3. Azimuthal dependence of 3-component RMS envelopes

1. Simulation of vector-wave envelopes in 3-D random elastic media for non-spherical radiation source based on the stochastic ray path method Kaoru Sawazaki, Haruo Sato, and Takeshi Nishimura (sawa@zisin.geophys.tohoku.ac.jp)Geophysics, Science, Tohoku University, Japan S41C-1866 1. Introduction 3. Azimuthal dependence of 3-component RMS envelopes <Parameters for the simulation> 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. e=5%，a=5km，k=0.5，Dr=2km VP=6.0km/s，VS=3.46km/s Frequency: 10Hz ES/EP: 23.4 Number of particles: 500,000 Intrinsic absorption is not included 2. Simulation method 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 rayat the distance r with the scattering angle distribution , we obtain the angular spectrum at the distance r+Dr as • The envelope amplitude appears at the Null-axis (q=0,f=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 (q=90， f=45) and the B-axis (q=90, f=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. Figure 1. von-Karman type PSDF (Saito et al., 2005). (1), a: Correlation distance e: RMS value of the velocity fluctuation k: Parameter that controls the decay of PSDF (2), Figure 3.Squared amplitude of the normalized radiation pattern for P and S waves for a point shear dislocation source. (3), Figure 4.Azimuthal dependence of the 3-comp. RMS envelopes for P and S waves at the 100km distance. 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 4. Envelopes for different hypocentral distances and frequencies (4). Solving eq. (1) by the Monte-Carlo method, we chase the ray bending process. <Stochastic ray path method (Williamson, 1972)> • A random inhomogeneous medium from a source to a receiver is divided into N spherical layers. • Energy 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. • The particle is scattered at the layer boundaries following the scattering angle distribution given by eq. (2), which is treated by the Monte-Carlo method. • The oscillation direction of the energy particle at the receiver is projected into radial (r) and transverse (f and q) components. • The histogram of the accumulated travel times of the particles is calculated, which represents the 3-component MS envelope. Figure 5.Square root of 3-comp. sum S wave envelopes for 10Hz at the different hypocentral distances. Figure 6.Square root of 3-comp. sumP and S wave envelopes for 10Hz and 2Hz at the 100km distance. • 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. 5. Conclusion 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. Figure 2. Schematic illustration of the stochastic ray path method for a point shear dislocation source.