1. SSA 2016 Annual Meeting, April 20 – 22, 2016, Tuscany 1/2, Peppermill Hotel, Reno, Nevada
Directional Dependent H/V Spectral Ratio of Microtremors at Onahama, Japan
Shinichi Matsushima DPRI, Kyoto University
Hiroyuki Kosaka Institude of Construction Technology, Toda Corporation (Former graduate student)
Toga Kobayashi Sumitomo Corp. (Former undergraduate student)
Hiroshi Kawase DPRI, Kyoto University

2. Acknowledgements
Kind understanding and cooperation by the Tohoku Harbor Office of Ministry of Land, Infrastructure and Transportation
This study was partially supported by the PRENOLIN project
PRENOLIN Project: a benchmark on numerical simulation of 1-D non-linear site effect
PRENOLIN is a part of two larger projects: funded by the ANR (French National Research Agency) and SIGMA, funded by a consortium of nuclear operators (EDF, CEA, AREVA, ENL)
This study was also partially supported by JSPS KAKENHI Grant Numbers , and 15H02989, as well as a DPRI internal funds
Dr. Florent De Martin helped with the calculation using EFISPEC (Spectral Element Method (SEM)) developed by Dr. De Martin
April 20th, 2016
SSA 2016 Annual Meeting

3. Background - Microtremor H/V Spectral Ratios (MHVRs) at Uji, Kyoto, Japan -
Site C’’
Site C
Site C’
Matsushima et al. (2014)
Site C
- Observed MHVRs show significant directional dependency
- Theoretical MHVRs calculated by SEM based on diffuse field assumption considering a simplified basin model of Uji, qualitatively reproduces the observed MHVRs
April 20th, 2016
SSA 2016 Annual Meeting

4. Objective of this Study
In this study, we observed MHVRs at a strong motion observation site of Port and Harbor Research Institute in Onahama, Japan as a part of the European project “PRENOLIN”
We found that directional dependence exists in some parts of the area surrounding the site
The directional dependence is more apparent and has a higher dominant frequency, at around 5 Hz, compared to those observed in Uji
We conducted microtremor observations to detect the distribution of directional dependent MHVRs in order to find the cause of the directionality and model the velocity structure
April 20th, 2016
SSA 2016 Annual Meeting

5. Location of Onahama, Fukushima, Japan
Port of Onahama
April 20th, 2016
SSA 2016 Annual Meeting

6. Microtremor Observations inside the Tohoku Port Office Premises Line-1 to Line-7
Line-1 48m
Line-2 50m
Line-3 51m
Line-4 72m
Line-6 15m
Line-7 55m
Line-5 35m
April 20th, 2016
SSA 2016 Annual Meeting

7. Observed MHVRs of Line-3
South
NS/UD
EW/UD
Line-1 48m
Line-2 50m
Line-3 51m 12
MHVR
0.1 10
Freq (Hz)
North
April 20th, 2016
SSA 2016 Annual Meeting

8. Observed MHVRs of Line-4
East
NS/UD
EW/UD
Line-4 72m
Line-6 15m
Line-7 55m
Line-5 35m 12
MHVR
0.1 10
Freq (Hz)
West
April 20th, 2016
SSA 2016 Annual Meeting

9. Microtremor Observations in and around the Tohoku Port Office Line-A to Line-I
April 20th, 2016
SSA 2016 Annual Meeting

10. Observed MHVRs of Line-A & Line-C
North
North
NS/UD
EW/UD
South
South
Line-A
Line-C 12
MHVR
Line-C
0.1
Freq (Hz) 10
Line-A
April 20th, 2016
SSA 2016 Annual Meeting

11. Difference of Peak Freq. of NS/UD and Directional Dependent Power g
γ= 1 N ∙ f 1 f | NS 2 − EW 2 | 1 RMS
f1 = 2 Hz, f2 = 5 Hz
Distribution of Peak Freq. of NS/UD
Distribution of g
April 20th, 2016
SSA 2016 Annual Meeting

12. Model of Wedges assumed from MHVRs to Calculate Numerical MHVRs using SEM
East
West
South
North
-840m
840m
-840m
840m
Vs = m/s
Vp = m/s
ρ = 1710 kg/m3
Vs = m/s
Vp = m/s
ρ = 1710 kg/m3
Vs = m/s
Vp = m/s
ρ = 2050 kg/m3
Vs = m/s
Vp = m/s
ρ = 2050 kg/m3
840m
840m
East-West Wedge
North-South Wedge
April 20th, 2016
SSA 2016 Annual Meeting

13. Numerical MHVRs for East-West Wedge10
NS/UD
EW/UD
MHVR
0.1
Freq (Hz) 10
2-1
1-4
Vs = m/s
Vp = m/s
ρ = 1710 kg/m3
Vs = m/s
Vp = m/s
ρ = 2050 kg/m3
April 20th, 2016
SSA 2016 Annual Meeting

14. Numerical MHVRs for North-South Wedge10
MHVR
0.1
Freq (Hz) 10
NS/UD
EW/UD
April 20th, 2016
SSA 2016 Annual Meeting

15. Summary
The observed MHVRs with significant directional dependence lie in two straight lines, forming a T-like shape
We constructed a 2-D model of the two wedges, one in East-West direction and one in North-South direction
We calculated the numerical MHVRs by SEM using the diffuse field assumption
The numerical MHVRs resemble the observed MHVRs pretty well, except the site inside the North-South wedge
April 20th, 2016
SSA 2016 Annual Meeting

16. April 20th, 2016
SSA 2016 Annual Meeting

17. Mesh Model for North-South Wedge
Conditions of SEM calculation
Max. Freq.
20Hz
Min. Mesh Size
7.25m
No. Nodes
550,428
All Calc. Nodes
609,046
No. Elements
511,511
Integral Points
34,237,288
Calculation model
Close-up of the detailed mesh model near
the North-South wedge
April 20th, 2016
SSA 2016 Annual Meeting

18. Formulation (1)
Within a 3D diffuse, equipartitioned field, the average cross correlations of displacement at points and can be written as;
where is energy density of S waves
In order to calculate the theoretical energy density at a given point , we rewrite the above equation assuming as;
where is the shear modulus
This equation is valid even if the summation convention is ignored so can be written as , which is directional energy density (DED) along direction m
April 20th, 2016
SSA 2016 Annual Meeting

19. Formulation (2)
We may express the H/V spectral ratio in terms of energy densities.
For instance, is proportional to
It is common to eliminate the angular brackets while writing the expression for the average H/V spectral ratio as;
If we assume that microtremors constitute a diffuse field
Average spectral densities may be regarded as DEDs
Invoke the connection between the normalized average of energy densities of diffuse field with the imaginary part of Green’s function at the source
Then we can write as;
April 20th, 2016
SSA 2016 Annual Meeting

20. Formulation (3)
In an equipartitioned field, it will be valid even if we take only one horizontal component of the ratio of DEDs, so the directional H/V spectral ratio can be derived as;
From the relation between energy densities of diffuse field with the imaginary part of Green’s function, we can obtain the directional H/V spectral ratio as;
This relation is valid for 3D media, meaning that 1D or horizontal layering assumption is not needed, if we can assume a diffuse field
April 20th, 2016
SSA 2016 Annual Meeting

21. Direction of the Highest g
Direction of highest g from Magnetic North* g
Site
Angle
(deg.) H3 1 C3 2 I1 16 I4 62 H3
Rotation Angle (deg) C3 I1
MHVR
*Magnetic North is about 7 deg. west of true north I4
Frequency (Hz)
Frequency (Hz)
Rotated 2 deg.
Rotated 46 deg.
Site C3
April 20th, 2016
SSA 2016 Annual Meeting

22. Direction of the Highest g
Rotation Angle (deg)
Rotation Angle (deg)
MHVR
MHVR
Frequency (Hz)
Frequency (Hz)
Rotated 2 deg.
Rotated 46 deg.
Rotated 1 deg.
Rotated 47deg.
Site C3
Site H3
April 20th, 2016
SSA 2016 Annual Meeting

23. Direction of the Highest g
Rotation Angle (deg)
Rotation Angle (deg)
MHVR
MHVR
Frequency (Hz)
Frequency (Hz)
Rotated 16 deg.
Rotated 60 deg.
Rotated 62 deg.
Rotated16 deg.
Site I1
Site I4
April 20th, 2016
SSA 2016 Annual Meeting

24. Comparison with old maps Late 19th Century
April 20th, 2016
SSA 2016 Annual Meeting

25. Observed Acceleration at Strong Motion Network of Port and Airport Research Institute Onahama station
Downhole (GL-11.05m)
Surface
April 20th, 2016
SSA 2016 Annual Meeting

26. Geological Features at Strong Motion Network of Port and Airport Research Institute Onahama station
April 20th, 2016
SSA 2016 Annual Meeting

27. Background
As observational evidence of 3-D microtremor H/V spectral ratios (MHVRs), we have shown that significant directional dependency is observed in and around Uji campus, Kyoto University, Japan
At this site, the bedrock depth varies from east to west about 400m in depth within the distance of 1 km
The observed microtremor at Uji campus showed that the NS/UD has higher peak amplitude and EW/UD has higher peak frequency
This directional dependence is considered to be the result of 2-D surface geology
April 20th, 2016
SSA 2016 Annual Meeting

28. April 20th, 2016
SSA 2016 Annual Meeting