3. Azimuthal dependence of 3-component RMS envelopes

Simulation of vector-wave envelopes in 3-D random elastic media for non-spherical radiation source based on the stochastic ray path methodKaoru Sawazaki, Haruo Sato, and Takeshi Nishimura (sawa@zisin.geophys.tohoku.ac.jp) 　 Geophysics, Science, Tohoku University, Japan

1. Introduction　 The Markov approximation is very useful for the synthesis of wave envelopes near the direct wave arrival in random media. However, this method has not been precisely studied for an non-isotropic radiation source. The motivation of our study is to propose a method to synthesize vector-wave envelopes for a point shear dislocation source by using the stochastic ray path method, which treats seismic ray bending as a stochastic random process.

2. Simulation method

ddi drAAkekr d rrk rk 0exp,, 2

00

0'10

''201 ,,,,

2

1,, krkrdkrr

kkkkk

Figure 3. 　 Squared amplitude of the normalized radiation pattern for P and S waves for a point shear dislocation source. Figure 4. 　 Azimuthal dependence of the 3-comp. R

MS envelopes for P and S waves at the 100km distance.

　 We have synthesized three-component seismogram envelopes in a random medium for a point shear dislocation source by using the stochastic ray path method. The envelopes synthesized show a clear azimuthal dependence especially at the maximum peak arrival for short distances; however, such an azimuthal dependence disappears with travel distance or frequency increasing. Those envelopes explain the characteristics of observed seismograms of small earthquakes well in short periods.

5. Conclusion

4. Envelopes for different hypocentral distances and frequencies

Figure 5. 　 Square root of 3-comp. sum S wave envelopes for 10Hz at the different hypocentral distances.

The decay rate of the maximum amplitude against the hypocentral distance differs by azimuth.The azimuthal dependence of the maximum amplitude becomes more unclear for 10Hz envelopes than for 2Hz ones.

Figure 1. von-Karman type PSDF (Saito et al., 2005).

S41C-1866

①A random inhomogeneous medium from a source to a receiver is divided into N spherical layers.

②Energy particles are shot from a point shear dislocation source with the weight of the radiation pattern, where the particles propagate with a constant velocity of VP or VS.

③The particle is scattered at the layer boundaries following the scattering angle distribution given by eq. (2), which is treated by the Monte-Carlo method.

④The oscillation direction of the energy particle at the receiver is projected into radial (r) and transverse ( and ) components.

⑤The histogram of the accumulated travel times of the particles is calculated, which represents the 3-component MS envelope.

The envelope amplitude appears at the Null-axis (=0,=0) direction, which is contribution of the detoured particles that have experienced scatterings.

The largest P and S wave amplitudes appear at the A-axis (=90 ， =45) and the B-axis (=90, =0) directions, respectively, which reflects the original radiation pattern.

The azimuthal dependence is clear at the maximum peak arrival, however, it becomes unclear as the lapse time increases.

=5%， a=5km， =0.5， r=2km VP=6.0km/s， VS=3.46km/sFrequency: 10HzES/EP: 23.4Number of particles: 500,000Intrinsic absorption is not included

<Parameters for the simulation>

a: Correlation distance: RMS value of the velocity fluctuation : Parameter that controls the decay of PSDF

Figure 2. Schematic illustration of the stochastic ray path method for a point shear dislocation source.

2322

3223

1

238

ma

aP m

where P is the power spectral density function (PSDF) of the velocity fluctuation. We assume the von-Karman type PSDF (figure 1) which is given by

mmr erm dePdzA Zd zid 22

1

(1),

(2),

(3),

(4).

We describe the seismic energy propagation in a random inhomogeneous medium as a ray bending process under the assumption of the Markov approximation (backward scattering and PS, SP conversions are neglected. See Sato and Fehler (1998) for the detail). Convolving the angular spectrum of seismic ray at the distance r with the scattering angle distribution , we obtain the angular spectrum at the distance r+r as

1

Solving eq. (1) by the Monte-Carlo method, we chase the ray bending process.

Figure 6. 　 Square root of 3-comp. sum P and S wave envelopes for 10Hz and 2Hz at the 100km distance.

<Stochastic ray path method (Williamson, 1972)>