Details
of the Synthetic Data
The
synthetic data were generated under the
assumption that the field of microtremors satisfied
the following conditions.
1) Chacateristics
of the microtremor wavefield
(signals)
- The field of microtremors is dominated by surface waves (Rayleigh and
Love waves).
- The waves arrive as
plane waves in the array.
- The wavefield
is stationary in both time and space.
- The Rayleigh and Love
waves are mutually uncorrelated.
2) Phase velocities of
Rayleigh and Love waves
Phase velocities as
illustrated in the figure below were prescribed to the Rayleigh and Love waves
(red and green, respectively).
3) Arrival directions and
intensities of Rayleigh and Love waves
Rayleigh and Love waves
were made to arrive as plane waves in the array as illustrated in the figure
below. We assumed that both Rayleigh and Love waves arrived from all directions
with equal intensities, but that Rayleigh and Love waves had different
intensities. More specifically, we set the Rayleigh-to-Love power ratio at 4:1.
The horizontal-to-vertical amplitude ratio of the Rayleigh waves (which we
call R/V in this manual) was set at 1:10. The ratios were
fixed at these values for all frequencies.
4) Noise
On top of the Rayleigh-
and Love-wave signals we added incoherent noise with the following properties.
- Records of noise at
different stations are mutually uncorrelated.
- Noise is stationary in
time.
- Noise is uncorrelated
with the signals.
We calculated the noise
intensity corresponding to an SN ratio of 100 for all UD, NS and EW components,
and added noise on top of the signals composed of Rayleigh and Love waves. The
term NS ratio, which we use repeatedly in this manual, refers to the inverse of
the SN ratio.
