**3. Bouguer gravity anomaly**

[59] pointed out that all basins formed in the Ishikari-Teshio Belt in this stage are pull-apart basins. Tamaki et al. [38] showed that using dislocation modeling, a 30 km right-lateral strikeslip is required to restore the actual distribution and volume of the basin. Kurita and Yokoi [60] also stated that lateral faulting was dominant in forming some of the tectonic structures during

The Kawabata stage is the sedimentation stage of the Kawabata Formation, the Ukekoi Formation, the Fureoi Formation, the Kotanbetsu Formation and the Masuporo Formation. During the Neogene, Japan was affected by the opening event of the back-arc basin of the Sea of Japan. In this stage, sedimentary basins "A", "B", "D", "E", "F1" and "F2" were formed (Figure 5E), and from well data their depths are estimated to be 2000 m, 4000 m, 4000 m, 3500 m, 2000 m and 2000 m, respectively. As mentioned above, a lateral motion of the crust was dominant during the early Neogene [37, 38, 59]. Although a building of the Hidaka Mountains

**Figure 5.** Shapes of sedimentary basins in (A) early Ishikari stage (48-45 Ma), (B) late Ishikari stage (45-40 Ma), (C) Hor‐ onai stage (40–32 Ma), (D) Minami-Naganuma stage (34–20 Ma) and (E) Kawabata stage (15–12 Ma). Isopach maps of the Horonai stage and the Kawabata stage are after Association of Natural Gas Mining and Association for Offshore

in around 13 Ma has been pointed out (e.g., [45]), details are unknown.

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

the late Oligocene.

Petroleum Exploration [75].

Numerous geological and geophysical surveys have been carried out in the Hokkaido area, and each survey has played an important role in the understanding of crustal characteristics and tectonic events in the area. In particular, seismic prospecting has proved very useful in obtaining information relating to subsurface structures. However, seismic prospecting is almost two-dimensional, and it is difficult to intuitively understand the subsurface structures as three dimensional structures, even when provided with data from more than one profile. In contrast, the characteristics of gravity anomaly maps are easy to interpret and can be used to roughly estimate three dimensional subsurface structures from the data. Figure 6 shows the Bouguer gravity anomaly map of the study area. This map is based on the gravity mesh data by Komazawa [61]. The Bouguer density of 2670 kg/m3 was employed.

**Figure 6.** Bouguer gravity anomaly map. This map is based on the gravity mesh data by Komazawa [61], and the Bou‐ guer density of 2670 kg/m3 was assumed. Contour interval is 10 mGal.

There are negative gravity anomalies in the southern and northern parts of central Hokkaido. The negative gravity anomaly in the northern part reaches -20 mGal (Figure 6 and Area I in Figure 7) and the southern negative gravity anomaly is less than -100 mGal (Figure 6 and Area III in Figure 7). The southern negative gravity anomaly located at the curved subduction zone is the lowest in the country. From seismic prospecting, it is known that this negative gravity anomaly consists of a very thick sedimentary layer (5–8 km), with a velocity of 2.5–4.8 km/s (e.g., [50]). The sedimentary layer was formed by imbrications associated with the collision process of the Northeast Japan arc and the Kurile arc (e.g., [46-48]). In contrast, there is a positive gravity anomaly in the area of the mountains, and the mountain elevations are roughly less than 2000 m. It would not be necessary to consider isostasy for the mountains, because the mountain elevations are not very high and the gravity anomaly in this area is positive.

A flat gravity anomaly of less than 20 mGal is distributed like a belt between the northern and southern gravity anomalies (Figure 6 and Area II in Figure 7.). Figure 7 is the gravity anomaly map that the area less than 20 mGal was painted by gray. This painted area corresponds to the area where the Paleogene strata distribute under the surface (Figure 4). We show four cross section profiles (three E-W profiles, A-C, and one N-S profile, D) of the Bouguer gravity anomaly in Figure 7. From these profiles, the gravity anomalies in the region are shown to

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**1.** Gravity anomalies in the west-east direction have a regional trend which tilts toward the

**2.** Gravity anomalies less than 20 mGal have a steep gradient on the east side, while those on the west side vary gently. These patterns of gravity anomalies indicate a depression structure called a "half-graben". Since there are many confirmed lateral faults and reverse faults in this region and no normal faults, it is considered that these patterns of gravity anomalies are caused by structures formed by the activities of lateral faults and/or reverse

**3.** Gravity anomalies in the north-south direction are relatively high and flat at the center of Hokkaido. It is possible that the high density of metamorphic belts near this region affect the observed gravity anomalies. Another cause to be considered could be the effect of subsurface structures such as a reduction of low density materials (e.g., a thin sedimentary

In general, gravity anomalies are caused by spatial variations of subsurface structures, and indicate a deficiency or an excess of mass under the surface. In general, high gravity indicates the existence of a mass excess or of high density materials, and low gravity indicates the existence of a mass deficiency or of low density materials. These deficiencies or excesses, of

( ) <sup>1</sup> , <sup>2</sup> *M g x y dxdy*

( ) <sup>1</sup> , <sup>2</sup> *<sup>S</sup> M g x y dxdy*

p*G*

Here, g(*x, y*) is the gravity anomaly data given on *xy* mesh with a constant interval. *G, π* and *ΔM* are the universal gravitational constant, circular constant and deficiency or excess of mass, respectively. Equation (1) is described by an infinite integration and it is difficult to perform an infinite integration with actual field data. Consequently, we understand this as being an approximate calculation and perform a numerical integration within a finite area (S) as follows:

D= D òò (1)

D= D òò (2)

layer) or an increase of high density material (e.g., uplift of the mantle).

mass can be evaluated quantitatively using Gauss's theorem (e.g., [62]).

p*G*

east. This could indicate the regional gravity field in Hokkaido.

have the characteristics as follows:

fault.

**Figure 7.** Bouguer gravity anomaly map. Gray indicates gravity low area less than 20mGal. A-A', B-B', C-C' and D-D' show gravity anomalies along each profile of four red lines shown in the Bouguer gravity anomaly map.

A flat gravity anomaly of less than 20 mGal is distributed like a belt between the northern and southern gravity anomalies (Figure 6 and Area II in Figure 7.). Figure 7 is the gravity anomaly map that the area less than 20 mGal was painted by gray. This painted area corresponds to the area where the Paleogene strata distribute under the surface (Figure 4). We show four cross section profiles (three E-W profiles, A-C, and one N-S profile, D) of the Bouguer gravity anomaly in Figure 7. From these profiles, the gravity anomalies in the region are shown to have the characteristics as follows:

There are negative gravity anomalies in the southern and northern parts of central Hokkaido. The negative gravity anomaly in the northern part reaches -20 mGal (Figure 6 and Area I in Figure 7) and the southern negative gravity anomaly is less than -100 mGal (Figure 6 and Area III in Figure 7). The southern negative gravity anomaly located at the curved subduction zone is the lowest in the country. From seismic prospecting, it is known that this negative gravity anomaly consists of a very thick sedimentary layer (5–8 km), with a velocity of 2.5–4.8 km/s (e.g., [50]). The sedimentary layer was formed by imbrications associated with the collision process of the Northeast Japan arc and the Kurile arc (e.g., [46-48]). In contrast, there is a positive gravity anomaly in the area of the mountains, and the mountain elevations are roughly less than 2000 m. It would not be necessary to consider isostasy for the mountains, because the mountain elevations are not very high and the gravity anomaly in this area is positive.

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

**Figure 7.** Bouguer gravity anomaly map. Gray indicates gravity low area less than 20mGal. A-A', B-B', C-C' and D-D'

show gravity anomalies along each profile of four red lines shown in the Bouguer gravity anomaly map.


In general, gravity anomalies are caused by spatial variations of subsurface structures, and indicate a deficiency or an excess of mass under the surface. In general, high gravity indicates the existence of a mass excess or of high density materials, and low gravity indicates the existence of a mass deficiency or of low density materials. These deficiencies or excesses, of mass can be evaluated quantitatively using Gauss's theorem (e.g., [62]).

$$
\Delta M = \frac{1}{2\pi G} \iint \Delta g \left(\mathbf{x}, \mathbf{y}\right) d\mathbf{x}d\mathbf{y} \tag{1}
$$

Here, g(*x, y*) is the gravity anomaly data given on *xy* mesh with a constant interval. *G, π* and *ΔM* are the universal gravitational constant, circular constant and deficiency or excess of mass, respectively. Equation (1) is described by an infinite integration and it is difficult to perform an infinite integration with actual field data. Consequently, we understand this as being an approximate calculation and perform a numerical integration within a finite area (S) as follows:

$$
\Delta M = \frac{1}{2\pi G} \iint\_S \Delta \mathbf{g}\left(\mathbf{x}, \mathbf{y}\right) d\mathbf{x}d\mathbf{y} \tag{2}
$$

We applied equation (2) to three areas, I, II and III, and we attempted to estimate the magnitude of mass deficiency for the formation of a gravity anomaly less than 20 mGal in each area. In the calculations, we employed the Gauss-Legendre numerical integral formula (e.g., [63]).

As a result, mass deficiencies of 4.7×103 Gton, 8.6×102 Gton, and 1.5×104 Gton were estimated in areas I, II, and III, respectively. There are large mass deficiencies in areas I and III, where the negative gravity anomalies observed are very large and a small mass deficiency in area II. In central Hokkaido, the amount of mass deficiency is different by about two digits in both the maximum and the minimum values.

The amount of mass deficiency can be transformed into the volume (*V*) of sediment by the following equation, under a condition assuming an appropriate density contrast (*Δρ*).

$$V = \frac{\Delta M}{\Delta \rho} \tag{3}$$

**Figure 8.** Distribution of the horizontal gradient of the Bouguer gravity anomalies more than 2 mGal/km. Contour

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In general dislocation modeling, the dislocation plane is assumed in the modeled crust by referring to the distribution of existing active faults and/or tectonic lines, and the surface deformations are calculated by assigning displacements on the plane. If the area for modeling is small, or if the tectonics and faults assumed for modeling are clear, such a modeling

However, when details of the tectonics and/or the moved faults are not so clear (as in our study), the faults and their displacements for modeling are assumed experientially from characteristic distributions of target structures, by referring to more regional rough tectonics and fault distributions. The faults and their displacements (appropriately assumed) can then be considered as an initial model and can then be corrected by trial and error, so that the

There are numerous small faults in central Hokkaido. As mentioned above, the details of tectonics and faulting in this area are unclear. It would, therefore, be impossible to attempt to

interval is 1 mGal/km.

**4. Restoration of sedimentary basins**

procedure is useful and practical (e.g., [35, 36, 38, 67]).

calculated results fit to the actual structures or their distribution pattern.

As an example, when a density contrast of 300 kg/m3 is assumed, volumes of sediment of 1.6×104 km3 , 2.9×103 km3 and 5×104 km3 are estimated in areas I, II and III, respectively.

As mentioned above, gravity anomaly indicates also spatial variations of subsurface structures including the location of tectonic lines and/or faults. It is well known that if there is a tectonic line or a fault with a large gap in the vertical direction, the spatial distribution of the gravity anomaly varies steeply around these structures. The variation rate of the spatial distribution of the gravity anomaly is called the "horizontal gradient of gravity anomaly", and it is given by the first derivative (e.g., [64, 65]) or the second derivative (e.g., [4, 66]). In general, the first derivative of the gravity anomaly is more practical, because the calculation used is very simple and the geophysical and geological interpretations for the calculated results are straightfor‐ ward.

We employed the first derivative of the gravity anomaly defined by the following equation (4), and calculated the horizontal gradient of the gravity anomaly (Figure 8):

$$
\sqrt{\left[\frac{\partial \mathbf{g}\left(\mathbf{x}, \mathbf{y}\right)}{\partial \mathbf{x}}\right]^2 + \left[\frac{\partial \mathbf{g}\left(\mathbf{x}, \mathbf{y}\right)}{\partial \mathbf{y}}\right]^2} \tag{4}
$$

Figure 8 shows the distribution of the horizontal gradient of the Bouguer gravity anomaly more than 2 mGal/km. The contour interval is 1 mGal/km. Although there are no continuous horizontal gradient anomalies within the area where the gravity anomaly is less than 20 mGal, the continuous horizontal gradient anomalies appear around this area. This may indicate that there are not tectonic lines including faults having large vertical deformation within this gravity low area less than 20 mGal and/or that gravity anomalies due to these tectonic lines are hidden by thick sediments, although faults with large vertical deformations actually exist. Numerical Modeling of Sedimentary Basin Formation at the Termination of Lateral Faults in a Tectonic Region… http://dx.doi.org/10.5772/56558 285

**Figure 8.** Distribution of the horizontal gradient of the Bouguer gravity anomalies more than 2 mGal/km. Contour interval is 1 mGal/km.
