The plan of a Metropolitan Crustal Deformation Monitoring System

by Communications Research Laboratory

Fujinobu Takahashi*, Michito Imae, Taizoh Yoshino, Kosuke Heki,

Hiroo Kunimori, Noriyuki Kurihara and Toshimichi Ohtubo

Communications Research Laboratory, 4-2-1, Nukui-kitamchi, Koganei-shi, Tokyo 184 Japan

TEL: 0423-27-7554, FAX: 0423-27-6687 [TEL and FAX number of first author]

Abstract

Communications Research Laboratory (CRL) plans and proceeds a Metropolitan Crustal Deformation Monitoring Program called "Key Stone Project (KSP)" using space geodetic measurements. This system will use both Very Long Baseline Interferometer (VLBI) and Satellite Laser Ranging (SLR) to monitor the three dimensional displacement of sites at four locations around the Metropolitan Tokyo region. The Tokyo region is situated above the three-fold structure of major tectonic plates; the North American, the Philippine Sea and the Pacific plates.

VLBI and SLR are expected to offer the horizontal relative displacements and the absolute vertical positions with regard to the Earth's gravitational center with the precision better than 1 cm, respectively. The program will play a basic role for the earthquake prediction in this area.

This paper emphasizes the necessity of space geodetic techniques and the importance of the cooperation both among techniques and institutes.

1. Introduction

Tokyo Metropolitan Area is on the edge of the North American Plate and also very near the boundaries of three other plates: Pacific Plate, Philippine Sea Plate and Eurasian Plate (Fig. 1(a)). It is now an urgent subject to monitor the preseismic signals of "the earthquake occurring directly under Metropolitan Area (EDUMA)".

From mid 1980's, space geodetic techniques, such as Very Long Baseline Interferometer (VLBI), Satellite Laser Ranging (SLR) and Global Positioning System (GPS) have been available to monitor the global crustal motion with the precision better than a few centi-meters.

VLBI and GPS measure the baseline vectors and VLBI is suitable for longer baselines. SLR, however, measures the absolute position with regard to the earth mass center.

Recently routine base GPS geodetic networks have been started by Geographic Survey Institute (GSI) and National Institute For Disaster Prevention and Earth Science (NIED). Communications Research Laboratory (CRL) and GSI have established the Metropolitan Diamond Cross (MDX) VLBI funded by Science and Technology Agency of Japan. Based on these background, CRL promotes the new plan "Key Stone Project (KSP)" to observe the crustal deformation around the Tokyo Metropolitan area (Takahashi et al., 1993)

We describes the planned observation methods in KSP and evaluate the precision expected by this system. We also calculate the coseismic and preseismic crustal deformation caused by typical earthquakes expected there using the dislocation theory by Okada (1992b).

2. Observation methods

The observable τof relative geodesy using VLBI is approximately given by the following equation:

τ=τ_g+τ_p+τ_c (1)
where τ_g,τ_p and τ_c are a geometrical delay, a propagational excess path and a between-site clock differences. τ_g is calculated by :

τ_g = B･s/c (2)
where B, s and c are a baseline vector, a radio source direction vector and the light velocity. The partial derivatives are as follows:

∂τ/∂B = s/c ∂τ/∂s = B/c (3a)

∂τ/∂τ_p=1 ∂τ/∂τ_c=1 (3b)
while ∂τ/∂B and ∂τ/∂s are highly independent parameters and ∂τ/∂τ_p, ∂τ/∂τ_c have large correlation with the vertical site coordinate. Unless we determine the τ_p and τ_c using other method precisely, it is difficult to improve the vertical components accuracy.

The observable range ρ of SLR is approximately given by the following equation:

ρ=|X - x|+τ_Bc (4)
where X and x are the position vectors of a satellite and a ground stations, and τ_B (B means "bias") is the internal bias offset delay in the ground station. Eq. (4) is transformed to next equation:

(ρ-τ_Bc)²=(X - x)² (5)

Considering τ_B<<ρ, the partial derivatives are as follows:

∂ρ/∂X=(X - x)/(ρ-τ_Bc)=(X - x)/ρ (6a)

∂ρ/∂x=(x - X)/(ρ-τ_Bc)=(x - X)/ρ (6b)

c・∂ρ/∂τ_B=1 (6c)
while ∂ρ/∂X,∂ρ/∂x are highly independent parameters as mentioned above, ∂ρ/∂τ_B is strongly dependent on the vertical site coordinates However SLR's τ_B is measured locally with the accuracy better than a few millimeters, though measurements of VLBI's τ_c is very difficult because of the global distance.

In the estimation in Sec. 3, we assume the τ_B is determined accurately by a separate calibration method. Other significant point of SLR is to offer the absolute station position vector with respect to the earth mass center, because the reference satellites' orbits are determined very precisely and their focuses are absolutely fixed to the earth mass center.

3. Precision of KSP system

Fig. 1(b) illustrates the 3-dimensional plate structure beneath the Metropolitan Area and four KSP stations: Koganei, Kashima, Miura and Boso. Assumed KSP observation network consists of four K-4 VLBI systems with 11 mφ antenna and four most advanced SLR systems with 60 cmφ telescopes.

Fig. 2(a) shows the estimated formal errors of KSP VLBI stations. It shows that 4 or 5 hours observation offers the 1 cm precision for the vertical component and several milli-meters precision for the horizontal two components.

Similarly Fig. 2(b) shows the results of formal error estimations of SLR stations. Four LAGEOS passes offer milli-meter-level formal errors for all the three components of SLR stations positions in the geocentric coordinate system. However, both global cooperation to determine the satellite orbit and accurate calibration of station biases are necessary to get this performance.

Thus relative VLBI and geocentric SLR observations play very complimentary roles each other.

4. Models of EDUMA

The types of EDUMA are classified into the following five types by Okada (1992a) (see Fig. 3(a).):

(1) shallow crustal earthquakes

(2) earthquakes at the surface of the Philippine Sea Plate

(3) earthquakes within the Philippine Sea Plate

(4) earthquakes at the surface of the Pacific Plate

(5) earthquakes at within the Pacific Plate

Among the five types, our major concern is Type-1 and particularly Type-2, because of the weak signals of preseismic deformation for other types.

The amount of crustal deformation by Type-2 EDUMA strongly depends on the surface depth of Philippine Sea Plate. The depths of the Philippine Sea and the North American Plates was are reported by Ishida (1992) (Fig. 3(b)). She gave the surface depth Z (km) of the Philippine Sea Plate by the next equation:

Z=c₀₀+c₁₀X+c₂₀X²+c₀₁Y+c₂₁X²Y+c₀₂Y²+c₁₂XY²+c₂₂X²Y² (7)
where

c₀₀=-36.0 c₀₁=-0.288288 c₀₂= 1.24665E-03

c₁₀=0.0620664 c₁₁=0.0035786 c₁₂= 1.10536E-05

c₂₀=2.98745E-3 c₂₁=-9.06574E-6 c₂₂=-5.88048E-07

X and Y are the E-W and N-W distance in km from the reference point (latitude: 35°37.5' N and longitude: 139°52.5’E).

Beneath the Tokyo Metropolitan area, three-fold plate structure is a particularly important characteristics (see Fig. 1(a) and Fig. 3(b)). KSP's role is to monitor the precursory crustal deformation signals caused by Type-2 or Type-1 earthquakes.

5. Coseismic crustal deformation

In Table 1 three cases of EDUMA model parameters are given to calculate deformation distributions around the Tokyo Metropolitan area. The first case is a EDUMA of Type-1, magnitude 7 at the Ayasegawa Fault. The second case is Type-2, magnitude 7 beneath Boso Peninsula and the third is Type-2, magnitude 7 beneath Tokyo Bay.

Figs. 4(a) and (b) show the estimation results of coseismic deformation in the first and second cases, respectively. Fig. 4(a) shows that the deformation much more than 30 cm occurs almost all over Tokyo Metropolitan area. Type-1 EDUMA, however, does not have any information about the occurrence period. Thus our major concern is the Type-2 EDUMA. Fig. 4(b) shows that the southern Tokyo Metropolitan area has the coseismic crustal deformation more than 30 cm.

The interesting characteristics of Type-2 deformation is that their major components are horizontal. VLBI with high horizontal sensitivity is effective to monitor this Type-2 EDUMA.

6. Conclusion

Fig. 4(c) shows the calculation result of preseismic crustal deformation of the case 3 (Type-2, Magnitude 7 at Tokyo Bay). We assume the 5% pre-slip occurs before the main rupture. This will cause the preseismic crustal slip more than several milli-meters in the major southern part of Tokyo Metropolitan area. Our system has a sufficient sensitivity for both Type-1 and -2 EDUMA in southern Tokyo Metropolitan area. In northern Tokyo Metropolitan area, it has a suitable sensitivity for Type-1.

To realize the successful KSP system, the following points are also important:

(1) to promote the cooperative operations among geodetic techniques such as VLBI, SLR, GPS and conventional ground surveying.

(2) to continue cooperation between domestic and international communities and institutes.

Acknowledgments

The authors wish to thank Dr. Okada of NIED for his offer the program of the crustal deformation model and also thank to the fund of STA to perform MDX VLBI experiments.

References

Ishida M.(1990): Plate structure beneath the Tokyo Metropolitan Area, Zisin Journal (in Japanese), 10, 7-13

Ishida, M.(1992): Geometry and relative motion of Philippine Sea Plate and Pacific Plate beneath the Kanto-Tokai district, Japan, J. Geophys. Res. 97, 489-513

Okada Y. (1992a) Classification of earthquakes in the Tokyo Metropolitan Area (in Japanese), Abstr. Seismol. Soc. Jpn, 169, Oct.

Okada, Y.(1992b): Internal deformation due to shear and tensile faults in a half-space, Bull. Seis. Soc. America Vol. 82, No. 2, 1018-1040

Takahashi F., Imae M., Yoshino T., Heki K., Kunimori, H., Kurihara N. and Ohtubo T. (1993): The plan of a Metropolitan Crustal Deformation Monitoring System by Communications Research Laboratory, presented at CRCM'93, Dec.

Figure Captions

Fig. 1(a) Tokyo Metropolitan Area is on the edge of North American Plate and also very near the boundaries of other three plates: Pacific Plate, Philippine Sea Plate and Eurasian Plate.

Fig. 1(b) A illustration of 3-dimensional plate structure beneath the Metropolitan Area and arrangements of four KSP stations: Koganei, Kashima, Miura and Boso.

Fig. 2(a) Results of formal error estimation of KSP VLBI network. The horizontal axis means the length of observation time in hours and the vertical axis shows the formal errors of three components of station positions.

Fig. 2(b) Results of formal error estimations of KSP SLR network. The horizontal axis means the number of LAGEOS passes and the vertical axis shows the formal errors of three components of station positions.

Fig. 3(a) Five types of EDUMA proposed by Okada (1992a)

Fig. 3(b) The depth of Philippine Sea and North American Plates estimated by Ishida (1992).

Fig. 4(a) Estimation results of coseismic crustal deformation by first cases. Deformation much more than 30 cm occurs almost all over Tokyo Metropolitan area.

Fig. 4(b) Estimation results of coseismic crustal deformation by second cases. Southern Tokyo Metropolitan area has the coseismic crustal deformation more than 30 cm.

Fig. 4(c) Calculation result of preseismic crustal slip by case 3

Table 1 Three cases of EDUMA models to calculate crustal deformation distributions around Tokyo Metropolitan area

Items: / Cases: Case 1 (Ayasegawa) Case 2 (Boso) Case 3 (Tokyo Bay)

Position of the reference

point of the Fault Plane

(lat.) 36.09N 35.18N 35.25N

(lon.) 139.49E 140.11E 139.80E

(depth)

Orientation of the Fault Plane (degree)

(dip.) 80 161.6 157.2

(strike) 135 89.9 103.7

Dimension of the Fault plane

(along-strike: L1, l2) 0.0, 42.0 km -21.0, 21.0 km -21.0, 21.0 km

(along-dip: W1, W2) -21.0, 0.0 km -10.5, 10.5 km -10.5, 10.5 km

Dislocation

(along-strike) 0cm -102.7cm -118.3cm

(along-dip) 130cm -79.3cm -52.0cm

TITLE

The plan of a Metropolitan Crustal Deformation Monitoring System

by Communications Research Laboratory

The author to receive the proof

Fujinobu Takahashi, Dr.

Communications Research Laboratory, 4-2-1, Nukui-kitamchi, Koganei-shi, Tokyo 184 Japan

TEL: 0423-27-7554, FAX: 0423-27-6687 [TEL and FAX number of first author]