**1.1. Pull-apart basin forming at the termination of lateral faults**

When a sedimentary basin forms at the termination of a lateral faults, it is known as a pullapart basin. It is well known that tectonic basins, such as pull-apart basins, are generally formed at the termination of right-lateral, right-stepping and left-lateral, left-stepping fault systems (e.g., [1]). This is mainly caused by the formation of subsidence at the fault termination by the lateral motion of the faults. Subsidence is therefore likely to be found piled up at the termina‐ tion of right lateral right-stepping and left lateral left-stepping fault systems. In contrast, uplift structures are formed at the termination of right-lateral left-stepping and left-lateral rightstepping fault systems, because the terminations are located in an area where uplift is piled up, due to the lateral motion of the fault (Figure 1). Such structures are found in many places globally, and their fundamental formation mechanisms have been numerically simulated by numerous researchers (e.g., [2, 3]).

Katzman et al. [3] attempted to restore the subsurface structures of the Dead Sea, estimated from gravity anomalies (e.g., [4]), by means of Boundary Element Modeling (BEM), and indicated that it is necessary to assume long overlapping faults and a very high Poisson's ratio in order to restore the Dead Sea pull-apart basin. Rodgers [2] attempted to simulate the formation of a pull-apart basin by means of dislocation modeling (e.g., [5]), and this was probably the first study which discussed the formation of a pull-apart basin using numerical modeling.

© 2013 Kusumoto et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Kusumoto et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In this study, we employ the analytical solutions of Okada [8] for the numerical simulation of

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For a typical example of a pull-apart basin formed by dislocation, it would be appropriate to use a restoration model of Beppu Bay and Figure 1 for a numerical simulation. Beppu Bay is located at the junction between the Honshu and Ryukyu arcs, and it is formed at the western end of the Median Tectonic Line (MTL), which is the largest right-lateral tectonic line in southwestern Japan (c.f., [33]). Another right-lateral fault, the Kurume-Hiji Line (KHL: [34]), is located 30 km north of the MTL. The MTL and the KHL are arranged as a right-lateral rightstepping fault system, and the potential for producing a pull-apart basin exists. Kusumoto et al. [35] therefore applied the simple dislocation plane concept of Okada [8] to this fault system and showed that Beppu Bay was formed as a pull-apart basin by the right-lateral faulting of the MTL and KHL. In addition, they suggested that two major tectonic events (namely, the formation of half-graben caused by a north–south extension, and the formation of the pull-

In Figure 1 and in [35], a single motion of the fault was assumed on the dislocation planes. However, it is well known that active faults undergo multiple movements over geological time scales. In order to reflect this effect in the simulation, as the Okada's solution [8] is based on linear elasticity, we attempted to introduce the history of fault activity into the numerical model by superimposing analytical solutions for different fault parameters on a single fault. For example, if the geological evidence suggests that the active zone of a lateral fault shifted along its strike direction over time, we express its tectonic history by superimposing analytical

**Figure 2.** Illustration reflecting fault propagations in the dislocation modeling. Analytical solutions for different fault parameters are superimposed onto a single fault plane. Vertical displacements are normalized by the maximum value

Itoh et al. [36] introduced this simulation technique while attempting to interpret topography and paleomagnetic data for the Takayama basin, central Japan. They showed that the basic

of absolute values of the total vertical displacement field, and they do not have a unit.

apart basin caused by east–west compression) occurred in this region.

solutions for different fault lengths (Figure 2).

sedimentary basin formation.

**Figure 1.** Schematic illustration of sedimentary basin and uplift at the terminations of lateral fault system. In this fig‐ ure, right lateral motion was assumed to each vertical fault (pink line). Vertical displacements are normalized by the maximum value of absolute values of the total vertical displacement field, and they do not have a unit.

## **1.2. Dislocation modeling**

In general, dislocation modeling is used for the quantitative interpretation of crustal defor‐ mation caused by earthquakes and/or volcanic activity (e.g., [6, 7]). Surface or interior dis‐ placements or strains can be calculated by considering dislocations on a plane embedded in an elastic isotropic half-space (e.g., [8, 9]).

Studies on dislocation theory and its applications began with Steketee [10] and were refined by Okada [9], who derived closed analytical solutions for surface and internal deformations or strains due to shear and tensile faults, with arbitrary dip angles in a half-space. During this period, many researchers applied dislocation theory to inhomogeneous media and considered the effects of viscoelasticity and poroelasticity (e.g., [11-18]). Such basic theories and their applications to earth science have been described in many textbooks (e.g., [19-21]). In addition, the fundamental idea of dislocation theory has been applied to theory for the interpreting the gravity and potential changes due to large earthquakes (e.g., [22-24]). In particular, Okubo's formula [23] was applied to an interpretation of gravity changes due to the 2011 Tohoku-Oki earthquake, as observed by the Gravity Recovery And Climate Experiment (GRACE) [25], and Wang et al. [26] were successful in discussing co- and post-seismic deformation independently of GPS data.

As mentioned above, many useful solutions have been derived, although all solutions cannot be referred to as being "closed analytical solutions." Closed analytical solutions (derived by [8, 9]) for a dislocation plane embedded in an elastic isotropic half-space are often employed for the quantitative interpretation of crustal movements, because they are very simple and are successful in explaining observational data. Consequently, some useful simulation software have been developed using Okada's formula [9], (for example Coulomb (e.g., [27, 28])) and/or stress evaluation methods (for example ΔCFF (e.g., [29])), and the method has been applied to the interpretation of crustal movements and/or the evaluation of stress changes due to earthquakes (e.g., [30-32]).

In this study, we employ the analytical solutions of Okada [8] for the numerical simulation of sedimentary basin formation.

For a typical example of a pull-apart basin formed by dislocation, it would be appropriate to use a restoration model of Beppu Bay and Figure 1 for a numerical simulation. Beppu Bay is located at the junction between the Honshu and Ryukyu arcs, and it is formed at the western end of the Median Tectonic Line (MTL), which is the largest right-lateral tectonic line in southwestern Japan (c.f., [33]). Another right-lateral fault, the Kurume-Hiji Line (KHL: [34]), is located 30 km north of the MTL. The MTL and the KHL are arranged as a right-lateral rightstepping fault system, and the potential for producing a pull-apart basin exists. Kusumoto et al. [35] therefore applied the simple dislocation plane concept of Okada [8] to this fault system and showed that Beppu Bay was formed as a pull-apart basin by the right-lateral faulting of the MTL and KHL. In addition, they suggested that two major tectonic events (namely, the formation of half-graben caused by a north–south extension, and the formation of the pullapart basin caused by east–west compression) occurred in this region.

In Figure 1 and in [35], a single motion of the fault was assumed on the dislocation planes. However, it is well known that active faults undergo multiple movements over geological time scales. In order to reflect this effect in the simulation, as the Okada's solution [8] is based on linear elasticity, we attempted to introduce the history of fault activity into the numerical model by superimposing analytical solutions for different fault parameters on a single fault. For example, if the geological evidence suggests that the active zone of a lateral fault shifted along its strike direction over time, we express its tectonic history by superimposing analytical solutions for different fault lengths (Figure 2).

**1.2. Dislocation modeling**

of GPS data.

earthquakes (e.g., [30-32]).

an elastic isotropic half-space (e.g., [8, 9]).

In general, dislocation modeling is used for the quantitative interpretation of crustal defor‐ mation caused by earthquakes and/or volcanic activity (e.g., [6, 7]). Surface or interior dis‐ placements or strains can be calculated by considering dislocations on a plane embedded in

**Figure 1.** Schematic illustration of sedimentary basin and uplift at the terminations of lateral fault system. In this fig‐ ure, right lateral motion was assumed to each vertical fault (pink line). Vertical displacements are normalized by the

maximum value of absolute values of the total vertical displacement field, and they do not have a unit.

274 Mechanism of Sedimentary Basin Formation - Multidisciplinary Approach on Active Plate Margins

Studies on dislocation theory and its applications began with Steketee [10] and were refined by Okada [9], who derived closed analytical solutions for surface and internal deformations or strains due to shear and tensile faults, with arbitrary dip angles in a half-space. During this period, many researchers applied dislocation theory to inhomogeneous media and considered the effects of viscoelasticity and poroelasticity (e.g., [11-18]). Such basic theories and their applications to earth science have been described in many textbooks (e.g., [19-21]). In addition, the fundamental idea of dislocation theory has been applied to theory for the interpreting the gravity and potential changes due to large earthquakes (e.g., [22-24]). In particular, Okubo's formula [23] was applied to an interpretation of gravity changes due to the 2011 Tohoku-Oki earthquake, as observed by the Gravity Recovery And Climate Experiment (GRACE) [25], and Wang et al. [26] were successful in discussing co- and post-seismic deformation independently

As mentioned above, many useful solutions have been derived, although all solutions cannot be referred to as being "closed analytical solutions." Closed analytical solutions (derived by [8, 9]) for a dislocation plane embedded in an elastic isotropic half-space are often employed for the quantitative interpretation of crustal movements, because they are very simple and are successful in explaining observational data. Consequently, some useful simulation software have been developed using Okada's formula [9], (for example Coulomb (e.g., [27, 28])) and/or stress evaluation methods (for example ΔCFF (e.g., [29])), and the method has been applied to the interpretation of crustal movements and/or the evaluation of stress changes due to

**Figure 2.** Illustration reflecting fault propagations in the dislocation modeling. Analytical solutions for different fault parameters are superimposed onto a single fault plane. Vertical displacements are normalized by the maximum value of absolute values of the total vertical displacement field, and they do not have a unit.

Itoh et al. [36] introduced this simulation technique while attempting to interpret topography and paleomagnetic data for the Takayama basin, central Japan. They showed that the basic structure of the Takayama basin, and changes in the declination of the thermoremanent magnetization, can be restored by considering the cumulative activity of two right-lateral faults (the Enako Fault and the Makigahora Fault) and a reverse fault (the Harayama Fault). In addition, they showed that the reverse fault can be divided into two segments that moved independently with a time lag between their active periods. Because this modeling technique can take into account the type and amount of fault motion, we can reflect the history of fault activity based on certain geological evidence, including paleomagnetic studies, in the numer‐ ical modeling, and can discuss the tectonics in detail.

In the following sections, we describe the basic background and gravity anomaly in central

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Hokkaido is located on the North American plate, at a junction of the Northeast Japan arc and the Kurile arc (Figure 3). Using recent GPS observations, an east-west compressive strain field has been observed in the northern part of Hokkaido, and this strain field is considered to be caused by the convergence of the Eurasia plate with the northern part of Hokkaido functioning

**Figure 3.** Location map of our study area. Hokkaido is located on the North American plate, at a junction of the North‐ eastern Japan arc and the Kurile arc. Gray dashed line indicates the old plate boundary between the Eurasian and

Although the present plate boundary between the North American plate and the Eurasian plate exists in the Sea of Japan, it is known that the plate boundary was located in central Hokkaido at around 13 Ma. This period of time corresponds to the stage when the uplifting of the Hidaka Mountains began (e.g., [45]). This tectonic framework is controlled by the dextral oblique collision between the Eurasian and North American Plates and the oblique subduction

North American Plates. Rectangular area by gray thin line indicates the study area of Itoh and Tsuru [58].

Hokkaido, and we attempt the restoration of the sedimentary basins.

**2. Basic background of central Hokkaido**

**2.1. Geophysical background**

as a part of the plate boundary (e.g., [44]).

This modeling technique has also been applied to the formation of pull-apart basins located in Hokkaido by Itoh et al. [37] and Tamaki et al. [38]. Tamaki et al. [38] found that a strike-slip fault motion reaching 30 km, is required to restore the distribution and volume of the Minami-Naganuma Basin located in southern central Hokkaido.

Here, we describe the disadvantages of the dislocation modeling defined using elasticity, and the solutions for the dislocation plane are given as a range of the linear elasticity. Since fracture, flow and other non-linear phenomena seen in the general solid material are not considered in the model, it is difficult to directly compare the amount of displacement between the modeled structure and the actual structure in long-time scale modeling. In general, dislocation modeling (including visco-elasticity effects) is often employed in discussions on crustal movements over a long time-scale such as on a geological time scale (e.g., [18, 39, 40]). In addition, Finite Element Modeling (FEM), Finite Difference Modeling (FDM) and Discrete Element Modeling (DEM) can simulate the formation processes of sedimentary basins or the building processes of mountains over a geological time-scale and can quantitatively discuss the mechanisms of their formation on a time axis (e.g., [41-43]).

As mentioned above, dislocation modeling defined using a range of the linear elasticity has disadvantages in the ability to directly compare the amount of displacement between the modeled structures and the actual structures. However, when we simply discuss the essential aspects of tectonics from the distribution pattern of structures caused by fault motions, dislocation modeling is a very useful tool because it provides the pattern of displacement using easy calculations.

#### **1.3. Aims of this study**

The aims of this study are to simplify the complex formation processes of sedimentary basins through numerical simulations and to show that the simplification enables us to estimate deductively which processes cause materialization. Central Hokkaido was selected as the field in which to achieve these aims, as many sedimentary basins are distributed in this area.

As will be described later in the paper, many sedimentary basins were formed from 48 to 12 Ma in central Hokkaido, and it is difficult to discuss their formation processes using only observational data because of their complex distribution both at and below the surface. In order to simplify the complex formation processes of sedimentary basins, we attempted to restore sedimentary basins using the advanced technique already mentioned, and we evaluated the fault type and the amount of movement required to form these sedimentary basins.

In the following sections, we describe the basic background and gravity anomaly in central Hokkaido, and we attempt the restoration of the sedimentary basins.
