the second-order derivatives of the potential in the Fourier domain and Fourier inverse transformation emphasise short wavelength signals including noise, we obtained components of the gravity gradient tensor by numerical differentiation of *g*
_{
x
}, *g*
_{
y
}, and *g*
_{
z
} in the space domain. The components of *g*
_{
x
} and *g*
_{
y
} were calculated by the method of Mickus and Hinojosa (2001). The horizontal derivatives of *g*
_{
x
}, *g*
_{
y
}, and *g*
_{
z
} were calculated using simple finite-difference methods (e.g. Blakely 1996). The vertical gravity gradient, *g*
_{
zz
}, has been computed as *g*
_{
zz
} = −(*g*
_{
xx
} + *g*
_{
yy
}), since the gravity potential satisfies the Laplace’s equation.

## Dip estimation of fault or density structure boundary

*v*

_{1}) of the gradient tensor of the potential field indicates the direction of the causative body (Beiki and Pedersen 2010), Beiki (2013) suggested that the dip of the causative body can be estimated from the respective

*x*,

*y*, and

*z*components (

*v*

_{1x },

*v*

_{1y },

*v*

_{1z }) of the maximum eigenvector,

*v*

_{1}, as follows:

*I*

_{1}and

*I*

_{2}are invariants of the gravity gradient tensor. Each invariant is given by three eigenvalues (

*λ*

_{1},

*λ*

_{2},

*λ*

_{3}) of the tensor as follows:

Kusumoto (2015) considered that a basement consists of an assembly of high-density columns (Fig. 4b) and applied this idea to analysis of fault dip. To effectively estimate the dip of the fault or density structure boundary, Kusumoto (2015) recommended that the estimation would be conducted at areas of high horizontal gravity gradient. In this study, the dip of the structure boundary was estimated in the area satisfying the conditions of which tectonic lines are extracted precisely and are 2-D structure, namely the areas of HG ≥ 25 E and DI ≤ 0.5.

## Results and discussion

In part of the Median Tectonic Line, the dip is very high and exceeds 70° in some areas. It is well known that the Median Tectonic Line had moved as a right-lateral fault in the Quaternary; thus, the high dips reaching 70° or 80° are expected. The dips of the Median Tectonic Line become low gradually to the north in the Beppu Bay area. Although Kusumoto (2015) reported that this dip estimation technique tends to underestimate the actual dip in deep parts when applied to normal faults, seismic reflection surveys have confirmed dips of normal faults distributed in Beppu Bay to be 17° and 7° by seismic reflection surveys (e.g. Itoh et al. 2014). Therefore, the dip distribution calculated from the gravity gradient tensor agrees with the observed data.

In part of the Oita–Kumamoto Tectonic Line, the general dip was estimated to be about 65°. Because large-scale seismic survey has not been conducted around this tectonic line, its actual dip is unknown. However, the dip estimated from the gravity gradient tensor agrees with the fault dip obtained from crustal movement due to an earthquake in the Futagawa fault system.

The largest earthquake, *M* = 7.3, occurred on 15 April 2016 in a series of earthquakes at the centre of the Futagawa fault system; its fault parameters are estimated from crustal movement data observed by GNSS (The Headquarters for Earthquake Research Promotion 2016). According to The Headquarters for Earthquake Research Promotion (2016), the earthquake source fault is right lateral with a normal fault component, and the upper depth, length, width, azimuth, dip, slip angle, and slip amount of the fault are estimated to be 0.1, 27.1, 12.3 km, 235°, 60°, −161°, and 3.5 m, respectively. Figure 5 shows that the dips estimated from the gravity gradient tensor are 30°–40° at the northern side and roughly 55°–65° at the southern side. Because the earthquake source fault dips to the north, and this technique tends underestimate the actual dip in deep part for normal faults, the dips estimated from the gravity gradient tensor were found to agree with the fault dip obtained by crustal movement in the central eastern part of the Futagawa fault system.

From these discussions, it appears that the dip estimation technique using eigenvectors and eigenvalues of the gravity gradient tensor effectively provided the dip of the Oita–Kumamoto Tectonic Line, which we conclude to be generally about 65°. In detail, the dip of the Oita–Kumamoto Tectonic Line tends to be higher towards its eastern end and exceeds 70° at the area connecting to the Median Tectonic Line. The dip in the Futagawa fault system area is relatively low at about 60°. This variation or trend is divided into eastern and western areas by the Aso caldera. Although a series of earthquakes occurred along the Oita–Kumamoto Tectonic Line, the cause or origin and formation processes of this tectonic line might be different in each segment.

Although the tectonics in the western part of the Aso caldera are unknown in detail, the eastern part of the Aso caldera is known as the Hohi volcanic zone (e.g. Kamata 1989), which consists of a half-graben with volcanic activities that began in 6 Ma (e.g. Kamata 1989) and pull-apart basins that were formed after the half-graben formation in about 1.5 Ma (e.g. Itoh et al. 1998). These structures and their formation processes have been restored by numerical simulations assuming high-dip (80°) normal faulting and right-lateral faulting (e.g. Kusumoto et al. 1999). It appears that the formation of the half-graben in 6 Ma plays an important role in understanding the spatial variation of dip distribution because the Oita–Kumamoto Tectonic Line is the boundary between Cenozoic volcanic rocks and Palaeozoic and Mesozoic Erathems.

In this study, we used the existing gravity anomaly database (Komazawa 2004) which compiled 1 km × 1 km mesh data of the Bouguer gravity anomaly obtained by Bouguer density of 2670 kg/m^{3}. Although changes of the mesh size and the Bouguer density vary aspects of some maps, it seems that they would not make serious differences in the general situation. However, to obtain a detailed fault shape and to discuss the cause of a series of earthquakes tectonically, in addition to discussions on change of the Bouguer density, it is effective to use a dense gravity database or to conduct gravity gradiometer survey and seismic reflection survey around fault zones in the future studies.

## Conclusion

In this study, we estimated the dip distribution of the Oita–Kumamoto Tectonic Line where a series of earthquakes began on 14 April 2016. For dip estimation, the method using the dip of the maximum eigenvector of the gravity gradient tensor was employed. Because gravity gradiometry survey has not been conducted in the study area, the tensor was obtained by calculations from the Bouguer gravity anomaly. The estimation was conducted in an area satisfying the following conditions: (1) a horizontal gravity gradient larger than 25 E and (2) a dimensionality index <0.5.

We obtained that the dip of the Oita–Kumamoto Tectonic Line is generally about 65°. The fault dip around the largest earthquake of *M* = 7.3 in a series of earthquakes was estimated to be about 60°, which agrees with the dip of the earthquake source fault obtained by GNSS data analysis.

In addition, we found that the dip distribution of the Oita–Kumamoto Tectonic Line tends to be higher towards its eastern end, exceeding 70° at the area connecting with the Median Tectonic Line. On the other hand, the dip in the Futagawa fault system area is relatively low. This spatial variation of dip distribution has been attributed to the formation of a half-graben with volcanic activities that began in 6 Ma. However, more observations and discussions including numerical simulations are needed to understand these results because details of the tectonics in the Futagawa fault system area are unknown.

## Declarations

### Acknowledgements

This work was supported partially by the Integrated Research for Beppu—Haneyama Fault Zone (East part of Oita Plain—Yufuin Fault) by MEXT and by JSPS (Japan Society for the Promotion of Science) KAKENHI Grant Number 15K14274. The author is grateful to these agencies. Lastly, we are most grateful to two anonymous reviewers for their constructive reviews and comments on the manuscript and to Hiroyuki Tsutsumi for his editorial advice and cooperation.

### Competing interests

The author declares that he has no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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