**4. Restoration of sedimentary basins**

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]).

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

Gton, 8.6×102

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

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*).

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‐

We employed the first derivative of the gravity anomaly defined by the following equation

( ) ( ) 2 2 *gxy gxy* , , *x y* é ùé ù ¶ ¶ ê úê ú + ¶ ¶ ë ûë û

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.

(4), and calculated the horizontal gradient of the gravity anomaly (Figure 8):

*<sup>M</sup> <sup>V</sup>* r

Gton, and 1.5×104

<sup>D</sup> <sup>=</sup> <sup>D</sup> (3)

are estimated in areas I, II and III, respectively.

is assumed, volumes of sediment of

Gton were estimated

(4)

As a result, mass deficiencies of 4.7×103

maximum and the minimum values.

1.6×104

ward.

km3

, 2.9×103

km3

As an example, when a density contrast of 300 kg/m3

and 5×104

km3

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

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

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 model each fault for restoring the distribution of the sedimentary basins by trial and error. Consequently, in this study, we assumed that the dislocation plane used for the modeling was not a fault plane, but a typical or average plane of a fault zone. After trial and error, we defined the nine fault zones as shown in Table 1 and Figure 9, and employed them for numerical simulations. Each fault included in these fault zones is listed in Table 1 (with literature).

**No. Fault zone Preference (recognition as**

1 Horonobe Research Group for Active

2 Tenpoku Ikeda et al. [74];

5 Rumoi-

8 Hidaka-North (a)

9 Hidaka-South (b)

Shintotsu

**tectonic zone)**

Faults [73]

Itoh et al. [37]

3 Chikubetsu this study Shosanbetsu Fault [78]

4 Onishika this study Onishika Fault [80]

Association of Natural Gas

Association for Offshore

to modeling in the geological time scale (e.g., [3, 36-38, 68]).

Mining and

Petroleum Exploration [75] **Specific faults [reference]**

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287

Enbetsugawa Tectonic Line [79]

Chikubetsu Anticlinal Fault [78]

Tenguyama Thrust Fault [81] Okinaiyama Fault [82]

Shisenzawa Fault [82]

Horoshin Fault [82]

Shozuzawa Fault [83] Horonuka Fault [83] Chashinai Fault [84] Sorachi Fault [85]

buried with sediments.)

buried with sediments.)

6 T1 Itoh and Tsuru [58, 59] N/A (Most of the fault trace is in offshore area and

7 T2 Itoh and Tsuru [58, 59] N/A (Most of the fault trace is in offshore area and

**Table 1.** Fault zones. Definition of each fault zone, and relationship fault zone and specific faults. (a) Hidaka-North Fault Zone is collectively defined as the eastern margin of N-S serpentinite zone along the longitudinal mountainous range in northern Hokkaido. (b) Hidaka-South Fault Zone is assigned to the western margin of the area of the highest recent uplift rate in Hokkaido (i.e. Hidaka Mountains), of which tectonic and structural context is still controversial.

In the following subsections, we give the results of numerical simulations, accompanied by simple explanations. The faults moved during each stage and their fault parameters are listed in Table 2. In calculations, the total movement of each fault plane was expressed by fault motions of 1000 times, and a high Poisson's ratio of 0.4 was assumed because of its application

this study See footnote.

this study See footnote.

Shimokinebetsuzawagawa Fault [82]

Poroshiriyama-Higashi Fault [82]

Horonobe Fault [76] Higashino Fault [77, 78]

Numerical Modeling of Sedimentary Basin Formation at the Termination of Lateral Faults in a Tectonic Region…

**Figure 9.** Fault zones defined in this study. Each fault included in these fault zones is listed in Table 1 with literature.

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model each fault for restoring the distribution of the sedimentary basins by trial and error. Consequently, in this study, we assumed that the dislocation plane used for the modeling was not a fault plane, but a typical or average plane of a fault zone. After trial and error, we defined the nine fault zones as shown in Table 1 and Figure 9, and employed them for numerical simulations. Each fault included in these fault zones is listed in Table 1 (with literature).

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

**Figure 9.** Fault zones defined in this study. Each fault included in these fault zones is listed in Table 1 with literature.


**Table 1.** Fault zones. Definition of each fault zone, and relationship fault zone and specific faults. (a) Hidaka-North Fault Zone is collectively defined as the eastern margin of N-S serpentinite zone along the longitudinal mountainous range in northern Hokkaido. (b) Hidaka-South Fault Zone is assigned to the western margin of the area of the highest recent uplift rate in Hokkaido (i.e. Hidaka Mountains), of which tectonic and structural context is still controversial.

In the following subsections, we give the results of numerical simulations, accompanied by simple explanations. The faults moved during each stage and their fault parameters are listed in Table 2. In calculations, the total movement of each fault plane was expressed by fault motions of 1000 times, and a high Poisson's ratio of 0.4 was assumed because of its application to modeling in the geological time scale (e.g., [3, 36-38, 68]).


**Table 2.** Fault zones moved in each stage. Values in (A, B) shown in Table indicate total slip (A: km) amount assumed on the fault plane and fault initial length (B: km). Width, depth and dip angle of fault moved as right lateral fault are assumed to be 15km, 15km and π/2, respectively. Width, depth and dip angle of fault moved as reverse fault are assumed to be 17.32km, 15km and π/3, respectively.

#### **4.1. Early Ishikari stage (48–45 Ma)**

We attempted to restore the sedimentary basins formed in the early Ishikari stage, named "A", "B" and "C" (Figure 5A). Results are shown in Figure 10A. Right lateral movements of fault zones were required, (including the T1 fault, T2 fault, the Rumoi-ShinTotsu tectonic line and the Hidaka-North fault), in order to restore these three sedimentary basins. The amount of movement of each fault was determined by trial and errors, and results are shown in Table 2 and are as follows:

> **Figure 10.** Distribution pattern of sedimentary basins in each stage restored by the dislocation modeling. A: early Ishi‐ kari stage. B: late Ishikari stage (45-40 Ma). C: Horonai stage (40–32 Ma). D: Minami-Naganuma stage (34–20 Ma). E: early Kawabata stage (15–13 Ma). F: late Kawabata stage (13-12Ma). Vertical displacement amounts are given in m.

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From geological observations it is known that sedimentary basin "C" is the biggest basin and reaches to a depth of 1000 m. In our modeling, the depth of the modeled basin reached 1400 m. Sedimentary basins, "A" and "B" reach about 600 m and 500 m depths, respectively, and


From these amounts of displacement on each fault plane, it is estimated that during this tectonic stage, a horizontal movement reaching around 100 km occurred.

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**No. Fault zone (fault type) Early**

<sup>1</sup> Horonobe (Right lateral

<sup>2</sup> Tenpoku (Right lateral

<sup>3</sup> Chikubetsu (Right lateral

<sup>4</sup> Onishika (Right lateral

<sup>5</sup> Rumoi-Shintotsu (Right lateral

<sup>8</sup> Hidaka-North (Right lateral

Hidaka-North (Reverse

Hidaka-South (Reverse

assumed to be 17.32km, 15km and π/3, respectively.

**3.** Rumoi-ShinTotsu tectonic zone: 22 km

**4.** Hidaka-North fault zone: 36 km

**4.1. Early Ishikari stage (48–45 Ma)**

and are as follows:

**1.** T1 fault zone: 14 km **2.** T2 fault zone: 25 km

9

**Ishikari**

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

**Late Ishikari**

motion) - - (88, 500) (94, 500) (36, 61) -

motion) - - (28, 24) (14, 500) (41, 32) -

motion) - - - - (21, 36) -

motion) - (48, 150) (61, 63) - - -

motion) (22, 47) - (61, 94) (48, 78) (44, 73) -

motion) (36, 500) (36, 500) (29, 500) - - -

motion) - - - - - (2.5, 500)

motion) - - - - - (2.5, 212)

**Table 2.** Fault zones moved in each stage. Values in (A, B) shown in Table indicate total slip (A: km) amount assumed on the fault plane and fault initial length (B: km). Width, depth and dip angle of fault moved as right lateral fault are assumed to be 15km, 15km and π/2, respectively. Width, depth and dip angle of fault moved as reverse fault are

We attempted to restore the sedimentary basins formed in the early Ishikari stage, named "A", "B" and "C" (Figure 5A). Results are shown in Figure 10A. Right lateral movements of fault zones were required, (including the T1 fault, T2 fault, the Rumoi-ShinTotsu tectonic line and the Hidaka-North fault), in order to restore these three sedimentary basins. The amount of movement of each fault was determined by trial and errors, and results are shown in Table 2

From these amounts of displacement on each fault plane, it is estimated that during this

tectonic stage, a horizontal movement reaching around 100 km occurred.

6 T1 (Right lateral motion) (14, 500) (14, 500) (14, 500) - - - 7 T2 (Right lateral motion) (25, 500) (25, 500) (61, 500) (44, 500) (92, 500) -

**Horonai**

**Minami Naganuma**

**Early Kawabata**

**Late Kawabata**

**Figure 10.** Distribution pattern of sedimentary basins in each stage restored by the dislocation modeling. A: early Ishi‐ kari stage. B: late Ishikari stage (45-40 Ma). C: Horonai stage (40–32 Ma). D: Minami-Naganuma stage (34–20 Ma). E: early Kawabata stage (15–13 Ma). F: late Kawabata stage (13-12Ma). Vertical displacement amounts are given in m.

From geological observations it is known that sedimentary basin "C" is the biggest basin and reaches to a depth of 1000 m. In our modeling, the depth of the modeled basin reached 1400 m. Sedimentary basins, "A" and "B" reach about 600 m and 500 m depths, respectively, and both depths of restored basins (modeled basins) corresponding to these basins are 1000m as a result of dislocation modeling. Differences between the actual basin depth and the modeled basin depth, namely "the modeled basin depth–actual basin depth," were +400 m, +400 m and +500 m for basins "C", "A" and "B", respectively. The amount of restored subsidence may be a little large.

**1.** T1 fault zone: 14 km

**2.** T2 fault zone: 61 km

**4.** Onishika fault zone: 61 km

**5.** Tenpoku fault zone: 28 km

**6.** Horonobe fault zone: 88 km

**7.** Hidaka-North fault zone: 29 km

**4.4. Minami-Naganuma stage (34–20 Ma)**

**2.** Rumoi-ShinTotsu tectonic zone: 48 km

**1.** T2 fault zone: 44 km

**3.** Tenpoku fault zone: 14 km

**4.** Horonobe fault zone: 94 km

**3.** Rumoi-ShinTotsu tectonic line zone: 61 km

ment reaching about 342 km occurred during this tectonic stage.

m, and -500 m in basin "A", "B", "C", "D", "E" and "F", respectively.

amount of fault movement is shown in Table 2 and as follows:

ment reaching about 200 km occurred during this tectonic stage.

From the amount of displacement of each fault plane, it is estimated that a horizontal move‐

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291

From geological observations, it is known that depths of the sedimentary basins "A", "B", "C", "D", "E" and "F" reach to 3500 m, 1200 m, 1200 m, 600 m, 300 m and 1500 m, respectively. In our model, depths of modeled sedimentary basins "A", "B," "C", "D", "E" and "F" reached 1000 m, 600 m, 1800 m, 1100 m, 900 m and 1000 m, respectively. The differences between the actual basin depth and the modeled basin depth were -2500 m, -600 m, +600 m, +500 m, +600

We attempted to restore sedimentary basins "B", "D", "E" and "F" in the Minami-Naganuma stage (Figure 5D), and the results are shown in Figure 10D. The right lateral movements of fault zones, (including the T2 fault, the Rumoi-ShinTotsu tectonic line, Tenpoku fault and the

In this stage, Tamaki et al. [38] have restored already the Minami-Naganuma basin (corre‐ sponding to basin "B": pull-apart basin) located in south central Hokkaido. We referred to their results and determined the amount of movement of each fault by trial and error. The

From the amounts of displacement on each fault plane, it is estimated that horizontal move‐

From geological observations it is known that the depth of sedimentary basins "B", "E" and "F" reached 2000 m, 300 m and 1500 m, respectively. As already mentioned, the maximum depth of basin "D" is unknown. In our model, the depths of the modeled sedimentary basins "B", "D", "E" and "F" reached 1200 m, 1100 m, 700 m and 1200 m, respectively. The differences

Horonobe fault), were required in order to restore these four sedimentary basins.

Here, we assigned the right lateral motion to each fault as mentioned above, in order to restore the spatial patterns of basin distribution. If the amount of lateral motion of each fault is reduced to adjust to the depth component of each basin, it is not possible to restore the spatial distri‐ bution patterns of the basins.
