__MODERN MICROZONATION METHODOLOGIES FOLLOWED BY
UPSL__

**Prediction of Ground Motion**Prediction of ground motion is the first step of earthquake damage assessment. Many local governments in Japan have done this kind of assessment, and prediction of ground motion is generally consists of two processes as shown in Fig. 1.1. The first process is prediction of ground motion on seismic bedrock and the second process is evaluation of soil effects. When both processes are calculated, ground motion at surface can be predicted. There are cases where the second process is divided into two processes further.

Fig. 1 Schematic illustration of wave propagation through seismic bedrock and soil surface

The 1st Process: Wave propagation in seismic bedrock

The 2nd Process : Wave propagation in soil surface**Ground Motion on Seismic Bedrock**On the first process as shown in Fig. 1.1, ground motion on seismic bedrock are predicted for a hypothetical source. The method of this process is classified into two groups.

(a) The method that considers rupture pattern of fault

(b) The attenuation formula for ground motionIn the group (a) hypothetical seismogenic fault is divided into subfaults, and rupture pattern can be considered. Therefore, the method of this group explains the phenomenon that the observed waveform at the same distance from source are different each other according to rupture pattern. However, there is a problem that it has uncertainty on setting rupture direction for hypothetical earthquake that have never occurred.

In the group (b) the empirical relationship is derived from regression analysis for the observed data. This is an easy method to calculate ground motion and there are many attenuation formulas for each ground motion index such as peak acceleration, peak velocity, response spectrum and so on . Recently the observed data near source is used for regression analysis and attenuation formula can be adapted to calculation of ground motion near source region. There are attenuation formulas that can consider rupture direction also. However the attenuation formula can’t fully explain the distribution of strong motion because the actual earthquake has complex rupture process.

__Midorikawa and Kobayashi (1979, 1980)__*Input/Output*- Pre-Condition

- Divide hypothetical seismogenic fault into subfaults
- Set rupture velocity
- Set rupture pattern
- Set rupture starting point
- Set S-wave velocity from seismogenic fault to observation point
- Set position and shape of seismogenic fault

*Input Data*

- Seismic moment
- Hypocentral distance

*Output Data*

- Peak acceleration on seismic bedrock
- Velocity response spectrum on seismic bedrock

__Outline of the Method__In this method, fault plain is modeled to consist of small subfaults as shown in Fig. 1.2 (a), and seismic waves are radiated when rupture front arrives at each subfault.

The chracteristic of this method is as follows:

1) Evaluate ground motion with velocity response envelope

2) Divide fault plain into small subfaults and think of subfault as point source

3) Deal with S wave with period of approx. 0.1-5 sec.Fig. 2 Schematic illustration of round motion prediction using response envelopes

(Midorikawa and Kobayashi, 1979)(a) Dividing fault plain into small subfaults

(b) An approximate model of response envelope for ground motion

(c) Superpositon of response envelopes from each subfaultResponse envelopes from each subfault are illustrated as shown in Fig. 1.2 (c).

When the size and rupture velocity of subfault is , respectively, duration of response envelope is given by.

Envelope has coda duration as a result of scattering effect on ray as follows:

where is proportional coefficient to express the time lag that is the difference between arrival time of first arrived wave and arrival time of last arrived wave from subfault.

Peak amplitude for each response envelope from subfault is given by

.

Total response envelope at observation is calculated by superposition of response envelopes from each subfault in consideration of travel time and delay time by rupture propagation. Velocity response is given by attenuation formula for velocity response spectrum as follows:

Duration is given as

.

In this method calculation output is velocity response spectrum. According to Kawasaki City (1988) peak ground acceleration is given as

.

*Note*This method provides velocity response spectrum with damping factor of 5% on seismic bedrock in which S-wave velocity is approx. 3 km/s.

Analyzed data in this method don’t contain record observed near source region and the shortest distance between source and observation is no less than approximate 50km. Therefore this method cannot explain ground motion near fault. When this method is used near source region, the calculation result overestimated.

In order to solve this problem, other attenuation formula for response spectrum is used. For example, Miyagi Prefecture (1996) uses the following formula that is calibrated by the recorded data for the 1995 Southern Hyogo Prefecture Earthquake.

__Irikura (1986)__*Input/Output**Pre-Condition*

- Set hypothetical seismogenic fault
- Divide hypothetical seismogenic fault into elements
- Set rupture pattern

*Input Data*

- Seismic moment of hypothetical earthquake
- Seismic moment of element earthquake
- Seismogram of element earthquake (=)
- Rise time (=)
- Rupture velocity
- S-wave velocity in propagation-path
- Position of observation point

*Output Data*

- Time-history waveform inferred for hypothetical earthquake

*Outline of the Method*Ground motion for large earthquake, which reflects rupture pattern, ray path and site effect, can be synthesized by convolving waveform of small event which is observed at same location from same fault area as follows:

is corresponding to summation with respect to number of elements. indicates summation with respect to time in rupture process. is dislocation time function at point on fault. is time lag between origin time and rupture starting time of element. is delay time related with rupture propagation. is the Green’s function from point on fault to observation point , and indicates convolution with . In this Empirical Green’s Function method, the observed record for element earthquake is used as .

*Note*To estimate ground motion by this method, it is necessary that observed waveform for small event that occurs near hypothetical source is recorded. But it is rare that necessary waveform was recorded. In this case, Green’s function is obtained by using numerical calculation or statistical technique.

For example, there is Somerville (1993) technique as deterministic method. In that method, Green’s function is estimated by use of ray tracing method and source time function calculated from observed data.

__Reference__

Irikura, K. (1986) Estimation of near-field
ground motion using empirical Green's function, *Proc. of Ninth World
Conference on Earthquake Engineering*, Tokyo-Kyoto, JAPAN, 8,
37-42.

Irikura, K. (1986) Prediction of strong
acceleration motion using empirical Green’s function, *Proc. 7 th Japan
Earthq. Engnrg. Sympo.,* 151-156.

Somerville, P. (1993) Engineering
applications of strong ground motion simulation, *Tectonophysics*, 218,
195-219.

__Goto__*et al.*(1995)*Input/Output*- Pre-Condition

- Set hypothetical seismogenic fault
- Set rupture pattern (bilateral faulting or unilateral faulting)

*Input Data*

- Moment magnitude
- The closest distance to the fault rupture
- Azimuth

*Output Data*

- Peak acceleration on seismic bedrock

__Outline of the Method__Goto

*et al.*(1995) computes peak ground acceleration on seismic bedrock by multiplying acceleration that is obtained by attenuation formula (Joyner and Boore, 1981) and coefficient of directivity effect corresponding to rupture pattern together.When directivity effect is not considered, horizontal peak ground acceleration on seismic bedrock can be calculated by attenuation formula of Joyner and Boore (1981) as follows:

where is peak ground acceleration in gal, is the closest distance to the fault rupture in km and is moment magnitude

*Case of bilateral faulting*In this case rupture propagates along fault line toward both the ends from hypocenter that is located center of the fault line. Then peek ground acceleration is given by

*Case of unilateral faulting*

In this case rupture propagates along fault line toward the end from hypocenter that is located another end of the fault line. Then peak ground acceleration is given by

Azimuth is the angle that is measured clockwise from the direction of rupture propagation to the direction of observation , and is 0.72 that is given as average value.

*Note*Joyner and Boore already modified their attenuation formula from Joyner and Boore (1981).

__Fukushima and Tanaka (1990, 1991)__*Input/Output**Pre-Condition*

- Set hypothetical hypocenter (or seismogenic fault)

*Input Data*

- The closest distance to the fault rupture
- Surface-wave magnitude

*Output Data*

- The mean of the peak acceleration from two horizontal components

__Outline of the Method__Fukushima and Tanaka (1990, 1991) proposes the attenuation formula of peak ground acceleration, which is derived from ground motion data recorded in Japan, the United States and so on. This attenuation formula showed the good agreement also with observed data for the 1995 Southern Hyogo Prefecture Earthquake.

Fig. 4 Analyzed data and attenuation relation for peak horizontal acceleration

(Fukushima and Tanaka, 1991)*Note*Since this formula calculates peak acceleration at the surface, correction is required when this formula is applied to estimating ground motion on bedrock. For example, it is possible to use the ratio of the observed acceleration to predicted acceleration for each soil type, which is described at the original paper.

__Reference__

Fukushima, Y. and T. Tanaka (1990) A new
attenuation relation for peak horizontal acceleration of strong earthquake
ground motion in Japan, *Bull. Seism. Soc. Am.*, 84, 757-783.

Fukushima, Y. and T. Tanaka (1991) A new
attenuation relation for peak horizontal acceleration of strong earthquake
ground motion in Japan, *Shimizu Technical Research Bulletin*, 10,
1-11.

__Annaka__*et al.*(1997)*Input/Output*- Pre-Condition

- Set hypothetical hypocenter (or seismogenic fault)

*Input Data*

- JMA (Japan Meteorological Agency) Magnitude
- Focal depth (or depth at center of seismogenic fault)
- Hypocentral distance (or the closest distance to the fault rupture)

*Output Data*

- Peak velocity on (engineering) bedrock
- Peak acceleration on (engineering) bedrock

*Outline of the Method*This method provides peak ground motion on engineering bedrock in which S-wave velocity is the range from 300m/s to 600m/s. Compared with other attenuation formulas, the characteristic of this method is that the focal depth is taken into consideration.

Table .1 Regression coefficients

Parameters

C

_{m}C

_{h}C

_{d}C

_{0}Peak acceleration [gal]

0.606

0.00459

2.136

1.730

Peak velocity [cm/s]

0.725

0.00318

1.918

-0.519

*Note*---

__Midorikawa (1993)__*Input/Output**Pre-Condition*

- Set hypothetical hypocenter (or seismogenic fault)

*Input Data*

- Moment magnitude
- The closest distance to the fault rupture

*Output Data*

- Peak ground velocity on stiff site (Vs=600m/s)

*Outline of the Method*Since it is thought that there is a high correlation between earthquake damage and peak ground velocity, in Midorikawa (1993) method, peak ground velocity is used as a measure for ground motion severity. This method provides peak ground velocity on stiff site with S-wave velocity of 600m/s.

*Note*According to the magnitude range of analyzed data, it is valid to use this formula for earthquakes with moment magnitude of 6.5 to 7.8

*Refference*

Midorikawa, S. (1993) Preliminary analysis for attenuation of peak ground velocity on stiff site, Proceedings of the International Workshop on Strong Motion Data, Vol. 2, 39-48.

__Evaluation of Soil Effects__The following methods are generally used as response analysis of soil surface in earthquake damage assessment.

(a) Multi-reflection theory

(b) Equi-linearized technique

(c) Calculation to apply Multi-reflection theory to deep subsurface and apply equi-linearized technique to shallow subsurfaceMulti-reflection theory is basic method in response analysis, and built in early 1960s (e.g. Haskell, 1960). This method can explain that ground motion tends to be amplified at soft-soil site. However if incident wave has large amplitude, ground motion at soft-soil site is weaker than at stiff site. This phenomenon is called nonlinear behavior of soil and observed when large earthquake occurred, but multi-reflection theory can’t explain this phenomenon.

In order to take nonlinear behavior into consideration, equi-linearized technique was developed. In earthquake damage assessment, SHAKE (Schnabel

*et al.*, 1972) has been often used as equi-linearized technique, but recently the method which can consider frequency-dependent effect of shear modulus and damping factor, e.g. FDEL (Sugito*et.al*., 1994), is used more and more.On the other hand there are simple methods for evaluating site amplification factor. For example, Matsuoka and Midorikawa (1994) can calculate site amplification factor from geomorphological unit or geology, altitude and the shortest distance from a river. The advantage of this method is that it does not need detailed parameters about soil which is obtained from field investigation such as boring data. On the other hand, the disadvantage is that it cannot explain nonlinear behavior of soil.

__Multi-Reflection Theory__*Input/Output**Pre-Condition*

- Set soil model with S-wave velocity, shear modulus, density and thickness for each layer

*Input Data*

- Time-history waveform or response spectrum of incident wave

*Output Data*

- Transfer function
- Time-history waveform or response spectrum at surface corresponding to the input data

*Outline of the Method*As shown in Fig. 1.5, soil surface is modeled as the horizontal layered media.

変位

S波速度

剛性率

密度

層厚

層

u

_{1}V

_{1}μ

_{1}2

_{1}d

_{1}1

u

_{2}V

_{2}μ

_{2}2

_{2}d

_{2}2

：

：

：

：

：

：

u

_{m}V

_{m}μ

_{m}2

_{m}d

_{m}m

：

：

：

：

：

：

u

_{n-1}V

_{n-1}μ

_{n-1}2

_{n-1}d

_{n-1}n-1

u

_{n}V

_{n}μ

_{n}2

_{n}d

_{n}n

Fig. 5 Soil model with horizontal layered structure

Displacement amplitude of incident S wave at upper boundary of th layer (=bedrock) is given by

,

where is the angular frequency and is a constant. Displacement in any th layer is expressed with summation of downward transmitting wave and upward transmitting wave . Because is expressed by and , displacement and stress in th layer is given by

,

where is depth from upper boundary of th layer and .

Derived from continuity condition of displacement and stress between th layer and ()th layer,

,

where is called layer matrix.

By using this recurrence formula iteratively, displacement and stress at ground surface can be computed by

.

Stress at ground surface is zero and displacement amplitude of incident S wave is given by , then an above equation is developed as

.

Therefore frequency-transfer function, it is the ratio of surface to incident amplitude in frequency domain, is given by

.

Taking intrinsic attenuation parameter into consideration, you have to substitute complex shear modulus for shear modulus in above-mentioned equations.

*Note*Because this method does not consider nonlinear behavior of soil, predicted amplitude at soft-soil sites, particularly sand deposit, is overestimated compared with observed amplitude when incident S wave has large amplitude.

This method need many parameters for each layer, but it is exceptional that parameters such as S-wave velocity is observed in research area even if there are many boring data. So it is necessary to infer unknown parameters using conversion formulas with N value as input, because N value is usually recorded in boring data in Japan.

*Reference*

Haskell, N. A. (1960) Crustal reflection of
plane SH waves, *J. Geophys. Res.*, 65, 4147-4150.

__Equi-Linearized Technique__*Input/Output**Pre-Condition*

- Strain-dependent curves of shear modulus and damping factor for each soil types
- Set soil model with S-wave velocity, density, thickness and soil type for each layer

*Input Data*

- Time-history waveform or response spectrum of incident

*Output Data*

- Transfer function
- Time-history waveform or response spectrum at surface corresponding to the input data

*Outline of the Method*In general, soil has characteristic that shear modulus decreases and damping factor increase as shear strain increases. In this method, to consider this characteristic calculation is executed with following process (see also Fig. 1.6).

__Process 1__Set up soil structure model with parameters necessary for calculation. Then compute shear modulus and damping factor on the assumption that shear strain is slight.__Process 2__Do response analysis for given incident waveform and calculate time series of shear strain for each layer.__Process 3__Calculate new shear modulus corresponding to 60 percent of maximum shear strain which is given by response analysis, using strain-dependent curves of shear modulus and damping factor.__Process 4__Calibrate soil structure model with newly gained shear modulus and damping factor.__Process 5__Iterate calculation from process 2 to process 4 until shear modulus and damping factor converge.*Note*The nonlinear technique called SHAKE (Schnabel

*et.al.*, 1972) is one of the typical methods which consider strain-dependency in physical properties of soil. The nonlinear technique is more suitable to actual behavior of soil than multi-reflection theory as described in 1.2.1. However, predicted amplitude at soft-soil sites, particularly sand deposit, is underestimated compared with observed amplitude, because shear strain become too large when incident S wave has large amplitude.To improve this problem in SHAKE, in FDEL (Sugito

*et.al*., 1994) the frequency dependent effect of shear modulus and damping factor is taken into consideration.These methods need many parameters for each layer, but it is exceptional that parameters such as S-wave velocity is observed in research area even if there are many boring data. So it is necessary to infer unknown parameters using conversion formulas with N value as input, because N value is usually recorded in boring data in Japan.

*Reference*

Schnabel, P. B., J. Lysmer and H. B. Seed
(1972) SHAKE a computer program for earthquake response analysis of horizontally
layered sites, *EERC*, 72-12.

Sugito, M., G. Goda and T. Masuda (1994)
Frequency dependent equi-linearized technique for seismic response analysis
of multi-layered ground, *Proceedings of JSCE*, 493, 49-58 (in Japanese
with English abstract).

__Matsuoka and Midorikawa (1994), Midorikawa__*et.al.*(1994)*Input/Output**Pre-Condition*---

*Input Data*

- Geomorphological unit or Geology
- Altitude
- The shortest distance from a river
- Peak ground acceleration or velocity on Tertiary ground

*Output Data*

- The amplification factor for peak ground acceleration or velocity to Tertiary ground
- Peak ground acceleration or velocity at surface

*Outline of the Method*Using the observed strong motion data for the 1987 Chiba-ken-toho-oki, Japan earthquake, Midorikawa

*et al.*(1994) proposes the following equations which can calculate the site amplification for peak ground acceleration () and velocity () with the time-weighted average shear wave velocity to a depth of 30m ( in m/s) as input.Where is given by the following equation for each soil type (Matsuoka and Midorikawa, 1994).

The regression coefficients of are summarized in Table 1.2.

Table .2 Regression coefficients for each soil type (Matsuoka and Midorikawa, 1994)

Geomorphological

unit or Geology

Data #

Reclaimed Land

2.23

0

0

0.14

132

Artificial Transformed Land

2.26

0

0

0.09

7

Delta, Back Marsh ()

2.19

0

0

0.12

36

Delta, Back Marsh ()

2.26

0

0.25

0.13

57

Natural Levee

1.94

0.32

0

0.13

18

Valley Plain

2.07

0.15

0

0.12

26

Sand Bar, Dune

2.29

0

0

0.13

13

Fan

1.83

0.36

0

0.15

20

Loam Plateau

2.00

0.28

0

0.11

95

Gravel Plateau

1.76

0.36

0

0.12

12

Hill

2.64

0

0

0.17

22

Other Geom. Units

(e.g. Volcanic Mountain)2.25

0.13

0

0.16

10

Pre-Tertialy

2.87

0

0

0.23

3

Peak ground acceleration (or velocity) at surface can be obtained by multiplying the amplification factor and peak ground acceleration (or velocity) on bedrock together. In this method bedrock indicates the layer with .

*Note*Because this method derived from the dataset mainly recorded in Kanto district in Japan, calculation result is not compensated except Kanto district.

In order to be able to use this method in other area in Japan, Geological Survey of Japan (1996) decided maximum and minimum value for , , for each geomorphological unit or Geology.

Table .3 Maximum and minimum value for , ,

(Geological Survey of Japan, 1996)Geomorphological

unit or Geology

*V*_{S}*H**D*Reclaimed Land

170

－

－

Artificial Transformed Land

180

－

－

Delta, Back Marsh ()

155

－

－

Delta, Back Marsh ()

155～250

－

0.5～4.0

Natural Levee

160～250

5～30

－

Valley Plain

165～300

10～500

－

Sand Bar, Dune

195

－

－

Fan

180～450

15～200

－

Loam Plateau

170～400

10～150

－

Gravel Plateau

200～500

30～400

－

Hill

435

－

－

Other Geom. Units

(e.g. Volcanic Mountain)200～400

5～500

－

*Reference*

Matsuoka M. and S. Midorikawa (1994) The
digital national land information and seismic microzoning, *22nd symposium of earthquake ground
motion*, 23-34 (in Japanese with English abstract).

Midorikawa, S., M. Matsuoka and K. Sakugawa
(1994) Site Effects on Strong-Motion Records Observed during the
1987-Chiba-ken-toho-oki, Japan Earthquake, *Proc. Ninth Japan Earthq. Engnrg.
Sympo.*, E085-E090.